Do People in Public Life Have a Right to Privacy? Essay

People, famous or not, have a right to privacy, which is a basic human right. Although some of them have voluntarily made themselves known to the world, they are still entitled to live a life without others following them all the time, eavesdropping on what they say and being under surveillance. However, in the case of politicians or other powerful people, the right to privacy comes into conflict with another right, the public’s right to know. The entitlement and the necessity to get informed are essential to guarantee democracy; this can only be achieved by the freedom of the press. Therefore the right to privacy of certain politicians sometimes has to be neglected to ensure a rightful running of our country. But do we need to get informed about everything there is? We have to distinguish between famous people. Basically there are those who were seeking a public life – or at least knew to some extent what they were going into – and those who were not. Politicians, athletes, actors, musicians, entertainers and members of royalty belong to the former. The latter are ordinary citizens who become significant, because of their extraordinary experiences, for example victims of crimes or tragedies, but also criminals. The amount of ordinary citizens who receive their celebrity status unwillingly is quite big and the privacy of those people needs to be especially respected and maintained. Names, addresses or pictures that could lead to the identification of a person should never be made public. It is not of interest for the readers, and it usually does not make a difference for them, what the name of someone is, but for the one concerned publication of identity could mean embarrassment and harassment. Suspected criminals, for instance, could lose their jobs, their families could break up or their whole lives could get destroyed, even when they are innocent. Apart from that, as soon as someone is well known, they are pursued and harassed by journalists demanding interviews. Also in cases where a family just had to experience the loss of a dear person, the press usually shows little respect for that. While we tend to despise the way the press is treating ordinary people and feel the justification for their right to privacy, we have problems applying the same to people who were seeking a public role. In those cases we tend to think we have a right to the invasion of their privacy, since they have put themselves into the public eye on purpose. We demand to know about their personal lives, but we don’t see that this interest is only greediness for amusement. The press is using this human phenomenon and is sacrificing individual privacy for the entertainment of a general public to increase the circulation of a paper. We are satisfying our voyeurism and we even claim that we have a right to it, but by that we submit ourselves to the tabloid values of a mainstream media and put that under the cover of public interest. What is public interest? Journalists usually widen this term to use it as an excuse for all forms of reporting, in order to cover up every detail of one’s life. But public interest is not necessarily what the public is interested in, which is usually sex and crime; it is not what increases the circulation of a paper; it is not gossip. Public interest is the necessity to have access to essential information that allows us to keep a critical eye on our society. A person’s personal lives or gossip about it is not news and not of public interest. But unfortunately, reports about politicians’ sex lives are more popular than reports about someone’s policies and public actions. The position of politicians in the eye of the public is especially difficult to judge. On the one hand politicians use their happy family and home in campaigns, on the other hand we know personal particulars and behaviour have nothing to do with competence in running a country and private details, even if completely irrelevant, can still ruin careers. Sometimes only due to the intrusion of privacy, corruption or similar crimes can be made public, but at the same time not everything in one’s life is connected to one’s office. When personal morality and family values are deliberately used by politicians  as a reason for them to be elected, they have chosen to make it a public issue rather than a private one. This is a sad fact, but it does not justify intrusion of the personal lives of all politicians. A politician still is, like everyone else, entitled to privacy. Unfortunately, the press and the public seem to have grown bored covering politicians who aren’t celebrities and so personal gossip wins over public issues. Since their private lives are so closely observed, politicians are concentrating a lot on their image and consequently they have less time to spend on their actual job. This close scrutiny is not only humiliating, it also makes poor political performances more likely. If the public lost its big interest in private lives, political coverage and also politicians themselves would have to focus more on policies and actions. Everyone would have to stop making privacy an issue, which has no place in politics. However, competence seems to count less and less nowadays and politicians are rather supposed to have a good character. People are inclined to think that one who betrays his wife also betrays his country, which generally not the case. But character is not determinable by personal behaviour and moreover there is no connection between private morality and someone’s ability to do a job well. Would we rather have a morally integer, but less competent person in power? A lot of good leaders of the past would probable fail today, for example Kennedy, who committed adultery, or Kreisky, who had a speech impediment. Many talented people do not manage to reach a high position today, because they have no blameless personal lives and many are kept from seeking a public office, because they fear the intrusion of privacy. Politicians have to be observed in some respects. The press, being independent from any authorities, plays an important role in informing the public; it is the instrument that can expose corruption, wasting of taxes, hidden agendas or other crimes by examining actions and words of politicians. Naturally, there is no clear dividing line between public and private matter. Generally you can say, everything that has to do with the particular person’s profession has a public interest justification and can  thus be reported about. Intrusion of privacy should only be allowed in cases where privacy is strongly connected to the public office. Any other information revealed, which is irrelevant to the politician’s skills and competence, is not irrelevant to the image one has of that person. It just prejudices people against them and this can clearly not be in the public interest. Watergate, for instance, was one example of a journalist revealing illegal political actions, but h ere only information connected with the person’s profession was made public. Clinton’s sex-affair, however, was an example of going too far into privacy. People claimed the whole scandal was not about sex, but about committing perjury, which is not quite true. A perjury of Clinton about a land deal would have probable not interested as many, but this one was about sex, so the interest was enormous. Clinton was asked something he should have never been asked. Private questions – such as: â€Å"Have you ever committed adultery?† – ought definitely not be put to someone. Because if one refuses an answer to a query like that, it is a signal that there is something to hide. Since you hardly find someone who has never done anything wrong or illegal, it is especially unlikely to find a politician like that. Everyone knows they can’t admit little sins of their youth or sex affairs, because they know it would ruin their careers. So politicians have two possibilities when they are asked questions about their private lives: not answeri ng, the same as admitting, or lying. For celebrities, other than politicians, it is even more difficult to argue for their right to privacy, since so many of them use their status of being popular and seem to enjoy sharing private details and creating sensational news to stay well known or to make money. Publicity should be expected by them and loss of privacy is said to be the prize for fame. But does every skier, musician or actor really just want to be in the public eye? Is not also imaginable that a tennis player just loves to play tennis and detests being on television? We can reduce those people to the fact that they are famous, but it would show little acknowledgement for their talents or abilities. After all, the celebrity status is in many cases just by-product of someone’s success in a particular field. Fame does not rob anyone the  right to privacy and journalists go way too far for interviews or pictures of celebrities. Sometimes this has great consequence as in the case of Princess Diana, who died in a car accident after being chased by reporters. We are all obsessed with privacy, protecting our own on the one hand, and invading other people’s privacy on the other hand. If people similar to us, ordinary people, get their privacy invaded, we are outraged. But someone different to us, someone famous, somehow has the duty to uncover everything there is. Since they have voluntarily thrown themselves into the public light, they now belong to the public. Political scandals have shown the need for close observation of public figures, especially if they have power, but in most cases we hypocritically claim to have a right to know about something that is actually none of our business. Privacy is classed as a right under the European Convention of Human Rights and it applies to everyone.

