The Negative Effects of Oil Spills Have on Nigeria, A letter

Dear President My name is John Doe. I am writing this letter to inform you about the negative effects in Nigeria oil spills have on its people and the environment around them. Oil spills pollute the water, killing animals and plant life that inhabit the area around the spill. It is important that this problem is to be looked at and solved. Nigerias Niger Delta is one of the most oil-polluted places on the planet with more than 6,800 recorded oil spills. Millions of barrels of oil were spilled into the Niger Delta.. Some people inhabit the land around it. The water is there main resource to use. They use it for irrigation, drinking, and bathing. They use the water for their everyday needs. The water is too polluted for them to drink anymore and they can’t use the water for irrigation because it is killing all of their crops. Multiple people have suffered from illnesses from drinking the oil polluted water. Cleanups don’t â€Å"clean† the land very well even though they are supp osed to clean deep into the ground. A percent of Nigerian mangrove ecosystems have been destroyed out by oil. The known effects of oil on mangroves are making the soil into acid, stop cellular respiration, and they do not let the roots get oxygen. The loss of mangrove forests does not only decrease the life of plants and animals. They also affect humans. The indigenous people living in the affected areas highly value these systems. The local people by the mangrove forest use the wood as a majorShow MoreRelatedGreenwashing: Petroleum and Oil3155 Words   |  13 PagesGreenwashing It is now popular to be environmentally conscious in American society. It is completely acknowledged by the populace that oil will, indeed, run out within a lifetime, leaving a demand for a different kind of energy source. Hybrid cars, such as the Prius are now mainstream, recycling is day-to-day, finding organic fruits, vegetables, and meat is as easy as walking to the nearest grocery store, and using plastic bags has been deemed unacceptable. Global warming, while debated and questionedRead MoreThe And Environmental Energy Conservation2791 Words   |  12 Pagesmore demand for energy resources particularly global fossil fuel consumption, clean water supply, electricity as well as food, public health services and shelter. Having grown up in Nigeria, a country with a population of 167 million persons and ranked as the seventh crude oil producer in the world and the largest oil-producing country in Africa, it is ironic that about 117.8 million Nigerians rely on fuels such as animal dung, crop residues, wood, charcoal and kerosene as sources of energy to cookRead MoreThe And Environmental Energy Conservation2578 Words   |  11 Pagesthis growth would result in more demand for energy resources particularly global fossil fuel consumption, clean water supply, electricity as well as food and shelter. Having grown up in Nigeria, a country with a population of 167 million persons and ranked as the seventh crude oil producer in the world, the largest oil-producing country in Africa, it is ironic that about 117.8 million Nigerians rely on fuels such as animal dung, crop residues, wood, charcoal and kerosene as sources of energy to cookRead MoreThe Effect of Globalisation on the Development of Underdeveloped1 Economies7888 Words   |  32 PagesTHE EFFECT OF GLOBALISATION ON THE DEVELOPMENT OF UNDERDEVELOPED1 ECONOMIES By MUSA JEGA IBRAHIM The existing wide disparities between the developed and the underdeveloped economies makes globalisation a tool for stultifying the industrialisation process, and by extension, retarding the growth and development of underdeveloped economies. Trade liberalisation, the cardinal instrument of globalisation ensures that industrialised countries have access to world markets, which enhances furtherRead MoreImplication of Oil and Gas Investment in Ghana15418 Words   |  62 Pages1. O INTRODUCTION The purpose of this chapter is to give an introduction to the motive for selecting the implications and importance of oil and gas investment as the main subject of this project work. The background and history of this project are followed by the subject, providing an introduction to the main theme of this work. The problems for discussion are further presented in order to illustrate the main problems of this study. This chapter was completed by illustrating the structure ofRead MoreThe Role of Advertising in Marketing Communications9872 Words   |  40 Pageslater. 2. SALES PROMOTION – A variety of short term incentives to encourage trial or purchase of a product or service. Companies use sales promotion tools to draw a stronger and quicker buyer response. Sales promotion can be used for short – run effects such as to highlight product offers and boost sagging sales. The advantages of sales promotion are as follows: Communication: They gain attention and may lead the consumer to the product. Incentive: They incorporate some concession, inducementRead MoreInternational Management67196 Words   |  269 PagesInternational Management Education iii This page intentionally left blank Preface C hanges in the global business environment continue unabated. The global financial crisis and economic recession have challenged some assumptions about globalization and economic integration, but they have also underscored the interconnected nature of global economies. Most countries and regions around the world are inextricably linked, yet profound differences in institutional and cultural environments persistRead MoreIgbo Dictionary129408 Words   |  518 Pages............................................ 29 IGBO DICTIONARY ..................................................................................................................................... 1 Abbreviations: Parts of speech of headwords have been indicated in this edition as follows adj. aux. v. cf. coll. conj. dem. E. enc. esp. ext. suff. H. infl. suff. int. int. lit. n. num. p.n. prep. pron. poss. quant. usu. v. Y. adjective auxiliary verb compare colloquial conjunction demonstrativeRead MoreEdexcel Igcse Economics Answer49663 Words   |  199 Pagesfor negotiations to begin. The price a car is eventually sold for will nearly always be lower than the price displayed. (c) The locations in all of the photographs may be described as markets. Question 1: (a) The prices of CDs in Tamer’s shop have been falling recently. He has not been able to sell the CDs because people do not want to buy them. This is because many people prefer to download music from the internet and listen to it using an iPod. Tamer has lowered prices to encourage his customers Read MoreFinancial Analysis of General Electric98175 Words   |  393 PagesGE Works 2011 Annual Report CONTENTS 2 Letter to Shareowners 10 Business Overview 29 Board of Directors 31 Financial Section 142 Corporate Information 2011 SUMMARY CONSOLIDATED REVENUES (In $ billions) 2007 170 NBCU 155 2008 180 163 154 139 150 133 2009 2010 ï ¬ nancial and strategic highlights 2011 147 142 22% GROWTH CONTINUES 22% increase in Operating EPS excluding impact of the preferred stock redemption, and 20% rise in Operating earnings. $200B RECORD INDUSTRIAL

