Corporation Law case study Essay Example | Topics and Well Written Essays - 2500 words

Corporation Law case study - Essay Example The main issue is if the selling of stocks and the responsibility of the directors. Its nesassry to tell a few words about dealing with outsiders. Also the seconde question deals with the problem of outsider trading. Express authority4 In the context of a Co, actual authority will be conferred by the Co const or, in its absence in accordance with the replaceable rules of the CA. In general, in the case of any Co with more than 1 D, authority is vested in the Board collectively - s 198A Any act lying outside the authority of the D's or the Board can be performed by the members in general meeting - s 198A(2) Implied authority of Co officers The Board may appoint someone as Managing Director (must be one of their own number - replaceable rule s 201J), conferring on that person the powers of the Board - s 198C(1). According to the articles concerning duties of directors one of theliste every managing director is obliged to act in good faith in the best interests of the corp and to use powers for a proper purpose - s 181.5 In this case the managing director haven't acted in the best iint of the company because the board of directors had rejected the contract. So mister Lam is responsible for comensation the losses to the company. Also he have to take responsibility of information given about the information given on the new project because he promised the increase in productivity of about 100%. The law prohibits insider trading. Generally, D's do not owe a fiduciary duty to individual s'holders Percival v Wright [1902] 2 Ch 421 - shareholders offered to sell shares to directors - directors already negotiating to sell shares at much higher price but did not inform s'holders - court held no fiduciary duty to shareholders,... The second question concerns different articles of the corporate law. There is some information about the corporations' law. The main issue is if the selling of stocks and the responsibility of the directors. Its nesassry to tell a few words about dealing with outsiders. Also the seconde question deals with the problem of outsider trading. According to the articles concerning duties of directors one of theliste every managing director is obliged to act in good faith in the best interests of the corp and to use powers for a proper purpose - s 181.5 In this case the managing director haven't acted in the best iint of the company because the board of directors had rejected the contract. So mister Lam is responsible for comensation the losses to the company. Also he have to take responsibility of information given about the information given on the new project because he promised the increase in productivity of about 100%. The law prohibits insider trading. Percival v Wright [1902] 2 Ch 421 - shareholders offered to sell shares to directors - directors already negotiating to sell shares at much higher price but did not inform s'holders - court held no fiduciary duty to shareholders, and so they could not recover. Primary prohibition in s 1043A(1) - insider may not purchase or sell shares in Co or get anyone to do that for him.

Contemporary Architectural Design and Property Development Essay

Contemporary Architectural Design and Property Development - Essay Example In general, a religion means a strict, unwritten code of essential rules (including morals and traditions) established by humans in order to control social life of their society. Vastu and Feng-Shui is a part of old traditions and culture of Chinese and Indian societies. In a time, they became popular in all Asian countries. Both of the concepts refer to the science of planning buildings, travelways, and graves such that they will get maximum benefits and minimum damage from the 'the cosmos'. More specifically, Feng-Shui addresses wind, water, and other natural forces. "Natural forces" in this case include good and bad luck, which are explicitly compared to wind. The idea of both approaches is that inhabitants of a well-sited home, or descendants of someone buried in a good gravesite, can expect wealth, sons, status, and security to flow to them. Rajgopal (2002) explains: The rebirth of Vastu Shastra parallels contemporary spiritual movements arising all over the world that seek to connect with a higher energy, draw closer to the mysteries of the universe, and contribute to a major paradigm shift (p. 33). However, focally, Vastu and Feng-Shui in... s a true folk science, as recognized by the first Western observer to comment extensively on it and by many Chinese and Westerners since Vastu and Feng-Shui also involve an emotional response to landscapes (Freeman, 2005). In India, excellent work is being done which shows not only that modem architecture can be given a worthy landscape setting, but also that it may soon be possible to find landscape architects who can deal imaginatively with the vast new opportunities created for them by modern town and country planning. But no large body of recognizably modern landscape architecture exists, and in only a few countries is there a strong school of designers (Pegrum, 2000). In modern Asian (and Indian) architecture the two great motive forces of the modern movement are on the one hand the new opportunities being created by technical and social progress and on the other the new structural techniques. In landscape architecture new opportunities are certainly being created, but the technique of garden construction is still fundamentally the same as it was in the eighteenth century. "The three main principles of Veda are right orientation, right placement, and right proportion" (Rajgopal, 2002, p. 34). Even the invention of modern earth-moving machinery, which may seem revolutionary, has in fact merely accelerated and cheapened processes which were used by old builders. Rajgopal (2002) explains that: The reason for da Gama's consternation was that all buildings constructed in Kerala, regardless of the faith of their inhabitants, were built according to the principles of Vastu Shastra by takshagans-- skilled craftsmen-carpenters well versed in the ancient science (p. 34). Today, in Vastu and Feng-Shui, in spite of the advance of science and the discovery of new plants,

How Does Hydro And Wave Energy Work Environmental Sciences Essay

How Does Hydro And Wave Energy Work Environmental Sciences Essay Energy also known as electricity is an important source of energy use all around the world. Electricity Energy helps do a lot of work such as it gives people light. It warms our bodies and homes. It runs our TVs and our cars. It makes us grow and move and think. Energy is the power to change things. It is the ability to do work. Light is a type of energy we use all the time. We use it so we can see. We get most of our light from the sun. At night people must make there our own light. Usually, we use electricity to make light. In todays world with the help of latest technology energy can be created by using heat from sun, power of wind and the force of falling water or wave. Currently government from all around the world are keen in investing a lot of money in these projects. The projects are met to be environmentally friendly, low in cost, easy to maintain and noise free. Hydro energy system provides energy that normally comes from water force and converts to electricity. Hydro energy can be created by using many ways. In most of the leading countries, the most reliable and cheap common method of generating energy from water are hydroelectric dams, where water comes down through an area that causes turbines to rotate and then energy can be captured to run a generator. Power can also be generated from the energy of tidal forces or wave power, which uses the energy created by waves. 1.2 Technology in different countries Technological advances in the plants and in power transmission make it feasible to build hydroelectric plants in remote locations, far from where the power will be used. The Itaipu Dam on the Paranà ¡ River between Paraguay and Brazil can produce up to 12,600 megawatts of power. This plant, opened in 1982, supplies nearly all Paraguays electricity and one-quarter of that needed for Brazil. Tasik Kenyir (Lake Kenyir) Sultan Mahmud hydroelectric power station in Malaysia has a capacity of 400 megawatts of power. One of the largest hydroelectric projects in the world is Chinas Three Gorges project on the Yangtze River. The dam, designed to control the devastating floods on the river, includes a large hydroelectric plant. With a capacity of 18,200 megawatts, Three Gorges is projected to be able to provide up to one-ninth of Chinas electricity needs. China has also built many small hydroelectric plants for local use around the country. 1.3 Stage of development of Hydro Energy Hydroelectric power grew rapidly after that. In 1886 there were 45 hydroelectric plants in the United States. By 1889, 200 plants were generating electricity by using water for some or all of the power. At the same time, hydroelectric power plants opened around the world. Italy built its first hydroelectric plant in 1885 at Tivoli, in the mountains outside Rome. The plant initially powered lights in the nearby town. But by 1892 a second plant in the same location was providing power to Rome, the first long-distance power transmission in Italy. Other countries with good conditions for hydroelectric power soon built plants. Canada, France, Japan, and Russia were among the first on board. During the period from 1900 to 1950 the use of hydroelectric power increased rapidly. 1.4 Economics and politics involved Hydro energy systems have a big impact economically as the system provides energy to public where they are charged for the serviced. While this process go on capital usually comes in the market where every one gets a portion of the business or makes profit for there business. Politically the system can make a difference for example if there is a natural disaster the government will make a loss. 1.5 Cultural and decision making in different countries Many countries in the world use hydro energy system to create electricity in a lower cost. Currently Canada comes up top of the list for high usage and the United States comes in second. One of the main reasons the following countries took the decision to use hydro energy system the most to produce electricity is because its a renewable energy, which means it will not be depleted over time and it will consistently be replenished. It is also a clean energy source. 1.6 Possible Problems when using Hydro Energy One problem that can happen when using hydro energy is that it sometime can change the natural flow of the water which can make it possible to harm plants and animals in the water. It can also damage areas and wildlife, as when creating a hydro electric dam, areas should be flooded. 1.7 Profitable Hydro Energy system Other reasons that many countries want to use hydro energy is that it is cheaper than using other methods to convert energy to electricity. It is also reliable and can be used almost immediately when turned on to meet the demand for electricity. Therefore, one must weigh the pros and cons before deciding to use hydro energy to supply their demand for electricity. 1.8 Application of Hydro Energy our Major A hydro energy plant can absorbs the energy of falling water to generate electricity then a turbine can converts the energy of falling water into mechanical energy. Then a generator has to convert the mechanical energy into electrical energy.  Hydro plants can be in different size from micro-hydro that power only very few homes. A Dam can raise water level of a river to create falling water.  Also the dam can control the flow of water. The reservoir that is created is will practically stored energy. The force of falling water should push against the turbines blades causing the turbine to turn in one direction. A water turbine is similar to a windmill,  except that the energy is provided in different way, falling water instead of wind. The turbine should convert the kinetic energy of falling water into a mechanical energy. Generator that is connected to the turbine via shafts so  when the turbine turns it makes the generator to rotate also convert the  mechanical energy from the turbine into electric energy. Wave Energy 2.1 Background of wave energy Waves are naturally caused by the wind which blows over the sea level. In many part of the world, the wind blows with different force to provide waves that can be used to produce energy. There is high level energy and force in the ocean waves.  Wave power can devices  and extract energy directly from the surface ocean waves or from pressure fluctuations below the surface. Wave can also be generated wave when earth quack takes place. Wave power  varies widely  in different parts of the world, and wave energy cant be usefull effectively everywhere. Wave-power can be found in different areas of the world include the western coasts of Scotland, northern Canada, southern Africa, Australia, and the  north-western coasts of the United States. 2.2 Technology In the current market technologies and design in wave Energy system has improved tremendously. The industrial wave power station/plant has to use a shoreline chamber, in which seawater comes and goes naturally. As the water come, the air in the chamber is pressurised and forced to go through a hole into the turbine, to make it turn. As the water recedes, the air is goes back, leaving the turbine turning. The turbine then can be connected via a shaft but the new technology is using belt to the generator where energy will be converted into electricity. 2.3 Impact on environment In todays world wave power is considered as environmentally friendly. Most complain usually come from local neighbours as it can be a bit noisy, landscape, or affect of roads leading to the sites. These complains are currently seen as disadvantage. 2.4 Political and Economical Impact Wave energy has made a big impact economically and politically from years. Economically in a way when a project take place it brings capital together which means everyone small business, contracts labourers, shops and many get a portion of the business and earn them profit. Politically it can affect the government if the project does not work because of a natural disaster. 2.5 Application of wave energy Kinetic energy naturally has to be in the wave that moves in the ocean. The energy can be used to power and run a turbine. Following the example in diagram 1 below wave should rise while reaching the chamber. The forces of the rising water actually have to push air out of the chamber. The moving air in red colour shown in the diagram spins the actual turbine which will manually turn the generator. After this process wave down, air flows through the turbine and back into the chamber through doors that are normally closed. Others system actually uses up and down motion of the wave to power piston that moves up and down inside the cylinder. That piston should be able to turn a generator. Tidal Power Wave Energy Diagram 1 Comparison of different energy system Hydro Energy Hydroelectric power has other benefits as well. Dams and hydroelectric plants last a long time. This means that once the costs of building are paid off, a hydroelectric plant becomes a relatively inexpensive source of electricity. Wave Energy Wave energy system is as good as hydro energy. Advantages are it does not disturb public in case there of noise. Disadvantages are it can cause damages in case there are sea storm and also mite be difficult for engineers to do any maintenance. Wind Energy Wind Energy system work nearly the same way wave energy works. Before engineers used to place big turbines in land but now technology has improved same system can be build on sea and works as good as any other system. Conclusion Following the discussion between different kind of energy systems. Energy is a very important factor in todays world. As technology level is rising better energy system is been design and tested. Currently a new energy system has been tested which works under water. The turbine system is fixed on the ground to protect against vibration. The turbine system rotates with the help of sea water pressure. Engineers and government of all the leading countries are investing more energy system because they are pollution free and do not need any expensive fuel.

Incidents In The Life Of A Slave Girl Essay -- essays research papers

Incidents in the Life Of A Slave Girl CHAPTER I   Ã‚  Ã‚  Ã‚  Ã‚  The conditions of this master-slave relationship are that the slave (Linda) is there to do work for her mistress, or master, which is now her sister' s daughter. Linda is supposed to take care her new owner's five year old daughter, help plant things, take care of any animals and anything else she is told. As a slave, she should also do everything else she is told by her master. â€Å"After a brief period of suspense, the will of my mistress was read, and we learned that she had bequeathed me to her sister's daughter, a child of five years old.† I think that before her former master died and she was sent to her master's sister's daughter, the conditions were different. Linda's master taught her how to read and spell, which was a privilege, because most slaves were not taught how to do this. â€Å"While I was with her, she taught me to read and spell; and for this privilege, which so rarely falls to the lot of a slave, I bless her memory.† Chapter II The author's purpose for including this chapter is to show just how unfairly, and cruelly slaves (she) were treated. People saw the slaves as scapegoats and were blamed for everything. She gives many examples of situations in which someone (one of the masters or mistresses) wasn't happy with something and blamed it on the slave(s), forcing them to deal with the harsh consequences. An example is when the cook sends dinner out to Dr. Flint....