A Rose for Emily: a Themes of Death and Change Essay

William Faulkner explains why the story is not about him, but his details about a lonely poor woman named Miss Emily is very unpredictable. Miss Emily is unable to grip the idea of death and suffers from denial. After the death of her father, the people from the town expected her to be in a state of grief but she is not. Instead, she proceeds to say that her father is very well with her and alive. William Faulkner’s idea of grieving is clear in this story because he shows his audience that it is better to accept death than to ignore it through the accounts of Miss Emily’s journey. William Faulkner’s story takes place in the South, during a time period of racial discrimination and major changes. By using reader response criticism, a reader can analyze â€Å"A Rose for Emily† through the aspects of the secret held within the story, race found through anthropology, and gender found through anthropology. To begin with, one can analyze â€Å"A Rose for Emily† by examining the hidden message found in the story. The hidden message that William Faulkner tried to convey in his story was the themes of death and change. For example, Emily told them that her father was not dead. Miss Emily tried to defy death by holding on to her father’s corpse and treating it as if he were still living and how fearful she was of change. She later killed Homer to ensure that he would never leave her. Miss Emily continually tried to prevent any sort of change through death or other means from occurring in her town. She was so frightened of change that she wouldn’t allow the city to put numbers on her house for mail. The next step to analyzing â€Å"A Rose for Emily† is to examine race found through anthropology. The South was once known for its extreme prejudice and racism. William Faulkner’s attempts to convey this racism is made clear in â€Å"A Rose for Emily†. Mr. Faulkner explains the roles of women in the South and how they were seen through the eyes of men. When Miss Emily Grierson died the whole town went to her funeral. The men out of respectful affection for a fallen monument and the women mostly out of curiosity. In conclusion, there are many aspects that were incorporated into â€Å"A Rose for Emily†. William Faulkner was able to create a story involving many ideas about society and how it functioned in a specific time period in the South. To further examine â€Å"A Rose for Emily†, one can use the reader response criticism and analyze the aspects of the hidden message found within the story, race found through anthropology, and gender found through anthropology. â€Å"A Rose for Emily† is an important element in literature due to examination of the effects of change created in the olden South.

Ethical issues in medicine Essay Example | Topics and Well Written Essays - 2000 words

Ethical issues in medicine - Essay Example n europe regarding a suicidal act was that if any person performs a suicidal act upon him, then the court of law used to order the local police to drag the body of that person on the streets, just to set an example for those, who wished to perform a suicidal act upon them (Emanuel, 1805-1810). By the end of the 18th century, Euthanasia was quite a controversial topic of discussion. Many experts had ejected the idea of euthanasia and considered to be morally and ethically illegal. But in 1828, for the first time ever in history of mankind, The constituiton of USA made assisted suicide illegal. However, By 1930, Euthanasia had started to gain strong support in USA and other westernicized socities of the world and they were in favor of it. By the 20th and ealy 21st century, Euthanasia has made strong progress in Europe. Countries like Netherlands and Belgium have made it legal. Even Australia and USA have made steps to legalize it. Euthanasia can be either an active euthanasia or passive euthanasia. Passive euthanasia refers to taking the life of the other person, at his request, by removing the life supporting means. There can be two kinds of life supporting means, ordinary life supporting means and extraordinary life supporting means. Ordinary life supporting means, such as food and water, are basic human needs, which are required by a person at regular intervals, in order to continue his life. In addition, any such death which is caused by the failure to provide the ordinary life supporting means does not comes under the definition of euthanasia. However, it is not necessary for a person to use extraordinary life supporting means to continue his life and a person also has an absolute freedom to discontinue any such medical treatment which can be categorized as an extraordinary life supporting mean. This is because, as there are many intricacies involved in deaths which are caused by the removal of extraordi nary life supporting means, so each such case of death

Subtle Expressions of Patriotism Essay Example | Topics and Well Written Essays - 750 words

Subtle Expressions of Patriotism - Essay Example It is not the cultures of the Irish, Hispanics, and Germans that dot this continent. America is a set of principles, values, and ideals that have remained unchanged for over two centuries. Giving our continual vigilance and support to these abstract concepts is what patriotism is. A colorful hat or a flag on the lawn does little to strengthen our nation or bind us together as a people. Living the principles and ideals of our founding fathers is a subtle, yet powerful, way to not only show our patriotism, but to put it to work to strengthen our nation. Practicing the founding principle of equality binds us together in a nationalistic environment that creates the strength of numbers with the peace of individualism. We practice equality in our day-to-day lives by acting on the immortal words "We hold these Truths to be self-evident, that all Men are created equal, that they are endowed, by their Creator, with certain unalienable Rights" (Declaration of Independence). We live up to this ideal by treating our fellow citizens with dignity and respect. This calls us to do more than simply profess to be fair and equal in our treatment of minorities, religions, and opposing political opinions. It means that we must also accept them as legitimate and equal in terms of allowing them to exist, flourish, and grow. The practice of equality is a subtle expression of patriotism that is built upon the foundation of our nation's beliefs. Equality helps our nation assure that we are allowed to remain free and have the liberty that our independence granted us. Founding father Thomas Jefferson warned us that, "The price of freedom is eternal vigilance" (qtd. in Quotation Page). Our subtle patriotism is shown by our continued watch over our government, its excesses, and its direction in forming our domestic and foreign policies. As with equality, this expression of patriotism also requires action on the part of the citizenry. It requires us to stay informed of the issues that affect America. It demands that we participate in government when possible and whenever necessary. This may mean taking the simple action to vote, or may require running for public office. In addition, as Mark Twain said, we need to support our government when it deserves it. Freedom is a right that must be lived and watched over to assure it remains a part of our American tradition. As a nation that is built on equality and liberty, we have a patriotic obligation to support our country when we can, and criticize it when we can't. While we see our brave soldiers as true patriots, some patriots may be subtler in their approach. Visiting a veteran's hospital to thank the courageous men and women that have placed their life in harms way for our freedom is a quiet, yet forceful, show of patriotism. In addition, we must be willing to criticize our government when our conscience tells us that the government is taking action that is not in the best interest of the people. Civil disobedience can be as patriotic as enlisting in the armed forces. In both cases we are defending the principles and values that make this nation America. In conclusion, patriotism is an action that must be lived and incorporated into our daily lives. It isn't displayed by our once a year display of flags and fireworks. Patriotism is an

History Paper on the Portrayal of Women in Advertising Research

History on the Portrayal of Women in Advertising - Research Paper Example In this context, it can be stated that portrayal of women in advertising is nothing new. The gender-based advertisement has shown a growing trend and has become more diverse over the years. It is a known fact that repetitive themes shown in advertisement influence the perception of people and society to a great extent. The mode of advertisement using media and print media such as magazines has shown profound transition over centuries. Notwithstanding, it is often argued that the role of women in advertising are much narrower than that of men. In this regard, many scholars have claimed that advertising characters of women are portrayed as subordinates to men and in a passive role. Sexual portrayal and sexuality has been used in advertisement since long. The gender stereotype was clearly visible earlier centuries and the role of women in advertising profoundly affected the perception of society towards women (Jacobson and Mazur 75-82). Historically, women in advertising had been represented as a sex object and had been subject to widespread exploitation. Besides, gender biases and racial biases were clearly apparently in the historical context with respect to women advertising. The image of women during the earlier centuries particularly in 19the century extremely suffered in the society due to objectification as well as sexism. It is evident that women are used in advertisement and their image is sometimes manipulated and distorted in order to promote women as a stereotype sex object. This is again due to the fact that women were given no power in the earlier days. The theme of using women as a sexual object initiated in the year 1850 when women were used and exposed to sell the product. For instance, the portrayal of nude women for the sale of tobacco in the 1850’s was normal due to the perception and mindset of people. Gender role was high in the initial years when advertisement through television or mag azines initiated. The

