Monday, December 30, 2019

Real Interest Rate And Nominal Interest Rate Finance Essay - Free Essay Example

Sample details Pages: 10 Words: 3042 Downloads: 3 Date added: 2017/06/26 Category Finance Essay Type Argumentative essay Did you like this example? Interest is defined as the price paid for the money borrowed from a lender. It is sometimes described as the reward for postponing consumption. It was considered by Classical economists as the earnings of capital; hence the marginal productivity of capital was called the rate of interest. Real Interest rate and Nominal Interest rate The nominal rate of interest is the annual rate that must be paid on borrowed funds. It is the rate of interest, which is quoted in all financial market. However, the real rate of interest takes account of inflation. In order to calculate the real rate of interest we simply deduct the rate of inflation from the nominal rate of interest. It can be described properly by the Fisher equation. 1 + i = (1 + r) (1+E(I)) Where; i is the nominal interest rate, r is the real interest rate, E(I) is the expected inflation rate. Don’t waste time! Our writers will create an original "Real Interest Rate And Nominal Interest Rate Finance Essay" essay for you Create order THEORIES OF INTEREST RATE The Classical Theory The classical theory explains interest rate in relation to demand and supply on savings. It suggests that demand comes from those in need of money, for example investors and entrepreneurs, and supply comes from those who are restricting their consumption in order to save their incomes. Interest is viewed as a reward for the savings of their incomes. Interest is a price for abstinence It was Nasau Senior who first claimed that interest was the price paid for the sacrifice involved in savings. According to him, it is the willingness of the consumer that determines whether he or she will abstain from consumption in order to make savings. Therefore interest act as a compensation for the individual to abstain from consumption. However Karl Marx, an economist, argued that the main source of savings comes from rich people and they do not need to undergo the sacrifice of abstinence in order to save. So Marshall substituted the term waiting for abstinence and interest is the reward for the sacrifice of postponing consumption when an individual saves money since it does not abstain completely from consumption. The Agio Theory Another explanation proposed by Bohm-Bawerk was that people prefer present enjoyment to future enjoyment on goods of the same kind and quality which means there is an agio or premium on the present goods. In order to encourage people to skip the enjoyment of present goods, interest must be paid to them. Three reasons put forward by the economist were: People tend to underestimate the future wants. Present wants are felt more strongly than future wants. Present goods possess a technical superiority over future goods. Fishers Theory (Time Preference Theory) Irving Fisher emphasized much on time preference as the cause of interest and he also considered marginal productivity of capital (rate of return over sacrifice) as a factor that determines interest. He defined interest as the compensation for the time preference of an individual. Time preference is the preference of having the same amount of goods and services at one time instead of some other time. The greater the preference of individual for the present enjoyment of good, the higher will be the rate of interest paid to persuade them to lend the money. The time preference depends on the following factors: Size of income: Large incomes imply less time preference which means a relatively lower rate of interest rate. Distribution of income over time: If income increases with time, people will be impatient to spend in the present and thus time preference will be greater. Degree of certainty regarding enjoyment in the future: If someone is sure of future enjoyment, the lat ter will not be willing to spend in the present, therefore the time preference will be less. Liquidity Preference Theory of Interest Rate Keynes pointed interest as the reward for separating with liquidity for a specified period of time in his book The General Theory of Employment, Interest and Money. He explains liquidity preference as the desire for someone to save cash, in other words which leads to the demand for money. The three motives from which demand for money arises are: Transactions motive: It refers to demand for money for current transactions of individuals or firms. This demand depends on: Size of income: If income is high. This implies that there will be more transactions. Time gap between receipts of income: The greater the time gap will induce a greater demand for money. Spending habit: If a person has the habit of spending, he will perform more transactions and therefore demand for money will be greater. Precautionary motive: It relates to the holding of cash balances of a firm or individual to meet unexpected incidents, for example accidents. Factors that affect this type of demand are: Size of income: A greater size of income will cause more to be preserved for the future. Nature of the person or firm: It depends whether the person or firm is optimistic or pessimistic and this will determine whether the demand for precautionary motive will be high or less. Rationally pessimistic firms will want to have more cash with them. Farsightedness: Usually a farsighted person or firm can have a good prediction of the