The Reconstruction of African History

The Reconstruction of African History This context will analyze the contribution of historian B.A Ogot in the reconstruction of the African History. It will explore Kenya as one of the African nations and/ or countries where the work of B.A Ogot has contributed a lot in historical reconstruction. His significance in history can be accredited to the fact that his life was surrounded by the major events with specific reference to the independence period among other events that has built the history of this nation. In order to understand his contributions to the study topic, both his past and current dispositions will be analyzed by reviewing his literature that he has produced over the years. Following this, this study will also highlight various historical processes from the pre-colonial time to colonial administration in Kenya based on the Mau Mau organization, composition and its impacts. His reconstruction of Africans History The work of B.A Ogot presents various aspects of both pre-colonial history and colonial era in Africa. According to the researches conducted based on his contribution into the African history with reference to Atieno (2002) in The challenges of History and leadership in Africa, his main role was to offer defense for humanity, durability, historicity, complexity and wealth of African societies together with their culture. He offered criticism on studies based on African institutions and customary practices that were said to have failed in offering any defense to African history through adherence to African ideas of the universe, destiny and its existence. He examines the main aspects of Nilotic societies and cultures based on the concept of Jok  [1]  . This term is found in different forms of Nilotic languages whose meaning is God, spirit, Ghost among others. Ogot had immense interest in the institutional practices and the history of African thought for instance religion which was captured in his three essays he wrote. On making of a sanctuary is the essay that examines padhola religion that has been said to be contented in Jok concept and cannot be understood beside Nilotic culture. Ogot trace changes imposed in Padhola religion by the migration of Nilotes to the south, establishment of Bura shrine as a worshipping place, other denominational rivals and the infiltration of strangers among padhola in nineteenth century. Ogot embarked on effects of European religiosity on the lives of the Luo people, which led to religious contradictions in Nyanza. According to Ogot, there exists a complex process of converting first African Christians based on their motivations, training, sacrifices and evangelical activities among others. He presented how the first African Christians faced troubles from the European missionaries, African chiefs and the c olonial government. The religious struggle led to the establishment of Anglican Church in which Mango broke and founded his own church the holy ghost church. Both religious contradictions and conflicts resulted to the murder of Mango in 1934 during an attack that sprouted on the village he belongs. The essay A community of their own Ogot looked at both the rise and effects of the Maria legion of African church that resulted from a reformation of Roman Catholic Church in Nyanza. Ogot is argued to have been normalizing African initiatives, cultural systems, choices, activities and adaptations through analyzing religious based on their terms. He also showed how religion resisted toward the colonial rule in Africa. The emergence of the Nomiya Luo church and Church of Christian Africans offer a better indicator of resistance to colonial rule and/ or power. In his essay on Kingship and statelessness Among the Nilotes, he challenged the racist hypothesis that holds that, there exists a correlation between degr ee of political evolution and the peoples hamitic blood. Based on this hypothesis, he suggested that the establishment of both Shilluk and Bunyoro kingdoms was based on factors such as political, economic and military. In his work, Ogot identified segmentary states that were observed to be less advanced as compared to the Bunyoro Kingdom. Examples of these segmentary states include the Ruothships that belongs to Luo and Acholi and the stateless societies of the Dinka and Nuer. The work of Ogot showed that the process of state formation comprises different groups of people and other historical contexts. Ogot produced many essays that enable one to trace his contribution to the reconstruction of the African history from Kenyans independence to date  [2]  . There was only one essay that concentrated on the colonial state alone while others lay emphasis on the anti-colonial resistance: For instance, the Mau Mau movement that was Kenyas liberation movement during the colonial period or era. Ogot highlighted the colonial rule and its contradiction nature in Kenya and Africa as a whole. His work presented the view that the colonial state and/ or the conquest were observed to be both authoritarian and weak as it lacked legitimacy. Another contribution of Ogot is that through his work, he describes how illiterate and incom petent officials in Africa struggled to cope with colonial version of administration, the missionarys roles, impacts of both the first and Second World War, religious movements and the reformist political associations that resulted from the educated elite. Through the work of Ogot, it is clear that a connection exists between local and national manifestations of what was referred to as nationalism. Ogot explains why the nationalist party KAU failed to establish itself in Nyanza. He argued that Kikuyu leadership in KAU was the major cause of its failure in Nyanza since they only focused on land grievances in kikuyu, which had little connection with Nyanza. According to Ogot, Mau Mau movement had historical significance since it was based on Kenyas decolonization. The goals of this movement were to make Kenya a nation in other words, to nationalize Kenya but we cannot call this movement a national movement since it was confined to one part of Kenya that is the Central Kenya. In addition, B.A Ogot focuses on both the ideology and social composition of Mau Mau and its origin in the context of African imagination and colonial era.  [3]  His writing focused on the people especially those who supported the movement and who opposed it amon g the kikuyu community. He indicated that the class and ideological divisions among kikuyu people mainly implicated the variations between the loyalist and fighters. These variations were based on access to land, affinities to Christianity and traditional culture, attitudes based on constitutionalism among others. He further showed that the differentiation of memories, age, political ecologies in terms of location and dreams about the future accounts for variations. It has been argued that, songs played a major role in peoples culture because people use songs to express their visions, problems, social values and appropriate possibilities. It was therefore through songs that the Mau Mau movement came into practice in Kenya as people expressed their demand for decolonization after a long period of suffering from the colonial states. Through songs, people were able to mobilize each other therefore reinforcing their strength and spirits of other supporters. According to him, the use of songs implicated that the Mau Mau movement was anti-colonial movement fighting for the decolonization of Kenya. These songs were sang in kikuyu language, symbols, history and legends and this explains why they were said to limit their accessibility and their national appeal. Another contribution of B.A Ogot in the reconstruction of African history is showed on his analyses of The birth of national language. During colonial era most of Africans in Kenya lacked national language since the European language used by the elite lacked nationality in it The researches conducted by B.A Ogot on national language showed that kikuyu was first made a national language because the origin of Mau Mau movement took its roots in Central Kenya  [4]  . The elites borrowed their language from the European and/ or colonial state but were few to make the language a national one. Mau Mau left behind legacy in Kenya based on the inherent biases and propaganda that its still in practiced in Kenya of today. He analyses how different and important figures of Mau Mau movement were arrested and detained with unintended outcomes. Ogot has addressed several critical issues that faced African societies from the colonial period to independence. He examined Africa in terms of politics, leadership, culture, development, identities, and functions of universities and impacts of globalizalisation on Africa. Through his work, Ogot urge writers to investigate more into the social realities that resulted to the current forms of leaders and treat Africans as evil.  [5]  The corruption presented by the modern African elite began during the colonial period with writers such as Elspeth Huxley who was said to have had distrusted the over educated African elite. It was argued that most of African nationalist used political slogans of the western during their struggle against the colonial states. In conclusion, the African history is a complex process of historical events that occurred from colonial era to date. The study highlights that the struggle for African history began with the view of Ogots generations and continue s to the current generation meaning that as we come up with new topics, theories and methodologies we must adhere to the mission that Inspired Ogott generation.

