[0.1] Questions about integers and primes It is easy to formulate questions about integers and primes, though not easy to distinguish those questions that have deeper meanings. More than 2000 years ago, contemporaries of Euclid knew that there are infinitely-many prime numbers. Quantifying the distribution of primes is still essentially an open question! Chebyshev (1848-50), Riemann (1857-8), H...

In this paper we present the simplest possible color balance algorithm. The assumption underlying this algorithm is that the highest values of R, G, B observed in the image must correspond to white, and the lowest values to obscurity. The algorithm simply stretches, as much as it can, the values of the three channels Red, Green, Blue (R, G, B), so that they occupy the maximal possible range [0,...

We derive a closed master equation for an individual-based population model in continuous space and time. The model and master equation include Brownian motion, reproduction via binary fission, and an interaction-dependent death rate moderated by a competition kernel. Using simulations we compare this individual-based model with the simplest approximation, the spatial logistic equation. In the ...

in this paper a modification of he's variational iteration method (vim) has been employed to solve dung and riccati equations. sometimes, it is not easy or even impossible, to obtain the first few iterations of vim, therefore, we suggest to approximate the integrand by using suitable expansions such as taylor or chebyshev expansions.

in this paper, we present a computational method for solving boundary integral equations with loga-rithmic singular kernels which occur as reformulations of a boundary value problem for the laplacian equation. themethod is based on the use of the galerkin method with cas wavelets constructed on the unit interval as basis.this approach utilizes the non-uniform gauss-legendre quadrature rule for ...

In a nucleonic propagation through conical crossings of electronic energy levels, the codimension two conical crossings are the simplest energy level crossings, which affect the Born– Oppenheimer approximation in the zeroth order term. The purpose of this paper is to develop the surface hopping method for the Schrödinger equation with conical crossings in the Eulerian formulation. The approach ...

in this paper, a new spectral-iterative method is employed to give approximate solutions of fractional logistic differential equation. this approach is based on combination of two different methods, i.e. the iterative method cite{35} and the spectral method. the method reduces the differential equation to systems of linear algebraic equations and then the resulting systems are solved by a numer...

In this paper we proposed the estimation of the characteristic impedance, effect of dispersion, and the effective dielectric constant of Coplanar Waveguide (CPW) using conformal mapping theory and performances are analyzed. Numerically efficient and accurate formulae based on the conformal mapping method for the analysis of coplanar waveguide structures are presented. The analysis formulas for ...

In many fields of science including population dynamics, the vast state spaces inhabited by all but the very simplest of systems can preclude a deterministic analysis. Here, a class of approximate deterministic models is introduced into the field of epidemiology that reduces this state space to one that is numerically feasible. However, these reduced state space master equations do not in gener...