New method for the determination of adsorption space volume for sorbents with an arbitrary porous structure from excess gas adsorption isotherm measurements

A new method for the determination of adsorption space volume has been proposed, which is applicable to adsorbents with an arbitrary porous structure, including nonporous adsorbents with open surfaces. The method is based on the use of an experimental excess adsorption isotherm measured over a wide range of pressures in the equilibrium gaseous phase (as a rule up to 100–150 MPa) and the absolute adsorption isotherm equation with unspecified parameters in the most general form, given by statistical physics. The method has been tested for a number of adsorption systems, and it has been found that the result was always unambiguous, correct, and stable in the sense of input data.Translated fromIzvestiya Akademii Nauk. Seriya Khimicheskaya, No. 12, pp. 2381–2385, December, 1995.     

关于有限域上一类方程零点个数的估计

By establishing the connection between graph colouring and the solution of some equation systems in finite fields, we obtain some formulas to the number of solutions of some equation systems in finite fields, in terms of chromatic polynomial of a graph.     

关于Smarandache ceil函数的一个方程

研究了关于Sm arandache ceil函数的一个方程,并用初等方法得到了它的所有解.     

A Singular Equation of Length Four Over Groups

Let G be a group and t an unknown. In this paper we prove that the equation atbtct^–1dt^–1 = 1 (a,b,c,d G, a² 1, c² 1, bd 1) has a solution over G. This forms part of a program to investigate precisely when an equation, whose associated star graph contains no admissible paths of length less than 3, fails to have a solution over G.2000 Mathematics Subject Classification: 20E06     

PERIODIC SOLUTION AND ASYMPTOTICITY OF ABEL EQUATION

Inarticles[1]and[2]theexistenceandstabilityofperiodicsolutionofAbelequation:werediscllsscd,wb')lteth'3coefficientsa(t),b(t),c(t)andd(t)areradalcollt,inuouslyp(3riodicfunctions.111thispal)erwenotonlystudythegeneralI\)rnlofeqllation(A),hiltalsodiscllssitssomespecialcases.FOT'example,as(l(l-)=0l,hcAbelequationbecomesfWeshallobtainsomeinterestingresultsfromit,suchdoubleperiodicsolution,etc.Equation(B)alsohassomeapplication,weknowthattheOdum(1971)*ThispaperissponsoredbyNationalScienceFundation…     

环与环上矩阵的正则性

本文主要研究环及其上矩阵的正则性 .当 R是一个有单位元的环时 ,本文引进并刻划了Mm× n( R)的正则性并由此重新证明了环 R与全矩阵环 Mn( R)正则的等价性 ,这种方法比原有的证明方法简捷     

Equations of similitude

A general technique is developed to enlarge the Galois group of an equation from a subgroup of a finite classical isometry group towards the corresponding similitude group. Abhyankar’s work was partly supported by NSF grant DMS 97-32592 and NSA grant MDA 904-97-1-0010, and Loomis’s work was partly supported by a Sloan Doctoral Dissertation Fellowship.     

一个包含Smarandache函数的方程

对于任意正整数n,我们用S(n)表示Smarandache函数,即S(n)=min{m:n|m!}.本文的主要目的是运用初等方法研究方程∑_(d|n)S(d)=n的可解性,并给出它的所有正整数解.     

Propagation of light in(2+1)-dimensional nonlinear optical media with spatially inhomogeneous nonlinearities

The(2 1)-dimensional nonlinear Schr(o)dinger(NLS)equation with spatially inhomogeneous nonlinearities is investigated,which describes propagation of light in(2 1)-dimensional nonlinear optical media with inhomogeneous nonlinearities.New types of optical modes and nonlinear effects in optical media are presented numerically.The results reveal that the regular split of beam can be obtained in (2 1)-dimensional nonlinear optical media with inhomogeneous nonlinearities,by adjusting the guiding parameter.Furthermore,the stability of beam regular split is discussed numerically,and the results reveal that the beam regular split is stable to the finite initial perturbations.     

Theoretical investigation of a backward wave oscillator

From the linear Vlasov equation,the theoretical investigation on relativistic backward wave osciUator is performed.The relationship between the microwave power and the guiding magnetic field,which accords with the results of the particle simulation and experiments,is deduced.