College Athletes Should Not Be Paid - 1140 Words

Bailey Duggan Professor Gina Rho Freshman composition 111 21 march, 2016 Money and sports Collegiate athletes attend college to master their craft before going professional, and should not be paid. This also does not factor in other things such as injury and other issues that could arise. Colleges paying students to perform is not merited and would only cause more problems. Scholarships are important because they allow a student who could not usually attend college for free with the only requirement being that they play on the football team. That is why student athletes should not get paid, because they are already receiving a free education. The National Collegiate Athletic Association (NCAA) of college football would be nothing without its players. The NCAA is broken up into three divisions, going from best known and talented universities in division one to the least known and talented universities in division three. Depending on the talent of the high school player he can pick from any of the three divisions. If that same player reaches the ultimate go al of a college football player, which is to be recruited to the Nation Football League (NFL) then that player is known as a Premium college player. Universities that would pay college football players would set a precedent that sports are more important than an education, which is why they should not get paid. The argument that college football student athletes should be paid originated from these divisions’ threeShow MoreRelatedShould College Athletes Be Paid?1578 Words   |  7 PagesAshay Mehta Nou Per 8 Should College Athletes Be Paid? One of the hottest debates in the sports industry is if college athletes should be paid. If you want to pay these athletes, how would the college determine the dollar amount that should be paid? Should the basketball team make more than the football team? Should the the soccer team be paid as well? Cheerleading? Chess team? Should everyone on the team get a salary? What if your college is good at football and your basketball team is awfulRead MoreShould College Athletes Be Paid?1398 Words   |  6 Pagesbelieve that college athletes at the highest performing schools are better treated than others. Although they do not get paid, they do receive some benefits for being athletes that other students would not get. One advantage for playing a sport is access to scholarships that some schools reserve for their athletes. Depending on the school and the athlete’s performance, money towards tuition is often given. Only some schools are willing to grant â€Å"full-ride† scholar ships for certain athletes. AccordingRead MoreShould College Athletes Be Paid?1289 Words   |  6 PagesThroughout the years college sports have been about the love of the game, filled with adrenaline moments. However, the following question still remains: Should college athletes get paid to play sports in college? Seemingly, this debate has been endless, yet the questions have gone unanswered. The National Collegiate Athletics Association (NCAA) plays a vital role in this debate. The NCAA is a billion dollar industry, but yet sees that the athlete should get paid for their hard work and dedicationRead MoreShould College Athletes Be Paid?1334 Words   |  6 Pagesrising to the surface is â€Å"Should college athletes be paid?†. This has become a burning question. The NCAA is a multibillion-dollar industry, that makes millions, if not billions, in revenue. Yet it’s still maintains the non-profit status meaning that the industry is not set on making a profit and none of the revenue that is made is distributed to its members, managers, or officers. While most players who play in college sports are under a scholarship, that pays for the college tuition, books, and housingRead MoreShould College Athletes Be Paid?1364 Words   |  6 PagesHave you paid attention to all of the news that has been surfacing about collegiate sports lately? It is a big topic now days in the world of sports on weather college athletes should be getting paid to play sports. College athletics have gained great popularity of the past few decades, and have brought schools lots of revenue. A lot of college athletes think they should be getting paid for their services they do for their school. College sports like basketball and football generate over six billionRead MoreShould College Athletes Be Paid?1130 Words   |  5 PagesWhat college athlete would not want to be paid to play the sport that he or she loves? The real question is, though, should college athletes be paid fo r their roles in a college’s athletics? They are many points to each side of this recent controversial topic, which is why this has been made into such a hot debate in the past couple of years. As of right now, these athletes are not getting paid, but many of them truly believe that they should. Others believe that they already are being paid throughRead MoreShould College Athletes Be Paid?986 Words   |  4 PagesPaying the College Athlete The college athlete has steadily grown in popularity in the United States over the span of the past decades. Monetarily speaking, this increased publicity has been extremely beneficial for National Athletic Association (NCAA) and all the colleges involved in athletics which has sparked the dispute of whether or not the athlete should be paid for their hard work and dedication on the field and to their school or if the athletic scholarship is more than enough. College athletesRead MoreShould College Athletes Be Paid?1239 Words   |  5 PagesLindsey Simmerman Speech 102 T/Th 1:00-2:15 October 25, 2016 Should college athletes be paid to play? Specific Purpose: To persuade the class to agree with my stance on paying college athletes to play sports Thesis: College football is the hours players spend practicing and performing, the number of injuries the players face, and the persona these athletes must portray every day all the while watching their schools, coaches, and the National Collegiate Athletic Association (NCAA) get all the compensationRead MoreCollege Athletes Should Be Paid1254 Words   |  6 PagesSome college athletic departments are as wealthy as professional sports teams. The NCAA has an average annual revenue of $10.6 billion dollars. College athletes should be paid because of the amount of revenue that they bring to their college. Each individual college should pay its athletes based on how much revenue they bring to the college in which they attend. The colleges that win their Division title, their Conference title, or the National championship, give bonuses to the Head coach of thatRead MoreCollege Athletes Should Not Be Paid1558 Words   |  7 Pagesstudent-athletes participate in a variety of different s ports, and currently they do not receive paychecks for their performances. College athletics have attained an extensive popularity increase among Americans over the past few decades. This has resulted into increased revenues for the National Collegiate Athletic Association [NCAA] and the participating colleges, which has fuelled the debate of whether or not college athletes should collect an income. College athletes should not be paid to play