Heineken in Cambodia

Heineken Overview of controversial business practices in 2008 Sanne van der Wal & Rob Bleijerveld April 2009 Heineken Overview of controversial business practices in 2008 Sanne van der Wal & Rob Bleijerveld Amsterdam, April 2009 Heineken Overview of controversial business practices in 2008 Colophon Heineken Overview of controversial business practices in 2008 April 2009 By: Sanne van der Wal & Rob Bleijerveld Cover Design: Annelies Vlasblom Funding This publication is made possible with co-funding from the Vereniging van Beleggers voor Duurzame Ontwikkeling (VBDO) Published byStichting Onderzoek Multinationale Ondernemingen Centre for Research on Multinational Corporations Sarphatistraat 30 1018 GL Amsterdam The Netherlands Phone: + 31 (20) 6391291 E-mail: [email  protected] nl Website: Hwww. somo. nl This document is licensed under the Creative Commons Attribution-NonCommercial-NoDerivateWorks 2. 5 License. 1 Introduction This company report has been prepared by SOMO (Centre for R esearch on Multinational Corporations). It provides an overview of business practices that could be regarded as unsustainable or irresponsible which occurred (or might have been addressed) in 2008.The overview below describes only controversial practices and not the positive achievements of a company in the same year. Information on positive achievements can usually be found in a company’s annual and/or sustainability report and on the company’s website. The purpose of this report is to provide additional information to shareholders and other stakeholders of a company on controversies that might or might not be detected and reported by the company itself.This report does not contain an analysis of a company’s corporate responsibility policies, operational aspects of corporate responsibility management, implementation systems, reporting and transparency, or total performance on any issue. For some controversies, it is indicated which standards or policies may hav e been violated and a brief analysis is presented. Apart from this, the report is mainly descriptive.The range of sustainability and corporate responsibility issues eligible for inclusion in this overview is relatively broad and mainly based on the OECD Guidelines for Multinational Enterprises. These Guidelines are used as a general frame of reference in addition to the company-specific standards. Sources of information are mentioned in footnotes throughout the report. The main sources were obtained through SOMO’s global network of civil society organisations, including reports, other documents, and unpublished information.Media and company information databases and information available via the Internet are used as secondary sources where necessary. Heineken has been informed about the research project in advance and was given two weeks to review the report and provide corrections of any factual errors in the draft version. The overview of controversial practices in this rep ort is not intended to be exhaustive. Instead, it focuses on a limited number of issues and cases that might merit further attention or reflection.Where information about the latest developments, either positive or negative, was unavailable, it is possible that situations described in the overview have recently changed. Taking into account these limitations, SOMO believes that the report can be used for improvement and for a more informed assessment of a company’s corporate responsibility performance. For more information, please contact SOMO: SOMO (Centre for Research on Multinational Corporations) Sarphatistraat 30, 1018 GL Amsterdam, The Netherlands Tel. 31 (0)20 6391291 Fax +31 (0)20 6391391 e-mail: [email  protected] nl website: www. somo. nl 2 Heineken Overview of controversial business practices in 2008 Precarious working conditions of Heineken Beer sellers in Cambodia This short overview deals with only one issue: the continuing bad labour and health conditions of s ocalled ‘beer sellers’ in Cambodia, salaried women who wear distinctive Heineken uniforms while exclusively selling Heineken beer in bars and restaurants, alongside those working for its partly owned partner brands (e. . , Tiger, ABC, etc†¦), and for competitors.The work conditions of these women, who are hired by most of the international brewers and their distributors operating in Cambodia 1 , have been criticised for several years, by the Cambodian NGO (Non-Governmental Organisation ) Siem Reap Citizens for Health, Educational and Social Issues (SiRCHESI) 2 . In 2002 the CEO and the Boards of both Heineken Breweries Ltd and Heineken Holding N. V. from here: Heineken) were first notified by SiRCHESI of concerns about the health and welfare of their beer sellers, who continued, in 2008, to be at high risk for HIV/AIDS and alcohol- related health problems, who experience sexual harassment and violence at their workplaces, and who are not paid a ‘living wage'- a salary for a full-time job on which they can support themselves and their family dependents. Press reports going back to 1998, and particularly a story in the Wall Street Journal (2000) had already clearly described the problems before social scientists began systematic data collection. Also SOMO's overview of controversial business practices of Heineken during 2006 for VBDO of April 2007 has called attention to this critical issue. 4 Recent inquiries and research in Cambodia –as part of a longitudinal study (2004-2009) 5 – reconfirm that these bad labour and health conditions still exist. Heineken – and other brands, with whom they both compete and co-operate – have not made significant progress in 2007, nor in 2008 to reduce the high risks to the health and safety of the women beer-sellers in Cambodia nor meet their monthly financial needs.So far, industry efforts to resolve these issues – through the formation in late 2006 of â€Å"Beer Sell ing Industry Cambodia† as a professional brewers association with a code of conduct (COC) for beer sellers – have failed. 1 2 3 4 5 See e. g. â€Å"Heineken en promotiemeisjes in Cambodja – deel A,† R. Feilzer and F. P. van der Putten (p. 85-96) and F. P. van der Putten, â€Å" – deel B† (p. 109-13), in: Bedrijfsgevallen, Eds. W Dubbink and H. van Luijk (Assen: Van Gorcum, 2006). SiRCHESI website, . and ,, and . SiRCHESI’s website http://www. fairtradebeer. com press reports section. Heineken – Overview of controversial business practices in 2006,† Francis Weyzig (SOMO), April 2007 Performed by Staff, volunteers ,researchers and students located in Siem Reap with SiRCHESI, or at Siem Reap Provincial AIDS Office, of University of Guelph (CA), National Center in HIV Social Research (University of New South Wales, AU), Macquarie University (Sydney, AU), University of Melbourne (AU), Australia Volunteers International, Duke Un iversity (North Carolina, US), Oxford University (Oxford, UK), University of Technology Sydney (AU), as welll as University of Maastricht, NL, National University of Singapore, and Staffordshire University (UK).Data and analyses were provided through Ian Lubek, international advisor to SiRCHESI. The SIRCHESI interviews with beer sellers were conducted either in the workplaces or during health workshops. 213 interviews were conducted from 2004-6, and 324 from 2007-9. 22 beer sellers worked for Heineken and partner brands, 57 worked for Carlsberg brands such as Angkor; 56 sold AB-INBEV brands, 1 sold a SAB-Miller brand, and the remaining 201 sold other brands including Dutch brands Bavaria, Hollandia, as well as Corona, San Miguel, Singha, Oettinger, Asahi, etc. 3 Below, some controversial aspects of the situation in 2008, revealed by SiRCHESI, are described. More background data can be found on the SiRCHESI website dedicated to this issue www. ethicalbeer. com. On the same website mo re new details on the longitudinal study, including data for 2008-9, are published by SiRCHESI 6 as well. Low income and transparency As in 2006, SiRCHESI research 7 confirms that Heineken is not paying a â€Å"living wage† in 2008.If Heineken and its Asia Pacific Breweries partner brands (Tiger, ABC, Anchor, Cheers,etc. paid their beer sellers the current industry standard (2008) of just over 8 US dollar per beer case as commission, they would earn – based on SiRCHESI’s observations of sales of more than 3 cases per night – about 700 US dollars per month which amounts to about 10 times the current fixed salary. BSIC brand sellers are consistently paid less each month than non-BSIC brands yet increasingly sell manifold more beer each year 8 . In fact workers get less than 2. 5 percent of the sale, and face severe nightly workplace health and safety risks. Part of this profitability for Heineken is based on the sellers’ own nightly consumption of ab out 6 percent of sales, which adds harm and risk to their working situation.For a number of years, Heineken officials reported paying bonuses to the beer servers, yet SiRCHESI interviews showed that from 2002 onwards these were not being received by the beer sellers. In fact in 2008 they reported receiving monthly earnings of 71 US dollars which is considerably lower than the 84 US dollars reported by non-BSIC sellers and the 85 US dollars Heineken headquarters reports paying 9 . SiRCHESI estimates that 71 US dollar monthly is still less than half of what would be enough to provide for them and their family dependents. This situation of underpayment –first reported to Heineken executives in 2002 and unchanged ever since- puts terrible pressures on the women to support their families and to make ends meet, compelling some to sell unsafe sex to customers in desperation to supplement insufficient income.In general it is difficult for Heineken beer sellers to know to what benefit s and bonuses they are entitled because Heineken is failing to provide beer sellers copies of their work contracts specifying working conditions, benefits such as severance pay and maternity leave, and exact earnings– all, transparently. In 2008, no beer seller could show SiRCHESI a copy of their signed contract. Several Heineken beer sellers said they did have signed contracts but that these contracts had gone to the distributors' Head Quarters in Cambodia. In 2008 SiRCHESI asked the distributor and BSIC for copies of these contracts they but were told they were â€Å"proprietary† and could not be disseminated. 6 7 8 9 See for example: â€Å"Ab-Inbev, Carlsberg, Heineken and other international brewers are yet again in 2008-9 behaving badly to women beer sellers in Cambodia†, SiRECHESI, April 2009, http://www. ethicalbeer. com/read/April2009-INFO.df AND â€Å"Professor criticizes international beer companies for not being proactive enough in Cambodia (2008-9) to protect their women beer sellers from hazardous, harmful, and potentially mortal workplace health and safety risks: Citing recent research, he urges company executives, brand consumers and shareholders to implement immediate changes. †, SiRCHESI, April 2009, http://www. ethicalbeer. com/read/APRIL2009Press-info. pdf This overview builds on SiRCHESI published (see footnote directly above) and unpublished information provided/communicated directly to SOMO by As Tiger Beer seller Sophea wrote to management at Cambodian Breweries Ltd. asking for a salary increase to 100 US dollars monthly: â€Å"Our claim is absolutely justified. The quantity of our sales increased, and the price of beer increased too†¦. Now it {Tiger Beer} is sold for 2. 90 US dollars. â€Å" (Cambodge Soir, 18-25 June, 2008). â€Å"Biermeisjes bezorgen Heineken hoofdpijn,† Financiele Telegraaf (p. 27) 10 mei 2008 4 Heineken Overview of controversial business practices in 2008 Workplace health an d safety issues Heineken’s HIV/AIDS policy of 2002 has promised coverage to all its workers world-wide 10 . However the company and partner brands are still not providing free HAART (highly active anti-retroviral therapy) for their HIV positive beer sellers as they do for their personnel in Africa.What compounds the situation is that most beer-sellers are currently excluded from Government ARVT (anti-retroviral therapy) programs due to Cambodia and the Global Fund’s inability to implement access in 2008-9 for all persons living with HIV. Simple factors such as lack of daily transportation to a distribution site mean that many beer-sellers cannot receive ARVT. In Africa Heineken has solved this problem through workplace distribution of HAART. Heineken is also not providing enough effective workplace health and safety education about HIV/AIDS, reproductive health and alcohol risks before employment begins. Although Heineken proactively developed the Selling Beer Safely ( SBS) Program in 2003 it has not been offered to every employee; moreover, the number of beneficiaries of SBS is declining markedly.Of 224 Heineken family sellers in the SiRCHESI research sample of 2004 to 2009, 31. 2 percent had received no health training at the time of the interview. It should be mentioned that this is better than the industry average of 43. 3 percent that received no health and safety training about being a beer seller. In 2004, 22 percent of Heineken or Tiger beer sellers had received SBS training. However in 2008 this share had declined to 4. 7 percent. However, when SiRCHESI asked whether they had received either the SBS or any other in-house training program 11 , BSIC beer sellers did modestly better: 27. 8 percent reported in-house training, while only 8. 3 percent non-BSIC sellers reported in-house training.But the most serious criticism is the procrastination in supplying this education. Of 224 Heineken family beer sellers interviewed, 16 (7. 1 percent) re ceived training before they started, and a further 6 (2. 7 percent) received it on the first day. 80/224 or 35. 7 percent had received it in the next 6 months, while the remainder had training in the next 18 months or not at all (122 or 54. 5 percent). Hence only 9. 8 percent had been given some early-warning training – before or on the first day of work- about the risks and harm possible for beer-sellers themselves, damage to the fetus during pregnancy, or contraction of HIV/AIDS or a sexually transmitted infection (STI).Although the BSIC COC which Heineken claims to uphold explicitly forbids workplace drinking of alcohol, SiRCHESI found that only 6% of Heineken (7. 6% of BSIC brands) beer sellers were in fact abstaining in 2008. For those who continue to drink, the mean alcohol consumed nightly by BSIC sellers in 2008 was 1. 48 litres nightly or 6 standard drinks (N=103), while 1. 53 litres (7 standard drinks) were consumed nightly by Heineken beer family servers (N=89). Al l of these levels are well above levels of national guidelines for responsible drinking as set for women by 23 countries surveyed by the International Center For Alcohol Policies (ICAP) 12 including the Netherlands.This means that these women have an increased risk for physical (raised blood pressure, stroke, and liver cirrhosis), mental, and social problems associated with alcohol abuse. While (excessive) workplace drinking continues to be a critical issue in Cambodia it has been observed by SiRCHESI to no longer exist in nearby Singapore. 10 11 12 â€Å"Heineken's HIV/AIDS Policy – contribution of a private company,† HEINEKEN COR P. COMMUNICATION ~ 02 92857455 NO. 023, by Heineken International, 18 April 2002 (at http://fairtradebeer. com/reportfiles/heinekenaidspolicy2002. pdf) SiRCHESI: â€Å"other in house-training† are mostly shorter than the 3 day SBS training some just get 1-2 hours – the â€Å"refresher courses† International Center For Al cohol Policies (ICAP) in International Drinking Guidelines Reports 14

Human Resource Management Overview Essay

Introduction Most go through their day to day actions giving no thought to all of the people that are behind the scenes making everything that they do go smoothly. From making important business calls on your cell phone while traveling, to getting your lunch in a timely fashion so that you can get back to work. Without human capital none of this would be possible, these businesses are nothing more than a bunch of empty building once the human capital is removed from them. IT is the job of the Human Resource Management (HRM) to make sure that there are qualified people filling all of these positions to make business flow as smoothly as possible every day and to make your experience the best that it can be. The following paper will address what Human Resource management is as well as what the primary function of this department is. Lastly it will address the role that HRM plays in an organizations strategic plan. What is Human Resource Management? Human Resource Management is a function of a group of a group of people or a department that has the primary tasks of recruiting, training, and compensating employees, as well as ensuring that all rules and regulations are followed and that all of the tasks being completed are in line with the organizational goals. This is accomplished through the six core functions of HR which are; Workforce Management, Total Rewards, Risk Management, HR Development, Employee Relations, and Strategic Management (DeCenzo & Robbins, 2013). The workforce management function of HRM is primarily concerned with workforce planning and employment strategies. This includes determining what skills are necessary to complete the jobs, recruiting and  selecting the best possible people to fill the position, and maintaining the records of each employee as well as those that have been terminated. The total rewards function of HRM is the function that deals with all aspects of employee compensation, from salaries to benefit packages and everything in between. Receiving ones paycheck, a raise, bonus, or enrolling in medical or dental coverage that you are eligible for are all things that are taken care of through the total rewards function of HRM. The primary job of those who work in the risk management function of HR is to identify any labor related risks to the employees and the organization, and then to assess, manage and monitor these risks. This is not only limited to safety issues but also includes improper or inadequate training and failure to comply with legal regulations regarding labor laws. The employee relations function of HR deals with just that, Employee relations. It is their job to try and build and maintain positive relationships between the employers, mangers and employees. They are also the ones that will be contacted when there is a dispute that needs resolved or workplace policies or procedures need to be implemented or changed. Lastly the strategic management function of HR is a combination of all of the other core functions as they have been listed above. The strategic management function is primarily concerned with ensuring that all other aspects of HRM interact effectively throughout the organization and all contribute to the goals or support of others in reaching the goals of the organization. What is the primary function of HRM? The primary function of HRM can become quite foggy at times. You see the primary of function of HRM will vary depending upon which area of HR you are immediately dealing with. However, since it is impossible for a business to operate without human capital then clearly the primary function of HRM is to manage the human capital within an organization and provide a clear link between the goals of the organization and all whom work there (DeCenzo & Robbins, 2013). Mind you the HRM team is not the ones that are making the decisions; they are merely making suggestions and bringing insight to those that do make the decisions for the organization that they work for. When the HR is performing well then it should be easy for the employees to see the link between what it is that they do and how it contributes to the  achievement of the organizations goals. What is the role of HRM in an organization’s strategic plan? The role of HRM in an organizations strategic plan is actually quite complex. HRM’s role is to work with the decision makers in the organization and evaluate and develop and organizational strategy. This is in part accomplished through identifying, analyzing, and balancing of external opportunities and threats with the internal strengths and weaknesses. By identifying external opportunities and threats they are then able to work closely with the decision makes to develop a clarified business strategy after which they will realign the HR functions and the key people practices so that they work best with the organizational strategy. They will then create and needed competencies and behaviors to get everyone on the same page and realizing the strategy of the business and the results that are to be expected. Lastly they will re-evaluate the strategy and refine it where necessary to help the business stay aligned an on track to accomplish the goals that it has set out to accomplish. Conclusion Businesses would be nothing other than hollowed out building without the people that are involved in running them daily. Without the human aspect of a business then a business would not be. It is for this reason and this reason alone that makes the HR department or team of any business to be that of a highly valued one, because without the proper people in the proper places, with the proper vision and goals, any organization is going to fail. HRM makes it possible to accomplish all of these and do so consistently. Reference DeCenzo, D., & Robbins, S. (2013). Fundamentals of Human Resource Management (11th ed.). Hoboken, NJ: John Wiley & Sons.

