De Morgan classifying toposes

We present a general method for deciding whether a Grothendieck topos satisfies De Morgan's law (resp. the law of excluded middle) or not; applications to the theory of classifying toposes follow. Specifically, we obtain a syntactic characterization of the class of geometric theories whose classifying toposes satisfy De Morgan's law (resp. are Boolean), as well as model-theoretic criteria for theories whose classifying toposes arise as localizations of a given presheaf topos.     

Opération de la cohomologie elliptique définie par l'opérateur de Hecke T2

In this Note we show that isomorphism of formal group law classification, naturality of C-oriented multiplicative cohomology theories, and the strict isomorphism between the formal group law associated to Tate's curve and the multiplicative one, give a stable cohomology operation of degree 0 for elliptic cohomology of level 2, which induces the Hecke operator T₂ on coefficient group.     

Vortex dynamics for the nonlinear wave equation

Vortex dynamics for the nonlinear wave equation is a typical model of the “particle and field” theories of classical physics. The formal derivation of the dynamical law was done by J.Neu. He also made an interesting connection between vortex dynamics and the Dirac theory of electrons. Here we give a rigorous mathematical proof of this natural dynamical law. © 1999 John Wiley & Sons, Inc.     

The scope of Feferman’s semi-intuitionistic set theories and his second conjecture

The paper is concerned with the scope of semi-intuitionistic set theories that relate to various foundational stances. It also provides a proof for a second conjecture of Feferman’s that relates the concepts for which the law of excluded middle obtains to those that are absolute with regard to the relevant test structures, or more precisely of ${\Delta }_1$ complexity. The latter is then used to show that a plethora of statements is indeterminate with respect to various semi-intuitionistic set theories.     

Realisierung formaler Gruppen durch Kohomologiefunktoren

To any multiplicative cohomology theory h with the property that complex line bundles are h-oriented corresponds a formal group law F(X,Y) over the ring h(pt) which describes the Euler class of a tensor product of line bundles by means of the Euler classes of its factors. We consider this formal group as an invariant of h and give sufficient conditions under which a morphism between formal groups of cohomology theories h,k can be extended in one and only one way to a transformation of theories hk. Some typical applications will be discussed.     

云南省就业问题的趋势与控制模型研究

基于因果关系理论、因子分析理论、协整分析、自回归分布滞后模型和误差修正模型,对云南省就业问题进行了研究.建立了云南省就业的趋势和控制模型,揭示了云南省就业发展的内在规律及其与各宏观因素之间的系统作用关系.     

Dynamic crack propagation in a 2D elastic body: The out-of-plane case

Already in 1920 Griffith has formulated an energy balance criterion for quasistatic crack propagation in brittle elastic materials. Nowadays, a generalized energy balance law is used in mechanics [F. Erdogan, Crack propagation theories, in: H. Liebowitz (Ed.), Fracture, vol. 2, Academic Press, New York, 1968, pp. 498-586; L.B. Freund, Dynamic Fracture Mechanics, Cambridge Univ. Press, Cambridge, 1990; D. Gross, Bruchmechanik, Springer-Verlag, Berlin, 1996] in order to predict how a running crack will grow. We discuss this situation in a rigorous mathematical way for the out-of-plane state. This model is described by two coupled equations in the reference configuration: a two-dimensional scalar wave equation for the displacement fields in a cracked bounded domain and an ordinary differential equation for the crack position derived from the energy balance law. We handle both equations separately, assuming at first that the crack position is known. Then the weak and strong solvability of the wave equation will be studied and the crack tip singularities will be derived under the assumption that the crack is straight and moves tangentially. Using the energy balance law and the crack tip behavior of the displacement fields we finally arrive at an ordinary differential equation for the motion of the crack tip.     

Describing a Basis in Semireduced Form for Inference Rules of Intuitionistic Logic

It is shown that a set of all rules in semireduced form whose premises satisfy a collection of specific conditions form a basis for all rules admissible in IPC. The conditions specified are quite natural, and many of them show up as properties of maximal theories in the canonical Kripke model for IPC. Besides, a similar basis is constructed for rules admissible in the superintuitionistic logic KC, a logic of the weak law of the excluded middle.     

可拓营销理论研究

利用物元理论、事元理论和可拓集合理论 ,对需要、产品、市场、资源、企业等进行可拓分析 ,提出可拓营销的基本理论——产品开拓规律、可拓市场、可拓资源、健全企业等     

Well-posedness Results for Models of Elastomers

Existence and uniqueness of weak solutions are shown for different models of the dynamic behavior of elastomers. The models are based on a nonlinear stress-strain relationship (satisfying a locally Lipschitz and affine domination property) and incorporate hysteretic effects as well. The results provide alternatives to previous theories that required monotonicity assumptions on the nonlinearities. Results with a nonlinear constitutive law and nonlinear internal dynamics are presented for the first time.     

A nonlocal higher-order model including thickness stretching effect for bending and buckling of curved nanobeams

An analytical approach for static bending and buckling analyses of curved nanobeams using the differential constitutive law, consequent to Eringen’s strain-driven integral model coupled with a higher-order shear deformation accounting for through thickness stretching is presented. The formulation is general in the sense that it can be deduced to examine the influence of different structural theories, for static and dynamic analyses of curved nanobeams. The governing equations derived using Hamiltons principle are solved in conjunction with Naviers solutions. The formulation is validated considering problems for which solutions are available. A comparative study is made here by various theories obtained through the formulation. The effects various structural parameters such as thickness ratio, beam length, rise of the curved beam, and nonlocal scale parameter are brought out on bending and stability characteristics of curved nanobeams.     

