Mathematical modelling of rock bolt systems I

The main goal of the paper is to give a variational formulation of the behaviour of bolt systems in rock mass. The problem arises in geomechanics where bolt systems are applied to reinforce underground openings by inserting steel bars or cables. After giving a variational formulation, we prove the existence and uniqueness and some other properties.     

Quantitative characterization of spatiotemporal patterns II

Disorderness of spatiotemporal patterns which are obtained by nonlinear partial differential equations is characterized quantitatively. The mean Lyapunov exponent for a nonlinear partial differential equation is given. The local Lyapunov exponent which is a finite time average of the mean Lyapunov exponent is shown to have close relation to the spatiotemporal patterns. It is suggested that the systems which are described by nonlinear partial differential equations are characterized statistically through the probability distribution function of the local Lyapunov exponent.     

Resonance Problems Which Intersect Many Eigenvalues

We study semilinear problems in which the nonlinear part is linear at infinity but behaves like a function intersecting many of the eigenvalues of the linear operator. The asymptotic linear operator can have a null space of any finite dimension.     

Effect of the conditions of isolation on the physicochemical properties of human serum albumin in the norm and with pathology

Differential scanning calorimetry and IR spectrosocopy were used to investigate the effect of the procedure of isolation of human serum albumin on its physicochemical characteristics. It is shown that fractionation of blood plasma with ethylene glycol followed by ion exchange chromatography can be used to obtain albumin of normal donors that is similar to the albumin in the nonfractionated plasma according to melting thermograms. Endotherms of human serum albumin samples that were obtained by affinity chromatography and preparative electrophoresis are bimodal, unlike the monophasic for albumin obtained by polyethylene glycol precipitation. These changes result from a higher content of nonetherified fatty acids in the albumin samples obtained by affinity chromatography and from modification of the secondary protein structure in the samples obtained by electrophoresis. Analysis of melting thermograms of serum albumin from patients with uremia, chronic hepatitis, and peritonitis shows that fractionation of blood with polyethylene glycol preserves the thermodynamic characteristics of the various pathological serum albumins to the greatest extent. The present results demonstrate the advantage of polyethylene glycol fractionation for isolation of native preparations of normal and “pathological” human serum albumin. Translated from Zhurnal Prikladnoi Spektroskopii, Vol. 64, No. 1, pp. 32–37, January–February, 1997.     

On the pth moment exponential stability criteria of neutral stochastic functional differential equations

The paper discusses the pth moment exponential stability for a general class of neutral stochastic functional differential equations of the Ito type. This investigation can be very complicated, even in many special cases, by using usual methods based on Lyapunov functionals. In this paper we present criteria which are relatively easy to verify the pth moment exponential stability of the solutions of such equations.     

奇摄动非线性边值问题

§ 1 .　Introduction　　AclassofintegraldifferentialequationsDirichletboundaryvalueproblemsforordinarydif ferentialequationandellipticequationarediscussedin [1]and [2 ]respectively .Andin [3]akindofnonlocalproblemsforsingularlyperturbedreactiondiffusionsystemsarestudied.Inthispaper,whatisworthpointingoutisaclassofnonlinearboundaryvalueproblemsdiscussed,applyingthemethodofcompositeexpandandthetheoryofdifferentialinequalities.εy″ =f(x ,y ,Tεy ,ε) y′ +g(x ,y ,Tεy,ε) ,0 相似文献   

单层介质膜保偏全反射直角三棱镜镀膜材料的选择及其微分相位特性研究

入射角、基底玻璃折射率、膜介质折射率、膜厚等因素会影响单层介质膜保偏全反射直角三棱镜的保偏特性，且各因素的影响程度并不相同。本文分析了上述各因素的微小变化对保偏特性的影响，并提出了选择膜介质的方法     

An Oscillation Criterion for Second Order Superlinear Differential Equations

61.IntroductionConsiderthesecondordersuperlinearequationx'(t) p(t)X'(t) q(t)1x(t)l"sgnx(t)=o,t>to,(1)wherea>l,pandq:[t,'co)-R=(-co,oo)arecontinuous.Weconsideronlysuchsolutionsxofequation(l)whichexistonsomeinterval[t.,oo),t.>t,>o.Asolutionofequation(l)issaidtobeoscillatoryifithasarbitrarilylargezerosandotherwise,itissaidtobenonoscillatory.Equation(l)iscalledoscillatoryifallofitssolutionsareoscilllatory.Forthespecialcasewherep(t)=Oli.e.,forthedifferentialequationx'(t) q(t)lx(t)l"sgnx(t)=o,a>1-…     

中立型抛物方程解的强迫振动性

本文讨论中立型抛物方程解的强迫振动，其中Ω是Rn中具有光滑边界Ω的有界区域，     

中国现行财政体制下“买税”行为的博弈分析

博弈论为理论依据,通过对高、低两种任务下买税利益团体和上级监管部门的利益偏好和行为特征进行建模对比分析,考察影响其行为的各种因素,从经济学角度探求引起“买税”行为的根源,并试着给出建议.