Tosco Marketing Company Quality Control :: GCSE Business Marketing Coursework

Tosco Marketing Company Quality Control TOSCO MARKETING COMPANY Quality control comes in many forms. For some it is following a specific philosophy, such as those developed by Demming or Juran. For others it is achieving a specific degree of merit as that established by the Malcolm Baldridge Awards, or International Standard Organizations (ISO). However, the petroleum industry as a whole has compromised, shifted, and remained adaptable to an ever-changing world filled with government regulations and restrictions. The negative environmental impact of the petroleum industry is either not understood, grossly downplayed, or it is blatantly ignored. Government agencies have amended and abolished amendments in many of their policies so quickly that establishing best practices is nearly impossible. However, one thing in the petroleum industry remains the same. Safety is a key quality concept that must be adhered to. Tosco Corporation made a bad name for itself by ignoring certain safety issues. Quality control in the safety department was ineffective, and people died because of their neglect. Only recently have they outsourced the development of their safety program to Dupont. Introduction to Government Standards The Department of Energy (DOE) and the Environmental Protection Agency (EPA) require an insurmountable amount of data, reports, testing, and auditing to ensure the compliance of all U.S. Oil Companies around the world. The most recent concern regarding the petroleum industry is that of methyl tertiary butyl ether (MTBE’s) that are put in our fuel. Early on it was believed that adding MTBE’s to fuel would result in cleaner burning gasoline. However, according to the â€Å"Ground Water Monitor† small amounts seeped into the ground water and caused an unacceptable amount of contamination. The conception of MTBE’s was in 1967 with the passage of the Clean Air Act. This is the primary statute governing air quality in the United States. It assigns responsibilities to government and industry to reduce emissions from pollution sources such as automobiles, refineries, chemical plants, and power plants. However, it seems as though every solution to meet the stringent requirements poses another problem. The Clean Air Act has been amended several times, and most recently it is to be amended to ban MTBE’s by the year 2002.