Undecided Essay Example | Topics and Well Written Essays - 1250 words - 4

Undecided - Essay Example ysis will consider the core components that defined the way in which the system evolved and held on to power only to eventually decline as all systems are bound to do in one form or another. As a further function of such an analysis, it is the hope of this author that the reader will be able to gain some very clear insights as to the reasons why and ultimately how this power evolved and eventually declined as a means of providing key insights into the nature, growth, and decay that all forms of governance will ultimately experience over the course of time. With respect to the creation of Gaddafi’s modern Libya, this was fundamentally centered upon the fact that a highly tribalized Libya was not effectively governed by the monarchy that loosely held sway over the various and far flung groups that defined the Libyan state. Longing for a sense of purpose and sensing the fundamental shifts that decolonization had effected on neighboring regions within the Arab world, there was a strong sense of unease and dissatisfaction that pervaded the society of the time; making it ripe for systemic change. Sensing the weakness, Gaddafi and others were able to organize a coup with a core cabal of willing individuals that had formed key and strategic alliances with many of the tribes that constituted Libya (Hauslohner 39). A further human need that was seemingly sought to be recognized within the context of the revolution was the ability of the individual citizen to have a say with regards to the way in which government undertook the process of governance. This right to self-determination has long been a central and key role in undermining existing systems of government; however, as was seen in the case of Libya, the extent to which this self-determination was ultimately realized was quite limited. As a means of creating the power that could seek to congeal this non-uniform and highly tribalized representation of a nation into a single unit, a unique coalescence of Islamic

Redo psychology in education Essay Example | Topics and Well Written Essays - 1000 words

Redo psychology in education - Essay Example In spite of their individualistic cognitive and behavioral differences, there are certain areas in which students from the 9th to 12th grade equally need guidance and education. Such areas include but are not limited to the study of ethics, and corporate social responsibility. There is need to teach such subjects at all levels, though their content can be customized to match the level of complexity understandable for the students at different levels. Learner diversity in the curriculum is fostered not only by the inclusion of diversity in he curriculum, but also by keeping a diverse force of teachers that have to teach that curriculum to the students. So there is a need to work on both levels i.e. curriculum and faculty because underestimating the need to work on one would have an adverse impact on the other. For example, let’s talk about a school teaching different languages to the students because the knowledge of different languages is fundamental to social integration in the contemporary multicultural society. The languages being taught include English, Urdu, French, and Arabic. Now there is a need to either have a teacher who is well-equipped with the knowledge of each of the four languages or the school needs to hire four different teachers each having expertise in his/her own language to teach the students effectively. On the other hand, curriculum can be made diverse by including content from different cultures de pending upon which area a certain culture is more developed in or what a certain culture has more to offer in comparison to other cultures. From this standpoint, the subjects of science and technology can be based on Western knowledge since advanced economies are more advanced in the research and knowledge of science and technology as compared to the third world countries whereas the subjects of arts and craft, including performing arts can be based on the knowledge of South Asian cultures

The Oil Supply Dependence Of The Automobile Industry Research Paper

The Oil Supply Dependence Of The Automobile Industry - Research Paper Example The paper tells that considering the rising oil prices worldwide, there were recent attempts to pave the way to alternative sources of energy so as to gradually reduce the demand for oil. In 2010, Li, Xiaogu, Clark, Christopher, et. al. conducted a survey of the peoples’ likelihood that they will prefer flexible-fuel or hybrid automobile given the choice when they purchase one. The result showed positive response to less dependence on oil for automobiles. Statistics show a declining dependence on foreign petroleum since 2005, according to the U.S. Energy Information Administration in mid-2011. Nonetheless, what has been the actual situation pertaining to a dependence on automotive oil? There was an increase in the use of domestically produced biodiesel, ethanol, and natural gas. However, by the mere fact that crude oil from domestic production realized increase in demand, dependence on oil as source of energy remains high. Imported oil declined. As can be seen from Figure A, c onsumption of oil also declined in 2010. But there will be a growing demand for liquid fuels including oil in the coming years as shown in Figure B. For automobiles, the trend in demand for Motor Gasoline also shows a projected increase in demand. See Figure C. Even as the production volume of crude oil will be increased in the USA, the prices of oil will also increase in the coming years. This can be clearly seen in Figure D. Apparently, the people are feeling the financial impact of the seemingly endless price increases of oil in the world market as well as in the local market. There is a domino effect on even the prices of basic goods whenever oil price increases are announced. Oil price increases eventually jack up the prices of goods and services since sources of energy like gasoline, motor oil, and liquefied petroleum gas are part of the cost of production and operating expenses like transportation or travelling expenses. It reduces the value of family income because each doll ar will have a lower value in the sense that the same amount of money can only buy less and less as the prices of oil increase to push up the prices of prime commodities. Thus, people have been adjusting to these trends by finding ways and means to reduce dependence on oil. Many have resorted to alternative energy sources. 2. Analysis of the Problem The world has limited supply of oil while there has been increasing demand for oil. Tverberg, Gail E. wrote that oil supply of our world had stopped increasing since 2005 (Abstract). As a matter of fact, his report mentioned (3): â€Å"We show in this section that world oil supply constriction started about 2004 based on price trends, and that restriction affected primarily OECD countries†. It will take about 20 years to mitigate the decline in oil supply by producing alternative sources and by replacing vehicles capable of utilizing alternative sources (4). It was estimated that wind and solar energy sources can only contribute a n insignificant capacity for the production of energy compared to the total energy supplied by oil-based power generators. â€Å"Growth of emerging economies† (1) certainly led to an oil shortage given such a fact about no more rise in the production of oil supply. To confirm this phenomenon as of a very recent date, January 3, 2012, Brad Plumer of the Washington Post reported the prediction of Goldman Sach’s Investment Bank pertaining to oil production in the world, which says that demand will hit the production capacity of oil by the year 2013. China and India have reached 2.5 billion population. Their demand for oil in order to achieve economic growth was reported to be rising as a result of these two countries’ fast developments. In contrast, oil supply production

Financial Leasing in the Context of Uniform Commercial Code of the Essay

Financial Leasing in the Context of Uniform Commercial Code of the United States - Essay Example nless the lessee has selected that person and directed the lessor to acquire the goods or the right to possession and use of the goods from that person, (b) that the lessee is entitled under this Article to the promises and warranties, including those of any third party, provided to the lessor by the person supplying the goods in connection with or as part of the contract by which the lessor acquired the goods or the right to possession and use of the goods, and (c) that the lessee may communicate with the person supplying the goods to the lessor and receive an accurate and complete statement of those promises and warranties, including any disclaimers and limitations of them or of remedies.2 For lessors the essential challenges in financial leasing are the length of time the financial institution’s investment is exposed which is the duration of the financial lease. Since the financial institution only holds the title of ownership of the asset in financial leases they do not ha ve possession of the asset therefore the care, maintenance, state and condition of the asset is not within the control of the financial institution. This exposure is considered a risk by financial institution since in the event of a default or failure of the lessee to satisfy his part of the agreement the state and condition of the asset may not make it marketable or commercially viable for the financial institution or the lessor to recover his investment at the onset. Taking the above into consideration the lessor can exercise his right by virtue of Article 9 of the Uniform Commercial Code of the United States to secure his investment supported by Article 1 203 of the same Code which states that: A transaction in the form of a lease creates a  security interest if the consideration that the... For lessors the essential challenges in financial leasing are the length of time the financial institution’s investment is exposed which is the duration of the financial lease. Since the financial institution only holds the title of ownership of the asset in financial leases they do not have possession of the asset therefore the care, maintenance, state and condition of the asset is not within the control of the financial institution. This exposure is considered a risk by financial institution since in the event of a default or failure of the lessee to satisfy his part of the agreement the state and condition of the asset may not make it marketable or commercially viable for the financial institution or the lessor to recover his investment at the onset. Taking the above into consideration the lessor can exercise his right by virtue of Article 9 of the Uniform Commercial Code of the United States to secure his investment supported by Article 1 203 of the same Code which states that: A transaction in the form of a lease creates a security interest if the consideration that the lessee is to pay the lessor for the right to possession and use of the goods is an obligation for the term of the lease and is not subject to termination by the lessee, and: the original term of the lease is equal to or greater than the remaining economic life of the goods; the lessee is bound to renew the lease for the remaining economic life of the goods or is bound to become the owner of the goods;