Expansion of U.S. Companies in Africa Essays

Expansion of U.S. Companies in Africa Essays Expansion of U.S. Companies in Africa Essay Expansion of U.S. Companies in Africa Essay Expansion of U.S. Companies Introduction Over the years, America has developed various companies in some African countries. The companies are aimed at increasing the economy in the U.S. while strengthening its resources overseas and enhancing international relations. Some of the companies in Africa have influenced politics in America and the related countries to allow smooth business operations. If a country’s economy is strong, it increases its wealth and promotes good business relations with the outside world. Expansion of companies shows the growth of a business. This leads to opportunities that benefit all people and countries associated with the company. Expansion mainly increases employment opportunities, which in turn improves the development of a nation. Expansion of a company is usually triggered by the need to increase market and maximize profits. However, it has various effects on the development and economy of a country. The issues, effects and significance of expansion are an important topic for discussi on especially in the growing world economy. Several U.S. companies have expanded in Africa and the implication of their growth on stocks, government policies, employment and the development of America. Issues Recently, the U.S. developed an interest of conducting business in some African countries. These interests were triggered by factors such as the nature of land, good climate and availability of resources in the countries. However, the establishment of Chinese companies in Africa has hindered efficient expansion by the U.S. As a result, some companies have grown in Africa but have faced many barriers during expansion. Despite the barriers, some companies have taken advantage of the loopholes to increase the economy. Examples of these companies that have expanded immensely are, Coca Cola Company, General Motors, Isuzu Motors Limited, Ford Motors and Cummins Incorporation. The growth of these companies has affected America and Africa in many ways. The need for expansion of companies in Africa by America was fueled by the rise in China’s economy. It led to an urge by American companies to compete for market with China. The market opportunities in Africa influenced the struggle between China and America to dominate business. Cummins Incorporation, which is an American company that deals with the supply of trucks and engines, has taken drastic measures of increasing sales of its products in Africa, to restore stiff competition between America and China. Last year, it was noted that China had gained much more popularity in South Africa from the design and production of truck engines and equipment. Another measure that America has taken is generated from a company like Caterpillar Incorporation, which deals with making construction products. The company has invested funds used to train personnel and build infrastructure to accommodate its workers in countries like Mozambique and Zambia. General Electric Company, which deals with the supply and manufacture of aircrafts, has developed an aircraft-leasing administrative center in Ghana as another measure. The administrative centre serves as the company’s headquarters for the west and central part of Africa. All these measures were aimed at improving the stock value and economy of the U.S. Analysis The measures outlined above show the main reason behind the expansion of American companies in Africa. It is evident that the Chinese rapid growth in economy affected the market of many products in the U.S. China developed companies that shared the same goals as American firms, but both countries were competing for market and exploration of resources in Africa. China discovered opportunities in Africa before the U.S. and utilized them to strengthen the economy. The strong economy in China influenced an increase of stock value by the U.S. in order to bridge the gap in the economy between the two countries. However, increasing the stock value has negative effects on market. This forced the U.S to develop interests in Africa to maintain balance. Worldwide statistics show the interests of other continents in Africa are extremely high. This is because Africa is the largest source of market and it is developing rapidly in terms of resources and infrastructure. There are many changes being made in Africa currently that will make it a market hub. Improvement of infrastructure has influenced the growth and expansion of many companies in various countries. In South Africa and Nigeria, for example, the development of sophisticated buildings has led to the expansion of existing restaurants and hotels. A restaurant such as KFC has led to imports of poultry products by the U.S to Africa. Good climate, agriculture and tourist attractions in countries like Kenya and Ethiopia have played a major role in expansion of U.S companies. This is because these factors are influential in determining the location of a company. The healthy climate gives favorable working conditions and China has focused most of its development there by building large telecommunications networks in Ethiopia. America was aimed at expanding more in Asian countries that lacked these resources. Upon the discovery of Africa’s potential, America reevaluated its plans and focused more towards expansion in Africa. China has also developed equipment for processing products electronically in Africa. Products such as pharmaceuticals and processed perishables have gained a vast market in Africa, therefore, increasing China’s economy. By producing and marketing these products in Africa, China incurs minimal costs of production while creating opportunities for Africans such as employment and training. China is also a leading developer of mobile phone networks through Huawei Technologies Company. This is due to the development programs established in Africa that provide the Chinese with contracts for installing networks in various areas. However, America has not taken advantage of these opportunities, and this has not fully exploited its potential in developing technology. Some American government policies affect relations between the U.S and Africa. Since most African countries have one-party governments, establishing strong business relationships with America is difficult. However, the Chinese government has less strict policies, which facilitate smooth interactions with Africa. The African growth and opportunity act of 2000 of America allows trading between African countries that are viewed to be developing politically, socially and economically. This act affected the development of some companies in remote countries that have good land and favorable climate. However, China had no such policies. In fact, the state council of china encouraged mutual gain when conducting business in Africa with the aim of promoting social progress. American companies have faced some challenges in expanding in Africa. The development of infrastructure in the past years has led to congestion in countries like Nigeria. This has made it difficult to arrive on time in various working places due to the perils of traffic. As a result, it has forced American companies to construct on the outskirts of Nigeria, which also poses a challenge for workers in a company in terms of transport. This challenge is faced because America delayed in establishing its companies in Africa due to the lack of knowledge and confidence in the continent. This enabled China to take time to develop appropriately especially with the availability of oil in Nigeria. Conclusion According to the article, it is evident that America is struggling maintain competition with China. China has exploited Africa, and as a result, stocks in America are reducing in value. This has forced many leading companies in America to expand in Africa because of its rapid growth and available resources. The delay in discovering potential market in Africa by the U.S. is highlighted as a threat to the economy of America. Currently, the U.S. is struggling to keep up with China economically, and this has led to the rise of companies in Africa. Kindly find the article at: http://online.wsj.com/article/SB10001424052748703841904576257233342891732.html

Dorothy Parker Quotes

Dorothy Parker Quotes Dorothy Parker was a writer and critic for such magazines as Vogue, Vanity Fair, and the New Yorker. She also wrote a number of screenplays, poetry, and short fiction. A founder of the Algonquin Round Table, she was known for her pointed verbal wit and satire, often focused on the life of middle class young women, newly liberated from Victorian restrictions. Selected Dorothy Parker Quotations Im never going to be famous. I dont do anything, not one single thing. I used to bite my nails, but I dont even do that anymore.I dont care what is written about me so long as it isnt true.Wit has truth in it; wisecracking is simply calisthenics with words.Oh, I said it, alright. You know how it is. A joke. When people expect you to say things, you say things. Isnt that the way it is?I know that there are things that never have been funny, and never will be. And I know that ridicule may be a shield, but it is not a weapon.You cant teach an old dogma new tricks.Women and elephants never forget.I might repeat to myself slowly and soothingly, a list of quotations beautiful from minds profound- if I can remember any of the damn things.I havent got a visual mind. I hear things.Men seldom make passes at girls who wear glasses.Four be the things Id have been better without:  Love, curiosity, freckles, and doubt.A girls best friend is her mutter.I require only three things of a man. He mus t be handsome, ruthless, and stupid. Take care of luxuries and the necessities will take care of themselves.Salary is no object; I want only enough to keep body and soul apart.Money cannot buy health, but Id settle for a diamond-studded wheelchair.As I was saying to the landlord only this morning: You cant have everything.The two most beautiful words in the English language are cheque enclosed.As far as I am concerned, the most beautiful word in the English language is cellar-door.If you want to know what God thinks of money, just look at the people he gave it to.The cure for boredom is curiosity. There is no cure for curiosity.Inertia rides and riddles me; /  The which is called Philosophy.The best way to keep children home is to make the home atmosphere pleasant- and let the air out of the tires.Now, look, baby, Union is spelled with 5 letters. It is not a four-letter word.It serves me right for keeping all my eggs in one bastard.All I need is room enough to lay a hat and a few friends. Heterosexuality is not normal, its just common.Scratch a lover, and find a foe.Scratch an actor and find an actress.Men dont like nobility in woman. Not any men. I suppose it is because the men like to have the copyrights on nobility- if there is going to be anything like that in a relationship.That woman speaks eighteen languages, and cant say no in any of them.People are more fun than anybody.I like to have a martini,Two at the very most.After three Im under the table,after four Im under my host.Did I enjoy the party? One more drink and Id have been under the host.Id rather have a bottle in front of me, than a frontal lobotomy.You can lead a horticulture, but you cant make her think.Ducking for apples- change one letter and its the story of my life.Brevity is the soul of lingerie.This is not a novel to be tossed aside lightly. It should be thrown with great force.She runs the gamut of emotions from A to B.The only -ism Hollywood believes in is plagiarism. If all the young ladies who attended the Yale prom were laid end to end, no one would be the least surprised.As only New Yorkers know, if you can get through the twilight, youll live through the night.He (Robert Benchley) and I had an office so tiny that an inch smaller and it would have been adultery.Misfortune, and recited misfortune especially, may be prolonged to that point where it ceases to excite pity and arouses only irritation.Constant use had not worn ragged the fabric of their friendship.Brendan Gill, in introducing  The Portable Dorothy Parker:  The span of her work is narrow, and what it embraces is often slight.To a man she found annoying:  With the crown of thorns I wear, why should I worry about a little prick like you?About being refused admittance to a casino in Monte Carlo in 1926 because she did not have stockings on:  So I went and found my stockings and then came back and lost my shirt.When being questioned by the FBI, 1952: Listen, I cant even get my do g to stay down. Do I look like someone who could overthrow the government? When asked whether she was Dorothy Parker:  Yes, do you mind?Summer makes me drowsy.Autumn makes me sing.Winters pretty lousy,But I hate Spring.Razors pain you; Rivers are damp;Acids stain you; And drugs cause cramp.Guns arent lawful; Nooses give;Gas smells awful; You might as well live.Oh, both my shoes are shiny new /  And pristine is my hatOh, life is a glorious cycle of song,A medley of extemporanea;And love is a thing that can never go wrong;And I am Marie of Romania.The pure and worthy Mrs. StoweIs one we all are proud to knowAs mother, wife, and authoress- Thank God, I am content with less!After the death of her husband a conversation with a neighbor:Neighbor:  Ã¢â‚¬Å"Is there anything I can do?†D.P.: â€Å"Yes, get me another husband.†Neighbor:  Ã¢â‚¬Å"Dottie, thats a terrible thing to say!†D.P. â€Å"All right, get me a ham and cheese on rye.†That would be a good thing for them to cut on my tombstone: Wherever she went, including here, it wa s against her better judgment.I like to think of my shining tombstone. It gives me, as you might say, something to live for. To Lillian Hellman, her executor, a few days before dying:  Lilly, promise me that my gravestone will carry only these words: If you can read this, youre too close. About These Quotes: Quote collection assembled by Jone Johnson Lewis. This is an informal collection assembled over many years. I regret that I am not be able to provide the original source if it is not listed with the quote.

Redundant Object Pronouns in Spanish

Redundant Object Pronouns in Spanish Although by definition, pronouns are words that stand for nouns, it is common in Spanish to use a pronoun, particularly an object pronoun, in addition to the noun it stands for. Such use of redundant object pronouns occurs most commonly in the following situations. When the Object of a Verb Precedes the Verb Placing the object before the verb, while certainly common in Spanish (and possible in English to give a sentence literary flavor), can be at least slightly confusing to the listener. So placing a redundant object pronoun helps make it clearer which noun is the subject of the verb. The redundant object pronoun in these cases is mandatory or nearly so, even when the form of the verb (such as it being plural) might seem sufficient to indicate what the subject and object of the verb are. For example, in the sentence El buffet de desayuno lo tenemos de mià ©rcoles a domingo (We have the breakfast buffet from Wednesday to Sunday), buffet de desayuno is the object of the verb tenemos. The lo (which isnt translated but in this case would be the equivalent of it) is redundant but still required. Some examples, with the redundant object and pronoun in boldface: Al presidente le vamos a preguntar quà © es lo que ha ocurrido. Were going to ask the president what it is that has happened.La piscina la encontramos muy sucia. We found the swimming pool very dirty.Los instrumentos los compraron gracias al apoyo financiero de su madre. They bought the instruments thanks to the financial support of their mother. Youll probably come across the redundant object pronoun most often with gustar and verbs similar to gustar, which normally put the object ahead of the verb. Note that when these verbs are used, they are usually translated with the object in Spanish being the subject of the English translation. A Cristal le gusta estar rodeada de gente. Cristal likes to be surrounded by people.A Sakura le encantaba ir al parque a jugar. Sakura loved going to the park to play. To Provide Emphasis Sometimes, especially in Latin America, the redundant pronoun may be used even when the object appears after the verb in order to provide emphasis. For example, in Gracias a ella lo conocà ­ a à ©l (thanks to her, I met him), the lo remains even though the speaker added a à ©l to call attention to the person the speaker met. We might convey a similar thought in English by placing strong stress on him. When the Object of the Verb Is Todo   Although not required, todo (or its variations) as an object is sometimes accompanied by a redundant pronoun that matches it in number and gender. En sus ojos lo puedo ver todo. In your eyes I can see everything.Tengo mucha fà © que los van a rescatar a todos vivos. I have a lot of faith that they are going to rescue everyone alive. To Repeat the Object of a Verb in a Relative Clause   Sometimes people will use a grammatically unnecessary object pronoun in a relative clause (one that follows a  subordinate conjunction). For example, in Hay otros aspectos del gobierno que los aprendemos (There are other aspects of the government that we learned), the los isnt needed, but it helps link aprendemos to aspectos. This usage isnt particularly common and is sometimes considered grammatically incorrect.