An Athletes Secret of Success Essay -- Sports Athletes Fitness Essays

An Athletes Secret of Success Vince Lombardi says, â€Å"The price of success is hard work, dedication to the job at hand, and the determination that whether we win or lose, we have applied the best of ourselves to the task at hand.† A dedicated athlete puts forth their all by fully devoting themselves to their sport. They always try to give one hundred and ten percent before, during, and after practice. Athletes achieve their success knowing they worked hard to attain it and can truly say they accomplished something that makes them a better person.   Ã‚  Ã‚  Ã‚  Ã‚  A committed athlete devotes a great deal of time to practice. They arrive early in order to get in a better warm-up, give more than their best effort during practice, and stay after practice to repeat what they went over. Also, they p...

Report on field visit to SARDI (Aquatic Sciences)

Aquatic Sciences is a research division under SARDI with a main motto of the sustainable growth of South Australian Industries. The South Australian Aquatic Sciences Centre (SAASC) is located at West Beach on the shores of Gulf St. Vincent and most of the research works in aquatic biology are conducted here. The thrust areas of research include 1. Aquaculture: Here active research is being carried out for freshwater, brackish and marine aquaculture needs. This include development of diets, species selection etc. 2. Marine Environment and Ecology: conduct research on habitat mapping, environmental impact assessment, etc. . Oceanography: Research to understand the influence of oceanographic factors on climate. 4. Wild Fisheries: They carry out stock assessment works and provide necessary information to the industries involved for the sustainable exploitation of the stocks such as abalone, rock lobster, prawns, snapper, garfish and Australian sardines. Also undertakes surveys to measure the impact of fishing effort on fish stocks. 5. Inland Waters & Catchment Ecology: Undertake research on inland water habitats. There are 87 research and technical staff, 18 support staff and 40 postgraduate positions at West Beach research centre. The facilities include a central library with the most modern and comprehensive literature of different aspects of aquatic sciences. The pool farm has facilities to carry out research in both marine and freshwater environments with tanks of different capacities. We were allowed to visit the different research infrastructure facilities such as coastal finfish hatcheries, sophisticated aquaculture laboratories, controlled environment rooms, fish aging laboratories, image analysis rooms etc. As a whole, the trip was of great use to understand the various research activities that are going on in the field of marine biology.