future. If he/it expects fewer tragedies, he/it will keep less money with him. The demand for money for both transaction motive and precautionary motive are completely interest inelastic. Speculative motive: It refers the holding of resources in liquid form so as to take advantage of the rise and fall in prices of bonds and securities. According to Keynes, rate of interest is inversely proportional to bond prices. For instance, if bond price is expected to rise, normally investors will hold less money and will purchase bond in order to sell it when its price will increase. Determination of Interest Rates The classical theory determines interest rate by the demand of savings and supply for savings. Supply for savings depends on the abstinence of the savers whereas demand for savings depends on willingness of investors to invest in capital products. Rate of interest is determined by the intersection (E) of investment curve (II) and supply of savings curve (SS). Determination of the Rate of Interest through the Supply of Money and Interaction of Liquidity Preference According to Keynes, rate of interest is determined by the supply of money and liquidity preference which is the demand for money. The supply of money is usually determined by the policies of Government and the Central Bank of a country. It is perfectly inelastic The curve LP is the liquidity preference which is the demand for money. The money supply curve is S. The equilibrium rate of interest is the point E and at any interest above R, there will be an excess of money supply according to the demand for money. This will lead to a decrease in interest rate. There is a situation called the liquidity trap where changes in money supply does not influence the interest rate Direct intervention of Central bank. Central bank may directly intervene by imposing maximum or minimum prices of loans; depending on whether it wants to protect the money borrower or money lender. If the Central Bank fixes a minimum rate of interest, the intervention is to cheapen loans. It acts in favour of the borrowers. They pay a cost which is at the minimum price although maximum rate of interest may create shortages of loans. This is so because demand for loans is greater than supply of loans. If Central Bank fixes a maximum rate of interest, the measure is to protect the money lenders this guarantees them a higher market rate of interest although this may lead to a surplus of loans. Indirect intervention of Central bank through repo rate/ bank rate/ Lombard rate. The repo rate is the rate at which the central bank lends money to the commercial banks. Hence, repo rate is a cost to the suppliers of loans. Following an increase in repo rate, in order to maintain the spread, commercial banks will also increase their rate of interest; which also implies that following a fall in repo rate, commercial banks may reduce the rate of interest. Lombard rates provided by the Central Bank are rates that are charged for credit to banks. The Central Bank offers banks loans which they use to lend borrowers. The Central Bank usually set Lombard rates a little above standard rates. In order to make profit, the banks charge the borrowers an interest which above the Lombard rate and hence hedge against any loss on securities. Inflation rate. Following an increase in inflation rate and assuming the market rate of interest remaining unchanged, the real rate of interest will fall; which is a deterrent to save. Therefore, in order to maintain a positive real rate of interest, the market rate of interest has to be increased during inflation. Therefore the relationship is that interest rate increased as a result of inflation. The banking market structure. Here, a question needs to be asked. Is it a highly perfectly competitive or an imperfect banking market? If it is an imperfect banking market in form of a monopoly, duopoly, oligopoly it is not in favour of a borrowers market. Mauritius is an oligopolistic sector having 2 main players. Hence, it becomes a lenders market where they can resist any signal by the central bank through its repo rate. The rate of interest of trading partners influencing the domestic rate of interest. The rate of interest practiced by the trade partners may influence the domestic rate of interest. Following the liberalization of the capital account on the balance of payments, there is an unrestricted inflow and outflow of short -term investments which can be in terms of portfolio investments. If trade partners increase their rate of interest and the Mauritian economy maintains the same rate, there may be a net outflow of portfolio investments which will affect the supply of the Mauritian currency by depreciating it. Interest Rate Risk Interest rate risk is the risk associated with movements of interest rate in the net income and economic value of an institution. The Fed gazette pointed interest rate risk as the blood pressure for banks. This is so because banks normally act as financial intermediaries, that is, they accept deposits which they turn into loans with different maturities and interest rates. These activities result in an exposure which is the interest rate risk. Therefore it is important to have an efficient risk management that preserves interest rate risk at sound levels. Sources of Interest Rate Risk Being financial intermediaries, there are different sources of interest rate risk that banks face. The Basel Committee differentiates among four sources of interest rate risk. Repricing Risk It