Paper reaction of the book Money has no smell by Paul Stoller Essay - 1

Paper reaction of the book Money has no smell by Paul Stoller - Essay Example Furthermore, the process of Africanization pertains to the marginal spaces that society provides to minority immigrants. I agree with Stoller’s argument that globalization presents ironies in the production and representation of ethnic identity. Furthermore, this book makes me feel resentful at the materialist culture of Western capitalism and how it dilutes, rather than strengthen, African identities and cultures through emphasizing the overwhelmingly dominant role of economics in shaping everyday lives and aspirations. Globalization presents economic-political ironies. An interesting irony about globalization and business is that Stoller learns more about the bureaucratic political system of his nation from his interactions with Africans. African traders ask help from Stoller in filling out official business and resident forms and other documents needed to stay and work in New York. Stoller learns that he knows so little of his own political and economic infrastructures, and this is where the Africans, or the â€Å"others,† teach him about the complexity of New York and American economics. Moreover, the complexity of these structures defies logic at times. On the one hand, the African traders have simple economic thinking. They buy something and they sell it for a profit, and then they have to pay taxes. On the other hand, the political bureaucracy is not as simple and logical. Stoller helped Boubà © Mounkaila finish his numerous forms and applications for Manhattan. They already brought t hese documents to the INS office, but they were required to follow a much more impractical protocol that would result to delays in processing it: â€Å"Even though we were in the INS offices, they insisted that the forms be mailed to them† (Stoller 112). This anecdote shows that market economics is not as efficient as its proponents assert it is. In reality, the authorities create rules and regulations that hamper the efficiency

