Solvability of 2n-order m-point boundary value problem at resonance

The existence of solutions for the 2n-order m-point boundary value problem at resonance is obtained by using the coincidence degree theory of Mawhin.We give an example to demonstrate our result.The interest is that the nonlinear term may be noncontinuous.     

（Φ，△）－TYPE PROBABILISTIC CONTRACTOR AND SOLUTIONS FOR A NONLINEAR OPERATOR EQUATIONS IN MENGER PN－SPACES

（Φ，△）－ＴＹＰＥＰＲＯＢＡＢＩＬＩＳＴＩＣＣＯＮＴＲＡＣＴＯＲＡＮＤＳＯＬＵＴＩＯＮＳＦＯＲＡＮＯＮＬＩＮＥＡＲＯＰＥＲＡＴＯＲＥＱＵＡＴＩＯＮＳＩＮＭＥＮＧＥＲＰＮ－ＳＰＡＣＥＳ￥ＦａｎｇＪｉｎｘｕａｎ（方锦暄）（ＤｅｐａｒｔｍｅｎｔｏｆＭａｔ...     

足底压力统计变化规律测试与侦破技术

利用现场足迹特征,分析罪犯的性别、年龄、身高、体态、行走姿势等个人形体特点,常称为给罪犯“画像”。这一技术在侦破案件中起了一定作用。（１）研究人在常态下行走时留在地面上的平面足迹反映出压力的分布和变化规律,分析压力与年龄的相关性,从中研究出分析年龄的科学方法,提高分析年龄的准确率。（２）研究平面足迹压力与人的性别、身高、体态、行走姿势的相关性找出各自的科学分析方法。（３）从分析理论上全面加以提高,     

摩擦过程中真实接触面积的灰色分析

灰色系统理论是近几年以随机过程为研究对象而形成和发展起来的，在农业和自动控制等方面的研究与应用发展较快．为了使这种理论应用于摩擦学研究领域，从光全反射测量和计算机数值计算两方面，考察了粗糙表面接触时真实接触面积的随机特性，指出摩擦过程中的真实接触面积是一种含有随机成分的变化量，研究目标应当侧重于真实接触面积的变化趋势和范围，而不是它的精确解．在此基础上，首次利用灰色系统理论，分别对静态和动态接触条件下真实接触面积的变化规律进行了灰色分析，建立了精度比较高的预测真实接触面积的灰色模型ＣＭ（１，１）．这种模型对动、静接触面积的计算值与实测值具有良好的一致性，可以用于动态跟踪描述摩擦过程中真实接触面积的变化规律     

Nontangential Limit of the Weyl m-Functions for the Ergodic Schrödinger Equation

This paper deals with the spectral and qualitative problems associated with the one-dimensional ergodic Schrödinger equation. Let A ₂ be the set of those energies for which the real projective flow admits an invariant linear measure with square integrable density function. On this set we calculate the directional derivative of the Floquet coefficient and prove the existence of a nontangential limit of the Weyl m-functions in the L ¹-topology. In particular, we verify that the known Dieft–Simon inequality for the derivative of the rotation number obtained from Kotani's theory is in fact an equality. In the bounded orbit case we deduce the uniform boundedness of the Weyl m-functions and obtain necessary and sufficient conditions to assure their uniform convergence.     

Spectral Properties of Schrödinger Operators on Domains with Varying Orders of Thinness

We consider the Schrödinger operator on two types of domains depending on a small parameter : dumbbell domains and thin domains with varying orders of thinness. In both situations we compare the eigenvalues and eigenvectors of the Schrödinger operator with the corresponding eigenvalues and eigenvectors of a limit operator defined on the limit domain.     

Variable Order and Distributed Order Fractional Operators

Many physical processes appear to exhibit fractional order behavior thatmay vary with time or space. The continuum of order in the fractionalcalculus allows the order of the fractional operator to be considered asa variable. This paper develops the concept of variable and distributedorder fractional operators. Definitions based on the Riemann–Liouvilledefinition are introduced and the behavior of the new operators isstudied. Several time domain definitions that assign different argumentsto the order q in the Riemann–Liouville definition are introduced. Foreach of these definitions various characteristics are determined. Theseinclude: time invariance of the operator, operator initialization,physical realization, linearity, operational transforms, and memorycharacteristics of the defining kernels.A measure (m ₂) for memory retentiveness of the order history isintroduced. A generalized linear argument for the order q allows theconcept of `tailored' variable order fractional operators whose m ₂ memory may be chosen for a particular application. Memory retentiveness (m ₂) andorder dynamic behavior are investigated and applications are shown.The concept of distributed order operators where the order of thetime based operator depends on an additional independent (spatial)variable is also forwarded. Several definitions and their Laplacetransforms are developed, analysis methods with these operators aredemonstrated, and examples shown. Finally operators of multivariable anddistributed order are defined and their various applications areoutlined.     

三峡库区滑坡的时空分布特征与成因探讨

三峡库区地质灾害频繁发生,地质历史上大型滑坡广泛发育。近年库区滑坡灾害有逐年增加趋势。这些滑坡形成的堆积体成因复杂,不能单纯从传统的外动力或内动力作用来解释,给库区灾害的防治工程带来了很大困难。三峡库区大型古滑坡主要沿长江干流和支流的深切河谷两岸分布,与河流发育演化史密切相关。15万年以来,长江三峡地区经历了新构造期以来抬升速率最快的一次构造幕,山原期夷平面上升了100m,河流强烈下切,形成高陡岸坡,卸荷效应显著;同时,该时期三峡地区的气候受到青藏高原环境变化的影响,在间冰期可能存在相似的暖湿古气候环境,降水极为丰富。三峡库区的大型古滑坡在新构造快速抬升时期广泛发育,并且与暖湿多雨期相对应,表明库区滑坡的发育演化是新构造运动和气候变化内外动力耦合作用的结果。     

Influence of cyclic loading on crack growth kinetics in a viscoelastic orthotropic plate made of a composite material

The kinetics of crack growth in a viscoelastic orthotropic plate made of a composite material is analyzed. The external load is the superposition of a cyclic load and a constant tensile load. The level of the tensile load is assumed to exceed the amplitude of the cyclic load. The kinetic curves are compared with the constant tension curves. The effect of the cyclic component is studied.Translated from Prikladnaya Mekhanika, Vol. 40, No. 9, pp. 116–122, September 2004.     

One approximate solution of the Nekrasov problem

An approximate solution ω = A[ω, μ] of the nonlinear integral Nekrasov equation is obtained by successive replacement of the kernel of the integral operator by a close one. The solution is sought not directly at the bifurcation point μ₁ = 3 of the linearized equation ω = μL[ω] but at the point μ = 1 at which operator A[ω, μ], remaining nonlinear in ω, is linear in μ. __________ Translated from Prikladnaya Mekhanika i Tekhnicheskaya Fizika, Vol. 48, No. 6, pp. 50–56, November–December, 2007.