Northanger abbey Free Essays

Thesis In the history of English literature it’s difficult to specify a genre, even Gothic novel by resonance and measure the impact on other styles, trends, genres. Chronological framework of its existence, in the opinion of the vast majority of researchers limited the end of the XVIII – beginning of the nineteenth centuries. However, traces of â€Å"Gothic† poetics, especially its artistic language and philosophical thinking can be recognized in the work of writer Jane Austen. We will write a custom essay sample on Northanger abbey or any similar topic only for you Order Now Logical and important question is the tatus of the Gothic in Jane Austen, namely in the novel â€Å"Northanger Abbey† – the status of genre, poetological, aesthetic, ideological. In the main part we have given the definition of the Gothic genre, and have found his place in the novel † Northanger Abbey† identified writing style, tone, name origin, setting, we have analyzed plot, identified narrators point of view, found the used symbols. In conclusion, we have learned that the whole work is permeated with hidden quotations, allusions and reminiscences, including literary discussions between heroes around novel and orecasts developments, dense, albeit controversial, parallels at characters, perpetual comparison of weather and scenery of â€Å"udolfskymy† ; We observe the formula CL Pitt the transformation of the Gothic novel (romance) in the household (novel); Also we have explored favorite means writers with the help of which she deliberately changes and scale depicted in the novel offers a look at reality through the eyepiece, in which things, people, events are not given in a close-up, in Gothic but are quite smaller. How to cite Northanger abbey, Papers

Cognitive and Negative Symptoms in Medication †Free Samples

Question: Discuss about the Cognitive and Negative Symptoms in Medication. Answer: Introduction: A beautiful mind is a movie which was released in the year 2001 and is based on the life of John Nash, an exemplary brilliant but antisocial mathematical genius. In the movie John Nash is plagued with a life long illness with Schizophrenia. The film is set in a time frame where John Nash wax aware of his illness and moving to the point at which he and his wife find a way to manage his condition(Nasar,2011) Schizophrenia is the mental illness depicted in the movie. The illness groped John Nash at a very early age in his life, which later though he successfully overcame, after winning the noble prize. The illness refers to losing touch with the reality and displaying symptoms of mental illusions. In the movie it is shown that John Nash suffered from a very specific type of Schizophrenia called the Paranoid Schizophrenia (Rahman, 2017) The 5 major symptoms of the illness which are clearly visible can be divided into 5 categories. Behavioural symptoms lead to social isolation, disorganized behaviour, hostility, self-harm, repetitive movements (Carbon Correll, 2014). Secondly, there are signs in mood changes. Some of the moods which come along the illness are anger, loss of interest in activities, elevated mood and inappropriate emotional response. Thirdly, speech disorder, incoherent speech is some of the symptoms in speech. Fourthly, the patient faces psychological symptoms like hallucination, depression, fear, delusion and paranoia. Lastly, cognitive symptoms include mental confusion, memory loss, amnesia, having a belief that some ordinary vent has a special meaning attached to it, disorientation of thoughts etc. These are the major symptoms of the illness which are divided in the above mentioned 5 category. A person suffering from the disease is prone to have all or some of these symptoms, and experiences them on a day to day basis (Butcher, Hooley Mineka, 2015) The prevalence of the illness in UAE is 0.7% of the adult population, which is in sync with the global data from WHO (World health organization) .The problem with the illness in UAE, is that there are strong chances that it might go unnoticed, because of lack of education and a mental stigma. It is also mentioned in a health report that cases of this illness are under reported. The world figure states at 1.1% of the human population suffers from this illness, or in other world, 51 million people are suffering from this illness, and China being the country of most number of reported cases(Lee, Nurjono, Wong Salim, 2017) There are various impacts on the individual, family as well as the workplace in which the individual works. If Socio-cultural impacts are considered then individually the patient is kept in isolation, with not much of an interaction with the society. He is treated differently in a light of sympathy, rather than being empathetic. The family of such patient are put down by the society as not responsible parents, unable to take care of their child. The stigma present in the society disallows such families to be a part of social gatherings. Also, at the workplace, It will be difficult to justify the job role, biasedness will occur in the organization. Not giving the ownership for the work and enough responsibility. Spiritually as well the person and his environment are deeply affected. It is possible to have either of the two effects on the individual, either he may turn extremely spiritual and look forward to god saving his life, or in other case, being an absolute atheist. Most families end up becoming extremely devoted to god, and wait for gods charisma to shower on their child. Workplace involves a lot of teamwork, in this particular case, people will be very judging of ones behaviour which might not give him mental peace, resulting in frustration, anger and disappointment in the individual at the workplace. In the movie, the nursing diagnoses with the patient are careful and appropriate. Visiting