Management Case Study Essay Example for Free

Management Case Study Essay The case study below takes place at the Sir Charles Wilberforce Hospital’s cafeteria, which is experiencing problems with the change management. Due to the new management undertaken by Keith Davis, there was a major issue of inadequate communication channels, as Keith told his employees what to do rather than consult them, especially with the decision-making. The best alternative to rectify this problem is for Keith to adapt to a consultative management style, in order for employees to take ownership in their workplace through expressing their opinions and feel more valued, however still allowing Keith to still make the final decision. Another major issue addressed in the Cafeteria was the amount of unmotivated staff. As employees feel unsatisfied with their work, the best solution to this issue is Goal Setting. Through employees setting strategic goals they will increase their motivation through achievement of these goals which will lead them to set more challenging ones. Lastly, the third major issue recognised was Keith’s poor leadership skills which made it difficult for employees to fulfil expectations and find enjoyment in the workplace. The best alternative solution for this problem is to retrain Keith’s leadership abilities so he is able to adopt all the qualities needed to become a better leader in his managing role. Although this may be an expensive method, the new leadership qualities Keith will learn will make a happier work environment for his employees and build a better employer/employee relationship. 3. Problem identification Poor communication channels Keith focuses on top down communication channels, providing a one way communication which is from him to his employees, rather than two-way which provides his employees to communicate ideas with him. This negatively impacts the hospital as the Keith is unable to discuss problems or ask questions amongst employees to see if there are any problems going on amongst the workers and therefore leading to job dissatisfaction employees. Although Keith tried to soothe Julia when the issue between her and Madison was brought to his attention, he did not follow it up or treat it as an importance. Lack of staff motivation Prior to Keith’s managing, Anne’s original foundations of self-satisfaction and close family ties seemed to motivate the employees at Sir Charles Wilberforce hospital. Keith’s changes were made to become more efficient, employees were left struggling to gain satisfaction and motivation in order for themselves to achieve their hierarchy of needs (Maslow, 1954). In this hierarchy of needs Maslow developed, employees have five needs, physiological, safety, social, esteem, and self-actualisation, once they fulfil one of their needs they can graduate to the next one to fulfil it and so on. Without fulfilling the social needs of forming social ties or self-actualisation of gaining enough experience within the kitchen to become a supervisor, it became unknown to the employees of what they are capable of and decreased their enticements to complete tasks and feel satisfied. Insufficient leadership abilities Keith lacks major leadership qualities, as the organisational layout he uses is to tell employees what to do, depriving them of guidance and support. The Hersey Situations leadership model suggests that leadership focuses on follower’s readiness (Hersey, Blanchard Johnson, 2001). This theory suggests that at Sir Charles Wilberforce, if the employees feel they are unable to complete a task Keith should give those clear and specific instructions. If they are willing and confident Keith needs to provide them display high task orientation, and if employees feel able but are unwilling Keith would need to use a supportive approach. Lack of teamwork The teamwork environment of delegating tasks amongst of employees was not addressed by Keith. He believed that employees needed to finish work on time, plan menus monthly and take on cleaning responsibilities, whereas, the use of team work would have provided a better suited time managed system. Through having each employee assist with cleaning duties, planning menus, helping out another if time was short as well as assisting each other to get all food out and made the kitchen would be less chaotic. This would have assisted with issues if someone was ill, allowing more than one person to prepare greater portions of meals. 4. Statement of Major Problems The three major problems that are brought to the attention at Sir Charles Wilberforce Hospital are: Inadequate communication channels Unmotivated staff Insufficient leadership abilities The poor communication channel Keith utilises is top-down communication from Keith to his employees. As this is a workplace that depends on seeking ideas from others and support from each other, two way communications between Keith and his employees is necessary. This will allow employees to feel part of the decision making and feel they can share their ideas to improve the workplace. Following this Keith must then improve his leadership skills, putting his employees first and assisting them with any help and support they need in order to achieve a positive workplace. This may involve Keith revising the organisation’s culture, or distinguishing the strength and weakness of each employee so he knows how to assist each of them. Once Keith’s leadership abilities are improved, staff motivation must be identified and given, in order for employees to become productive within the kitchen and gain job satisfaction, increasing their abilities and allowing them to feel the want to work. 5. Generation and Evaluation of Alternative Solutions Inadequate communication channels Regular work meetings Set regular meetings within the kitchen, in order to concerns amongst employees to be discussed as we as evaluation on how the business is going and openly discuss ways to improve or maintain it. Advantages Allows for feedback Employees can listen to each person’s idea and encourages discussion openly Evaluate the earnings to the previous week and that time the previous year, allowing each person to suggest ways to improve or maintain their profit margins. Disadvantages Some employees may not attend May be time consuming to discuss all ideas Consultative management style Implement a Consultative management style in order to increase two-way and open communication between Keith and the employees. Advantages Allows employees to feel ownership in decision making Allows employees to share their ideas and opinions Gives confidence to employees Disadvantages Employees may feel held back to express their opinions because they do not feel comfortable Employees may feel offended if their ideas are not taken into consideration Time consuming Unmotivated staff Goal setting Implement setting goals, which involve employees setting goals that motivate them to improve their capabilities. Advantages Gives self-satisfaction Increases productivity and performance levels Disadvantages Time consuming to distinguish appropriate and achievable goals Goals ay appear as unattainable and lead to employees to give up Job design Mr Dev can alter the job design to assist in identifying and correcting any deficiencies that affect performance and motivation. Advantages Job enlargement, can be used to increase motivation by giving employees more and varied tasks so the employee is motivation to try new tasks Job rotation allows an employee to work in different departments or jobs in an organization to gain better insight into operations motivating the employee to increase his/her skills and knowledge about other jobs. Disadvantages Job enrichment may lead the employee transferred too much responsibility in the kitchen and independence in the planning and control aspects of the job which may suppress motivation levels Reward and Recognition Evaluating each employee to identify which people are performing to their maximum, and rewarding them financially or non-financially for their hard work, therefore motivating other employees to improve their work standards. Advantages Employees will increase performance to obtain more rewards Will produce higher standards amongst the employees Self- enrichment Disadvantages Expensive to keep purchasing rewards and reassess each employee to recognise After a while employees may feel that rewards may not motivate them anymore Keith may not want to undertake the idea of rewarding and recognising employees Insufficient leadership abilities Retrain Keith Retraining programs for Keith within the company or externally will allow Keith to develop better leadership qualities and create a happier workplace. Advantages Positively effects employees to feel trust and support from Keith Keith can evaluate themselves as to what skills are expected to lead the employees Disadvantages May take a while for Keith to learn and adapt to these skills May be expensive Dismiss Keith Dismissing Keith will demolish the issue of poor leadership abilities and will allow the business to replace him with a more experienced manager. Advantages Re-appoint a new manager who possess all correct leadership skills Employees are in a happier environment where they can get the support they need More time appropriate and efficient than retraining Disadvantages May be hard to find a replacement Employees may find it hard to adapt to a new manager and may be resistant to give them a chance due to their bad experience with Keith 6. Recommendation Consultative management style A Consultative management style is the recommended alternative for Keith to address to his employees. The type of management style used by Keith at this point is autocratic, which involves him making decisions for the hospital kitchen unilaterally. Although regular meetings are a good alternative by providing mediation and assistant towards employees, the consultative management style involves a permanent change to the organisation. The consultative style would involve Keith discussing ideas of possible changes to be made within the kitchen, as well as employees being able to give their opinions and ideas. By implementing a consultative management style, employees at the cafeteria will be able to perform to their optimum level, concentrating on increasing common sense approach for Keith to meet the needs and wants of the employees, as well as making employees realise their own abilities and capabilities in performing tasks, (McClelland, 1987). Similarly to regular meetings, the consultative approach gives open communication, however unlike meetings the consultative approach is more permanent in the workplace and is used daily, for example in decision making, gaining assistance with a task or getting support with a concern. This will benefit the kitchen, as the employees will respond more positively to any changes to feel more a part of the workplace and a sense of belonging. Keith will benefit from this style, as he will be given a broader range of ideas as well as maintain his authority to make the final decision. Goal Setting Setting goals is the preferred alternative for Keith to use within the kitchen. Despite the fact being rewarded motivates someone to maintain if not improve performance to be rewarded again, goal setting gives motivation. Goal setting enables employees to measure their processes and work performance. This enables employees to gain feedback on their results, unlike rewards and recognition which just motivates employees to try harder to gain another reward rather than possessing the want to gain the self-satisfaction that they have improved. Edward Locke’s theory of goal setting outlines that in setting specific and challenging goals it enables process and outcome improvement (Locke ; Latham, 1990). Similarly, job design suggests a different form of motivating to increase their skills of different tasks, however it also does hold the ability to measure the improvement that setting goals do. If goal setting is adapted by Keith, his employees would be able to achieve towards a higher performance, as well as motivating them to set higher goals with increasingly difficult tasks, once they have been achieved. Through Maslow’s hierarchy of needs, this can assist in setting goals with Locke and Latham’s theory. Maslow theory suggests that ‘although no need is every fully satisfied, a substantially satisfied need no longer motivates an individual to satisfy that need’ (Robbins, Bergmann, Stagg and Coulter, 2012, p559). This suggests that in identifying each need, physiological safety social esteem and self-actualisation, employees at sir Charles Wilberforce can pinpoint what tasks they need to complete in order to graduate to the next level. For example one of the employees may find that they feel they don’t belong, in order to achieve this level they can set a goal to form relations with other employees on a professional basis. Once this goal is achieved they can move on to develop their esteem needs. Retraining Keith Although, retraining Keith may be considered a time consuming process, compared to the alternative of dismissing Keith, it appears to be a more logical approach. Through retraining, Keith is able to gain leadership skills that he may not be aware are essential skills he needs in order to be a manager. This will transform him from telling his employees what to do, to instead assisting and guiding them through changes. Despite the expenses of this method, it may also be difficult for Keith to cooperate as well as understand the concept of these skills however unlike dismissing, he will be able to improve and allow for a happier work. The trait theory suggests that it is impossible to identify and isolate characteristics from leaders from non-leaders. However there are seven traits associated with leadership, these being ‘drive, the desire to lead, honesty and integrity, self-confidence, intelligence, job-relevant knowledge and extraversion’, (Robbins, 2012, p605). Eventually with the retraining, Keith may possess these seven leadership abilities to involve his employees in decision making process and form a trust bond.

