Journal of Applied & Computational Mathematics

Using Markov-chains (formally a Markov process or Markov system) we will show how to estimate the probabilities of a capital gains tax rate changing from its current rate to another rate within a certain number of years. It is important to recognize that capital gains rates in the United States have their origins in every elected administration of the government that had the power to influence tax policy. The outcome of government elections is dependent on chance factors such as periods of war and peace, economic recession and expansion, current fiscal and monetary policy, changes in population demographics, just to name a few. The delicate balance between the government and the dynamic society that shapes tax policy is difficult to predict using deterministic modeling. Therefore, we look to stochastic modeling using the Markov-Chain processes to see if it could be of use in creating a useful model for capital gains tax rates in the United States.

In this paper we obtain some coefficient inequalities for subclasses of uniformly p−valent starlike and convex functions in the open unit disk denoted by SDp (β, α) and KDp (β, α). Growth bounds and distortion bounds are discussed for functions in these classes. For different values of the parameters p, α and β our results of this paper generalize those obtained by several authors in the literature.

This paper deals with the state-dependent functional differential equations x(x(t)). We give the strict proof of qualitative properties that Eder’s case and the solution of the state-dependent differential equation is not unique. In some conditions, we also extend Eder’s case.

Combination of weighted weibull distribution proposed by Ramadan and beta distribution gives a better distribution (beta-weighted weibull distribution) than each of them individually in terms of the estimate of their characteristics in their parameters. The combination was done by using the logic of beta function by Jones. We investigated in the new proposed beta-weighted weibull distribution some basic properties including moments, moment generating functions, survival rate function, and hazard rate function, skewness, and kurtosis, coefficient of variation, asymptotic behaviors and estimation of parameters. The proposed model is much more flexibility and has better representation of data than weighted weibull distribution. A real data set is used to illustrate the importance the potentiality of the new model.

In this paper we find all conjugacy classes of the first basic Renner monoid of type E6. They are listed in the tables of the paper.