happens where there is a time difference in the maturity usually for fixed rate and repricing for floating rate of bank liabilities, assets and off balance sheet positions. If the average yield of a banks assets or liabilities is sensitive to changes in market interest rate, therefore the bank will normally face repricing risk. This will result in different possible mismatches. Different maturities may happen in the fixed rate of assets and liabilities. There may also be different pricing periods with floating rate assets and liabilities. This floating rate may have base rates of different maturities. It is measured by comparing the amount of banks assets that reprice to its liabilities within the same period of time. In order to improve their earnings, some banks take this type of risk in their balance sheet structure deliberately. The current earnings performance of a bank usually gives an image of the repricing risk. Yield Curve Risk Yield curve risk represents the possible changes in the yield curve that can affect the banks assets and liabilities. It implicates the changes in the relationship between interest rates of the same markets but with different maturities. According to the Basle Committee, changes in the shape and slope of the yield curve can be caused by mismatches in repricing. Unexpected shifts in the yield curve can have a negative impact on the banks income and economic value. Basis Risk Basis risk arises due to changes in the relationship between interest rates from different market sectors. In a simpler term, it can be defined as the change in interest rate of one instrument in relation to another. This type of risk is also known as the spread risk. The changes in the relationship can affect the banks current net interest margin through changes in the paid spreads of instruments that are being repriced. Future cash flows can also be affected which in turn will affect the underlying net economic value of the bank. Banks can be exposed to basis risk when they use off-balance-sheet instruments such as options, swaps and futures in order to hedge interest rate risk. The risk is that off-balance-sheet contracts cash flows may change with changes in interest rates and in relation to the positions being hedged. Option Risk Option gives its holder the right to sell or buy financial instrument at the strike price over a specified period of time. This risk occurs when a banks customer has the right to alter the timing and level of flows of an instrument. Option can result with an unbalanced risk/ reward profile. The movement of interest rate is important because it will determine whether the bank will gain or lose. For example, a bank sells options to its members. The amount of earnings is favoured by the moment of interest rate. This will surpass the amount that the bank would have lost if the rate of interest moved in an unfavourable way. The bank will have more upside reward than downside exposure. Impact of Interest Rate Risk There are two perspectives on which a bank is assessed for its interest rate exposure. They are the earning perspective and the underlying economic value of the bank. Earnings Perspective Fluctuations in interest rate affect a banks reported earnings. This perspective considers the impact of changes in the interest rate on a banks reported earnings. The reported earnings are usually influenced through changes in a banks net interest income. The Net interest income varies with the movement of interest rate because differences in: Timing of accrual changes which is the repricing risk, Options position, Changing rate and yield curve relationships which represent the basis and yield curve risk. In order to predict an effect in their earnings, banks usually conduct analysis such as income sensitivity or consider different scenarios on changes of interest rate. Economic Value Perspective This perspective considers the impact of movements in interest rate on the economic value of a banks liabilities, assets and off- balance-sheet contracts. The economic value of a bank can be viewed as the present value of banks expected net cash flows. This perspective identifies risk arising from maturity gaps or long term repricing. The impact of interest rate changes on the value of all cash flows, the economic perspective provides a comprehensive measurement of interest rate risk. It can also give a leading indicator of the banks future earnings and capital values. Measuring Interest Rate Risk In order to have a sound management of interest rate risk, an accurate and timely measurement of it is important. It should be able to quantify and indentify the banks major sources of interest rate risk exposure. There are different approaches in measuring interest rate risk used by banks. Maturity Gap Analysis This analysis distributes interest rate sensitive assets, liabilities and off-balance-sheet positions into a certain number of predefined time band according to their maturity (if fixed rate) or time remaining to their next repricing (if floating rate). Its objective is to improve the net interest in the short run over discreet periods of time called the gap periods. The risk sensitive assets and risk sensitive liabilities are grouped into maturity buckets based on maturity and the time until the first possible repricing due to change in the interest rates. The gap (RSG) is then calculated by considering the difference between the absolute values of the interest Rate Sensitive Assets (RSAs) and interest Rate Sensitive