The Mandelbrot and Filled Julia Sets The Mandelbrot and Filled Julia Sets are sets of numbers that are composed of complex numbers that do not diverge for varying conditions of the function fc(z)=z²+c. For the Mandelbrot set, the function is iterated from z=0. The filled Julia set holds c constant for any complex number to look at the behavior of the iterated functions for each value of z in the complex plane. Both sets are derived from the iterations of simple functions in the complex plane,…
The Cost-of-Carry Model In the commodity market the Cost of Carry model is used to price the futures and forwards contracts based on the spot price of the traded asset. The cost of carry is all the costs to carry an asset from the present until a certain future period, those are the cost to finance the asset (the interest), the storage costs, the transportation cost, and the insurance costs. The cost of carry model looks at the price of the future or forwardcontract as a function of the spot…
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1. What are the least, and most, amount of distinct zeroes of a 7th degree polynomial, given that at least one root is a complex number? Answer: If the equation is 7th degree then it has 7 roots. Those roots can be complex or real. Complex roots always come in pairs, so if it has one, then it has 2, the other one being the conjugate of the first one. This in other words, if one complex root is a + bi, then the other complex root is a – bi. If at least one root were complex, then we would have a…
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;…
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…
2. The PZK Co will take out a forward exchange contract, the foreign exchange contract is define as an agreement of two sides to determine in a specified amount of currency exchange on a valid date. The advantages of PZK Co use forward contracts are that, the company can hedge their imports by locking the currency rate, to avoid the unfavourable exchange rate and fluctuations thus the company can make use of the forward contract to ensure the exchange rate is fixed at the deal day. Moreover, the…
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…
If R and r is the Circumradius and Inradius of a non-degenerate triangle then due to Euler we have an Inequality stated as and the equality holds when the triangle is equilateral. This ubiquitous inequality occurs in the literature in many different equivalent forms [4] and also Many other different simple approaches for proving this inequality are known. (some of them can be found in [2], [3], [5], [17], and [18] ). In this article we present a proof for this Inequality based on two basic…
As business becomes more globalized and trade continues to expand internationally, companies need to understand and reduce the risk associated with international business. Though there are many risks faced by companies when operating internationally, including political, financial, and cultural, this paper will specifically discuss the financial risk associated with exchange rates and how companies mitigate this risk through currency hedging. Foreign Exchange Risks Foreign exchange risk is “the…