the secret department of defence facility in pentagon, John Nash gets extremely baffled and disturbed after he breaks the code, assigned to him, and when he is asked to do a further analysis of it, he gets paranoid and highly delusional(Fortinash Worret, 2014). Alicai (Wife of John Nash) opens up the mailbox and retrieves the letter which John Nash had delivered to pentagon, the letters were unopened, it made John Nash realize that he has been hallucinating and it was his delusion making him belief that he got in touch with the secretory at pentagon and has provided him with confidential information. Also, his assumptions that the Soviets are spying on him got cleared at a later stage (Stuart, 2014) The nurse was keeping the voice in low tone while listening to the patient, using clear or simple words and keeping the direction as simple as possible. This was because it is proven that high pitched voice can lead to anxiety, which further elevates the problem, on the other hand, low pitch helps in better understanding thus helps to diagnose the problem in a much more efficient manner. Focussing and directing the attention of the patient towards the things which are actually present in the environment. Make him touch the things with his fingers to help him get out of his hallucination and paranoia. The direct relation of drawing the attention of the patient towards the things in the environment is linked with drawing focus to the reality. This helps the patient in moving away from delusions and focussing on the hard hit reality, very effective. Schizophrenia as explained earlier is a severe chronic mental disorder which is characterized by hallucinations, abnormal behaviour, and psychotic disorder and so on. In this illness a person finds it really difficult to identify with the reality (Scigliano Ronchetti, 2013) some of the different forms of treatment, which are in line with the side effects of the illness and there are various treatments available for the same. Weight Management is important as multiple anti-psychotic drugs cause increase in weight of the patient. Treating the weight problems might lead to better lifestyle and is also proven to cure the medical illness; regular exercise also helps in weight management (Khanra, Khess Srivastava, 2015) Cognitive Behavioural Therapy is a type of intervention with the patient can help in his changing patterns, his destructive thought might sublime and his disruptive way of living might improve. This also helps the patients to test the reality of their thoughts and strike a balance with the reality (Ohta, 2017) Some more forms of treatment are Social Skills Training, Supported employment and Medical treatments including Zyprexa, Risperdal, Seroquel, Geodon, Invega. There are various side effects of the treatment like uncontrollable movements. The drugs given to patient might lead to several complications like tremors, ticks, and muscle spasm. Such uncontrolled movements might be source of trouble in the daily life and can cause serious concern for the family of the patient (Carrier, 2016) Weight Increase is one of the strongest side effects of the illness is weight gain. In almost 60% of the cases of the illness patients tend to gain weight. Weight disorder alleviates the problem and hence it is very much advised to maintain proper eating habits, exercise on a daily basis and keep the weight under check (Australian, 2017) Some other side effects are Drowsiness, Dizziness, Dry Mouth, Restlessness, Constipation and Nausea. There are few ways to manage the illness. The most important ways are weight management, healthy diet, regular exercise and family support. Healthy Diet and regular exercise is proven by scientist and doctors that it is very important to prevent any illness and at the same time mask the effect of a chronic illness. A diet enriched in nutrition at regular intervals can create wonders for the illness. In the similar manner regular exercise, cardio, yoga and other such exercises keeps the patient in a good state of mind and helps in elevating his confidence level. Family Support is also very important as this illness has side effects of depression, sad thoughts, disorientation in his memory etc. At this point in time what he actually requires is the care of his family and the support they lend to him in his difficult times. A loving, caring and supportive family can do what sometimes medicine cannot. Thus highly advisable for families of such kind of illness to support the patient and t ry to spend as much time as possible with them. References: Australian, R. (2017). Royal Australian and New Zealand College of Psychiatrists clinical practice guidelines for the treatment of schizophrenia and related disorders.Australian New Zealand Journal of Psychiatry. Butcher, J. N., Hooley, J. M., Mineka, S. M. (2015).Abnormal psychology. Pearson Higher Ed. Carbon, M., Correll, C. U. (2014). Thinking and acting beyond the positive: the role of the cognitive and negative symptoms in schizophrenia.CNS spectrums,19(S1), 35-53. Carrier, C. (2016).TITLE: Reporting side effects of medication among individuals with schizophrenia: A qualitative study(Doctoral dissertation, McMaster University). Fortinash, K. M., Worret, P. A. H. (2014).Psychiatric Mental Health Nursing-E-Book. Elsevier Health Sciences. Khanra, S., Khess, C. R. J., Srivastava, N. (2015). Chronic non-fatal Datura abuse in a patient of paranoid schizophrenia: a case report.Addictive behaviors,43, 39-41. Lee, J., Nurjono, M., Wong, A., Salim, A. (2017). Prevalence of metabolic syndrome among patients with schizophrenia in Singapore. Nasar, S. (2011).A beautiful mind. Simon and Schuster. Ohta, H. (2017). Decreased thyroid-stimulating hormone and prolactin-releasing hormone concentration: case report.Reactions,1672, 45-7. Rahman, T. M. (2017).THE VIOLATION OF GRICES CONVERSATIONAL MAXIMS PERFORMED BY JOHN NASH IN A BEAUTIFUL MINDMOVIE(Doctoral dissertation, UIN Sunan Ampel Surabaya). Scigliano, G., Ronchetti, G. (2013). Antipsychotic-induced metabolic and cardiovascular side effects in schizophrenia: a novel mechanistic hypothesis.CNS drugs,27(4), 249-257. Stuart, G. W. (2014).Principles and Practice of Psychiatric Nursing-E-Book. Elsevier Health Sciences.

Comparison between Music and Style in 1950s and Music and Styles in 1970s

Maxima And Minima Of The Function Engineering Essay Essays