Liabilities (RSLs). RSG = RSAs RSLs The three possible scenarios are: RSA RSL = Positive Gap RSA RSL= Negative Gap RSA = RSL = Zero Gap The Gap ratio is calculated by the formula below: Gap Ratio = RSAs / RSLs Another formula where Gap is calculated is: Where; Earning Assets = Total Assets of the Bank, NIM = Net Interest Margin, ÃÆ' ¢Ãƒâ€¹Ã¢â‚¬  Ãƒ ¢Ã¢â€š ¬Ã‚  C = Acceptable Change in NIM, ÃÆ' ¢Ãƒâ€¹Ã¢â‚¬  Ãƒ ¢Ã¢â€š ¬Ã‚  r = Expected Change in Interest Rates. Duration Gap Analysis Duration is a measure of the percentage change in the economic value of a position that occurs given a small change in level of interest. It concentrates on the price risk and the reinvestment risk while managing the interest rate exposure. It also measures the effect of rate fluctuation on the market value of the assets and liabilities and net interest margin with the help of duration. Duration Gap is more difficult to measure than the simple gap model but it result in a more comprehensive measure of rate of interest rate. It also takes into consideration the time value of money. The sensitivity of the market value of assets and liabilities can be assessed using the Duration analysis. Ds x S= (DA x A) (DL x L) Where; Ds = Duration Gap/ Duration of surplus, DA = Duration of Assets, DL = Duration of Liabilities, A = Assets, L= Liabilities, S= Surplus. Ds = DL + (A/S) x (DA DL) L= A-S Where; ÃÆ' ¢Ãƒâ€¹Ã¢â‚¬  Ãƒ ¢Ã¢â€š ¬Ã‚  MV = Change in the M arket Value, D = Duration of assets or liabilities, ÃÆ' ¢Ãƒâ€¹Ã¢â‚¬  Ãƒ ¢Ã¢â€š ¬Ã‚  r = Change in the interest rate, r = Current interest rate, MV = Market Value. New MV = Current MV + ÃÆ' ¢Ãƒâ€¹Ã¢â‚¬  Ãƒ ¢Ã¢â€š ¬Ã‚   MV Simulation It is a financial model incorporating interrelationship of assets, prices, costs, volume, mix and other business related variables. It usually stimulates performance under alternative interest rate scenarios and assesses resulting volatility in net interest income, net interest margin and so on. With this technique, the timing of cash flows are captured accurately and the interpretation is easy. It also increases the value of strategic planning. It also requires highly skilled personnel and the accuracy depends on quality of data, strength of the model and the validity of assumptions. It is also known to be time consuming.

Sunday, December 22, 2019

The And Of Eating Disorders - 1438 Words

Introduction The EDI, as a multifaceted instrument and as one of the most widely used assessment tools, provides a standardized rating scale, which is used internationally (Garner, 1984). Eating disorder specialists frequently use EDI with adolescents who experience symptoms and present psychological features of eating disorders. According to the user’s manual, EDI-3 asses associated risk factors and outcomes of treatment and it can be used to assess the DSM-IV-TR diagnoses of Anorexia Nervosa, Bulimia Nervosa and Eating Disorders Not Otherwise Specified (Garner, 2004). However, the EDI-3 does not assess Binge Eating Disorders (Atlas, 2007). The EDI-3 is appropriate to use with females ages 13-53 (2007). In addition, EDI is used internationally not only in clinical settings but in research too (Clausen, Rosenvinge, Friborg, Rokkedal, 2011). EDI is constructed to inventory the severity of eating disorders (Garner, 1984). Test History Test 2- Eating Disorder Inventory The initial eating disorder inventory identification test was developed by David M. Garner in 1983 (Clausen, Rosenvinge, Friborg, Rokkedal, 2011). Since 1983, there have been two revisions. The first revision is Eating Inventory Two (EDI-2), which was completed in 1991. The second revision is Eating inventory three (EDI-3), which was completed in 2004 (Clausen et al., 2011). There are two additional forms of EDI-3: EDI-3 Symptom Checklist (EDI-3 SC) and EDI-3 Referral Form (EDI-3RF). The EDI-3 SC is a selfShow MoreRelatedEating Disorders : Eating Disorder1205 Words   |  5 PagesEating Disorders in Today’s World Eating disorders are alive and well in today’s world and they are a major problem. An eating disorder can look like a few different things, ranging from a severe reduction of food intake to over eating to feelings of negativity towards your body shape or weight (Lehigh University). While some disorders can only be found in specific age groups, races, etc., eating disorders can be found amongst all and it does not necessarily have to be pointed towards food (LehighRead MoreEating Disorders : An Eating Disorder1184 Words   |  5 Pagesas an eating disorder. Weir (2016) goes on to explain the origins behind eating disorders in individuals. This topic is important because, in the United States, many women and men suffer from a clinically significant eating disorder at some point in their life. It is important to know the influences that cause an individual to experience an eating disorder. Genetically, or environmentally, or both genetically and environmentally. Anorexia ner vosa, bulimia nervosa, and binge eating disorder are eatingRead MoreEating Disorders : Eating Disorder1028 Words   |  5 Pages Markehl Murray Mrs. Miller 4th period 6 January, 2016 Eating Disorders In US today, over 30 million men, women, and children suffer from an eating disorder. The most common eating disorders are; Anorexia, Binge eating, and Bulimia. Why do people resort to something so life threatening? Many people are turning towards eating disorders because they don’t accept who they are. Eating disorders are a mental illness that can have dangerous effects on the human