Second derivative test

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…

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…

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…

for velocity and acceleration, since the distance traveled remains constant and using a longer or shorter time than actually used will cause the acceleration to be slower or faster than it actually is. There was some variance in the way that the car started down the ramp, with either the front end of the car a little ahead of the starting distance or behind, which would have affected the distance traveled by the car. Since the initial dots had to be counted for the calculations in the lab…

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…

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…

Fundamental Theorem of Calculus The Fundamental Theorem of Calculus evaluate an antiderivative at the upper and lower limits of integration and take the difference. This theorem is separated into two parts. The first part is called the first fundamental theorem of calculus and states that one of the antiderivatives of some function may be obtained as the integral of the function with a variable bound of integration. The second part of the theorem, called the second fundamental theorem of…

timing of his confession, but he was proved right through the 87 letters exchanged between Bernoulli and L’Hospital from 1692 to 17075. These letters showed that Bernoulli did indeed teach L’Hospital a significant amount of the principles L’Hospital had claimed as his own. L’Hospital’s original statement of his rule in his textbook was formulated geometrically with the use of a curve. The curve AMD, with AP=x, PM=y, AB=a, allows for y to be expressed as a fraction whose numerator and…

mathematical point of view, there exist several approaches for solving partial differential equation constrained optimization problems; on the one hand, there is the treatment of the optimization problem in the partial differential equation context using adjoint equations deduced from the Lagrange principle. And, on the other hand, there is the possibility to derive a simplified model where the resulting discretized equations are interpreted as a mixed-integer problem relating the partial…