Maxima And Minima Of The Function Engineering Essay Essays Maxima And Minima Of The Function Engineering Essay Essay Maxima And Minima Of The Function Engineering Essay Essay This term paper nowadayss concise accounts of the topic s general rules and uses worked illustrations freely to spread out the thoughts about work outing the jobs by suited methods. Each illustration shows the method of obtaining the solution and includes extra explanatory techniques. For some subjects, where it would hold been hard to understand a solution given on a individual job, the solution has been drawn in bit-by-bit signifier. All the figures used have been taken from Google Book hunt. The term paper covers the necessary definitions on MAXIMA AND MINIMA OF THE FUNCTIONS and some of its of import applications. It covers the subject such as types of other method for work outing the large job in a cutoff method known. The facets of how to develop some of the most normally seen jobs is besides covered in this term paper. The motivation of this term paper is do the reader familiar with the constructs of application of upper limit and lower limit of the map and where this is used. Focus has been more on taking the simpler job so ( 2 ) that the construct could be made clearer even to the novices to technology mathematics. MAXIMA AND MINIMA Definition In mathematics, a point x*is a local maximumof a map fif there exists some I µ gt ; 0such that degree Fahrenheit ( x* ) a†°? degree Fahrenheit ( ten ) for all xwith |x-x*| lt ; I µ . Stated less officially, a local upper limit is a point where the map takes on its largest value among all points in the immediate locality. On a graph of a map, its local upper limit will look like the tops of hills. A local minimumis a point x*for which degree Fahrenheit ( x* ) a†°Ã‚ ¤ degree Fahrenheit ( ten ) for all xwith |x-x*| lt ; I µ . On a graph of a map, its local lower limit will look like the undersides of vales. A planetary maximumis a point x*for which degree Fahrenheit ( x* ) a†°? degree Fahrenheit ( ten ) for all x. Similarly, a planetary minimumis a point x*for which degree Fahrenheit ( x* ) a†°Ã‚ ¤ degree Fahrenheit ( ten ) for all x. Any planetary upper limit ( minimal ) is besides a local upper limit ( minimal ) ; nevertheless, a local upper limit or minimal demand non besides be a planetary upper limit or lower limit. The constructs of upper limit and lower limits are non restricted to maps whose sphere is the existent Numberss. One can speak about planetary upper limit and planetary lower limit for real-valued maps whose sphere is any set. In order to be able to specify local upper limit and local lower limit, the map needs to take existent values, and the construct of vicinity must be defined on the sphere of the map. A vicinity so plays the function of the set of tens such that |x x*| lt ; I µ . One refers to a local maximum/minimum as to a local extreme point ( or local optimum ) , and to a planetary maximum/minimum as to a planetary extreme point ( or planetary optimum ) . LOCAL MAXIMA AND MINIMA Functions can hold hills and vales : topographic points where they reach a lower limit or maximal value. It may non be the lower limit or upper limit for the whole map, but locally it is. You can see where they are, but how do we specify them? Local Maximum First we need to take an interval: Then we can state that a local upper limit is the point where: The tallness of the map at a is greater than ( or be to ) the tallness anyplace else in that interval. Or, more briefly: degree Fahrenheit ( a ) a†°? degree Fahrenheit ( ten ) for all x in the interval In other words, there is no tallness greater than degree Fahrenheit ( a ) . Note: degree Fahrenheit ( a ) should be inside the interval, non at one terminal or the other. Local Minimum Similarly, a local lower limit is: degree Fahrenheit ( a ) a†°Ã‚ ¤ degree Fahrenheit ( ten ) for all x in the interval The plural of Maximum is Maxima The plural of Minimum is Minima Maxima and Minima are jointly called Extreme point Global ( or Absolute ) Maximum and Minimum The upper limit or lower limit over the full map is called an Absolute or Global upper limit or lower limit. There is merely one planetary upper limit ( and one planetary lower limit ) but there can be more than one local upper limit or lower limit. A Assumingthis map continues downwards to left and right: The Global Maximum is about 3.7 The Global Minimum is -Infinity A Maxima and Minima of Functions of Two Variables Locate comparative upper limit, lower limit and saddle points of maps of two variables. Several illustrations with elaborate solutions are presented. three-dimensional graphs of maps are shown to corroborate the being of these points. More on Optimization Problems with Functions of Two Variables in this web site. Theorem Let f be a map with two variables with uninterrupted 2nd order partial derivativesfxx, fyyand fxyat a critical point ( a, B ) . Let D = fxx ( a, B ) fyy ( a, B ) fxy2 ( a, B ) If D gt ; 0 and fxx ( a, B ) gt ; 0, so degree Fahrenheit has a comparative lower limit at ( a, B ) . If D gt ; 0 and fxx ( a, B ) lt ; 0, so degree Fahrenheit has a comparative upper limit at ( a, B ) . If D lt ; 0, so degree Fahrenheit has a saddle point at ( a, B ) . If D = 0, so no decision can be drawn. We now present several illustrations with elaborate solutions on how to turn up comparative lower limit, upper limit and saddle points of maps of two variables. When excessively many critical points are found, the usage of a tabular array is really convenient. Example 1: Determine the critical points and turn up any comparative lower limit, upper limit and saddle points of map degree Fahrenheits defined by degree Fahrenheit ( x, y ) = 22+ 2xy + 2y2- 6x . Solution to Example 1: Find the first partial derived functions fxand fy. fx ( x, y ) = 4x + 2y 6 fy ( x, y ) = 2x + 4y The critical points satisfy the equations fx ( x, y ) = 0 and fy ( x, y ) = 0 at the same time. Hence. 4x + 2y 6 = 0 2x + 4y = 0 The above system of equations has one solution at the point ( 2, -1 ) . We now need to happen the 2nd order partial derived functions fxx ( x, y ) , fyy ( x, y ) and fxy ( x, Y ) . fxx ( x, y ) = 4 fxx ( x, y ) = 4 fxy ( x, y ) = 2 We now need to happen D defined above. D = fxx ( 2, -1 ) fyy ( 2, -1 ) fxy2 ( 2, -1 ) = ( 4 ) ( 4 ) 22= 12 Since D is positive and fxx ( 2, -1 ) is besides positive, harmonizing to the above theorem map degree Fahrenheit has a local lower limit at ( 2, -1 ) . The three-dimensional graph of map degree Fahrenheit given above shows that f has a local lower limit at the point ( 2, -1, degree Fahrenheit ( 2, -1 ) ) = ( 2, -1, -6 ) . Example 2: Determine the critical points and turn up any comparative lower limit, upper limit and saddle points of map degree Fahrenheits defined by degree Fahrenheit ( x, y ) = 22- 4xy + y4+ 2 . Solution to Example 2: Find the first partial derived functions fxand fy. fx ( x, y ) = 4x 4y fy ( x, y ) = 4x + 4y3 Determine the critical points by work outing the equations fx ( x, y ) = 0 and fy ( x, y ) = 0 at the same time. Hence. 