body, and several people are involvedRead MoreEating Disorders : Eating Disorder1235 Words   |  5 PagesEating Disorders Eating disorders are a very serious psychological condition that affects your mind so that you are more focused on your food and weight than you are on everything else. The most known and most commonly diagnosed eating disorders are anorexia, bulimia, and binge eating disorder; however, these are not the only eating disorders. Eating disorders cause psychical and psychological problems, which at their worst can even become life threating. Statistics show that more women are affectedRead MoreEating Disorders And Eating Disorder1410 Words   |  6 Pagesâ€Å"An eating disorder is about anxiety and control and healing from trauma and food and weight are just the tools of destruction† (Floyd, Mimms, Yelding, 2008). An eating disorder is defined as a severe disturbance in eating behavior. An eating disorder, as defined by our text book for class, is psychological disturbances that lead to certain physiological changes and serious health complications. The three most common a nd most easily identifiable forms of eating disorders include anorexia nervosaRead MoreEating Disorders And Eating Disorder1573 Words   |  7 Pagesaffects people called an â€Å"eating disorder.† Why did you choose this topic? I chose this topic because it is a very prevalent issue in our society today, and a close friend of mine is suffering from an eating disorder. What question(s) did you want to answer or what was your hypothesis regarding this topic? As mammals, there is no chance of escaping the need to consume food in everyday life. However, when it comes to food there can be a major concern of eating too much or eating too little. Doing eitherRead MoreEating Disorders And Eating Disorder1104 Words   |  5 PagesEating disorder is a serious problem happens in both men and women. Eating disorder is a sort of disease in which a person is having a strange routine of eating like consuming a huge amount of food each time they eat. This can incorporate not eating enough nourishment or indulging. Eating disorder influence many people around the world. The larger part of peoples who are dealing with this issue are ladies. A person with eating disorder issue may focus nonsensically on their weight and shape. EatingRead MoreEating Disorders : Eating Disorder966 Words   |  4 PagesEating Disorders Many people, both women and men of all ages, suffer from the psychological disorder, eating. Up to thirty million people in the world suffer from some kind of an eating disorder. There a two types of eating disorders, anorexia and bulimia, and have several methods of treatment. What is an eating disorder, and what do they cause? Eating disorders are maladaptive and very serious interruptions in eating. They can come in the form of overeating, or not eating enough, they are oftenRead MoreEating Disorders : Eating Disorder1031 Words   |  5 Pagesâ€Å"The eating disorder is a very jealous and abusive partner. It requires a lot of devotion in the extent that you have to devote yourself to tending to the anorexia. There s not a lot of time left over for adult life,† was stated by Dr. Doug Bunnell, a specialist in eating disorders. Eating disorders effect a variety of people. Age, race, and gender aren’t role playing keys in eating disorders. Not everyone gets an eating disorder, but if they do then, it will more than likely destroy their livesRead MoreEating Disorders And Eating Disorder1496 Words   |  6 PagesAn eating disorder is an illness that causes serious disturbances to your everyday diet, such as eating extremely small amounts of f ood or severely overeating. A person with an eating disorder may have started out just eating smaller or larger amount of food, but as some point, the urge to eat less or more has gotten out of control. Severe distress or concern about body weight or shape may also signal an eating disorder. Common eating disorders include anorexia nervosa, bulimia nervosa, and a binge-eating

Friday, December 13, 2019

Relating Pairs of Non-Zero Simple Zeros of Analytic Functions Free Essays

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 write a custom essay sample on Relating Pairs of Non-Zero Simple Zeros of Analytic Functions or any similar topic only for you Order Now 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 containing 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 Deform ation 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-intuitive: 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 Apple, 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 pair 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]. How to cite Relating Pairs of Non-Zero Simple Zeros of Analytic Functions, Papers

Thursday, December 5, 2019

Well As Breakfast Services To The Customers-Myassignmenthelp.Com