Arm Crank Ergometry Assignment Example | Topics and Well Written Essays - 2000 words

Arm Crank Ergometry - Assignment Example Previous studies have considered issues linked to exercise efficiency. This line of enquiry provides important information associated with the relationship between the energy required to achieve a given amount of external work. In the context of a competitive athlete or a patient in a clinical setting, exercise efficiency provides a useful insight into functional capacity. When presented in either gross or net terms, exercise efficiency has been shown to increase in line with workload during both cycling and ACE. Several studies have also demonstrated there to be a clear interaction between crank rate and workload with respect to oxygen consumption during cycling and ACE. Additionally, previous studies have considered exercise efficiency in a number of different ways, including the calculation of gross, net, and delta values. Powers et al. (1984) showed that VO2 during ACE increased in line with crank rate. At workloads of 15 and 30W, VO2 was lower and exercise efficiency was higher, using crank rate of 50 and 70 rev.min-1 compared to 90 rev.min-1. Furthermore, when the workloads were increased to 45 and 60W, exercise efficiency remained higher using 50 compared to 90 rev.min-1. ... Furthermore Smith et al. showed that while variations in crank rate (50, 70 and 90 rev.min-1) influenced measures of exercise efficiency a relatively low workloads (30 to 70w) during ACE, these discrepancies did not exist at 90w. These data are interesting as they question the previously reported interaction between crank rate, workload and exercise efficiency. The purpose of this practical will be to further investigate 1) if exercise efficiency parameters change in line with variations in crank rate and 2) to determine whether or mechanical efficiency varies according to the external workload being achieved. In these respects, values of gross, net and work efficiency will be considered. RESULTS. The results of the experiment are summarised in the table 1 in the Annex. You can see that the index FE02 (fractional concentration of oxygen in expired air) was varied in the range between 16.2 and 18.5 ml O2/kg/min (range is 2.3 ml O2/kg/min). Consequently the mean of 35 measurements was equal to 17.1 and its standard error is 0.09. The variance of FE02 gross value was 0.34 and standard deviation - 0.56. The distribution of the sample was asymmetric and not normal (skewness is 0.72 and kurtosis 0.29). The values of median, lower and upper quartile were equal to 17.0, 16.7 and 17.4 correspondingly. The mean value of FECO2 (fractional concentration of CO2-exhaled) was equal to 3.660.08 while the variance and standard deviation was 0.24 and 0.49 respectively. The median of the index was 3.73 and the first (lowest) and third (upper) quartiles were equal to 3.45 and 3.98 while the minimum and maximum were 2.52 and 4.44 (range is 1.92 ml CO2/kg/min). The skewness and kurtosis were not equal to zero thus the distribution was not symmetric. The data

Healthcare Programs Essay Example | Topics and Well Written Essays - 1000 words

Healthcare Programs - Essay Example TRICARE represents the healthcare program utilizing military healthcare systems as the main providers. This program is funded and supported through civilian providers and facilities, and includes provision of healthcare services to military personnel and their families of the USA, past or presently active. The introduction of tricare was primarily a strategy in the eighties and the nineties, in response to the increased healthcare costs in the USA, as well as the changes in the modernization trends. Tricare was perceived to be a feasible and economic way to save costs while improving access and choice to healthcare services. The development of TRICARE has expanded significantly, and has now come to be a part of 40% of the USA hospitals. Increasingly high numbers of healthcare personnel and providers now form a part of the TRICARE provision team. (Carrato, 2003) The effectiveness of Tricare is very evident if comparing to other healthcare systems such as CHAMPVA. The differences run from basic infrastructures of the plans. While TRICARE, formerly CHAMPUS, is a medical insurance program carried out by the department of defense, CHAMPVA is run through VA. The members differ with regards to their status as retired or non retired from military services, tricare being entertaining to the retired personnel. CHAMPVA restricts itself to those who are either 100% disabled personnel, or either dead. This does not to be so for tricare patients. CHAMPVA does not entertain veterans, which forms a large part of the tricare members. Also, CHAMPVA has rules about access and obtaining of prescriptions. The above mentioned differences help to understand some of the key differences that make tricare a much superior healthcare program over others. (Tricare for life, 2001) Tricare has many services at its disposal, which are both comprehensive as well as targeted in their approach to diseases. The triple option benefit in the system allows the enrollment of many people with a wide range of healthcare services. Now it has become active in the advanced medical areas of cancers, along with including age old programs of immunizations etc. The scope of tricare therefore is very vast, with much promise of improvement. Tricare gives these services through a range of programs, which include the Prime Preventive Services, the Pharmacy Program, and Dental Coverage etc. Tricare has proven its worth through its impressive reports of its performances. Perhaps the most demonstrative of Tricare's effectiveness is looking at the claims processing capacity and the speed with which these are carried out. Around 755 of the claims are addressed within 21 days of being placed, an impressive statement of the quality and the efficiency of Tricare. (Bailey, 1999) With the pr ojected increase of health costs by7.3% by the year 2011, Tricare's potential role in reducing these costs is highly promising. (Carrato, 2003) One of the proof that tricare has shown constant delivery with respect to healthcare is its successful maintenance of its enrollment fee. The active duty members have almost no costs for care, which is provided in the military settings. Pay for a service is very high

Personal ethics development Essay Example | Topics and Well Written Essays - 750 words

Personal ethics development - Essay Example The process of testing rules comprises of its universality i.e. can the rules be universally applied to everyone or it treats people as ends but not the means. Every individual has some of the sources where he or she draws some of the basic principles in life that forms the basis of what is wrong or right behavior. In several instances, the following are some of the major sources of ethics. Childhood upbringing- every person learns ethics from his or her parents through either words or most importantly through their actions. I learned some of the ethics by observing and listening and observing what my parents as I grew up. Life experience- at a later stage in life, some of the events directly and consciously shapes the ethics of an individual. For instance, an individual who was treated unfairly during a road accident may most likely have negative attitude in life towards people who treated him or her unfairly. Religious beliefs- nearly most of the religions in the world teach similar code of ethics that emphasizes on respect for other people’s rights, honest and selflessness. Therefore, whether in business or in business situations, religious people act in a manner that is seen as being ethical A person’s ethics can be displayed in the place of work since an individual and the organization can both affect each other’s actions and behavior. Team leaders have a great impact on their team’s behavior and ethics. A place of work is a good place to learn ethics since employees affect each other’s psychology and moral behavior. Therefore employees act as each other’s source of inspiration Good ethics assist an individual in understanding his or her working environment. It also assists an individual to wheedle with team members both in junior and senior positions in a friendly way. This assists in creating conducive working environment thus increasing the performance level. A

Math Edu Essay Example | Topics and Well Written Essays - 500 words

Math Edu - Essay Example First, students can be shown a square along with the length of its sides. Ask students to calculate its area. Next, pass out several cubes to the class so that there are enough for everyone to look at. These cubes should preferably have the same approximate side measurements as the square previously displayed. After explaining that surface area is the total area of the surface on the outside of an object, ask students how many sides there are, and what the shape of each side is. Ask them to make the connection themselves as to how to find the surface area of the cube. If they do not get it at first, hold up a picture of the square they just found the area of and compare it to the sides of the cube. They should be able to recognize that to find the surface area of the cube you multiply the area of the square by the number of squares/sides on the cube. Another good introduction or way to reiterate an understanding of how to find the surface area of a cube is to transform a two-dimensional drawing into a three-dimensional object. Pass out pieces of paper with six large squares on them. These squares should be arranged in a way that four are next to each vertically and one square is on each horizontal side of the third square. (It should resemble a cross).

The danger of smoking Research Paper Example | Topics and Well Written Essays - 1750 words

The danger of smoking - Research Paper Example Therefore, it is extremely essential to increase the level of awareness of the general public regarding the ill effects and hazards of smoking. The cigarette smoking might immediately change the precious life of the human being into death through stroke or heart attack. According to Gary Ford, it is stated that habit of consuming tobacco is more influential rather than health consciousness. Therefore, these individual consider tobacco smoking to be a passion or relaxation from their mental tension and so, they consume tobacco without any distress for health. Moreover, most of the individual treat smoking as a sense of status and style and so do not believe in the statistics of deaths presented by WHO or National Health Service (NHS). But they always remain in the top-most position in the list of deaths caused for excessive smoking of tobacco. Therefore, in order to decrease the rate of deaths or health related disorders, the passion of tobacco smoking needs to be reduced significantly. Tobacco smoking is extremely dangerous as it means the inhalation of numerous harmful chemicals or by-products of smoke such as nicotine, tar and carbon monoxide. Nicotine is the addictive constituent of tobacco (Ford 525). When nicotine is smoked, then immediately the molecules get inside the lungs of the individual. Then these nicotine molecules get absorbed by the blood stream and travel to the brain and lock the specific receptor regions. However by locking the specific receptor regions, the brain gets affected in a way that hinders the metabolism and appetite of the individual. Carbon monoxide is also another important ingredient of tobacco smokes. Carbon monoxide is also a poisonous gas inhaled into the lungs and absorbed by the blood cells of the body. After being inhaled, carbon monoxide reduces the amount of oxygen present in blood cells and so numerous cells die, because of lack of oxygen supply. However,

Marketing Essay Example | Topics and Well Written Essays - 2500 words - 1

Marketing - Essay Example The headquarters of the country is California United States, but HP operates its business around the world. HP was founded in 1939 by Bill Hewlett and David Packard. HP offers wide range of products such as laptops, printers, inks, toners, PCs, etc. HP launched its first inkjet and laser printers in the year 1984. However, these printers were specifically designed for the desktops. In the 90s, HP decided to enter the printer market with range of high quality and innovative printers. Now HP is among the top players in the printer industry. Companies are coming forward to invest their earning in planting more trees, reducing pollution and chemical wastes and gases. They are also bringing out several new eco-friendly and technologically improved products by using 100 % recyclable materials. In this study we would recommend a new product idea HP to introduce an eco-friendly technology in the printer which involves reprinting of the same paper by erasing its ink. This would not only give HP an edge over its competitors, but also make it a market leader from a major player. New Product HP can introduce a green or eco-friendly printer which would reduce the wastage and usage of paper. In this manner it would also assist in saving natural resources like trees and water. A new technology would be integrated in the green printer through which the printer can reprint on the same paper for many times. Not only the individual customers but also business houses, companies or firms are willing to pay higher prices for using eco-friendly products. This would also help in reducing the carbon footprints. It would be one of the most appropriate and innovative technology in the printer industry, so HP should patent the idea and the technology to protect the product manufacturing rights and the product idea. This technology can be also called the reverse printing technology. Though this product would be priced higher than the general printers because of its unique selling propositi on, but it would reduce the cost of papers for the customers. Target Market Target market involves a group of customers for whom the company designs, and develops a product or service. The marketing strategies and mix are designed and prepared by the marketers to satisfy the target customers. Targeting can be differentiated and undifferentiated. Differentiated targeting signifies focusing a particular type of customers and leaving out the rest, but in undifferentiated targeting, the marketer focuses on the mass, so customized product is not developed in this case. The printer market can be segmented into three divisions, first is the personal or individual users, second is the business houses, firms or companies using for their official purposes, and third is the printing businesses that use printers to print for other companies (Atkielsk, 2001, p. 1). Since reverse printing technology is niche and obviously HP would set the price of green printer higher than that of general printer s. So the individuals building for personal usage might not afford it. Moreover, the company cannot launch it at a low price because of its high cost of production, promotional and other costs. Therefore in the initial stage the target customer groups would be the firms, companies and the printing businesses that use it for commercial purposes. Another reason is that the printing companies, firms or organizations print millions of pages every day, so level

The danger of smoking Research Paper Example | Topics and Well Written Essays - 1750 words

The danger of smoking - Research Paper Example Therefore, it is extremely essential to increase the level of awareness of the general public regarding the ill effects and hazards of smoking. The cigarette smoking might immediately change the precious life of the human being into death through stroke or heart attack. According to Gary Ford, it is stated that habit of consuming tobacco is more influential rather than health consciousness. Therefore, these individual consider tobacco smoking to be a passion or relaxation from their mental tension and so, they consume tobacco without any distress for health. Moreover, most of the individual treat smoking as a sense of status and style and so do not believe in the statistics of deaths presented by WHO or National Health Service (NHS). But they always remain in the top-most position in the list of deaths caused for excessive smoking of tobacco. Therefore, in order to decrease the rate of deaths or health related disorders, the passion of tobacco smoking needs to be reduced significantly. Tobacco smoking is extremely dangerous as it means the inhalation of numerous harmful chemicals or by-products of smoke such as nicotine, tar and carbon monoxide. Nicotine is the addictive constituent of tobacco (Ford 525). When nicotine is smoked, then immediately the molecules get inside the lungs of the individual. Then these nicotine molecules get absorbed by the blood stream and travel to the brain and lock the specific receptor regions. However by locking the specific receptor regions, the brain gets affected in a way that hinders the metabolism and appetite of the individual. Carbon monoxide is also another important ingredient of tobacco smokes. Carbon monoxide is also a poisonous gas inhaled into the lungs and absorbed by the blood cells of the body. After being inhaled, carbon monoxide reduces the amount of oxygen present in blood cells and so numerous cells die, because of lack of oxygen supply. However,

Consumer Preference of Brighton & Hove Teenagers on Organic Food Essay Example for Free