4x 4y = 0 4x + 4y3= 0 The first equation gives x = y. Substitute ten by Y in the equation 4x + 4y3= 0 to obtain. 4y + 4y3= 0 Factor and solve for Y. 4y ( -1 + y2 ) = 0 Y = 0, y = 1 and y = -1 We now use the equation x = Y to happen the critical points. ( 0, 0 ) , ( 1, 1 ) and ( -1, -1 ) We now determine the 2nd order partial derived functions. fxx ( x, y ) = 4 fyy ( x, y ) = 12y2 fxy ( x, y ) = -4 We now use a tabular array to analyze the marks of D and fxx ( a, B ) and utilize the above theorem to make up ones mind on whether a given critical point is a saddle point, comparative upper limit or lower limit. critical point ( a, B ) ( 0,0 ) ( 1,1 ) ( -1,1 ) fxx ( a, B ) 4 4 4 fyy ( a, B ) 0 12 12 fxy ( a, B ) -4 -4 -4 Calciferol -16 32 32 saddle point comparative lower limit comparative lower limit A three-dimensional graph of map degree Fahrenheit shows that degree Fahrenheit has two local lower limits at ( -1, -1,1 ) and ( 1,1,1 ) and one saddle point at ( 0,0,2 ) . Example 3: Determine the critical points and turn up any comparative lower limit, upper limit and saddle points of map degree Fahrenheits defined by degree Fahrenheit ( x, y ) = x4- y4+ 4xy . Solution to Example 3: First partial derived functions fxand fyare given by. fx ( x, y ) = 43+ 4y fy ( x, y ) = 4y3+ 4x We now solve the equations fy ( x, y ) = 0 and fx ( x, y ) = 0 to happen the critical points.. 43+ 4y = 0 4y3+ 4x = 0 The first equation gives y = x3. Combined with the 2nd equation, we obtain. 4 ( x3 ) 3+ 4x = 0 Which may be written as. ten ( x4- 1 ) ( x4+ 1 ) = 0 Which has the solutions. ten = 0, -1 and 1. We now use the equation Y = x3to find the critical points. ( 0, 0 ) , ( 1, 1 ) and ( -1, -1 ) We now determine the 2nd order partial derived functions. fxx ( x, y ) = -122 The First Derivative: Maxima and Minima See the map degree Fahrenheit ( x ) =3x4a?’4x3a?’122+3A on the interval [ a?’23 ] . We can non happen parts of which degree Fahrenheit is increasing or decreasing, comparative upper limit or lower limit, or the absolute upper limit or minimal value of degree Fahrenheit on [ a?’23 ] by review. Graphing by manus is boring and imprecise. Even the usage of a charting plan will merely give us an estimate for the locations and values of upper limit and lower limit. We can utilize the first derived function of degree Fahrenheit, nevertheless, to happen all these things rapidly and easy. Increasing or Decreasing? Let f be uninterrupted on an interval I and differentiable on the inside of I. If f ( x ) 0 for all xI, so degree Fahrenheit is increasing on I. If f ( x ) 0 for all xI, so degree Fahrenheit is diminishing on I. Example The map degree Fahrenheit ( x ) =3x4a?’4x3a?’122+3 has foremost derivative degree Fahrenheit ( x ) A =A =A =A 12x3a?’12x2a?’24xA 12x ( x2a?’xa?’2 ) A 12x ( x+1 ) ( xa?’2 ) A A Thus, degree Fahrenheit ( ten ) is increasing on ( a?’10 ) ( 2 ) and diminishing on ( a?’a?’1 ) ( 02 ) . Relative Maxima and Minima Relative extreme point of f occur at critical points of degree Fahrenheit, values x0 for which either degree Fahrenheit ( x0 ) =0 or degree Fahrenheit ( x0 ) is vague. First Derivative Trial Suppose degree Fahrenheit is uninterrupted at a critical point x0. If f ( x ) 0 on an unfastened interval widening left from x0 and degree Fahrenheit ( x ) 0 on an unfastened interval widening right from x0, so degree Fahrenheit has a comparative upper limit at x0. If f ( x ) 0 on an unfastened interval widening left from x0 and degree Fahrenheit ( x ) 0 on an unfastened interval widening right from x0, so degree Fahrenheit has a comparative lower limit at x0. If f ( ten ) has the same mark on both an unfastened interval widening left from x0 and an unfastened interval widening right from x0, so degree Fahrenheit does non hold a comparative extreme point at x0. In drumhead, comparative extreme point occur where degree Fahrenheit ( x ) changes mark. Example Our map degree Fahrenheit ( x ) =3x4a?’4x3a?’122+3 is differentiable everyplace on [ a?’23 ] , with degree Fahrenheit ( x ) =0 for x=a?’102. These are the three critical points of degree Fahrenheit on [ a?’23 ] . By the First Derivative Test, degree Fahrenheit has a comparative upper limit at x=0 and comparative lower limit at x=a?’1 and x=2. Absolute Maxima and Minima If f has an utmost value on an unfastened interval, so the utmost value occurs at a critical point of degree Fahrenheit. If f has an utmost value on a closed interval, so the utmost value occurs either at a critical point or at an end point. Harmonizing to the Extreme Value Theorem, if a map is uninterrupted on a closed interval, so it achieves both an absolute upper limit and an absolute lower limit on the interval. Example Since degree Fahrenheit ( x ) =3x4a?’4x3a?’122+3 is uninterrupted on [ a?’23 ] , degree Fahrenheit must hold an absolute upper limit and an absolute lower limit on [ a?’23 ] . We merely necessitate to look into the value of degree Fahrenheit at the critical points x=a?’102 and at the end points x=a?’2 and x=3: degree Fahrenheit ( a?’2 ) A degree Fahrenheit ( a?’1 ) A degree Fahrenheit ( 0 ) A degree Fahrenheit ( 2 ) A degree Fahrenheit ( 3 ) A =A =A =A =A =A 35A a?’2A 3A a?’29A 30A A Thus, on [ a?’23 ] , degree Fahrenheit ( x ) achieves a maximal value of 35 at x=a?’2 and a minimal value of -29 at x=2. We have discovered a batch about the form of degree Fahrenheit ( x ) =3x4a?’4x3a?’122+3 without of all time charting it! Now take a expression at the graph and verify each of our decisions. Application The footings upper limit and lower limit refer to extreme values of a map, that is, the upper limit and lower limit values that the map attains. Maximal means upper edge or largest possible measure. The absolute upper limit of a map is the largest figure contained in the scope of the map. That is, if f ( a ) is greater than or equal to f ( ten ) , for all x in the sphere of the map, so degree Fahrenheit ( a ) is the absolute upper limit. For illustration, the map degree Fahrenheit ( x ) = -162 + 32x + 6 has a maximal value of 22 happening at x = 1. Every value of x produces a value of the map that is less than or equal to 22, hence, 22 is an absolute upper limit. In footings of its graph, the absolute upper limit of a map is the value of the map that corresponds to the highest point on the graph. Conversely, lower limit agencies lower edge or least possible measure. The absolute lower limit of a map is the smallest figure in its scope and corresponds to the value of the map at the lo west point of its graph. If f ( a ) is less than or equal to f ( ten ) , for all x in the sphere of the map, so degree Fahrenheit ( a ) is an absolute lower limit. As an illustration, degree Fahrenheit ( x ) = 322 32x 6 has an absolute lower limit of -22, because every value of x produces a value