The research on prime numbers is an interesting topic in Analytic Number Theory. The Fibonacci sequence is one of the most popular sequences in mathematics. In this paper, we will discuss the prime numbers of the Fibonacci sequence, which we call Fibonacci primes. The goal of this paper is to prove that starting with F5 = 5, all the Fibonacci primes p are satisfied with p≡1 (mod4), on the basis of the Pythagorean theorem.

The Perfect Bayesian equilibrium is not a refinement of the Nash equilibrium. The Perfect Bayesian equilibrium requires players to have beliefs that are consistent with the equilibrium strategies of other players. The Nash equilibrium does not explicitly specify the beliefs of the players. In any given Nash equilibrium, the default beliefs held by players are that the other players are playing the equilibrium strategies (or a particular subset of the equilibrium strategies in the case of multiple equilibriums). The default beliefs and equilibrium strategies in Nash equilibrium could be more narrowly defined than those allowed under Perfect Bayesian equilibrium. Consequently, the set of equilibriums under Perfect Bayesian equilibrium is not a subset of the set of equilibriums under Nash equilibrium.

This paper analyzes a generalized Stackelberg model of market competition with noisy observation. The current prevailing Stackelberg model and Cournot market are two extreme cases of this generalized Stackelberg model. In this generalized model, as the follower relies less on the inaccurate noisy observation and more on prior information and conjecture for his statistical inference and decision, the value of moving first and strategic commitment of the Stackelberg leader decreases and his profit lowers. On the other hand, the profit of the follower increases and the equilibrium moves towards the Cournot model and away from the Stackelberg model.

This paper uses a spectral algorithm for the numerical solution of unsteady periodic problems. This algorithm which is based on discrete Fourier transforms uses a Fourier representation for periodic conditions of problems and hence solves the periodic state directly, without resolving transients because the discrete Fourier transforms have the periodic property to confirm physics of flow. The algorithm has been proposed for the fast and efficient computation of periodic flows. The algorithm has been validated with Stokes’ second problem as a linear problem and Burgers' equation as a nonlinear problem. The same numerical results are compared with an analytical solution, second-order Backward Difference Formula (BDF) and finite difference method (FDM) results. By enforcing periodicity by using Fourier representation that has a spectral accuracy, a tremendous increase of accuracy has been obtained compared to using the conventional numerical methods like BDF and FDM. Results verify the small number of time intervals per oscillating cycle required to capture the flow physics in Stokes’ second problem. Moreover, they show that a small number of points in a computational grid are required to capture the flow physics in Burgers' equation. Furthermore, this algorithm is more able than a finite difference method to capture shock.

The solution of the financial application, be it asset pricing, portfolio allocation or risk management, relies on the simulation of discretized versions of the stochastic differential equations(SDEs). The simplest way to confront SDEs in numerical situations is to discretize them and use monte carlo simulation. The Euler scheme is most often used for discretization of SDEs. This discretization involves an approximation error. In this topic at the first we recall an introduction to SDEs and Monte carlo simulation. Then, we study the asymptotic error distribution of Euler approximations of solutions of SDEs. We also study the error distribution associated with a Doss transformation of the state variables. Convergence results for Euler schemes with and without doss transformation and the comparison of them with Milshtein scheme are presented at the end.

In this paper, a new method is suggested for image hiding using chaos signals. The combination of movement of pixels and adjusting quantity of gray level is simultaneously used in this method. The process of moving pixels is done by an order which is taken from logistic map and for adjusting gray level the order of standing of bits of pixel's quantity of gray level is changed by the means of chaos signal as well. Experimental results show that this method has a proper efficiency for prevalent terms. For example the amount of entropy obtained by this method is around 7.9949 that is so near to 8 its ideal amount.

The entrance region flow in channels constitutes aproblem of fundamental interest in engineering applications such as nuclear reactors, polymer processing industries, haemodialyzersand capillary membrane oxygenators. In such installations, the behavior of the fluid in the entrance region may play a significant part in the total length of the channel and the pressure drop may bemarkedly greater than for the case where the flow is regarded asfully developed throughout the channel. Recently, there has been anincreasing interest in problems involving materials with variable viscosity such as Bingham materials, Casson fluids and Hershel-Bulkley fluids which are characterized by an yield value. The entrance region flow of a Casson fluid in an annular cylinder has been investigated numerically without making prior assumptions onthe form of velocity profile within the boundary layer region. This velocity distribution is determined as part of the procedure by crosssectional integration of the momentum differential equation for agiven distance z from the channel entrance. Using the macroscopicmass and momentum balance equation the entrance length has been obtained at each cross section of the entrance region of the annulifor specific values of Casson Number and various value of aspectratio. The effects of non-Newtonian characteristics and channel width on the velocity profile, pressure distribution and the entrancelength have been discussed.

In multiple regression model, regression variables are usually assumed to be independent from each other. When this assumption is not established, the model would be inappropriate and therefore the results might be incorrect. So, biased regression methods are applied. Ridge regression and principal components regression are two methods of biased regression methods. In this paper, Monte Carlo simulation tests were used for estimating coefficients of ridge and principal components regression. These two methods were compared using minimum squared error (MSE).

In this paper, a new theorem on degree of approximation of conjugate of a function f ϵ Lip(ᶓ(t),r) using  (C,1)(E,q) product summability means of conjugate Fourier series has been established.

The agreement of measuring methods is one of the main problems in medicine and others science in related to measure. In this article we deal with one of these methods and performance the statistical test and finally show their result. This method is interclass correlation coefficient.

A numerical method is implemented to investigate the influence of an insoluble surfactant on the deformation of a falling drop normal to a solid surface. In the constructed model, the liquid drop falls due to the gravity. The front-tracking method is used to solve free boundary motion of the two-phase Navier-Stokes equations and the surfactant evolution. Results show that the surfactant affects to slow the falling drop; more significant for a relatively small drop than a big one. When the drop has attained the solid surface, the contained-surfactant drop deforms easier than the free-surfactant drop.

In this paper, we have presented a new method to solve second order nonlinear differential equations. Using the pseudo-operations given by monotone and continuous function g, the reduction of a nonlinear ordinary pseudo-differential equation isintroduced and investigated.