Consumer Preference of Brighton Hove Teenagers on Organic Food Essay There have been many studies investigating the influences on consumer purchasing and consumption of organic foods. It has a Journal of the Human Environment that argues that parts of researches have frequently taken the form of asking consumers directly about their reasons for purchase or nonpurchase of organic foods rather than seeking which types of beliefs and attitudes are actually related to purchase or consumption. (Shepherd, Magnusson, Sjoden, 2005) In recent year, other researchers have examined what beliefs and attitudes predict consumption. (Shepherd, Government office for Science, 2011) In several studies, a majority of the customers have a preference for and an interest in organic food. However, â€Å"the proportion of regular purchasers of organic food is low†. (Shepherd, Magnusson, Sjoden, 2005) So, this phenomenon showed a discrepancy between consumers’ attitudes and behavior, which is most of Consumers’ attitude are positively for organic foods, but not often to buy them. It seems the consumers not have a concerned the organic foods become an important purchase criterion. Since the 1920’s, the organic food has first appeared in Europe. (Baourakis, 2004) Until now, even the organic foods not take big market share, but in recent years, according to the British Food Standards Agency said ‘identifies the role that organic food plays in providing choice for customer. ’ (Food Standards Agency, 2011) Lampkin Padel (1994, cited in Baourakis, 2004) researched that consumer demand for organic food increased rapidly, thus, the number of famers increased reasonably, this phenomenon is not only in Europe, but also is in the United States. Problem Statement The problem to be explored is the purchase behavior of teenagers toward organic food in Brighton Hove. As mentioned before, the sales of organic food are increasing in UK. Nevertheless, Non-organic food still dominates in the food market. In addition, while there has some consumers who are already familiar and know with the organic food. It still has many consumers who are not yet know about them. Because of organic food produced without using any artificial chemicals, pesticides or fertilizers, which is better and fresher taste than other nonorganic foods. (Georgiou, 2002) There are different reasons why consumers tend to prefer to buy organic food. To discover the teenagers of Brighton Hove behavior on organic food, these are some of the variables that will be taken into account when do the research, which can separate to extrinsic factors and internal factors. External factors are environment influence, like education level influence, cultural influence, and family influence. Internal factors are product attributes, which are benefits of organic food, like environmentally friendliness, good for animal welfare, taste good and personal health. These may influence consumer buying decision. Research aims and objectives This research aims to explore teenagers’ behavior of Brighton Hove on organic food consumption in their daily life. This research will provide richer and deeper understanding of teenagers’ preference on organic foods and work to specific ages, thus the levels of education and collect the information about why they care about organic food. These research questions to be answered are: †¢Do the teenagers like to buy organic food in Brighton Hove? †¢Do the teenagers choose organic food influenced by environment (i.e. education level, cultural influence or family influence) in Brighton Hove? †¢What causes the teenagers care about organic food (i. e. the environment concern, animal welfare, personal health, taste) in Brighton Hove? In this particular case, it becomes more interesting to be more the teenager maybe will be influence by place cultural. Because Brighton Hove are famous resort which near the sea. Brighton and Hove is the UKs healthiest city that reason is its residents lifestyles, such as cycling to work, do yoga practice, and eating green food according to a study for Sky Travel. (University of sussex, 2010) The intention explore is the future development of organic food in Brighton Hove by asking questions and interview. This paper will propose use deductive way for research on specific consumer behavior on organic foods in Brighton Hove. Anticipated contributions Organic food is green food, these benefits lead to the market share of food were influenced, so, this academic research discuss about purchase behavior of teenagers on organic food consumption in Brighton Hove. Because teenager is our future, from their behavior, we can see the organic food development of Brighton Hove in next 50 years. Until now, it has some research about customer behavior on organic food, however, since there is lack of data for specific group people, like teenager. In this case, Kardes, Cronley, Cline argued that one of the contributions for study consumer behavior is that educate consumers and help them to make a better decision, also can understand make products for consumers actually needed and wanted. This becomes a marketing strategy, this research proposal discovers and satisfies customer needs and wants effectively and beneficial manner, while profiting the long-term interests for business. (Kardes, Cronley, Cline, 2011) Also this research proposal will investigate customer behavior information by primary research and secondary information, analysis the consumer’s performance, which showed the market tendency and understand the rival. It can help companies can get the market share of organic food in the future. Brief Review of Literature Wright Crea (2007) pointed that the UK organic food market rise approximately 10% annually with a value of 2 billion dollars, already become third largest in the world. According government statistics, the multiple supermarket retailers accounted for the major marketing share to the consumer with approximately 73 % of sales. The independent retailers and parts of farmers accounted for consumer 27 % of sales. The box schemes and internet order made up 8 percent. (dardni, 2010) Base on data, organic food is preferred by all age groups because of its health friendly benefits. These contained old people, adults and children. According to statistics, 70 % of the costumers are women, while 30 % are men. 57. 3 % of organic food consumers have job, while 23. 2 % do not have job. (Damin, 2011) Food standards Agency demonstrates that to eat â€Å"organic food is a way to decrease consumption of pesticide residues and additives. † (Food Standards Agency, 2011) Organic procurement reflects consumers are not only care about economic, but also concern with food production link to personal, social and environmental effect. (The Open University, 2006) Lockie argues that no artificial chemicals is one of the key point cause the sale growth of organic product around the world, which reflects people are more interested in personal health and family health, also care about the animal welfare, tradition, environmental protection, food traceability and sustainability. (Lockie, 2006) Food Standards Agency, â€Å"if they think theyre buying food with extra nutritional quality or extra safety. † (Food Standards Agency, 2011)) Stringer and Dennis argued that in UK recent research showed 21 percent of housewives ranked taste over other facts in what they ate in 1998s, while 14 percent of housewives because of health concern for their family and themselves in 1998s. (Stringer Dennis, 2000) According to ACNielsen research, the consumption of organic baby food jumped about 16 percent over the year before in 2005, it nearly double increasing of total organic food consumption. (Working Mother, 2006) In 2008, the Ferrell and Pride searched the mother behavior and investigate the age range from 25 to 40, are more prefer to buy organic food or clothing for their children no matter what their income. (Pride Ferrell, 2008) Mamatha Sarada revealed that child rights attitudes and participation in activities were influenced by their mother. (Mamatha Sarada, 2009) Brozina argued that culture can influence the consumers’ motives for organic food consumption. (Brozina, 2009) Samli argued that consumer behavior was influenced by social class, which related to not only economic well-being, but also other factors, such as education, family background and occupation. Secondly, it influenced by hierarchy of needs, which is more likely to be observed as different degrees of economic development, culture, and social psychology. Thirdly, it influenced by interpersonal influences from group member, like social consumption phenomenon and consumer want to buy luxury make a good impression on others. Fourthly, it depends on affective influences, like emotion. At last, cognitive will be influence the consumers choice, which is how much they know about that product. (Samli, 1995) While consumer express positive perspective on organic food, but it is not likely to expand beyond this niche market in the future, the major reason is premium prices, unless low-input can be made recognisable to consumers. . (Oppapers, 2011) Handlechner argued that organic producers are still only occupying a niche market now. Nevertheless, organic food may be having a larger potential in the future. (Handlechner, 2008) Hypotheses Hypothesis1. I expect that the teenagers in Brighton Hove may be having positive perspective on organic food due to Brighton Hove is a healthiest city. Hypothesis 2: I expect that the teenagers in Brighton Hove might concern about environment issue, animal welfare, and personal health, so they choose the organic food. Hypothesis 3: It is also my prediction that teenagers in Brighton Hove may not interested in organic food due to they do not possess economic income. Hypothesis 4: Maybe they like to buy the organic foods, but for teenager are too expensive that they do not possess enough money to pay for them. Methodology This research adopted the deductive way because the aim proved by separate several research questions that mentioned earlier before. This research design is exploratory due to this research proposal intends to explore the teenagers’ behaviour on organic food through survey in Brighton Hove. This study will consider descriptive because this proposal focus on survey the characteristic of certain group, teenagers. Accordingly, some writers in a journal demonstrated that descriptive study is the researchers are interested to survey a group such as education level, income, age or gender in some situations. (Kumar, Deb, Sinha, Sinha, 2001) The research is also adopt cross sectional because of this study will study in a particular phenomenon and particular time. It has time limited. (Scribd, 2011) Research method Primary research This research can either be qualitative or quantitative. Nevertheless, quantitative research may cover a larger number of populations, which will give generalized statistics results by questionnaire. This qualitative research intends to collect an in-depth understanding of teenagers’ behaviour and the reasons why they have that behaviour. This qualitative research is a non-numerical data collection by interview. Moreover, the qualitative and quantities research method inquires the how and why of decision making by teenagers, not only where, when, what. So, this easy chooses these methods on this particular case studied in order to seek empirical support for this research hypothesis. This research proposal will base on quantitative research due to it will give statistical evidence of data, which can be summarize teenagers behaviour specifically. Questionnaire is my first choice. Concerning the print cost, the questionnaires will be surveyed through email in the internet. The questionnaires will include an introduction that gives clearly explanation of purpose of this study. Furthermore, the questionnaires also will include clearly instructions that give a well-guided to the teenagers. Moreover, it will give clearly question which is easy to teenagers. More specifically, writing the letter to school headmaster get the permission in Brighton Hove. This questionnaire will be taken in the Junior high school and high school in 11th July 2011. This study will be randomly survey 1000 students in junior high school, 500 boys and 500 girls respectively. Other parts are 1000 students in high school, 500 boys and 500 girls. This will be more easily and faster when make analysis the data based on different education level and gender. Also, it will adopt anonymity, in order to keep the private information for teenager. This research proposal also will accord to qualitative research due to it will be get more detail with deeper conversational interview. It will not have predetermined questions are asked, because it can remain more open and adaptable get useful information due to nature and priorities of interview. It can directly get the exactly information for this research. More specifically, the interview will be taking at the school supermarket in Brighton Hove in 19th July 2011. More closely interview the staffs in supermarket in order to understand teenagers’ behaviour by real consumption. Moreover, the interview will be doing at teenagers’ home in 30th July 2011 and in order to have chance to understand their behaviour by face to face talking. It wills choice 10 families in high school, 10 families in junior high school. It could be though this interview can prove whether the teenager preference on organic foods influenced by their family background and mother. Secondary research â€Å"The value of using the secondary data for market research has been substantial throughout history, continues today, and promises to grow in the future. † (Patzer, 1995) Secondary research contains the collation, brief and synthesis of existing research that data is already done by government, company, organization or personal. When this research proposal chooses the secondary data source, it would be have a critical thinking and concern the academic source. Government research data is the good choice for this research. Moreover, Base on the books and journals, summarize others studies and result. It will filter information and get the clearly results. Another research approach would be reputation organization and news website. What is more, May be I can get record data form staff in school supermarket, for instance, it could be get the sales of every year or month in the school. Using the other cities’ secondary data compare with the primary data in Brighton Hove in order to know whether the Brighton Hove culture will influence the teenager behaviour on organic foods. Data Analysis â€Å"Thematic analysis focuses on identifiable themes and patterns of living or behaviour. † (Aronson, 1994) So in this case, the thematic analysis will be used to gather data and analyze them in interview. Moreover, another analysis is the content analysis, which will use in the interview, too. The questionnaire will be collect data by software for statistics, like Excel. Do the diagrams would be use the software, like word. Time chart JuneJulyAugustSeptemberOctoberNovember Research for Literature review Formulate research strategy, design and select methods Questionnaire Interviews Field Work/ Data collection Data Analysis Write up Conclusion. This research expects to explore the teenagers’ preference on organic food in Brighton Hove, which can get exactly information to answer the research question. I hope the teenagers will more concern their health and environment and animal in order to develop a sustainable society. The organic food company may take this kind research forward, which will bring long-term benefit if they grasp customer behavior and attitude. Maybe they will not only survey the teenager, but also research the householder behavior and psychology due to they have economic power. Bibliography Aronson, J. (1994). Nova. Retrieved 6 8, 2011, from A Pragmatic View of Thematic Analysis: http://www. nova. edu/ssss/QR/BackIssues/QR2-1/aronson. html Baourakis, G. (2004). Marketing trends for organic food in 21st century. World Scientific Publishing Co. Pte. Ltd. Brozina, S. (2009). EuroMed Journal of Business. Cultural influences on motives for organic food consumption , p. 185. Damin. (2011). dissertation. Retrieved 6 5, 2011, from Consumer behavior and organic food dessertation: http://www. dissertation-helper. co. uk/consumer-behavior-organic-food-dissertation/ dardni. (2010). Agriculture and Rural Development. Retrieved 6 5, 2011, from The market for organic products: http://www. dardni. gov. uk/ruralni/index/bussys/organic_production/organic_business_management/marketing. htm Food Standards Agency. (2011). Safe food,better business. Retrieved 5 28, 2011, from Organic food: http://www. food. gov. uk/foodindustry/farmingfood/organicfood/ GeorgiouDunnElisha. (2002). Everything you need to know about organic foods. The Rosen Publishing Group, Inc. Handlechner, M. (2008). Grin. Retrieved 6 7, 2011, from Organic Food: http://www. grin. com/ Kardes, R. F. , Cronley, L. M. , Cline, W. T. (2011). Consumer Behavior. Cengage Learning. Inc. Kumar, R. , Deb, K. J. , Sinha, B. N. , Sinha, V. K. (2001). Lithium Toxicity. A descriptive study , pp. 52-57. Lockie, S. (2006). Going Oorganic: mobilizing networks for environmentally responsible food production. London. Mamatha, T. , Sarada, D. (2009). Child rights: ICDS programme. Discovery Publishing House PVT. LTD. Oppapers. (2011). Oppapers. Retrieved 6 6, 2011, from Consumer Attitudes and purchase intentions in relation to organic food: http://www. oppapers. com/essays/Consumer-Attitudes-And-Purchase-Intentions-In/307542 PatzerL. Gordon. (1995). Using secondary data in marketing research: United States and worldwide. An imprint of Greenwood Publishing Group,Inc. Pride, W. M. , Ferrell, O. C. (2008). Marketing. Yaga Mamas: Todays Choosy Mothers , p. 134. Samli, A. C. (1995). International consumer behavior: its impact on marketing strategy development. An imprint pf Greenwood Publishing Groups,Inc. Scribd. (2011). Scribd. Retrieved 6 7, 2011, from Research Proposal on â€Å"TheConsumer Behavior On MP3Players†: http://www. scribd. com/doc/54718736/Research-Proposal-on-the-Consumer-Behaviour-of-MP3-s Shepherd, R. (2011). Government office for Science. Retrieved 6 8, 2011, from Societal attitudes to different food production models: http://www. bis. gov. uk/Foresight Shepherd, R. , Magnusson, M. , Sjoden, P. -O. (2005). AMBIO: A Journal of the Human Environment. Determinants of Consumer Behavior Related to Organic Foods , pp. 352-359. Sheth, N. J. (1985). Historical Perspective in Consumer Research: National and International Perspectives. HISTORY OF CONSUMER BEHAVIOR: A MARKETING PERSPECTIVE , pp. 5-7. StringerMichael, DennisC. (2000). Chilled foods: a comprehensive guide. Woodhead Publishing Limited. The Open University. (2006). Language of Food Politics. Retrieved 5 29, 2011, from Research Report: The Discourse of Organic Food Promotion: language, intentions: http://creet. open. ac. uk/projects/language-of-food-politics/documents/4_organic_food_report. pdf University of sussex. (2010). Sussexsport. Retrieved 6 3, 2011, from Healthy Articles: http://www. sussex. ac. uk/sport/1-4-9. html Working Mother. (2006). Is Organic Food Worth it? Working Mother , 88. Wright, S. , Crea, M. D. (2007). The International Market for Organic and Fair Trade Food and Drink. Blackwell Publishing Ltd.