greater than or equal to -22. In some instances, a map will hold no absolute upper limit or lower limit. For case the map degree Fahrenheit ( x ) = 1/x has no absolute upper limit value, nor does degree Fahrenheits ( ten ) = -1/x have an absolute lower limit. In still other instances, maps may hold comparative ( or local ) upper limit and lower limit. Relative means comparative to local or nearby values of the map. The footings relative upper limit and comparative lower limit refer to the largest, or least, value that a map takes on over some little part or interval of its sphere. Therefore, if f ( B ) is greater than or equal to f ( b A ± H ) for little values of H, so degree Fahrenheit ( B ) is a local upper limit ; if degree Fahrenheit ( B ) is less than or equal to f ( b A ± H ) , so degree Fahrenheit ( B ) is a comparative lower limit. For illustration, the map degree Fahrenheit ( x ) = x4 -123 582 + 180x + 225 has two comparative lower limit ( points A and C ) , one of which is besides the absolute low er limit ( indicate C ) of the map. It besides has a comparative upper limit ( point B ) , but no absolute upper limit. Finding the upper limit and lower limit, both absolute and comparative, of assorted maps represents an of import category of jobs solvable by usage of differential concretion. The theory behind happening maximal and minimal values of a map is based on the fact that the derived function of a map is equal to the incline of the tangent. When the values of a map addition as the value of the independent variable additions, the lines that are tangent to the graph of the map have positive incline, and the map is said to be increasing. Conversely, when the values of the map lessening with increasing values of the independent variable, the tangent lines have negative incline, and the map is said to be diminishing. Precisely at the point where the map alterations from increasing to diminishing or from diminishing to increasing, the tangent line is horizontal ( has slope 0 ) , and the derivative is zero. ( With mention to calculate 1, the map is diminishing to the left of point A, every bit goo d as between points B and C, and increasing between points A and B and to the right of point C ) . In order to happen maximal and minimal points, foremost happen the values of the independent variable for which the derived function of the map is zero, so replace them in the original map to obtain the corresponding upper limit or minimal values of the map. Second, inspect the behaviour of the derivative to the left and right of each point. If the derivative Figure 1. Illustration by Hans A ; Cassidy. Courtesy of Gale Group. is negative on the left and positive on the right, the point is a lower limit. If the derived function is positive on the left and negative on the right, the point is a maximal. Equivalently, find the 2nd derived function at each value of the independent variable that corresponds to a upper limit or lower limit ; if the 2nd derived function is positive, the point is a lower limit, if the 2nd derived function is negative the point is a maximal. A broad assortment of jobs can be solved by happening maximal or minimal values of maps. For illustration, say it is desired to maximise the country of a rectangle inscribed in a hemicycle. The country of the rectangle is given by A = 2xy. The hemicycle is given by x2 + y2 = r2, for Y a†°? 0, where R is the radius. To simplify the mathematics, note that A and A2 are both maximal for the same values of ten and Y, which occurs when the corner of the rectangle intersects the hemicycle, that is, when y2 = r2 x2. Therefore, we must happen a maximal value of the map A2 = 42 ( r2 -x2 ) = 4r2x2 44. The needed status is that the derivative be equal to zero, that is, vitamin D ( A2 ) /dx = 8r2x 163 = 0. This occurs when x = 0 or when ten = 1a?„2 ( R a?s +2 ) . Clearly the country is a maximal when x = 1a?„2 ( R a?s +2 ) . Substitution of this value into the equation of the hemicycle gives y = 1a?„2 ( R a?s +2 ) , that is, y = ten. Therefore, the maximal country of a r ectangle inscribed in a hemicycle is A = 2xy = r2. There are legion practical applications in which it is desired to happen the upper limit or minimal value of a peculiar measure. Such applications exist in economic sciences, concern, and technology. Many can be solved utilizing the methods of differential concretion described above. For illustration, in any fabrication concern it is normally possible to show net income as a map of the figure of units sold. Finding a upper limit for this map represents a straightforward manner of maximising net incomes. In other instances, the form of a container may be determined by minimising the sum of stuff required to fabricate it. The design of shrieking systems is frequently based on minimising force per unit area bead which in bend minimizes required pump sizes and reduces cost. The forms of steel beams are based on maximising strength. Finding upper limit or lower limit besides has of import applications in additive algebra and game theory. For illustration, additive programming consists of maximising ( or minimising ) a peculiar measure while necessitating that certain restraints be imposed on other measures. The measure to be maximized ( or minimized ) , every bit good as each of the restraints, is represented by an equation or inequality. The ensuing system of equations or inequalities, normally additive, frequently contains 100s or 1000s of variables. The thought is to happen the maximal value of a peculiar variable that represents a solution to the whole system. A practical illustration might be minimising the cost of bring forthing an car given certain known restraints on the cost of each portion, and the clip spent by each labourer, all of which may be mutualist. Regardless of the application, though, the cardinal measure in any upper limit or lower limit job is showing the job in mathematical footings. FINDING THE MAXIMA AND MINIMA OF THE FUNCTION WITH CONSTRAINED CONDITIOIN Lagrange s Method of Multipiers. Let F ( x, Y, omega ) and I ¦ ( x, Y, omega ) be maps defined over some part R of infinite. Find the points at which the map F ( x, Y, omega ) has maximums and lower limits subject to the side status I ¦ ( x, Y, omega ) = 0. Lagrange s method for work outing this job consists of organizing a 3rd map G ( x, Y, omega ) given by 17 ) A A A A A A G ( x, Y, omega ) = F ( x, Y, omega ) + I »I ¦ ( x, Y, omega ) , where I » is a changeless ( i.e. a parametric quantity ) to which we will subsequently delegate a value, and so happening the upper limit and lower limit of the map G ( x, Y, omega ) . A reader might rapidly inquire, Of what involvement are the upper limit and lower limit of the map G ( x, Y, omega ) ? How does this assist us work out the job of happening the upper limit and lower limit of F ( x, Y, omega ) ? The reply is that scrutiny of 17 ) shows that for those points matching to the solution set of I ¦ ( x, Y, omega ) = 0 the map G ( x, Y, omega ) is equal to the map F ( x, Y, omega ) since at those points equation 17 ) becomes A A A A A A A A A A A A G ( x, Y, omega ) = F ( x, Y, omega ) + I »I†¡0. Therefore, for the points on the surface I ¦ ( x, Y, omega ) = 0, maps F and G are equal so the upper limit and lower limit of G are besides the upper limit and lower limit of F. The process for happening the upper limit and lower limit of G ( x, Y, omega ) is as follows: We regard G ( x, Y, omega ) as a map of three independent variables and compose down the necessary conditions for a stationary point utilizing 1 ) above: 18 ) A A A A A A F1 + I »I ¦1 = 0A A A A A A A A A A A A A A A A F2 + I »I ¦2 = 0A A A A A A A A A A A A A A A A F3 + I »I ¦3 = 0 We so work out these three equations along with the equation of restraint I ¦ ( x, Y, omega ) = 0 to happen the values of the four measures x, Y, omega, I » . More than one point can be found in this manner and this will give us the locations of the stationary points. The upper limit and lower limit will be among the stationary points therefore found. Let us now observe something. If equations 18 ) are to keep at the same time, so it follows from the tierce of them that I » must hold the value A A A A A A A A A A A A If we substitute this value of I » into the first two equations of 18 ) we obtain A A A A A A A A A A A A F1I ¦3 F3I ¦1 = 0A A A A A A A A A A A A A A A A A A A A A A F2I ¦3 F3I ¦2 = 0A or A We note that the two equations of 19 ) are identically the same conditions as 8 ) above for the old method. Therefore utilizing equations 19 ) along with the equation of restraint I ¦ ( x, Y, omega ) = 0 is precisely the same process as the old method in which we used equations 8 ) and the same restraint. One of the great advantages of Lagrange s method over the method of inexplicit maps or the method of direct riddance is that it enables us to avoid doing a pick of independent variables. This is sometimes really of import ; it permits the keeping of symmetricalness in a job where the variables enter symmetrically at the beginning. Lagrange s method can be used with maps of any figure of variables and any figure of restraints ( smaller than the figure of variables ) . In general, given a map F ( x1, x2, , xn ) of n variables and h side conditions I ¦1 = 0, I ¦2 = 0, . , I ¦h = 0, for which this map may hold a upper limit or lower limit, equate to zero the partial derived functions of the subsidiary map F + I »1I ¦1 + I »2I ¦2 + + I »hI ¦h with regard to x1, x2, , xn, sing I »1, I »2, .. , I »h as invariables, and work out these n equations at the same time with the given h side conditions, handling the I » s as terra incognitas to be eliminated. The parametric quantity I » in Lagrange s method is called Lagrange s multiplier.

Arts and Politics - China, Germany, and the Soviet Union Essay

Arts and Politics - China, Germany, and the Soviet Union - Essay Example China, Germany, and the Soviet Union have been used as the target examples. This end of the article analyses the three choices, looks at their relationship and the reason as to why they were chosen as great choices for this report. In the 19th century, the Russian Tsars were clear in their articulation that revolutions stood in the offing, in the presence if outstanding masterpieces. There are situations in Russia where great artists of various forms were regarded as a threat to the government’ existence through their works of art. Pushkin, for example, as a great author who could express his thoughts in an articulate manner that was deemed as arrogant, with some freedom that made him make fun of official figures. His work, as per the governments, would rather have been used in public service. Art and politics have been closely related from past to present. There are some aspects that clearly point out the relationship between the two. The institutions of art, schemes in ideol ogy and some artists’ political dominance are just but a few. Over years, some authorities have tried to impose controls on ideologies in order to tame artists. Other governments have even attempted to thwart the freedom of expression as rolled out by artists. In China, the communist party pushed at gaining legitimacy in order to win cooperation from artists. The party tried to woo the artists to join in socialist constructions. The Chinese movements and the various notable interactions between the governments and artists place the country as one worthy of analysis for the purpose of this research. The artistic influence has grown in stages in China, with a recent period starting in the 1980’s after Mao’s death. This is a period that saw individual subjectivity on the rise and artists expressing themselves in minimal social reform. Germany has had its issues in the interactions between arts and politics as well. There were early attacks by the government to the artists, some of which indicate the magnitude that the artists had on the political arena. A good situation is in the 1940s when the national socialists banned all art that was in existence prior to 1933. There are examples of artists being forced to join certain groups, with those who refused being frustrated with professional dismissals. Looking at the mentioned issues, their effects and the reasons that led to their occurrence, art is an indispensable weapon in politics despite its autonomy, there is some coexistence that cannot be refuted. Looking at the Soviet Union, there is some inseparability between art and politics. According to Fox (1977), aesthetics and the style of art are led by the political exigencies. The politics of the day in the USSR dictate the Russian art. The styles of art in this country follow the trends that are in accord with the government. The links between art and politics in the Soviet can be traced from Karl Marx to Frederick Engels who asserted the i mportance of realistic representations to the state. The three countries have been able to showcase the tight bond between art and politics clearly as outlined b the examples stated above. A distinct relation is first evident in the manner in which the government controls the works of art. This may be represented vaguely, but political icons have treated artists with great suspicion from the word go, in all situations. In the USSR, the government dictated the styles; in Germany, the â€Å"degenerate art† exhibition indicated the government’s perception towards art and culture. In China, the government literally controlled the artistic movements.