Positive Negative Impacts Of Globalai Essay

What is meant by western culture: Western culture, sometimes equated with Western civilization or European civilization, is a term used very broadly to refer to a heritage of social norms, ethical values, traditional customs, religious beliefs, political systems, and specific artifacts and technologies. The term has come to apply to countries whose history is strongly marked by European immigration or settlement, such as the Americas, and Australasia, and is not restricted to Western Europe. Western culture stems from two sources: the Classical Period of the Greco-Roman era and the influence of Christianity. The artistic, philosophic, literary, and legal themes and traditions; the heritages of especially Latin, Celtic, Germanic, and Hellenic ethnic or linguistic groups; as well as a tradition of rationalism in various spheres of life, developed by Hellenistic philosophy, Scholasticism, Humanisms, the Scientific Revolution and Enlightenment; and including, in political thought, widespread rational arguments in favour of free thought, human rights, equality and democracy. The facts of bengali people which are affected by westernalization- 1.Cultural forms 2. Festivals and celebrations 3.Acculturation theory 4.Impact on language 5.Impact on education 6.Impact on food habit 7.Impact on dress pattern 8.Impact on family 9. Impact on social customs and values 10. Impact on rcommunication and technology 12.Impact on film and literatureeligion 11.Impact on 13. Impact on profession related issues Positive impacts of westernization Due to globalization, westernization is spreading out all over the world. Westernization has been placed in different countries because of globalization and needless to say, it has had an impact on the lifestyle of  Bangladeshi peopl. It has out-rooted the traditional Bengali culture and the rate at which westernization is happening to Bangladesh is surprising. Regional languages are on the process of redefined. In many ways instating of regional language people have been used to English especially in urban areas youngsters. It had started get fixing with western clothing, western languages, western mannerisms and everything else westernized.Bangladeshi culture is influenced by three great religions- Hinduism, Buddhism band Islam in successive order, with Islam having the most pervading and lasting impact. Like a colorful montage, the cultural tradition of the country is a happy blending of many variants, unique in diversity but in essence greatly symmetrical. Beside, the festival of PohelaBaishakh, people is now celebrating like other western cultural festivals especially in young group such as-  · Valentine’s Day,  · Friendship Day,  · Mother’s day,  · Father’s day.  · And other international celebrations. Now a day people are concern about how we think about globally, what the other country are doing in their cultural issue, just we observe and absorbing them. There is lot of issues that we automatically know about it; even he/she has a little knowledge about westernization. But, people are moving with it in all the way. Now a day’s every country in this world is treated as village, you can imagine whatever you can. That’s the way people are communicate easily to each other make things differences. Globalization has only one overarching feature–integration. It is all about collectiveness and ever increasing interconnectedness. It in effect influences everything, whether it is a company or a country. But here is a fact, is globalization all the way keeps help to connect to each other or build a strong communication in â€Å"borderless world†? If it is a question, then how it impacts in our society as well as in our culture? The Cable television has made different attraction in around  the world as well as in Bangladeshi household. Foreign movies have come and have reflected their culture in it. This has made a huge impact on the minds of the Bangladeshi people. Not to mention the easy availability of Internet whose reach even extends till rural areas? The internet has opened up opportunities for people to learn more about foreign cultures and places. It has made Bangladeshi more acceptable and open-minded towards change. Globalization has broken all borders. As a result, the new generation of Bangladeshi is more knowledgeable, more aware and more interested in the world around them. In our society, women who were once the exploited and ignored part of the population, now assert their rights of being a woman. Women now have more access to education and know more about their rights and their identity as a woman. Nowadays, you find women in the society who work alongside men. Men-dominated fields see the coming up of the woman. Men and women are slowly being treated equally. Negative impacts of westernization At the side of the positive, Bangladeshi people are involving day by day with negative activities which is destroying our own culture because of following western culture. However no matter have occurred by this way, what people are doing in our society.western dress is another factor that creates an imbalance in our society especially for woman group (whenever girls wear a shirt, t-shirt, and pant in our society, due to feel or sensation of comfortable) which does not permit within our culture as majority of Muslim nationality. For wearing that kind of dresses men are mostly thinking in negative sense. Children are involving some bad works which derived from western culture particularly from cable connection at their home. In some cases, young generation forget to respect their elder one., boys and girls are very much interested on going to DJ party at different night club. And, sometimes they want to live together before marriage which is extremely prohibited by our culture. Boys are using Tattoos on their body also. Bangladeshi people are now a day’s changing their behavior and habit in food. Easily converted to western ideas some cases it makes a question mark in our ethical perspective also. We referred those western materials by like fast food which is harmful for our health. Mostly, the young generation is very much interested on English movies, western music, dresses, foods and other things rather than Bengali culture. Now, young generation and even  also middle age people are not that much conscious about Bengali culture because of the globalization. In this way, Bengali culture is now no more originated by own culture, even it is losing her own value. Culture is the set of patterns of human activity within a society or social group and the symbolic structures that give such activity significance. Customs, traditions, laws, social standards and popular styles mainly constitute the cultural elements. There are many cultures currently existent in today’s modern world. Some cultures originated about a hundred of years back and are still surviving, whereas a few have evolved by absorbing the exciting and major elements of these already existent cultures. In this article, i am mainly going to focus on the two most talked about cultures of the world, the western culture and the Indian culture. The strength that this topic has been holding and the endless number of debates held over it has attracted me to express my opinion on it too. Undoubtedly, western culture and Indian culture are poles apart. There is a significant difference between the two in all aspect. Amongst all others the most noticeable difference between the two is that India has been a family oriented society, whereas America has been an individual oriented society. Openness and self dependency are a few words that define western culture, but Indian culture is the complete opposite of this. Globalisation and mass media has laid the basis of the merger of western culture with Indian culture and this collision can better be termed as westernisation. The damage that Indian culture has experienced can be broken down into three parts which are, pursuit of wealth, complex of the west and the most essential of all the power of western media. Cinema is the most powerful media, hence it is not only an entertainment industry, but is also seen as a role model. According to me, majority of the western ideas such as cohabitation, etc, have travelled through this medium. In other words, Hollywood has definitely influenced Bollywood and is responsible to a large extent for this clashing of culture. Respect for human rights, democracy, free speech and women’s rights are concepts which have had a wide ranging influence on Bangladesh. Even if they  have not as yet completely permeated to the level of the masses. The media is an effective way of influencing people. But unfortunately, in Bangladesh, always the negative side of all good things seems to influence people the most Bangladesh Television, which actually aired really good US TV serials, the Bangladeshi people soon began to become addicted to the Indian culture. They ate, drank, walked, talked, shopped, and slept like Indian people. They still do. As days passed, the number of Indian channels began to increase. Now there are more channels than there were channels on a TV set back in the 90s. The strongest influence of this culture is on children and women. There was a time when teenage boys never watched a single Hindi movie. Nowadays, from child to men all watch Hindi programmes including movies.This success is not for the Bangladeshi culture, but for Indian culture. Indian culture is eating up the creativity and productivity of many talented Bangladeshi individuals.