Hopf Algebra Project

Hopf Algebra Project Petros Karayiannis Chapter 0 Introduction Hopf algebras have lot of applications. At first, they used it in topology in 1940s, but then they realized it has applications through combinatorics, category theory, Hopf-Galois theory, quantum theory, Lie algebras, Homological algebra and functional analysis. The purpose of this project is to see the definitions and properties of Hopf algebras.(Becca 2014) Preliminaries This chapter provides all the essential tools to understand the structure of Hopf algebras. Basic notations of Hopf algebra are: Groups Fields Vector spaces Homomorphism Commutative diagrams 1.Groups Group G is a finite or infinite set of elements with a binary operation. Groups have to obey some rules, so we can define it as a group. Those are: closure, associative, there exist an identity element and an inverse element. Let us define two elements U, V in G, closure is when then the product of UV is also in G. Associative when the multiplication (UV) W=U (VW) à ªÃ¢â‚¬Å" ¯ U, V, W in G. There exist an identity element such that IU=UI=U for every element U in G. The inverse is when for each element U of G, the set contains an element V=U-1 such that UU-1=U-1U=I. 2.Fields A field Ã’Å“ is a commutative ring and every element b à Ã‚ µ Ã’Å“ has an inverse. 3.Vector Space A vector space V is a set that is closed under finite vector addition and scalar multiplication. In order for V to be a vector space, the following conditions must hold à ªÃ¢â‚¬Å" ¯ X, Y à Ã‚ µ V and any scalar a, b à Ã‚ µ Ã’Å“: a(b X) = (a b) X (a + b) X=aX + bX a(X+Y)=aX + aY 1X=X A left ideal of K-algebra is a linear subspace that has the property that any element of the subspace multiplied on the left by any element of the algebra produces an element of the subspace. We say that a subset L of a K-algebra A is a left ideal if for every x and y in L, z in A and c in K, we have the following: X +y is in L cx is in L zà ¢Ã¢â‚¬ ¹Ã¢â‚¬ ¦ x is in L If we replace c) with xà ¢Ã¢â‚¬ ¹Ã¢â‚¬ ¦ z is in L, then this would define a right ideal. A two-sided ideal is a subset that is both a left and a right ideal. When the algebra is commutative, then all of those notions of ideal are equivalent. We denote the left ideal as à ¢Ã…  Ã‚ ³. 4.Homomorphism Given two groups, (G,*) and (H, °) is a function f: Gà ¢Ã¢â‚¬  Ã¢â‚¬â„¢H such that à ªÃ¢â‚¬Å" ¯ u, v à Ã‚ µ G it holds that f(u*v)=f(u) °f(v) 5.Commutative diagrams A commutative diagram is showing the composition of maps represented by arrows. The fundament operation of Hopf algebras is the tensor product. A tensor product is a multiplication of vector spaces V and W with a result a single vector space, denoted as V    W. Definition 0.1 Let V and W be Ã’Å“-vector spaces with bases {ei } and {fj } respectively. The tensor product V and W is a new Ã’Å“-vector space,  Ãƒâ€šÃ‚   V      W with basis { ei fj }, is the set of all elements v    w= à ¢Ã‹â€ Ã¢â‚¬Ëœ (ci,j ei    fj ). ci,j à Ã‚ µÃƒâ€™Ã…“ are scalars. Also tensor products obey to distributive and scalar multiplication laws. The dimension of the tensor product of two vector spaces is: Dim(V   W)=dim(V)dim(W) Theorem of Universal Property of Tensor products 0.2 Let V, W, U be vector spaces with map f: V x W à ¢Ã¢â‚¬  Ã¢â‚¬â„¢ U is defined as f: (v, w) à ¢Ã¢â‚¬  Ã¢â‚¬â„¢vw. There exists a bilinear mapping b: V x W à ¢Ã¢â‚¬  Ã¢â‚¬â„¢ V   W , (v,w) à ¢Ã¢â‚¬  Ã¢â‚¬â„¢ v   Ãƒâ€šÃ‚   w If f: V x W à ¢Ã¢â‚¬  Ã¢â‚¬â„¢ U is bilinear, then there exist a unique function, f: V   Wà ¢Ã¢â‚¬  Ã¢â‚¬â„¢U with f=f °b   Extension of Tensor Products0.3 The definition of Tensor products can be extended for more than two vectors such as; V1 à ¢Ã…  -   V2à ¢Ã…  -  Ãƒâ€šÃ‚   V3 à ¢Ã…  -   à ¢Ã¢â€š ¬Ã‚ ¦..à ¢Ã…  -   VN = à ¢Ã‹â€ Ã¢â‚¬Ëœ( biv1à ¢Ã…  -   v2à ¢Ã…  -   à ¢Ã¢â€š ¬Ã‚ ¦.à ¢Ã…  -   vn )   (Becca 2014) Definition0.4 Let U,V be vector spacers over a field k and ÃŽÂ ½ à Ã‚ µ Uà ¢Ã‚ ¨Ã¢â‚¬Å¡V. If ÃŽÂ ½=0 then Rank (ÃŽÂ ½) =0. If ÃŽÂ ½Ãƒ ¢Ã¢â‚¬ °Ã‚  0 then rank (ÃŽÂ ½) is equal to the smallest positive integer r arising from the representations of ÃŽÂ ½= à ¢Ã‹â€ Ã¢â‚¬Ëœui à ¢Ã‚ ¨Ã¢â‚¬Å¡ vi à Ã‚ µUà ¢Ã‚ ¨Ã¢â‚¬Å¡V for i=1,2,à ¢Ã¢â€š ¬Ã‚ ¦,r. Definition0.5 Let U be a finite dimensional vector space over the field k with basis {u1,à ¢Ã¢â€š ¬Ã‚ ¦.,un}   be a basis for U. the dual basis for U*is {u1,à ¢Ã¢â€š ¬Ã‚ ¦.,un} where ui(uj)= ÃŽÂ ´ij for 1à ¢Ã¢â‚¬ °Ã‚ ¤I,jà ¢Ã¢â‚¬ °Ã‚ ¤n. Dual Pair0.6 A dual pair is a 3 -tuple (X,Y,) consisting two vector spaces X,Y over the same field K and a bilinear map, : X x Yà ¢Ã¢â‚¬  Ã¢â‚¬â„¢K with à ªÃ¢â‚¬Å" ¯x à Ã‚ µ X{0} yà Ã‚ µY: 0 and à ªÃ¢â‚¬Å" ¯y à Ã‚ µ Y{0} xà Ã‚ µX: 0 Definition0.7 The wedge product is the product in an exterior algebra. If ÃŽÂ ±, ÃŽÂ ² are differential k-forms of degree p, g respectively, then   ÃƒÅ½Ã‚ ±Ãƒ ¢Ã‹â€ Ã‚ §ÃƒÅ½Ã‚ ²=(-1)pq ÃŽÂ ²Ãƒ ¢Ã‹â€ Ã‚ §ÃƒÅ½Ã‚ ±, is not in general commutative, but is associative, (ÃŽÂ ±Ãƒ ¢Ã‹â€ Ã‚ §ÃƒÅ½Ã‚ ²)à ¢Ã‹â€ Ã‚ §u= ÃŽÂ ±Ãƒ ¢Ã‹â€ Ã‚ §(ÃŽÂ ²Ãƒ ¢Ã‹â€ Ã‚ §u) and bilinear (c1 ÃŽÂ ±1+c2 ÃŽÂ ±2)à ¢Ã‹â€ Ã‚ § ÃŽÂ ²= c1( ÃŽÂ ±1à ¢Ã‹â€ Ã‚ § ÃŽÂ ²) + c2( ÃŽÂ ±2à ¢Ã‹â€ Ã‚ § ÃŽÂ ²) ÃŽÂ ±Ãƒ ¢Ã‹â€ Ã‚ §( c1 ÃŽÂ ²1+c2 ÃŽÂ ²2)= c1( ÃŽÂ ±Ãƒ ¢Ã‹â€ Ã‚ § ÃŽÂ ²1) + c2( ÃŽÂ ±Ãƒ ¢Ã‹â€ Ã‚ § ÃŽÂ ²2).  Ãƒâ€šÃ‚  Ãƒâ€šÃ‚   (Becca 2014) Chapter 1 Definition1.1 Let (A, m, ÃŽÂ ·) be an algebra over k and write mop (ab) = ab à ªÃ¢â‚¬Å" ¯ a, bà Ã‚ µ A where mop=mà Ã¢â‚¬Å¾ÃƒÅ½Ã¢â‚¬Ëœ,Α. Thus ab=ba à ªÃ¢â‚¬Å" ¯a, b à Ã‚ µA. The (A, mop, ÃŽÂ ·) is the opposite algebra. Definition1.2 A co-algebra C is A vector space over K A map Ά: Cà ¢Ã¢â‚¬  Ã¢â‚¬â„¢C à ¢Ã…  -   C which is coassociative in the sense of à ¢Ã‹â€ Ã¢â‚¬Ëœ (c(1)(1) à ¢Ã…  -  Ãƒâ€šÃ‚   c(1)(2) à ¢Ã…  -   c(2))= à ¢Ã‹â€ Ã¢â‚¬Ëœ (c(1) à ¢Ã…  -  Ãƒâ€šÃ‚   c(2)(1) à ¢Ã…  -   c(2)c(2) )  Ãƒâ€šÃ‚   à ªÃ¢â‚¬Å" ¯ cà Ã‚ µC (Ά called the co-product) A map ÃŽÂ µ: Cà ¢Ã¢â‚¬  Ã¢â‚¬â„¢ k obeying à ¢Ã‹â€ Ã¢â‚¬Ëœ[ÃŽÂ µ((c(1))c(2))]=c= à ¢Ã‹â€ Ã¢â‚¬Ëœ[(c(1)) ÃŽÂ µc(2))] à ªÃ¢â‚¬Å" ¯ cà Ã‚ µC ( ÃŽÂ µ called the counit) Co-associativity and co-unit element can be expressed as commutative diagrams as follow: Figure 1: Co-associativity map Ά Figure 2: co-unit element map ÃŽÂ µ Definition1.3 A bi-algebra H is An algebra (H, m ,ÃŽÂ ·) A co-algebra (H, Ά, ÃŽÂ µ) Ά,ÃŽÂ µ are algebra maps, where Hà ¢Ã…  -   H has the tensor product algebra structure (hà ¢Ã…  - g)(hà ¢Ã…  -   g)= hhà ¢Ã…  -  Ãƒâ€šÃ‚   gg à ªÃ¢â‚¬Å" ¯h, h, g, g à Ã‚ µH. A representation of Hopf algebras as diagrams is the following: Definition1.4 A Hopf Algebra H is A bi-algebra H, Ά, ÃŽÂ µ, m, ÃŽÂ · A map S : Hà ¢Ã¢â‚¬  Ã¢â‚¬â„¢ H such that à ¢Ã‹â€ Ã¢â‚¬Ëœ [(Sh(1))h(2) ]= ÃŽÂ µ(h)= à ¢Ã‹â€ Ã¢â‚¬Ëœ [h(1)Sh(2) ]à ªÃ¢â‚¬Å" ¯ hà Ã‚ µH The axioms that make a simultaneous algebra and co-algebra into Hopf algebra is à Ã¢â‚¬Å¾:   Hà ¢Ã…  - Hà ¢Ã¢â‚¬  Ã¢â‚¬â„¢Hà ¢Ã…  -H Is the map à Ã¢â‚¬Å¾(hà ¢Ã…  -g)=gà ¢Ã…  -h called the flip map à ªÃ¢â‚¬Å" ¯ h, g à Ã‚ µ H. Definition1.5 Hopf Algebra is commutative if its commutative as algebra. It is co-commutative if its co-commutative as a co-algebra, à Ã¢â‚¬Å¾ÃƒÅ½Ã¢â‚¬ =Ά. It can be defined as S2=id. A commutative algebra over K is an algebra (A, m, ÃŽÂ ·) over k such that m=mop. Definition1.6 Two Hopf algebras H,H are dually paired by a map : H H à ¢Ã¢â‚¬  Ã¢â‚¬â„¢k if, =à Ã‹â€ ,Άh>, =ÃŽÂ µ(h) g   >=, ÃŽÂ µ(à Ã¢â‚¬  )= = à ªÃ¢â‚¬Å" ¯ à Ã¢â‚¬  , à Ã‹â€ Ãƒ Ã‚ µ H and h, g à Ã‚ µH. Let (C, Ά,ÃŽÂ µ) be a co-algebra over k. The co-algebra (C, Άcop, ÃŽÂ µ) is the opposite co-algebra. A co-commutative co-algebra over k is a co-algebra (C, Ά, ÃŽÂ µ) over k such that Ά= Άcop. Definition1.7 A bi-algebra or Hopf algebra H acts on algebra A (called H-module algebra) if: H acts on A as a vector space. The product map m: AAà ¢Ã¢â‚¬  Ã¢â‚¬â„¢A commutes with the action of H The unit map ÃŽÂ ·: kà ¢Ã¢â‚¬  Ã¢â‚¬â„¢ A commutes with the action of H. From b,c we come to the next action hà ¢Ã…  Ã‚ ³(ab)=à ¢Ã‹â€ Ã¢â‚¬Ëœ(h(1)à ¢Ã…  Ã‚ ³a)(h(2)à ¢Ã…  Ã‚ ³b), hà ¢Ã…  Ã‚ ³1= ÃŽÂ µ(h)1, à ªÃ¢â‚¬Å" ¯a, b à Ã‚ µ A, h à Ã‚ µ H This is the left action. Definition1.8 Let (A, m, ÃŽÂ ·) be algebra over k and is a left H- module along with a linear map m: Aà ¢Ã…  -Aà ¢Ã¢â‚¬  Ã¢â‚¬â„¢A and a scalar multiplication ÃŽÂ ·: k à ¢Ã…  - Aà ¢Ã¢â‚¬  Ã¢â‚¬â„¢A if the following diagrams commute. Figure 3: Left Module map Definition1.9 Co-algebra (C, Ά, ÃŽÂ µ) is H-module co-algebra if: C is an H-module Ά: Cà ¢Ã¢â‚¬  Ã¢â‚¬â„¢CC and ÃŽÂ µ: Cà ¢Ã¢â‚¬  Ã¢â‚¬â„¢ k commutes with the action of H. (Is a right C- co-module). Explicitly, Ά(hà ¢Ã…  Ã‚ ³c)=à ¢Ã‹â€ Ã¢â‚¬Ëœh(1)à ¢Ã…  Ã‚ ³c(1)à ¢Ã‚ ¨Ã¢â‚¬Å¡h(2)à ¢Ã…  Ã‚ ³c(2), ÃŽÂ µ(hà ¢Ã…  Ã‚ ³c)= ÃŽÂ µ(h)ÃŽÂ µ(c), à ªÃ¢â‚¬Å" ¯h à Ã‚ µ H, c à Ã‚ µ C.   