Question: Discuss About The Well As Breakfast Services To The Customers? Answer: Introducation I have been working in a restaurant sector for more than five years and have not faced with such situation anytime in the past. The restaurant I work for in involved in offering dining as well as breakfast services to the customers. The restaurant opens in two shifts; one is in the morning and the other in the evening. This kind of shift timing is maintained by the restaurant in order to get ample time for preparing the food items. This in turn helps the restaurant to serve best quality food to the customers. My role in this restaurant is of an operations manager. I look after all the operations in the store that is the kitchen, presentation if food and tables and responsible for maintaining the internal and external environment of the business. Being the operation manager, I was expected to stay the whole day for looking after the restaurant. The raw material for the food and other needs of the restaurant is bought under my supervision. I am the sole person to allow the entry of an item in the store after properly analyzing the quality and environmental considerations. The food is also cooked under my supervision as it is my duty to maintain the power consumption, waste disposal and recycling of waste when required (Montalbo, 2015). A restaurant should have some of these operations ethics for proper maintenance of the environment. As the waste disposed by our store also affects the external environment, being an operations manager it is my duty to supervise that. I handled all the operational responsibility of my store from preparation to waste. However, a few weeks before I got a message from my supervisor that I am not liable to look after the waste disposable duty from today. This was a shock for me as the company just informed me about the changes before prior discussion. It should be an ethical consideration of any business to discuss about any changes in the business before reaching to a decision (Su, 2014). Being a part of the organization and knowing that there must be some genuine reason behind such a decision, I decided to keep quiet and continue the duties I am allotted with. This shows that I followed the stage four of the Kohlbergs Thinking of moral improvement that states about obeying the decision of our authority due to social considerations (Nucci, Krettenauer Narvez, (Eds.)., 2014). I did not question on the decision taken by the restaurant manager due to moral ethics. This is because I was also relaxed that one of my responsibilities was reduced. With the passing time, I realized that due to improper supervision of the waste disposable system, the amount of waste was increasing in the restaurant. Moreover, improper ways of waste disposal was also affecting the external environment. After returning from a leave of two days, I also heard from some staffs working under me that the restaurant is hiring a new operations manager who will be looking for the waste disposal department. This was good news for me, as my responsibility will be fixed in one particular department. However, I was also afraid that this new hiring might be a threat for my position. This is because some of my colleagues also informed me that the new manager is more qualified and experienced than me. One decision by my supervisor or the restaurant manager has put me into two problems. One is being a store operation manager I need to see that the store operations are running smoothly with relation to the cleaning, safety and presentations. Second is the fear of losing my job if the new manager is highly educated. However, with the constraint of not going beyond the decision taken by the head of department, all the staffs in the restaurant was getting affected. A restaurant industrys sole aim is to serve the customers with best quality service and environment irrespective of anything (Huang, et. al., 2014). My operation staffs as well as I were afraid of losing the job with such bad situation of the store. I tried talking about the situation to the store manager about the worsening condition. However, due to some unknown reason he did not give much heed to the issue. In light of moral requirement in business (Weiss, 2014), there are reasons that make this situation a moral dilemma for me as well as for my staffs. This is because the consequences of the action taken by the authorities will affect me as well as my staffs. According to the business environment management, it has been widely recognized that a business is always affected by ethical, environmental and economic considerations (Crane Matten, 2016). Such considerations have to be met in any condition for proper revenue of the business. Moreover, the head manager did not think much before taking this action. He is not bothered that this action is going to affect me, my staffs as well as the reputation of the company. The long-term effect of this might be positive, however, it is presently affecting many people in the company. It becomes my ethical duty to make the authority informed about the situation and its affects. This puts me in stage six of Kohlbergs theory of post-conventional mor ality in which as person acts according to the internal environment principle (Nucci, Krettenauer Narvez, (Eds.)., 2014). In view of the stage five of the Kohlbergs model of morality, it was difficult to reach on any decision about the action that was taken. This is because any decision taken should be a balance between the social need and own rights (Nucci, Krettenauer Narvez, (Eds.)