Manufacturing Management

In simple terms, cash flow is how money moves into and out of your business or how the cycle of cash flows in and flows out of your business thereby helping to determine the solvency of your business (How, 2007). Cost flow in a manufacturing firm involves the expense of the direct materials the manufacturer will be needing for business, the cost of direct labor that will need to be paid for as part of the cash flow process along with the manufacturing overhead that needs to come out of the cash flow. Whereas the cash flow in a service firm would not as much involve physical materials in general but the cost of training, marketing, advertising, travel in addition to the expense involved in whatever particular service that firm specializes in. In general, in the operations of a manufacturing firm most of the work would be handled in a central location, namely if it is one firm, in that particular manufacturing firm’s location. Travel can be a necessity for the management in some manufacturing firms. Employees and especially management of a service firm would be less â€Å"centrally located† in that service firm employees generally travel to the places and customers which need their services. With manufacturing firms you may have a few individuals who travel to introduce their product but overall the energy and expense would be â€Å"product-related.† Service firms generally do not spend as much time, energy or development or industrial design as most of their time spent in research, development and advertising their particular services. The majority of their time and energy would be service-related and changes more from user to user than would a manufacturer who generally supplies to places that need the products they already manufacture. One would have more blue-collar employees within a manufacturing firm while more white-collar employees would be in the labor force of a service firm due to the different training, education and skills needed for the two different types of firms. Vertical analysis would be â€Å"dividing each expense item in the income statement of a given year by net sales to identify expense items that rise more quickly or more slowly than a change in sales (Vertical, 2007). In using the vertical analysis, an analyst would be able to give management the information results gained by comparing the percentage mark-up of asset items along with how they have been financed. In addition, an analyst would be able to observe the trend of the increase in the assets and liabilities over the years (Vertical 2007). The statements that would be used for the vertical analysis would come from comparing the financial statements of firms that vary in size. Using a balance sheet, the assets, liabilities and the assets would be expressed as 100% whereas each item in the various categories would be expressed as a percentage of the respective totals. In using the common size income statement all the items in the income statement would be expressed as a percentage of the sales while sales is expressed as 100%. Horizontal analysis would be â€Å"the process of dividing each expense item of a given year by the same expense item in the base year. This process allows assessment of changes in the relative importance of expense items over time and the behavior of expense items as sales change† (Vertical, 2007). The most important information the horizontal analysis provides management would be trend. Over several years the direction, speed and extent of the trend can be seen by the information provided by the horizontal analysis. The statement one would use to do the horizontal analysis would be setting consecutive balance sheets, income statement or statement of cash flow side-by-side and reviewing any changes in the various categories on a yearly or multiyear basis (Vertical, 2007). References (2007). â€Å"vertical analysis.† Retrieved April 12, 2007, from The Free Dictionary Web site: http://financial-dictionary.thefreedictionary.com/Vertical+analysis (2007). Vertical and Horizontal Analysis Technique. Retrieved April 13, 2007, from Financial Analysis Revisited Web site: http://cbdd.wsu.edu/kewlcontent/cdoutput/TR505r/page37.htm (2007). How to better manage your cash flow. Retrieved April 12, 2007, from Entrepreneur.com Web site: http://www.entrepreur.com/money/moneymanagement/managingcashflow/article66008.h