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 ¢

Improving Quality of Life for HIV Sufferers

Improving Quality of Life for HIV Sufferers Introduction It is esteemed that over thirty three million people in the world are living with HIV/AIDS, (WHO, 2009). The majority of people living with HIV are in developing countries, approximately 95% of the total. Sub-Saharan Africa has been hit especially hard. It is esteemed that nearly 70% of all HIV infected people live in this area and 90% of maternal-fetal transmission are occurring there. Compared with the adult transmission rate in developed countries which is lower than 1%, it is 8% in sub-Saharan Africa, (Boyle, 2000). New cases of HIV infection are reported every year and more and more people living with HIV are diagnosed AIDS as they get aged, (Vance, Struzick and Burrage, 2009). So far, there is no effective way to cure this disease. Antiretroviral treatment (ART) is the most effective way to treat people living with HIV. It significantly controls the virus load within patients bodies. It has been a great advance toward extending patients lifespan and improving their quality of l ife. Because of its therapeutic effect, many HIV positive people are able to live with this virus for many years. However, for many people, HIV/AIDS is still a stressful and demanding disease, (Van Dyk, 2007). On top of that, for many HIV infected people in developing countries, the cost of ART is prohibitively expensive. Poverty and a lack of resources are recognized as the most significant barriers which make caring for HIV-infected patients and effective prevention efforts virtually impossible in most developing countries, (Boyle, 2000). As social life is significantly effected in a negative way for this population by social stigma, life is only getting more difficult. People are afraid of being associated with HIV positive people due to two major seasons: A) the fear of being infected themselves; B) the discrimination surrounding the disease. Loneliness, helplessness and self-blame create a high suicidal ideation among HIV infected people. Therefore, they often need counseling a nd psychosocial support, (UNAIDS, 2008). There is a special sub-group of population that needs some extra attention: homosexual people. Research, (Kraaij, Van Der Veek, Garnefski, et al, 2008) shows that HIV infection rate among homosexual people is around thirty times higher than average. In addition, health equality is far from available for everyone. Most homosexual people have witnessed or experienced discrimination from heterosexual people, (Gonsiorek Weinrich, 1991, pp.15-20). This issue is much more severe in eastern countries due to the cultural background. Homosexual people may see HIV infection as blameworthy not only because of a self-protection motive but also because sexual risk reduction has been strongly promoted in the gay community. The relationship between sexual orientation an blame is anticipated, (Collins, 1994). No evidence shows that effective actions have been taken to stop highly risky behaviors which can cause HIV transmission, such as anal sex among men, drug abuse, et al. Statistics show that the estimated prevalence of past-5-year homosexual behavior among males was 6.2, 4.5 and 10.7 in the US, the UK and France, respectively. Similar or even higher prevalence was observed in other areas of the world, (Lau, Kim and Tsui, 2008). Therefore, new HIV infections are still taking place. Besides, prolonged lifespan of HIV infected people is also associated with more new HIV infections. Some qualitative studies may be able to reveal how being HIV infected and homosexual affects ones life. As Aggleton, Hart and Davies, et al., (1999), believed that social stigma is not equal throughout the world, and they argued being gay was a significant factor in migration for some. Homosexual people who cannot live a normal life in their home countries would like to leave for a foreign country where they can continue their lifestyles but have no relatives or close friends. It is potentially dangerous for their health status, especially after they are infected by HIV. The respond of a male interviewee from Brazil in their study is very strongly underpinning this point, you have to get married to leave the house. They (parent) see like if you are leaving the house its because youre not happy so you dont even have any need to talk to us any more, thats how they react. So we have to stay living with our parents so we cant have boyfriends. So that is why everyone leave the country In regard of friendship and social networks, homosexual people tend to be very limited in choosing friends. According to Aggleton, Hart and Davies, et al., (1999), gay people are very likely to have virtually exclusively gay friend and some only have a small mixture of friends of diverse sexuality. It suggests social stigma has negatively affected homosexual peoples socialization. In the UK, health policy surrounding sexual health of homosexual people is closely related to HIV epidemics. Department of Health promoted a ten year National Strategy for Sexual Health and HIV, which aims at reducing the transmission of HIV and STDs, improving health and social care for people living with HIV, and reducing the stigma associated with HIV and STDs, (2001). However, according to James, it is failing to significantly reduce the transmission of STD or HIV and to improve health and life quality for HIV infected people, despite millions of funding has been invested for sexual health service over three years. New research is required to provide better solution, (James, 2009). Therefore, it is important to find out the good practices in improving life quality for homosexual people living with HIV, not only from a medical perspective, but also from a social and humanitarian perspective. Importance of systematic appraisal To my knowledge, previous studies have seldom touched this area. The few existing studies were focusing the effectiveness of one or two interventions. Therefore, they could not present all the good practices in a more systematic way. Looking through Cochrane Library, several systematic reviews have been conducted in relation with quality of life for people living with HIV, (see appendix). However, none of them is focusing on homosexual population. The special health need has not been fully addressed. The aim of this appraisal is to find the most effective ways to help homosexual people with HIV cope this severe disease and the stress associated, and to provide the best evidence to present the good practices to improve quality of life for the targeted population. Research question for this appraisal can be summarized as what are the best ways of improving life quality for homosexual people living with HIV. To be more specific, this question can be interpreted by several small and more details questions: 1) Besides medical treatment, what do homosexual people living with HIV need the most? 2) What are the biggest obscures for these people to have a good life? 3) What are the good practices that have been used in improving HIV positive peoples life quality? 4) What are the strengths and limits of there practices? 5) From what aspects can these practices be further improved? Systematic Review Methodology In order to answer these questions, a systematic review methodology will be applied. A systematic review of literature synthesizes the evidence which is found in previous literatures that used valid and reliable research methods to conduct the experiments, (Evans, 2002). It is one essential skill for health care providers to acquire to base policy decisions on the best available evidence, besides their knowledge of research methodology, (Jubb, 2002). Therefore, systematic review are extremely important for making new policies. Originally, systematic reviews would only include study design that applied randomized control trials, but it has changed through the time. Today all kinds of research design methodologies can be included in the review as long as they have policy relevance. It has been widely acknowledged of the value of including diverse research methodologies based on the fact that randomized control trials cannot answer the entire question needed for evidence. However, for this particular dissertation, the fully structured systematic review would not be used because A) it is an individual work instead of a team work; B) assess to existing literatures is limited due to the fund and time. I am going to use the systematic appraisal instead, which adopts the same methodology as systematic review but doesnt include all the existing literatures related to the topic. Conclusion of the chapter The importance of finding the best ways of improving life quality for HIV infected homosexual people has been addressed in this chapter. In order to reach this goal, a systematic appraisal will be conducted. By selecting and reviewing previous studies in this context, evidences will provided to identify the good practices and suggestions for future practice and policy making will be given. Chapter Two Literature Overview Introduction to the chapter In this chapter, several key literatures will be carefully selected and critically reviewed to find the emerging themes on the topic of HIV transmission and ways of improving quality of life for homosexual people living with HIV. The purpose of this chapter is to provide a clear context in which this appraisal will be done. It will also put this appraisal in a national and international health management context to show its importance against a broader backdrop. Databases Searched NORA (online searching vehicle of Northumbria University) is the key searching engine because it provides the access to core health related databases such as ASSIA, HSWE, Web of Knowledge, and PubMed, et al. Using searching key words, HIV/ADIS, Homosexual/gay, quality of life/life quality, on NORA and other databases respectively, more than sixty articles were selected. Only studies that were published in referee journals were selected. Selected studies were not limited methodologically, so broader understanding on the research topic will be obtained. Similarly, research population of each study was not limited in terms of location, ethnics, or social-economical status. Emerging themes arising from key literatures Key literatures surrounding HIV/AIDS and homosexuality and life quality were carefully selected and reviewed. Throughout the literatures, three emerging themes were found: impacts of HIV infection on peoples