Aims. The so-called Limber equation is widely used in the literature to relate the projected angular clustering of galaxies to the spatial clustering of galaxies in an approximate way. This note gives estimates of where the regime of applicability of Limber's equation stops. Methods. This paper revisits Limber's equation, summarises its underlying assumptions, and compares its predictions to th...

Using concepts of noncommutative probability we show that the Löwner’s evolution equation can be viewed as providing a map from paths of measures to paths of probability measures. We show that the fixed point of the Löwner map is the convolution semigroup of the semicircle law in the chordal case, and its multiplicative analogue in the radial case. We further show that the Löwner evolution “spr...

This paper brings to light a method based on Multiphase algorithm for single variable equation using Newton's correction. Newton's method is derived through the logarithmic differentiation of polynomial equation. A correction term which enhances the high speed of convergence is hereby introduced. A translation of Newton's method to Total Step and Single Step Methods (T. S. M and S. S. M) re...

in this paper, a boussinesq equation is solved by using the adomian's decomposition method, modified adomian's decomposition method and homotopy analysis method. the approximate solution of this equation is calculated in the form of series which its components are computed by applying a recursive relation. the existence and uniqueness of the solution and the convergence of the propose...

le chatelier's principle is used as a very simple way to predict the effect of a change in conditions on a chemical equilibrium. . however, several studies have reported the violation of this principle, still there is no reported simple mathematical equation to express the exact condition of violation in the gas phase reactions. in this article, we derived a simple equation for the violati...