Relating Pairs of Non-Zero Simple Zeros of Analytic Functions

Relating Pairs of Non-Zero Simple Zeros of Analytic Functions Edwin G. Chasten June 9, 2008 Abstract We prove a theorem that relates non-zero simple zeros sol and z of two arbitrary analytic functions f and g, respectively. Preliminaries Let C denote the set of Complex numbers, and let R denote the set of real numbers. We will be begin by describing some fundamental results from complex analysis that will be used in proving our main lemmas and theorems.For a description of the basics of complex analysis, we refer the reader to the complex analysis text Complex Variables for Mathematics and Engineering Second Edition by John H. Mathews. The following theorems have particular relevance to the theorems we will be proving later in this paper, and will be stated with out proof, but proofs can be found in [1]. Theorem 1 (Deformation of Contour)(Mathews) If CLC and ca are simple positively oriented contours with CLC interior to ca , then for any analytic function f defined in a domain conta ining both contours, the following equation holds true [1]. F (z)adz -? CLC f (z)adz Proof of Theorem 1 : See pages 129-130 of [1]. The Deformation Theorem basically tells us that if we have an analytic function f defined on an open region D of the complex plane, then the contour integral off long a closed contour c about any point z in D is equivalent to the contour integral of f along any other closed contour co enclosing that same point z. The Deformation Theorem allows us to shrink a contour about a point z arbitrarily close to that point, and still be guaranteed that the value of the contour integral about that point will be unchanged.This property will be instrumental in the proof of a lemma we will be using in proving our main result that relates all ordered pairs (zoo , sol ) of non-zero simple zeros, zoo and sol , of any two arbitrary analytic functions, f and g, each having one of those points as a simple zero. This powerful result is both non-trivial, and counter-intuitiv e: there is no reason to think right owe that all pairs of non-zero simple zeros of analytic functions are related.The result is non-trivial because our result only works for pairs of non-zero simple zeros and does not in general carry over to more than two non-zero simple zeros. All of the statements above will be proven rigorously The author wishes to proper special thanks to Sean Apple, DRP. Edwin Ford, Ryan Mitchell, and Larry Washman for all of their insights and contributions to making this paper possible. Without each one of them, none of what is in this paper, however useful or not, would have been possible. In this paper.But before this, we wish to describe briefly one case where a more general result does hold; namely, that if the non-zero simple zeros of an analytic function g are closed under multiplication, then the non-zero simple zeros of any other arbitrary analytic function, say h, that is defined on a union of open regions in the complex plane containing all of the non-zero simple zeros of said function g, can be related using a slight modification of our main theorem to be proven. All but the last of these statements, too, will be proven rigorously in this paper, as the proof of he last statement is trivial.One particular application of this special case of our main theorem to be proved, is the reduction of the prime factorization problem down to evaluating contour integrals of any number of possible analytic functions over a closed contour. More specifically, the integral is taken over a closed contour containing information about the prime factors of a product of prime numbers. The product to be factored is contained in the argument of a product of analytic functions, f and g, each of whose only zeros in the complex plane occur at the integers, and the result is a factor of the product of prime numbers.This particular result was the main conclusion obtained via our two year research project consisting of the following researchers: Sean App le, DRP. Edwin Ford, Ryan Mitchell, and Larry Washman, math instructor at Pierce Community College. Our collaborative research on the integer prime factorization problem was of great inspiration to the author in the formation of the generalization that is the main theorem of this paper.This main theorem, itself, is a generalization of some machinery we had together developed to reduce the prime factorization problem to evaluating contour integrals of the product f two specially chosen functions in the complex plane during the two year research project. The author wishes to thank Sean Apple, DRP. Edwin Ford, Ryan Mitchell, and Larry Washman, for their inspiration and help in making this generalization possible, for without them, none of this, however useful or not, would have been discovered at this time.For the following discussion, see page 