life; impacts of sexuality; previous researches on health care strategies. How does HIV infection impact on peoples life? A progressive loss of immune functioning, as a main characteristic of HIV disease, will cause opportunistic infection, (Bormann Aschbacher, et al., 2009). Immune system functioning can be negatively affected by elevated levels of cortisol, a marker of stress-related neuroendocrine activity with substantial immunosuppressive and modulatory capabilities, (Borghetti, Saleri, Mocchegiani, et al., 2009). It is just one major impact of HIV infection on peoples life, medical-wisely. However, more literatures addressed issues surrounding HIV transmission and its severe impacts from social-cultural perspectives. As Hansen, Vaughan, and Cavanaugh, et al. (2009) argued antisocial or borderline personality disorder is a common sign among people living with HIV, which can be regarded as a significant predictor of low health related quality of life, putting social support, grief severity and HIV symptoms into consideration. Both direct and indirect impacts of this predictor can effect on patients life quality. It is also responsible for continued risky sexual behavior, poor medical treatment adherence and severe disease progression, (Berg, Michelson Safren, 2007). This argument is in line with other studies, such like Moskowiz, Hult and Bussolari, (2009) who believed that people who are infected by HIV are much more vulnerable to mental disorder problems, because many aspects of HIV infection are potentially stressful, such as the fear of death, the need to adhere to complex medication regimens, side-effects of the treatment, interactions with a complex medical system, symptoms associated with disease progression, financial difficulties, stigma, and the need to incorporate a new identity as someone with a serious illness are all potential stressors associated with being HIV positive. All these stressors are not unique to HIV, but they are more aggressive in HIV epidemic, (Armistead Forehand, 1995). Hansen, Vaughan, and Cavanaugh, et al., (2009), also accentuated that HIV positive people who are bereaved by HIV related death of beloved ones, are particularly vulnerable to the complicated grief reactions. Mental health of this population is an urgent issue for health care and health management. Health issues surrounding HIV are different from individuals to individuals, taking nationality, ethnics, gender and other social factors into consideration. The major difference of HIV infection between people in developed countries and people in developing countries is with regard to income level, availability of sufficient nutrition and equal access to basic health service, (Mahlungulu, Grobler, Visser, et al., 2007). HIV/AIDS changes people life to a large extend, both physically and psychologically. When facing societal discrimination and other hardships related to HIV/AIDS, a strong and supportive family is one of the first lines of defense, (Bor, Miller Goldman, 1993). A qualitative study from China, (Li Wu, et al, 2006), found that family support had multiple levels of positive impact on HIV infected people. Support from family members helped people living with HIV make important decisions which were beneficial to their health status, such as taking virus load test and taking medication regularly. It also helped improve family relationship, because with family supports, people living with HIV gained hopes for their future and valued their families more and had a positive attitude toward life in general, (Manopaiboon, Shaffer Clark, 1998). With family support, many of the participants expressed positive attitudes and made positive changes in their lives. Family members persuaded several participants to be tested for HIV. One female participant explained how initially she did not want to take the HIV test and how her father convinced her to do so. (Li Wu, et al, 2006). A study in the United States also stressed the relation between HIV awareness and family support, (Persson, Gullberg, Hanson, et al, 1994). According to the study, HIV seropositivity awareness of family member is closely related to the support one can get after being infected. More awareness of the family members would bring more support generally. However, the reality shows, there is a preference of HIV serostatus disclosure target within the family. More mothers were disclosed to than fathers; sisters were more likely to be aware of ones HIV infection than brothers, (Mason, Marks Simoni, 1995). How does being homosexual impact on peoples life? Being homosexual apparently puts any individual into a sexual minority. Life can be much more complicated, considering legal right of marriage, social stigma and discriminations, thread from homophobic people, and many other factors, (Sullivan Schneider, 2004). Multiple sexual partners are one big issue that has been talked a lot. Halkitis, Moeller and Siconolfi, et al., (2004), addressed a special issue against this backdrop. They found the prevalence of crystal meth use among men who have sex with men has been shown to be twenty times higher than the general population. More importantly, it was closely related to an increased sexual risking taking by this population. Crystal meth augments an individuals sexual drive and allows users stay high for an extended period of time, which may increase the odds of multiple sexual encounters with many sexual partnersCondom use was inconsistent and some people never used condom while on crystal, (Mimiaga, Fair Mayer, et al., 2008). Besides the complicated lifestyle of homosexual people, health inequality puts them further to a marginalized area of the society. Cochran, and Mays, (2007) found that people from sexual minorities, such homosexuals, bisexuals, transgender and heterosexual people who had experienced sex with the same sex people, may have unrecognized disparities in general physical health that go beyond the conditions specifically associated with STDs among homosexually active people, compared with exclusively heterosexual individuals. These disparities may include a higher risk for cardiovascular disease, lung cancer as a possible consequence of higher rates of smoking, and a higher risk for diabetes among lesbians and bisexual women, (Roberts, Dibble and Nussey, et al., 2003). It shows though reported being in good physical and mental health, people who identify themselves as homosexual or bisexual oriented are more likely to be exposed to health problems. Sexual orientation minorities are more vulnerable to higher risk of common health issues and limitations, (Ayala Coleman, 2000). Higher levels of psychological distress among people of sexual orientation are also observed, compared with their heterosexual counterpart. Even within sexual orientation minority population, health issues are not equally distributed, (Prado, Pratt Feaster, et al., 2004). Johnson, Wadsworth and Wellings, et al., (1992), also agree with the above studies. According to their research, men who have sex with men are more likely to suffer from health problems as a result of poor access to health care services caused by health inequalities. They also mentioned homophobia is another factor which can cause emotional distress. It could cause incidences of suicide, bipolar psychiatric disorders and depression, (Sell, Wells Wypij, 1995). Psychological issue of being homosexual has also been discussed by Mao and Kidd et al (2009). They stated that major depression was strongly associated with socio-economic deprivation, interpersonal isolation and personal withdrawal as part of life equality for homosexual people. Sexual function contributed as one factor for mental well-being too. The vicious cycle between depression, stress and social exclusion should be highlighted in this context, (Choenarom, Williams Hagerty, 2005). Both HIV positive and HIV negative gay men are found to have high rates of major depression. It could be explained by the impacts of marginalization and discrimination experienced by gay men. Low acceptance of homosexuality by oneself, by significant others and by society as a whole may well predispose gay men to more stressful life events and fewer social and sexual opportunities at an earlier stage of life than men in general, (Mao Kidd, et al., 2009). What did previous research attempt to do? What have they achieved? According to Bormann and Aschbacher, et al., (2009), HIV infection has become a long-term disease that can be managed with medical care and support, rather than an immediate death causing disease, after the introduction and utilization of highly active antiretroviral therapy. However, the prolonged life expectancy doesnt guarantee the quality of life. As Liu and Ostrow, et al (2006), argued that a balance between improvements through diminished HIV-related morbidity and potential declines posed by its side effects was always observed as a net effect of highly active antiretroviral therapy in treating HIV infection and impacting on patients overall quality of life. After receiving the therapy, patients physical health well-being would further decrease with high effect sizes, though mental health would improve after longer treatment with small effect size, (Miners, Sabin Mocroft, et al., 2001). As stress is a big issue for HIV infected people, stress management natural becomes one key research area. In general, different coping and stress management therapies for adults living with HIV infection were found effective in reducing emotional distress including anxiety, depression, and psychological distress. These interventions also reduced fatigue and improved quality of life, (Carey Fielder, 2008). However, as Moskowiz, Hult Bussolari, (2009) concluded that little consistency across studies regarding coping strategies and types of outcomes could be found because the literature on coping with HIV is large and heterogeneous with respect to measures of coping, outcomes, and conclusions. Therefore, it is important to identify all copy strategies in regards of stress management for HIV infection and compare them to find out the best practices and the common features shared by all good practices. Besides stress management by patients themselves, social support was observes as another key element in health care for people living with HIV. Social support and support from families member seem to be more precious in some part of the world because they are harder to get due to the huge stigma and discrimination surrounding HIV epidemic and homosexuality. As Songwathana