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...

thermophysical properties of fluorine are interesting because of its applications in different areas of technologyand industry. the computations of thermodynamic properties were performed with the gma equation of stateunder critical conditions. the present work reports calculations of density, volumetric, and thermodynamicproperties of liquid fluorine on extended ranges of pressure and temperat...

in this paper, we introduce an efficient method for solving the quadratic riccati differential equation. in this technique, combination of laplace transform and new homotopy perturbation methods (ltnhpm) are considered as an algorithm to the exact solution of the nonlinear riccati equation. unlike the previous approach for this problem, so-called nhpm, the present method, does not need the init...

Solving a quadratic equation P (x) = ax + bx+ c = 0 with real coefficients is known to middle school students. Solving the equation over the quaternions is not straightforward. Huang and So [2] give a complete set of formulas, breaking it into several cases depending on the coefficients. From a result of the second author in [10], zeros of P (x) can be expressed in terms of the zeros of a real ...

an optical system has been redesigned and used to measure detonation velocity as a function of condensed explosive density for rdx, hmx, petn. these measurements are then used to determine and fine tune parameters appearing in the bkw (beker-kistiakowsky-wilson) equation of state for gases at extremely high pressures. steady state form of conservation equations along with the bkw state equation...

Kung-Traub’s conjecture states that an optimal iterative method based on d function evaluations for finding a simple zero of a nonlinear function could achieve a maximum convergence order of 2d−1. During the last years, many attempts have been made to prove this conjecture or develop optimal methods which satisfy the conjecture. We understand from the conjecture that the maximum order reached b...

The aim of this research note is to prove the following new transformation formula begin{equation*} (1-x)^{-2a},_{3}F_{2}left[begin{array}{ccccc} a, & a+frac{1}{2}, & d+1 & & \ & & & ; & -frac{4x}{(1-x)^{2}} \ & c+1, & d & & end{array}right] \ =,_{4}F_{3}left[begin{array}{cccccc} 2a, & 2a-c, & a-A+1, & a+A+1 & & \ & & & & ; & -x \ & c+1, & a-A, & a+A & & end{array} right], end{equation*} wher...