113 of [1] for a formal definition of a contour. Now we shall discuss some more theorems that will be instrumental in proving our main results. The following theorem is called Cauchy Integral Formula. It provides us a way to represent arbitrary analytic functions evaluated at a point z in the domain of definition of the function in terms of a contour integral. This highly famous result is extremely powerful, and has many applications in both physics and engineering [1].It is also instrumental in proving a most counter-intuitive result: that if a function f is determinable on an open subset of the complex plane (I. E. If f is analytic on an open subset of the complex plane), then f has derivatives of all orders on that set [1]. In other words, if a function f has a first derivative on an open subset f complex numbers, then it has a second derivative defined on the same open subset of complex numbers, and it has a third derivative defined on the same open subset of complex numbers and so on ad infinitum [1].Theorem 2 (Cauchy Integral Formula)(Mathews) Let f be analytic in the simply connected domain D, and let c be a simple closed positively oriented contour that lies in D. If zoo is a point that lies interior to c, then the following holds true [1]. adz Proof of Theorem 2: see page 141 of [1]. The following theorem is called Leibniz Rule and along with Cauchy Integral Formula is instrumental in proving what is known as Cauchy Integral Formula for Derivatives, which has as a corollary, that functions that are analytic on a simply connected domain D, have derivatives of all orders on that same set [1].Without this theorem, we would need much stronger assumptions in the premise of our theorem relating pairs of non-zero simple zeros of analytic functions. Although we shall not use Leibniz rule directly in any of our proofs, Leibniz rule together with Cauchy Integral Formula form the back-bone of the machinery in the proof of Cauchy Integral Formula for Derivatives given in [1] on page 144, which we shall only outline. 2 Theorem 3 (Leibniz Rule)(Mathews) Let D be a simply connected domain, and let I : a t 0 b be an interval of real numbers.Let f (z, t) and its partial derivative fez (z, t) with respect to z be continuous functions for all z in D, and all t 2 1. Then the following holds true [1]. B f (z, t)dot fez (z, t)dot is analytic for z 2 D, and Proof of Theorem 3: The proof is given in [2]. The following Theorem is called Cauchy Integral Formula for derivatives and allows one to express the derivative of a function f at a point z in the domain off by a onto integral formula about a contour c containing the point z in its interior.The formula shows up in the remainder term in the proof of Tailor's Theorem. The remainder term mentioned above is used in the proof of Theorem (10), our main result. Theorem 4 [1](Mathews) Let f : D ! C be an analytic function in the simply connected domain D. Let be a simple closed positively oriented contour that is contained in D. If z is a point interior to c, then n! Ads z)n+l Proof of Theorem 4: We give here a sketch of the proof appearing in [1] . The proof is inductive and starts with the parameterization C : s = s(t) ND Ads = s (t)dot for a 0 t 0 b.Then Cauchy Integral formula is used to rewrite f in the form O f (s(t))so (t) dot s(t) z The proof then notes that the integrands in (B) are functions of z and t and the f and the partial derivative off with respect to z, fez , are derived and then Leibniz rule is applied to establish the base case for n = 1. Then induction is applied to prove the general formula. The main point of this is Corollary (5. 1) in [1] on page 144, which states that if a function f is analytic in a domain D, then the function has derivatives 3 of all orders in D, and these derivatives are analytic in D.Without this corollary, we could not relate the non-zero simple zeros of analytic functions as stated in Theorem (10); instead, the best we could do is to relate the non-zero simple zeros of functions whose second derivative exists on the intersection of the domains of the functions that contain the p air of non-zero simple zeros of the pair of given functions. But with Corollary (5. 1), we need only assume analyticity of the functions in question at the non-zero simple zeros, which significantly strengthens the results of our paper.Below we will give the definition of what is known in complex and real analysis as a ere of an analytic function f of a given order k, where k is a non-negative integer. What the order of a zero z tells us is how many of the derivatives of the function f are zero at z in addition to f itself. What is known is that if two functions, f and g, have a zero of order k and m, respectively, at some point zoo in the complex numbers, then the product of the two function f and g, denoted f g, will have a zero of order k + m at the point zoo [1].