., 2014). I realized that the company was going to benefit in the end with such experienced and qualified operation managers. Thus, it is not wise to directly go and ask about it to the authority. It might happen the head manager has informed the owner of the company before taking any such decision. The decision of the owner is just as he is the maximum stakeholder of the company. Unethical behavior is never accepted in any company and thus would prove to be a threat on my job (Giacalone Promislo, 2014). Unethical behavior is also bad for the business as it might lead to disputes between the management and the staffs, which will in return affect the servicing facility of the restaurant. Thus, it is beneficial that I follow the non-consequential theory of ethics that focuses on rights and integrity. The staffs of the restaurant have the rights to perform effectively and earn well from their job. There are employees who are in their initial stage of career development and such kind of actions will be detrimental to their career if they lose their job. However, raising my voice for their behalf would put my job at risk, as I am uncertain if the head manager took this action on some instruction from the owner of the restaurant. The next option for taking any decision is to follow the Utilitarianism act in consequential ethics (Mulgan, 2014). By following this theory, I will have a discussion with my head manager about the present condition of the restaurant and would try to reach to some kind of compromise that will be beneficial for the entire person affected as well as the company. In doing this I will request my supervisor to allow me to continue with the waste management operation of the business until the new manager joins the company. This will allow the staff to perform their task appropriately and benefit the restaurants environment. On the other hand, I will also have some idea of the view the head manager is holding about my position in the company. This decision will be beneficial for everyone. However, it might also backfire on me as the situation is sensitive and the management did not inform me about it themselves. Final approach that I can take to solve the issue is the egoistic approach (Knez, 2016). This approach usually involves getting our own work done without thinking much about others. I could just focus on completing the task that has been allotted to me without considering much about the staffs and the restaurant surroundings. Performing the task perfectly would help me be in the save side of not losing my job. Although I realize that the staffs also need to earn their living, yet I need to fulfill my own needs to some extent. Based on the above problems and the solutions that I suggested for dealing with that issue I realize that I have moved from one stage to another stage of Kohlbergs theory. I was initially on stage four where I believed on some moral concerns of the business. However, now I am at stage 6 of universal principles (Nucci, Krettenauer Narvez, (Eds.)., 2014). From all the above-mentioned solutions, I am certainly inclined towards the utilitarian approach of business ethics. I am aware that there are some negative impacts of egoistic behavior and an imperative leader always prefer for help others and work for everyones good. This will benefit the business and the employees. The debate on Ethical Leadership This Business School believes that ethical leadership is impossible in a shareholder focused economy According to the character of Mike, it is seen that he is against the topic given in the motion. His behavior is consistent with the ethics duties behavior given in the Maxim 1 of the Modernist theories. Mike is a retired lecturer from a renowned university and has been consistent with his though of business ethics. He believes a company should always have good people that can lead to good environment. However, his behavior towards his daughter puts him in the stage two of the Kohlbergs moral development model (Kurtines, 2014). This is because he is driven by his own interest and wants his daughter to seek his footsteps. This shows that h is demanding in his nature. His daughter is espousing new ethics in the organization that is different from the ethics used by shareholders. Thus, Mike displays stage two of Kohlbergs model and maxim 1 of Deontological ethics. Jan is also seemed to be against the topic suggested by the motion. According to her behavior, she believes in moral ethics, works for the good of her company, and does charitable work (Hoffman, Frederick, Schwartz, 2014). This puts her in the stage 6 of the moral development model and maxim 2 of human dignity. However, it is also seen that being the CEO of the company she has a dominant nature of doing what is right for the companys ethics. This puts her in utilitarian stage of consequentiality theory. She also displays egoism like Mike as she is using he employees for accomplishing her own needs. Mei-Hua is also against the claim given in the motion. She is a a successful and well renowned manager of one of the best pharmaceutical company of the world. She believes in ethics of the business and abides by the rules and governance of the business. This puts her in the utilitarian aspect of the consequential ethics and maxim 1 3 of deontological ethics as she is doing this for the good of all the employees and company (Paquette, Sommerfeldt, Kent, 2015). Moreover, her good intention behind the large settlement implies that she is stage 3 and 4 of the Kohlbergs model. She states that she is just following the rules of the company and working for everyones good. Deshi Chen was the only one person against the motion. He did not believe in ethical leadership. According to him corporate believe in profit and there is nothing as ethics in business. This act of his displays utilitarian thought. He is in the stage 5 and maxim 3 of the moral development model. However, his disagreement on business ethics and view of other teams shows that he believes in egoism of teleological ethics (Bonnemains, Claire, Tessier, 2016). He is