Definition1.10 A co-action of a co-algebra C on a vector space V is a map ÃŽÂ ²: Và ¢Ã¢â‚¬  Ã¢â‚¬â„¢Cà ¢Ã‚ ¨Ã¢â‚¬Å¡V such that, (idà ¢Ã‚ ¨Ã¢â‚¬Å¡ÃƒÅ½Ã‚ ²) à ¢Ã‹â€ Ã‹Å"ÃŽÂ ²=(ΆÃƒ ¢Ã‚ ¨Ã¢â‚¬Å¡ id )ÃŽÂ ²;   id =(ÃŽÂ µÃƒ ¢Ã‚ ¨Ã¢â‚¬Å¡id )à ¢Ã‹â€ Ã‹Å"ÃŽÂ ². Definition1.11 A bi-algebra or Hopf algebra H co-acts on an algebra A (an H- co-module algebra) if: A is an H- co-module The co-action ÃŽÂ ²: Aà ¢Ã¢â‚¬  Ã¢â‚¬â„¢ Hà ¢Ã‚ ¨Ã¢â‚¬Å¡A is an algebra homomorphism, where Hà ¢Ã‚ ¨Ã¢â‚¬Å¡A has the tensor product algebra structure. Definition1.12 Let C be co- algebra (C, Ά, ÃŽÂ µ), map ÃŽÂ ²: Aà ¢Ã¢â‚¬  Ã¢â‚¬â„¢ Hà ¢Ã‚ ¨Ã¢â‚¬Å¡A is a right C- co- module if the following diagrams commute. Figure 6:Co-algebra of a right co-module Sub-algebras, left ideals and right ideals of algebra have dual counter-parts in co-algebras. Let (A, m, ÃŽÂ ·) be algebra over k and suppose that V is a left ideal of A. Then m(Aà ¢Ã‚ ¨Ã¢â‚¬Å¡V)à ¢Ã…  Ã¢â‚¬  V. Thus the restriction of m to Aà ¢Ã‚ ¨Ã¢â‚¬Å¡V determines a map Aà ¢Ã‚ ¨Ã¢â‚¬Å¡Và ¢Ã¢â‚¬  Ã¢â‚¬â„¢V. Left co-ideal of a co-algebra C is a subspace V of C such that the co-product Ά restricts to a map Và ¢Ã¢â‚¬  Ã¢â‚¬â„¢Cà ¢Ã‚ ¨Ã¢â‚¬Å¡V. Definition1.13 Let V be a subspace of a co-algebra C over k. Then V is a sub-co-algebra of C if Ά(V)à ¢Ã…  Ã¢â‚¬  Và ¢Ã‚ ¨Ã¢â‚¬Å¡V, for left co-ideal Ά(V)à ¢Ã…  Ã¢â‚¬  Cà ¢Ã‚ ¨Ã¢â‚¬Å¡V and for right co-ideal Ά(V)à ¢Ã…  Ã¢â‚¬  Và ¢Ã‚ ¨Ã¢â‚¬Å¡C. Definition1.14 Let V be a subspace of a co-algebra C over k. The unique minimal sub-co-algebra of C which contains V is the sub-co-algebra of C generated by V. Definition1.15 A simple co-algebra is a co-algebra which has two sub-co-algebras. Definition1.16 Let C be co-algebra over k. A group-like element of C is c à Ã‚ µC with satisfies, Ά(s)=sà ¢Ã‚ ¨Ã¢â‚¬Å¡s   and ÃŽÂ µ(s)=1 à ªÃ¢â‚¬Å" ¯ s à Ã‚ µS. The set of group-like elements of C is denoted G(C). Definition1.17 Let S be a set. The co-algebra k[S] has a co-algebra structure determined by Ά(s)=sà ¢Ã‚ ¨Ã¢â‚¬Å¡s   and ÃŽÂ µ(s)=1 à ªÃ¢â‚¬Å" ¯ s à Ã‚ µS. If S=à ¢Ã‹â€ Ã¢â‚¬ ¦ we set C=k[à ¢Ã‹â€ Ã¢â‚¬ ¦]=0. Is the group-like co-algebra of S over k. Definition1.18 The co-algebra C over k with basis {co, c1, c2,à ¢Ã¢â€š ¬Ã‚ ¦..} whose co-product and co-unit is satisfy by Ά(cn)= à ¢Ã‹â€ Ã¢â‚¬Ëœcn-là ¢Ã‚ ¨Ã¢â‚¬Å¡cl and ÃŽÂ µ(cn)=ÃŽÂ ´n,0 for l=1,à ¢Ã¢â€š ¬Ã‚ ¦.,n and for all nà ¢Ã¢â‚¬ °Ã‚ ¥0. Is denoted by Pà ¢Ã‹â€ Ã… ¾(k). The sub-co-algebra which is the span of co, c1, c2,à ¢Ã¢â€š ¬Ã‚ ¦,cn is denoted Pn(k). Definition1.19 A co-matrix co-algebra over k is a co-algebra over k isomorphic to Cs(k) for some finite set S. The co-matrix identities are: Ά(ei, j)= à ¢Ã‹â€ Ã¢â‚¬Ëœei, là ¢Ã‚ ¨Ã¢â‚¬Å¡el, j ÃŽÂ µ(ei, j)=ÃŽÂ ´i, j à ¢Ã‹â€ Ã¢â€š ¬ i, j à Ã‚ µS. Set Cà ¢Ã‹â€ Ã¢â‚¬ ¦(k)=(0). Definition1.20 Let S be a non-empty finite set. A standard basis for Cs(k) is a basis {c i ,j}I, j à Ã‚ µS for Cs(k) which satisfies the co-matrix identities. Definition1.21 Let (C, Άc, ÃŽÂ µc) and (D, ΆD, ÃŽÂ µD) be co-algebras over the field k. A co-algebra map f: Cà ¢Ã¢â‚¬  Ã¢â‚¬â„¢D is a linear map of underlying vector spaces such that ΆDà ¢Ã‹â€ Ã‹Å"f=(fà ¢Ã‚ ¨Ã¢â‚¬Å¡f)à ¢Ã‹â€ Ã‹Å" Άc and ÃŽÂ µDà ¢Ã‹â€ Ã‹Å"f= ÃŽÂ µc. An isomorphism of co-algebras is a co-algebra map which is a linear isomorphism. Definition1.22 Let C be co-algebra over the field k. A co-ideal of C is a subspace I of C such that ÃŽÂ µ (I) = (0) and Ά (ÃŽâ„ ¢) à ¢Ã…  Ã¢â‚¬   Ià ¢Ã‚ ¨Ã¢â‚¬Å¡C+Cà ¢Ã‚ ¨Ã¢â‚¬Å¡I. Definition1.23 The co-ideal Ker (ÃŽÂ µ) of a co-algebra C over k is denoted by C+. Definition1.24 Let I be a co-ideal of co-algebra C over k. The unique co-algebra structure on C /I such that the projection à Ã¢â€š ¬: Cà ¢Ã¢â‚¬  Ã¢â‚¬â„¢ C/I is a co-algebra map, is the quotient co-algebra structure on C/I. Definition1.25 The tensor product of co-algebra has a natural co-algebra structure as the tensor product of vector space Cà ¢Ã…  -D is a co-algebra over k where Ά(c(1)à ¢Ã‚ ¨Ã¢â‚¬Å¡d(1))à ¢Ã‚ ¨Ã¢â‚¬Å¡( c(2)à ¢Ã‚ ¨Ã¢â‚¬Å¡d(2)) and ÃŽÂ µ(cà ¢Ã‚ ¨Ã¢â‚¬Å¡d)=ÃŽÂ µ(c)ÃŽÂ µ(d) à ¢Ã‹â€ Ã¢â€š ¬ c in C and d in D. Definition1.26 Let C be co-algebra over k. A skew-primitive element of C is a cà Ã‚ µC which satisfies Ά(c)= gà ¢Ã‚ ¨Ã¢â‚¬Å¡c +cà ¢Ã‚ ¨Ã¢â‚¬Å¡h, where c, h à Ã‚ µG(c). The set of g:h-skew primitive elements of C is denoted   by Pg,h (C). Definition1.27 Let C be co-algebra over a field k. A co-commutative element of C is cà Ã‚ µC such that Ά(c) = Άcop(c). The set of co-commutative elements of C is denoted by Cc(C). Cc(C) à ¢Ã…  Ã¢â‚¬  C. Definition1.28 The category whose objects are co-algebras over k and whose morphisms are co-algebra maps under function composition is denoted by k-Coalg. Definition1.29 The category whose objects are algebras over k and whose morphisms are co-algebra maps under function composition is denoted by k-Alg. Definition1.30 Let (C, Ά, ÃŽÂ µ) be co-algebra over k. The algebra (Cà ¢Ã‹â€ -, m, ÃŽÂ ·) where m= ΆÃƒ ¢Ã‹â€ -| Cà ¢Ã‹â€ -à ¢Ã‚ ¨Ã¢â‚¬Å¡Cà ¢Ã‹â€ -, ÃŽÂ · (1) =ÃŽÂ µ, is the dual algebra of (C, Ά, ÃŽÂ µ). Definition1.31 Let A be algebra over the field k. A locally finite A-module is an A-module M whose finitely generated sub-modules are finite-dimensional. The left and right Cà ¢Ã‹â€ --module actions on C are locally finite. Definition1.32 Let A be algebra over the field k. A derivation of A is a linear endomorphism F of A such that F (ab) =F (a) b-aF(b) for all a, b à Ã‚ µA. For fixed b à Ã‚ µA note that F: Aà ¢Ã¢â‚¬  Ã¢â‚¬â„¢A defined by F(a)=[a, b]= ab- ba   for all a à Ã‚ µA is a derivation of A. Definition1.33 Let C be co-algebra over the field k. A co-derivation of C is a linear endomorphism f of C such that ΆÃƒ ¢Ã‹â€ Ã‹Å"f= (fà ¢Ã‚ ¨Ã¢â‚¬Å¡IC + IC à ¢Ã‚ ¨Ã¢â‚¬Å¡f) à ¢Ã‹â€ Ã‹Å"Ά. Definition1.34 Let A and B ne algebra over the field k. The tensor product algebra structure on Aà ¢Ã‚ ¨Ã¢â‚¬Å¡B is determined by (aà ¢Ã‚ ¨Ã¢â‚¬Å¡b)(aà ¢Ã‚ ¨Ã¢â‚¬Å¡b)= aaà ¢Ã‚ ¨Ã¢â‚¬Å¡bb à ªÃ¢â‚¬Å" ¯ a, aà Ã‚ µA and b, bà Ã‚ µB. Definition1.35 Let X, Y be non-empty subsets of an algebra A over the field k. The centralizer of Y in X is ZX(Y) = {xà Ã‚ µX|yx=xy à ªÃ¢â‚¬Å" ¯yà Ã‚ µY} For y à Ã‚ µA the centralizer of y in X is ZX(y) = ZX({y}). Definition1.36 The centre of an algebra A over the field Z (A) = ZA(A). Definition1.37 Let (S, à ¢Ã¢â‚¬ °Ã‚ ¤) be a partially ordered set which is locally finite, meaning that à ªÃ¢â‚¬Å" ¯, I, jà Ã‚ µS which satisfy ià ¢Ã¢â‚¬ °Ã‚ ¤j the interval [i, j] = {là Ã‚ µS|ià ¢Ã¢â‚¬ °Ã‚ ¤là ¢Ã¢â‚¬ °Ã‚ ¤j} is a finite set. Let S= {[i, j] |I, jà Ã‚ µS, ià ¢Ã¢â‚¬ °Ã‚ ¤j} and let A be the algebra which is the vector space of functions f: Sà ¢Ã¢â‚¬  Ã¢â‚¬â„¢k under point wise operations whose product is given by (fà ¢Ã¢â‚¬ ¹Ã¢â‚¬  g)([i, j])=f([i, l])g([l, j])   