and Manderson, (2001) found that in Thailand, HIV infected people and their families were both afraid of disclosing their HIV seropositivity to the community because it would bring shame to the whole family. According to Li and Wu, (2006), it is similar in China. HIV/AIDS is always associated with over indulgent sexual intercourses, prostitution, and illegal drug abuse, all of which are considered as low moral status. The strong influence of culture in Asian countries makes it so hard for people living with HIV to seek for help and support. National and international context on health management Taking the UK for an example, Department of Health has promoted the strategy of sexual health and HIV nationwide. It is estimated that 30, 000 people in the UK are living with HIV, of who one third are not aware of their seropositivity. About 400 people die of HIV infection every year. The newly diagnosed HIV cases reached a new peak at the beginning for 21st century. Very noticeably, more HIV infect occurred among heterosexual population. However, sex between men still remains the major transmission route in the country. Combination therapy has improved the lifespan of people living with HIV. Unfortunately, it also provides the possibility of more new HIV infection cases. A survey targeted on gay men showed 58% guys under 20 did not use a condom when having sex with another man. Nearly half of HIV positive men have anal sex with a new partner not long time ago, and 40% of these people had unprotected sex with their partners. Highly active antiretroviral therapy is complex, prohibiti ve and extremely demanding on the patients. These patients may also be suffering from prejudice and social stigma. From a health management perspective, in order to promote HIV prevention and health care for HIV infected people, several actions will be taken by Department of Health in the UK. 1) continue to give a high priority to HIV prevention for gay men; 2) develop a national AIDS trust; 3) improve outreach services for people with undiagnosed HIV, particularly in targeted groups; 4) make sure HIV treatment and care services play a key role in HIV prevention by maintaining the sexual health of people living with HIV, diagnosing and treating STDs, reducing the transmission of HIV and providing information and advice, et al, (Department of Health, 2009). From a wider context, HIV is also a big concern of global epidemics. World Health Organization summarized in its bulletin that to manage global health in a more effective way in terms of HIV transmission, interventions must be targeted and they must be carried out in the right supportive environment. Thailand has set a good model for the rest, Close examination of the celebrated example of the 100% condom use campaign in Thailand shows its success to have depended on its being part of a package: HIV prevention became part of Thailands national sense of destiny, from the Prime Minister down. There was a nationwide debate on sexual mores, together with structural solutions such as regulation of the sex industry, intensive education, skills development and peer intervention with sex workers, and efforts targeting clients. World Health Organization As Piot and Seck, (2001) stated, it is also important to build synergies between prevention and health care. As the Declaration of Commitment adopted by the UN General Assembly recognized that prevention, care, support and treatment for those infected and affected by HIV/AIDS are mutually reinforcing elements of an effective response. Successful prevention and care build a common constituency for action. WHO also identified HIV-related stigma may well be the greatest obstacle to action against the epidemic, for individuals and communities as well as political, business and religious leaders. Therefore, defeating HIV related stigma is a key element in health care for people with HIV, (Piot Seck, 2001). Systematic appraisal arising from literature After reviewing relevant literatures, a need of a systematic appraisal which aims at finding the best ways of improving life quality for homosexual people living with HIV is emerging, because the impact of HIV infection and impact of being homosexual on peoples life are tremendous. Identifying good practices to improve life quality for this particular population is not only beneficial for the target group, but also will provide lots of inspiration for health care of other population. Conclusion of this chapter and link to next chapter In this chapter, key literatures surrounding HIV transmission and health care, life quality of homosexual people and people living with HIV, previous studies on HIV treatment and caring were carefully reviewed to identify the need of conducting this systematic appraisal. Details of how this appraisal will be done are explained in the next chapter. Chapter three: Methodology and Methods Introduction to the chapter In this chapter, the process of this systematic appraisal will be outlined, including explanation of research question in details, search theories and principles, literature searching strategy and vehicles, inclusion and exclusion criteria, and ethics concerns. A brief discussion of quantitative and qualitative research approaches will be conducted in a health management context. The purpose of this chapter is to explain how the public health studies were selected and how they were valid and reliable methodologically to provide evidence to answer the research question of this appraisal. Also explanation of inclusion/exclusion criteria will be given in this chapter. Qualitative and quantitative approaches in health sciences As Eriksson pointed, Public health needs to be evidence-based if it is to be done correctly, which means that learning and knowledge-production for public health must be comprehensive and include knowledge from four different domains: distribution of health, determinants or causal web, consequences, and intervention methods. Eriksson, 2000 To reach this goal, difference research methods have been applied. Generally, they can be put into two categories, namely, qualitative and quantitative. 1) Qualitative research Defined as a cover term for a variety of research traditions originating in philosophy, anthropology, psychology, and sociology that are epistemologically and methodologically similar,(Denzin Lincoln, 2005), qualitative research is based on an idealist philosophy, a subjective view that asserts that the world is known only through human beings perceptions, (Fawcett Alligood, 2003). Furthermore, qualitative research is regarded as a valid and important mode of scientific inquiry that generates distinctive nursing knowledge and complements the knowledge produced by quantitative research, (Fawcett Alligood, 2003). 2) Quantitative research According to Meadows, (2003), quantitative research is considered as the epitome of scientific research, which is focusing on hypothesis testing, reliability and validity. Quantitative research often involves experiment and survey. Typical quantitative experiment is randomized controlled trial, which regarded as the golden standard to provide evidence. Quantitative surveys are usually conducted by structured measures such as questionnaires and structured interviews, (Pool, Hiralal Ostelo, et al., 2010). The main strengths of qualitative research are its ability to examine the issue in detail and depth, the facts that it does not restrict the researchers to specific questions or lists and research framework and direction can be quickly revised as new information emerges, and its adaptability for use a wide range of subjects. However, in qualitative research, data are collected in a few cases or individuals. Research quality is heavily relied on the researchers skills. It takes more time to analyse and interpreter the data. Theres are the key limitations of qualitative research, (Patton, 1990). As the mainstay of traditional biomedical research, quantitative methods has been the gold standard for establishing the efficacy or applicability of a treatment or technique. However, there are frequently great difficulties pursuing this goalà ¢Ã¢â€š ¬Ã¢â‚¬ logistic, political, financial and ethical. Studies may be carried out using quantitative methods of less rigour, but the possibility of erroneous conclusions increases the further one moves from the classical prospective study, (Runciman, 2002). In fact, neither of the two research methodologies is perfect by itself. As Runciman, (2002), argued that quantitative and qualitative research are complementary; each provided the same information in the example chosen. A comparison of the two methodologies is seen in appendix. Each of them has its own strengths and limitations. As Eriksson (2000) said, The quantitative approaches need to be supplemented by more qualitative approaches. Evidence generated by such broader approaches gives excellent conditions for learning. To conduct this appraisal, I am searching for both qualitative and quantitative studies. By reviewing quantitative studies, I will be able to identify the existing problems and by reviewing qualitative studies, I will be able to build understanding of how the problems happen and how to solve them. HIV is an extremely complex health issue, as it is far more than a medical condition. Many other issues, such as social stigma, discrimination and psychological well-being, et al are closely related to HIV and people who are infected. Therefore, a mixed methodology is appropriate to be applied. As Rogers, Barton, and Pekarsky, et al., (2005) stated Two-way interaction occurred between themes arising from the qualitative and the quantitative analyses. This augmented and clarified the findings, and provided the integrated understanding needed to inform the larger debate about health care for marginalised groups. Explanation of research question in details HIV has been a global health threat for many years but so far there is no effective medication or therapy which can cure the disease or eliminate this virus. Therefore, it is necessary to find out the best way to improve the life quality for HIV patients as many new infected cases are reported every year.. As Shea, Grimshaw, and wells, et al (2007) said that a well conducted systematic review addresses a carefully formulated question by analyzing all available evidence, it is very important to form an explicit research question for this appraisal. The core research question of this appraisal is: What are the best ways to improve the life quality for homosexual people livin