Compared to the straight optimization of a non-transition state system to a ground state, transition states are more numerically sensitive and take more time to calculate. To achieve this level of accuracy, we continuously modified second derivative (force constants and frequencies) calculation criteria, which was either calculated initially by Gaussian and then approximated in further steps (Opt=CalcFC), or re-calculated at each step (Opt=CalcAll). Approximating the force constants was usually enough, though we turned to a detailed re-calculation of force constants at each step for particularly difficult optimizations, albeit at the expense of computational resources and time. Using the ModRedundant function, we also isolated the minima and maxima optimizations by freezing the active bond(s) of interest and forcing a minimization of the surrounding system, then unfreezing the active bond and optimizing the structure again to a local maximum. Monitoring the average root mean squared…
Jervand Asatrjan 1)summary of the major theme regarding the ability of quantitative financial models to consistently earn abnormally high returns? Why or Why not? Two risky positions taken together can eliminate risk idea stems from the Midas formula. The reason this was an important concept due to the discovery from a blind test that prices moved at random. Scientists made a conclusion that prices are not predicted by the investors rather it is by chance that some investor makes a very…
transitions), and α is absorption coefficient. Kubelka-Munk Equation (3): approximation of α .5 f(R)=(1-R)2/R=k/s (3) Where R is reflectance, k is the molar absorption coefficient, and is scattering coefficient. However, this method requires solid sample state analysis, which is not performed in this study. Therefore, trying to attempt a double derivative of the absorption by…
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…
use of sophisticated financial instruments to reduce the foreign exchange risk. One example of natural hedge is companies try to match revenues with expenditures in the same currency. In other words, companies require their customers to pay them in the same currency as their expenditures. Moreover, companies can build their manufacturing plant in the foreign country so that production costs are in the same currency as sales. With the increase in hedging costs, Airbus was looking for natural…
Semra Özal CONNECTIONS OF LOGARITHMIC FUNCTIONS Logarithm and exponential functions have close relationship and they are inverse function of each other in a way. Before explicitly clarifying this inverse relationship, we should analyze their definitions. Logarithm means, in mathematics, “The exponent that indicates the power to which a base number is raised to produce a given number “2 Exponential function means that “mathematical function in which an…
and also studied fractals in iterated functions in his landmark piece Mémoire sur l'itération des fonctions rationnelles.In the 1970’s, Benoit Mandelbrot formally defined what a fractal is, and popularized Julia’s work. He claims to have found the Mandelbrot Set, although this claim is contested. The Mandelbrot Set comes from the iteration of the function fc(z)=z²+c starting with z=0. Iteration is the process by which a function’s output is fed back into its input repeatedly. With this…
while selling the future contract (taking a short position). After one year the investor gives the gold to settle the contract and receives the $1,200 with which he pays the loan in addition to the interest, the amount of $1,155, and keeps the profit from transaction of $45.Table 1 below resumes the example. Table 1 Arbitrage 1 1-year gold future $1,200 Spot price of gold $1,100 Interest rate 5% Time t=0 Time t=1 Borrow $1,100 at 5% Buy gold in spot market for…
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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…