# Directional derivative

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This is done because real images have anomalies at some points caused by sensor errors and image deformation caused by errors of the local trajectory and residual scaled differences. The research into which type of restoration approach should be used and the equations presented which will be used was done by (M. Sistiaga, 1998). The selected method was to use Partial Derivative Equations (P.D.E.) as it successfully restored images and replaced linear filtering methods. A scheme that has been developed to restore images is multi-scale morphological analysis proposed by (L. Alvarez, 1992), which was used by (Lucido, 1997), the diffusion is based on an equation in the…

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For the application of Hopf’s bifurcation theory to the system (29) (see [Marsden J.E., M. Mckracken, 1976]), it is required to satisfy the following transversality condition (34) Substituting , and into (31), and calculating the derivatives with respect to , we obtain (35) where Since , we have , and . Hence there is a Hopf bifurcation at . We have the following result: Theorem 13. Suppose holds. Then the system (29) undergoes a Hopf…

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Introduction The problems of using derivatives as a risk management tool by financial institutions have been demonstrated in the Banc One case. The major objective of this paper is to provide more insight into the case through analysis of five specific questions in relation to Banc One’s performance between 1993 and 1994. We start by addressing the bank’s problems and potential reasons that lead to such issues. Evidences and facts show that both investors and managers blame the use of interest…

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Questions: Answer all questions given What kind of relationship did you see in your D vs T graphs (both hand and computer)? Do these relationships make sense? Explain! In the distance versus time graph for the hand graph, there is an exponential increase the in the distance traveled; as time progresses, the distance the car travels increases a little more, as the slope is not a straight line, but instead slopes upwards, with slopes later in the line being steeper than the slopes before. What…

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Results: At the start of the experiment, the initial flow rate was established as 20 ml min-1. This means that there is a steady flow of fluid or blood in your body (in this case, water) at a rate of 20ml min-1. In order to find the final concentration of the Eosin (2,5 mg ml-1) in the “blood” after 60 minutes a calibration curve had to be created by making up seven different solutions of eosin (11,25 μg ml-1) and water to compare it against their absorbance that was calculated in a…

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What are the factors affecting the prices of options? Explain the assumptions in the Black-Scholes model. In order to understand the factors that affect the prices of options, we need to understand what options are and how they work. Options are derivative assets. According to a California-based company called Optionetics (website: www.optionetics.com), "options are the most versatile trading instruments ever invented". This means, that you aren 't limited to making a profit only when the market…

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On 1705, Newton’s career was known by everyone and he was knighted by Queen Anne of England. He died on March 31, 1727. Back to the Fundamental Theorem of Calculus. This theorem is a simple theorem that establishes the relationship between the derivative and the integral and as we said before has two parts. The first part that talks about the relationship between the derivative and the integrals and the second part that tells us how to calculate a definite integral. The easiest way to…

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to him by Swiss Mathematician John Bernoulli. The Marquis de L’Hospital was born to Anne-Alexandre de L’Hospital and Elizabeth Gobelin in France in 1661. Initially, he was a cavalry officer, but unfortunately L’Hospital had to resign due to his nearsightedness. Because of this, L’Hospital became immersed in mathematics, a subject he was interested in from a young age, having solved a problem on the cycloid by age 15. L’Hospital later married Marie-Charlotte de Romilley de La Chesnelaye and had…

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Supply chains that are complex are commonly modeled as linear programs (LPs). They can effectively trade off broad range of criteria. To model FMCG supply chains accurately, one must include discrete aspects of decision making, which requires solving a mixed-integer program (MIP). It has become significantly important for managers, given the widespread use of linear models today, to be able to develop good, efficient models to aid them in the decision-making process. Three important factors;…

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Change is inevitable. It is no secret that advancements in time and ideas are destined to change the status quo, but the foresight to analyze the gray area where change occurs is often times unknown because change does not come easy. From the world’s most renowned scholars in ancient Greece detesting the shift from oral-based rhetoric to writing, to influential elites hindering the printing press from breaking long-standing institutions, these examples parallel the modern case of writing…

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