following whatever is best for him and not for the ethics of the business. On the other hand, it shows that Deshi might be considered on stage 2 because he is doing what is most beneficial according to his situation. The poverty that he and his family faced made him feel like this. Coming to myself I too believe in ethical leadership which is evident as I did not question my seniors and head of the restaurant about the new hire. The decision I took to stay on the side of utilitarian ethics puts me on stage 6 of universal principle of Kohlberg model. Thus, from the above discussion it is clear that everyone believes in ethical behavior in business environment except Deshi. The holiday case The case discusses about various types of dilemma coming from all people of the company, which played a role in helping Boris to reach on a decision. The first person to face a dilemma in this case study is Boris, the employee of the advertising agency company. He faced a dilemma between choosing his job and working for the client or going to his girlfriend Swee Lans place to meet her parents. Further, he also faced the dilemma while talking to his manager of choosing between his job and his holiday. He faced last dilemma when his friend questioned his decision and he was confused whether his decision was right or his friends are correct. Another person to face the dilemma is Swee Lan who was in a dilemma of choosing her parents happiness and Boris work. She was confused because if she supported Boris in giving up his holiday then she would have hurt her parents. On the other hand forcing Boris to choose the holiday would affect his career. Boriss manager was the third person to be affected by a dilemma between granting Boris his holiday and asking him to serve the client. His choice of allowing Boris to take a holiday would result in losing an important client of the company. Whereas, asking Boris to cancel his holiday would make one of his employee unhappy. The last person is Marcus, friend and colleague of Boris. He faced two sided problem, one is deciding to help Boris on taking a difficult decision he was facing and the other was blaming Boris of canceling his leave. This is because Boris canceling his leave would result in further cancelation of leaves of other employees in case of urgency in business. However, from the above four dilemma, Boris dilemma is the most important as he is the important character of the play. From the dilemma that Boris faced it is clear that he exhibits there characteristic of egoism. This puts him in the utilitarian theory of modernist ethical model. This is seen as Boris decides to cancel his holiday and stay back at office without even consulting his girlfriend. He is also in the stage two of the Kohlberg model as he cancels his holiday for which he will be rewarded in future. However, he is also in the stage 5 of the Kohlberg model where he realizes that there are people in his office and around which have different opinion and he decides to go against those opinions (Crane Matten, 2016). On the other hand, the dilemma that Boris face with his manager puts him in the Utilitarian stage of modernist theory of ethics where he decides to work for his company and get them better projects. This will benefit large number of people in his office as well. This also displays stage four in the nature of Boris as he realized his responsibility of obeying the rules of his office. However, again with Marcus he was egoist as he gave his own opinion that his decision of staying back was right (Mischel, 2013). This shows that Boris has been in ethical dilemma due to its social consciousness and morality towards his office. He will be in trouble in future because of giving up on his friends and girlfriend due to the needs of his office work. Interpersonal and team working skills The debate that we faced in this module was very interesting and helped us to learn many things about our behavior and thinking towards others. During this debate we were able to realize that we went through phase 2 and phase 5 of the Kohlberg theory of moral development. We gave our best in giving our views in all possible way we could. However, initially we saw ourselves at phase 2 of the Kohlberg model because at first we did not took active participation in the debate and was only waiting for good results (Zizek, Garz, Nowak, 2015). On the other hand there were ewe members who only focused on themselves and did not bother to give any response in the debate. They were facing the Utilitarian theory of egoism and self-development (Hayry, 2013). However, as the debate continued we found that it is interesting to be a part of it and give our view. This helped us to know that our thinking about the debate was wrong as it is not for harming anyone. It only helped the team members to share their views that they possess about the topic. As we moved forward the debate became more complex and conflicting and we moved to phase five. We realized that the situation of conflict and argument is an active part of the debate as every individual is sharing their own views on the topic (Lapsley, Carlo, 2014). There was an opposition team also which various kinds of views. The debate had put everyone in the non-consequential ethics which reflected the rights and justice that the people has (Nye, Plunkett, Ku, 2015). As there is no right or wrong answer for anything, it is just the views that differs about a single topic. 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