Asymptotics for stochastic reaction–diffusion equation driven by subordinate Brownian motion

We study the ergodicity of stochastic reaction–diffusion equation driven by subordinate Brownian motion. After establishing the strong Feller property and irreducibility of the system, we prove the tightness of the solution’s law. These properties imply that this stochastic system admits a unique invariant measure according to Doob’s and Krylov–Bogolyubov’s theories. Furthermore, we establish a large deviation principle for the occupation measure of this system by a hyper-exponential recurrence criterion. It is well known that S(P)DEs driven by $\alpha$-stable type noises do not satisfy Freidlin–Wentzell type large deviation, our result gives an example that strong dissipation overcomes heavy tailed noises to produce a Donsker–Varadhan type large deviation as time tends to infinity.     

On the transfer matrix of a MIMO system

We develop a deterministic ab initio model for the input–output relationship of a multiple‐input multiple‐output (MIMO) wireless channel, starting from the Maxwell equations combined with Ohm's law. The main technical tools are scattering and geometric perturbation theories. The derived relationship can lead us to a deep understanding of how the propagation conditions and the coupling effects between the elements of multiple‐element arrays affect the properties of an MIMO channel, e.g. its capacity and its number of degrees of freedom. Copyright © 2011 John Wiley & Sons, Ltd.     

Homogenization with the Quasistatic Tresca Friction Law:Qualitative and Quantitative Results

Modeling of frictional contacts is crucial for investigating mechanical performances of composite materials under varying service environments.The paper considers a linear elasticity system with strongly heterogeneous coefficients and quasistatic Tresca friction law,and studies the homogenization theories under the frameworks of H-convergence and small ε-periodicity.The qualitative result is based on H-convergence,which shows the original oscillating solutions will converge weakly to the homogen...     

Maximum friction law in plasticity

The maximum friction law postulates that the friction stress is equal to the maximum possible shear stress admissible by the constitutive equations. The boundary value problems including the maximum friction stress as a boundary condition reveal special mathematical features which are of interest in the development of theories and models, numerical simulation and engineering applications. The present paper shortly reviews the singularity in velocity fields that can occur in the vicinity of maximum friction surfaces. A large class of rigid plastic (in a broad sense that the elastic portion of the strain rate tensor is neglected) is considered. (© 2006 WILEY-VCH Verlag GmbH & Co. KGaA, Weinheim)     

湍流的Markov过程理论与Kolmogoroff理论的联系以及对制Kolmogoroff定律的推广——Ⅰ.对两个理论关系的分析

本文全文分为两部分(Ⅰ和Ⅱ).第Ⅰ部分讨论了关于大雷诺数湍流的两种理论——拉格朗日观点的Markov过程理论与欧拉观点的Kolmogoroff理论之间的联系.指出:对位置和速度的联合过程进行Markov描述所需雷诺数与Kolmogoroff第二相似性假设所需雷诺数同样大;周期与T_u和T_f同阶的旋涡分别对应于Kolmogoroff理论的含能范围与耗损范围;Richarson定律的适用范围T_*≤t≤β-1对应于Kolmogoroff理论的惯性子范围,从而指出,两种理论从不同侧面反映了大雷诺数湍流的流场结构.在本文第Ⅱ部分,我们将利用第Ⅰ部分中阐述的物理想法以适当方式建立两种理论之间的某种定量的联系.从而由拉格朗日观点的弥散运动的结果得出欧拉观点的结构函数、关联函数和能谱函数.所得结果不但适用于惯性子范围,而且适用于尺度更大(或波数更小)的全部范围.熟知的Kolmogoroff“2/3定律”和“(-5)/3定律”为本结果在惯性子范国的渐近解.因而本结果是Kolmogoroff“2/3定律”和“(-5)/3定律” 的推广.     

Damping sources interactions in impact of viscoelastic composite plates with damping treated SMA wires,using a hyperbolic plate theory

In the present paper, a comprehensive study is made on effects of the viscoelastic and the phase-transformation-based dissipations and their interactions on impact responses of viscoelastic composite plates with damping treated (structural hierarchy) shape memory alloy (SMA) wires, for the first time. In contrast to almost all of the available researches, a high-order hyperbolic plate theory that includes not only odd but also even functions of the transverse coordinate, is proposed and employed here. While a hierarchical viscoelastic constitutive law is employed for both the orthotropic and SMA materials, Brinson's constitutive law is refined to include the loading fluctuations and structural hierarchy of the SMA wire, simultaneously. The traditional Hertz and Yang-Sun contact laws are modified accordingly. The resulting highly nonlinear piecewise-defined integro-differential finite element governing equations are solved by an iterative algorithm within each time step. The presented discussions show that in contrast to the common belief, the zero-shear traction condition on the top and bottom surfaces of the viscoelastic orthotropic plate cannot be satisfied by the available plate theories, even for the symmetric lamination schemes. Results show that the viscoelasticity and phase-transformation effects on the resulting dynamic responses are more pronounced for the low and high energy impacts, respectively.     

A note on the integration of competing psychophysical theories

Virtually from its inception psychophysics has been caught on the horns of the dilemma as to the proper form of the fundamental psychophysical law. This paper illustrates an integration of two competing theories.     

一类不确定广义周期时变系统的鲁棒H_∞控制

本文研究了状态矩阵具不确定性广义周期时变系统的鲁棒H∞控制问题.利用线性矩阵不等式(LMI)方法,在给出不确定广义周期时变系统广义可镇定和广义二次可镇定且具有H∞性能指标概念的基础上,得到了该系统广义二次可镇定且具有H∞性能指标γ的充要条件,并给出了相应的鲁棒H∞状态反馈控制律的设计方法,推广了周期系统的鲁棒控制理论结果.最后,通过数值算例说明了设计方法的有效性.