ià ¢Ã¢â‚¬ °Ã‚ ¤là ¢Ã¢â‚¬ °Ã‚ ¤j For all f, g à Ã‚ µA and [i, j]à Ã‚ µS and whose unit is given by 1([I,j])= ÃŽÂ ´i,j à ªÃ¢â‚¬Å" ¯[I,j]à Ã‚ µS. Definition1.38 The algebra of A over the k described above is the incidence algebra of the locally finite partially ordered set (S, à ¢Ã¢â‚¬ °Ã‚ ¤). Definition1.39 Lie co-algebra over k is a pair (C, ÃŽÂ ´), where C is a vector space over k and ÃŽÂ ´: Cà ¢Ã¢â‚¬  Ã¢â‚¬â„¢Cà ¢Ã‚ ¨Ã¢â‚¬Å¡C is a linear map, which satisfies: à Ã¢â‚¬Å¾Ãƒ ¢Ã‹â€ Ã‹Å"ÃŽÂ ´=0 and (ÃŽâ„ ¢+(à Ã¢â‚¬Å¾Ãƒ ¢Ã‚ ¨Ã¢â‚¬Å¡ÃƒÅ½Ã¢â€ž ¢)à ¢Ã‹â€ Ã‹Å"(ÃŽâ„ ¢Ãƒ ¢Ã‚ ¨Ã¢â‚¬Å¡Ãƒ Ã¢â‚¬Å¾)+(ÃŽâ„ ¢Ãƒ ¢Ã‚ ¨Ã¢â‚¬Å¡Ãƒ Ã¢â‚¬Å¾)à ¢Ã‹â€ Ã‹Å" (à Ã¢â‚¬Å¾Ãƒ ¢Ã‚ ¨Ã¢â‚¬Å¡ÃƒÅ½Ã¢â€ž ¢))à ¢Ã‹â€ Ã‹Å"(ÃŽâ„ ¢Ãƒ ¢Ã‚ ¨Ã¢â‚¬Å¡ÃƒÅ½Ã‚ ´)à ¢Ã‹â€ Ã‹Å"ÃŽÂ ´=0 à Ã¢â‚¬Å¾=à Ã¢â‚¬Å¾C,C and I is the appropriate identity map. Definition1.40 Suppose that C is co-algebra over the field k. The wedge product of subspaces U and V is Uà ¢Ã‹â€ Ã‚ §V = Ά-1(Uà ¢Ã‚ ¨Ã¢â‚¬Å¡C+ Cà ¢Ã‚ ¨Ã¢â‚¬Å¡V). Definition1.41 Let C be co-algebra over the field k. A saturated sub-co-algebra of C is a sub-co-algebra D of C such that Uà ¢Ã‹â€ Ã‚ §Và ¢Ã…  Ã¢â‚¬  D, à ªÃ¢â‚¬Å" ¯ U, V of D. Definition1.42 Let C be co-algebra over k and (N, à Ã‚ ) be a left co-module. Then Uà ¢Ã‹â€ Ã‚ §X= à Ã‚ -1(Uà ¢Ã‚ ¨Ã¢â‚¬Å¡N+ Cà ¢Ã‚ ¨Ã¢â‚¬Å¡X) is the wedge product of subspaces U of C and X of N. Definition1.43 Let C be co-algebra over k and U be a subspace of C. The unique minimal saturated sub-co-algebra of C containing U is the saturated closure of U in C. Definition1.44 Let (A, m, ÃŽÂ ·) be algebra over k. Then, Aà ¢Ã‹â€ Ã‹Å"=mà ¢Ã‹â€ 1(Aà ¢Ã‹â€ -à ¢Ã‚ ¨Ã¢â‚¬Å¡Aà ¢Ã‹â€ - ) (Aà ¢Ã‹â€ Ã‹Å", Ά, ÃŽÂ µ) is a co-algebra over k, where Ά= mà ¢Ã‹â€ -| Aà ¢Ã‹â€ Ã‹Å" and ÃŽÂ µ=ÃŽÂ ·Ãƒ ¢Ã‹â€ -. ÃŽÂ ¤he co-algebra (Aà ¢Ã‹â€ Ã‹Å", Ά, ÃŽÂ µ) is the dual co-algebra of (A, m, ÃŽÂ ·). Also we denote Aà ¢Ã‹â€ Ã‹Å" by aà ¢Ã‹â€ Ã‹Å" and ΆÃƒ ¢Ã‹â€ Ã‹Å"= aà ¢Ã‹â€ Ã‹Å"(1)à ¢Ã‚ ¨Ã¢â‚¬Å¡ aà ¢Ã‹â€ Ã‹Å"(2), à ªÃ¢â‚¬Å" ¯ aà ¢Ã‹â€ Ã‹Å" à Ã‚ µ Aà ¢Ã‹â€ Ã‹Å". Definition1.45 Let A be algebra over k. An ÃŽÂ ·:ÃŽÂ ¾- derivation of A is a linear map f: Aà ¢Ã¢â‚¬  Ã¢â‚¬â„¢k which satisfies f(ab)= ÃŽÂ ·(a)f(b)+f(a) ÃŽÂ ¾(b), à ªÃ¢â‚¬Å" ¯ a, bà Ã‚ µ A and ÃŽÂ ·, ÃŽÂ ¾ à Ã‚ µ Alg(A, k). Definition1.46 The full subcategory of k-Alg (respectively of k-Co-alg) whose objects are finite dimensional algebras (respectively co-algebras) over k is denoted k-Alg fd (respectively  Ãƒâ€šÃ‚  Ãƒâ€šÃ‚  Ãƒâ€šÃ‚   k-Co-alg fd). Definition1.47 A proper algebra over k is an algebra over k such that the intersection of the co-finite ideals of A is (0), or equivalently the algebra map jA:Aà ¢Ã¢â‚¬  Ã¢â‚¬â„¢(Aà ¢Ã‹â€ Ã‹Å")*, be linear map defined by jA(a)(aà ¢Ã‹â€ Ã‹Å")=aà ¢Ã‹â€ Ã‹Å"(a), a à Ã‚ µA and aà ¢Ã‹â€ Ã‹Å"à Ã‚ µAà ¢Ã‹â€ Ã‹Å". Then: jA:Aà ¢Ã¢â‚¬  Ã¢â‚¬â„¢(Aà ¢Ã‹â€ Ã‹Å")* is an algebra map Ker(jA) is the intersection of the co-finite ideals of A Im(jA) is a dense subspace of (Aà ¢Ã‹â€ Ã‹Å")*. Is one-to-one. Definition1.48 Let A (respectively C) be an algebra (respectively co-algebra ) over k. Then A (respectively C) is reflexive if jA:Aà ¢Ã¢â‚¬  Ã¢â‚¬â„¢(Aà ¢Ã‹â€ Ã‹Å")*, as defined before and jC:Cà ¢Ã¢â‚¬  Ã¢â‚¬â„¢(C*)à ¢Ã‹â€ Ã‹Å", defined as: jC(c)(c*)=c*(c), à ªÃ¢â‚¬Å" ¯ c*à Ã‚ µC* and cà Ã‚ µC. Then: Im(jC)à ¢Ã…  Ã¢â‚¬  (C*)à ¢Ã‹â€ Ã‹Å" and jC:Cà ¢Ã¢â‚¬  Ã¢â‚¬â„¢(C*)à ¢Ã‹â€ Ã‹Å" is a co-algebra map. jC is one-to-one. Im(jC) is the set of all aà Ã‚ µ(C*)* which vanish on a closed co-finite ideal of C*. Is an isomorphism. Definition1.49 Almost left noetherian algebra over k is an algebra over k whose co-finite left ideal are finitely generated. (M is called almost noetherian if every co-finite submodule of M is finitely generated). Definition1.50 Let f:Uà ¢Ã¢â‚¬  Ã¢â‚¬â„¢V be a map of vector spaces over k. Then f is an almost one-to-one linear map if ker(f) is finite-dimensional, f is an almost onto linear map if Im(f) is co-finite subspace of V and f is an almost isomorphism if f is an almost one-to-one and an almost linear map. Definition1.51 Let A be algebra over k and C be co-algebra over k. A pairing of A and C is a bilinear map   ÃƒÅ½Ã‚ ²: AÃÆ'-Cà ¢Ã¢â‚¬  Ã¢â‚¬â„¢k which satisfies, ÃŽÂ ²(ab,c)= ÃŽÂ ² (a, c(1))ÃŽÂ ² (b, c(2)) and ÃŽÂ ²(1, c) = ÃŽÂ µ(c), à ªÃ¢â‚¬Å" ¯ a, b à Ã‚ µ A and  Ãƒâ€šÃ‚  Ãƒâ€šÃ‚  Ãƒâ€šÃ‚  Ãƒâ€šÃ‚  Ãƒâ€šÃ‚  Ãƒâ€šÃ‚   c à Ã‚ µC. Definition1.52 Let V be a vector space over k. A co-free co-algebra on V is a pair (à Ã¢â€š ¬, Tco(V)) such that: Tco(V) is a co-algebra over k and à Ã¢â€š ¬: Tco(V)à ¢Ã¢â‚¬  Ã¢â‚¬â„¢T is a linear map. If C is a co-algebra over k and f:Cà ¢Ã¢â‚¬  Ã¢â‚¬â„¢V is a linear map,à ¢Ã‹â€ Ã†â€™ a co-algebra map F: Cà ¢Ã¢â‚¬  Ã¢â‚¬â„¢ Tco(V) determined by à Ã¢â€š ¬Ãƒ ¢Ã‹â€ Ã‹Å"F=f. Definition1.53 Let V be a vector space over k. A co-free co-commutative co-algebra on V is any pair (à Ã¢â€š ¬, C(V)) which satisfies: C(V) is a co-commutative co-algebra over k and à Ã¢â€š ¬:C(V)à ¢Ã¢â‚¬  Ã¢â‚¬â„¢V is a linear map. If C is a co-commutative co-algebra over k and f: Cà ¢Ã¢â‚¬  Ã¢â‚¬â„¢V is linear map, à ¢Ã‹â€ Ã†â€™ co-algebra map F:C à ¢Ã¢â‚¬  Ã¢â‚¬â„¢C(V) determined by à Ã¢â€š ¬Ãƒ ¢Ã‹â€ Ã‹Å"F=f.   Ãƒâ€šÃ‚  Ãƒâ€šÃ‚  Ãƒâ€šÃ‚  Ãƒâ€šÃ‚  Ãƒâ€šÃ‚  Ãƒâ€šÃ‚  Ãƒâ€šÃ‚  Ãƒâ€šÃ‚  Ãƒâ€šÃ‚  Ãƒâ€šÃ‚  Ãƒâ€šÃ‚  Ãƒâ€šÃ‚  Ãƒâ€šÃ‚  Ãƒâ€šÃ‚  Ãƒâ€šÃ‚  Ãƒâ€šÃ‚   (Majid 2002, Radford David E) Chapter 2 Proposition (Anti-homomorphism property of antipodes) 2.1 The antipode of a Hopf algebra is unique and obey S(hg)=S(g)S(h), S(1)=1 and (Sà ¢Ã‚ ¨Ã¢â‚¬Å¡S)à ¢Ã‹â€ Ã‹Å"Άh=à Ã¢â‚¬Å¾Ãƒ ¢Ã‹â€ Ã‹Å"ΆÃƒ ¢Ã‹â€ Ã‹Å"Sh, ÃŽÂ µSh=ÃŽÂ µh, à ¢Ã‹â€ Ã¢â€š ¬h,g à ¢Ã‹â€ Ã‹â€  H.   Ãƒâ€šÃ‚  Ãƒâ€šÃ‚  Ãƒâ€šÃ‚  Ãƒâ€šÃ‚  Ãƒâ€šÃ‚  Ãƒâ€šÃ‚  Ãƒâ€šÃ‚  Ãƒâ€šÃ‚  Ãƒâ€šÃ‚  Ãƒâ€šÃ‚  Ãƒâ€šÃ‚   (Majid 2002, Radford David E) Proof Let S and S1 be two antipodes for H. Then using properties of antipode, associativity of à Ã¢â‚¬Å¾ and co-associativity of Ά we get S= à Ã¢â‚¬Å¾Ãƒ ¢Ã‹â€ Ã‹Å"(Sà ¢Ã…  -[ à Ã¢â‚¬Å¾Ãƒ ¢Ã‹â€ Ã‹Å"(Idà ¢Ã…  -S1)à ¢Ã‹â€ Ã‹Å"Ά])à ¢Ã‹â€ Ã‹Å"Ά= à Ã¢â‚¬Å¾Ãƒ ¢Ã‹â€ Ã‹Å"(Idà ¢Ã…  - à Ã¢â‚¬Å¾)à ¢Ã‹â€ Ã‹Å"(Sà ¢Ã‚ ¨Ã¢â‚¬Å¡Idà ¢Ã…  -S1)à ¢Ã‹â€ Ã‹Å"(Id à ¢Ã…  -Ά)à ¢Ã‹â€ Ã‹Å"Ά= à Ã¢â‚¬Å¾Ãƒ ¢Ã‹â€ Ã‹Å"(à Ã¢â‚¬Å¾Ãƒ ¢Ã‚ ¨Ã¢â‚¬Å¡Id)à ¢Ã‹â€ Ã‹Å"(Sà ¢Ã‚ ¨Ã¢â‚¬Å¡Idà ¢Ã…  -S1)à ¢Ã‹â€ Ã‹Å"(Ά à ¢Ã…  -Id)à ¢Ã‹â€ Ã‹Å"Ά = à Ã¢â‚¬Å¾Ãƒ ¢Ã‹â€ Ã‹Å"( [à Ã¢â‚¬Å¾Ãƒ ¢Ã‹â€ Ã‹Å"(Sà ¢Ã‚ ¨Ã¢â‚¬Å¡Id)à ¢Ã‹â€ Ã‹Å"Ά]à ¢Ã‚ ¨Ã¢â‚¬Å¡S1)à ¢Ã‹â€ Ã‹Å" Ά=S1. So the antipode is unique. Let Sà ¢Ã‹â€ -id=ÃŽÂ µs idà ¢Ã‹â€ -S=ÃŽÂ µt To check that S is an algebra anti-homomorphism, we compute S(1)= S(1(1))1(2)S(1(3))= S(1(1)) ÃŽÂ µt (1(2))= ÃŽÂ µs(1)=1, S(hg)=S(h(1)g(1)) ÃŽÂ µt(h(2)g(2))= S(h(1)g(1))h(2) ÃŽÂ µt(g(2))S(h(3))=ÃŽÂ µs (h(1)g(1))S(g(2))S(h(2))= S(g(1)) ÃŽÂ µs(h(1)) ÃŽÂ µt (g(2))S(h(2))=S(g)S(h), à ¢Ã‹â€ Ã¢â€š ¬h,g à ¢Ã‹â€ Ã‹â€ H and we used ÃŽÂ µt(hg)= ÃŽÂ µt(h ÃŽÂ µt(g)) and ÃŽÂ µs(hg)= ÃŽÂ µt(ÃŽÂ µs(h)g). Dualizing the above we can show that S is also a co-algebra anti-homomorphism: ÃŽÂ µ(S(h))= ÃŽÂ µ(S(h(1) ÃŽÂ µt(h(2)))= ÃŽÂ µ(S(h(1)h(2))= ÃŽÂ µ(ÃŽÂ µt(h))= ÃŽÂ µ(h), Ά(S(h))= Ά(S(h(1) ÃŽÂ µt(h(2)))= Ά(S(h(1) ÃŽÂ µt(h(2))à ¢Ã‚ ¨Ã¢â‚¬Å¡1)= Ά(S(h(1) ))(h(2)S(h(4))à ¢Ã‚ ¨Ã¢â‚¬Å¡ ÃŽÂ µt (h(3))= Ά(ÃŽÂ µs(h(1))(S(h(3))à ¢Ã‚ ¨Ã¢â‚¬Å¡S(h(2)))=S(h(3))à ¢Ã‚ ¨Ã¢â‚¬Å¡ ÃŽÂ µs(h(1))S(h(2))=S(h(2))à ¢Ã‚ ¨Ã¢â‚¬Å¡ S(h(1)). (New directions) Example2.2 The Hopf Algebra H=Uq(b+) is generated by 1 and the elements X,g,g-1 with relations gg-1=1=g-1g and g X=q X g, where q   is a fixed invertible element of the field k. Here ΆX= Xà ¢Ã‚ ¨Ã¢â‚¬Å¡1 +g à ¢Ã‚ ¨Ã¢â‚¬Å¡ X, Άg=g à ¢Ã‚ ¨Ã¢â‚¬Å¡ g, Άg-1=g-1à ¢Ã‚ ¨Ã¢â‚¬Å¡g-1, ÃŽÂ µX=0, ÃŽÂ µg=1=ÃŽÂ µ g-1, SX=- g-1X, Sg= g-1, S g-1=g. S2X=q-1X. Proof We have Ά, ÃŽÂ µ on the generators and extended them multiplicatively to products of the generators. ΆgX=(Άg)( ΆX)=( gà ¢Ã‚ ¨Ã¢â‚¬Å¡g)( Xà ¢Ã‚ ¨Ã¢â‚¬Å¡1 +gà ¢