A variational inequality formulation of equilibrium models for end-of-life products with nonlinear constraints

Variational inequality theory facilitates the formulation of equilibrium problems in economic networks. Examples of successful applications include models of supply chains, financial networks, transportation networks, and electricity networks. Previous economic network equilibrium models that were formulated as variational inequalities only included linear constraints; in this case the equivalence between equilibrium problems and variational inequality problems is achieved with a standard procedure because of the linearity of the constraints. However, in reality, often nonlinear constraints can be observed in the context of economic networks. In this paper, we first highlight with an application from the context of reverse logistics why the introduction of nonlinear constraints is beneficial. We then show mathematical conditions, including a constraint qualification and convexity of the feasible set, which allow us to characterize the economic problem by using a variational inequality formulation. Then, we provide numerical examples that highlight the applicability of the model to real-world problems. The numerical examples provide specific insights related to the role of collection targets in achieving sustainability goals.     

Variational Operators,Symplectic Operators,and the Cohomology of Scalar Evolution Equations

For a scalar evolution equation u_t = K(t, x, u, u_x, . . . , u_2m+1) with m ≥ 1, the cohomology space H^1,2() is shown to be isomorphic to the space of variational operators and an explicit isomorphism is given. The space of symplectic operators for u_t = K for which the equation is Hamiltonian is also shown to be isomorphic to the space H^1,2() and subsequently can be naturally identified with the space of variational operators. Third order scalar evolution equations admitting a first order symplectic (or variational) operator are characterized. The variational operator (or symplectic) nature of the potential form of a bi-Hamiltonian evolution equation is also presented in order to generate examples of interest.     

Geometrically distinct solutions for Klein–Gordon–Maxwell systems with super-linear nonlinearities

This paper is concerned with the following Klein–Gordon–Maxwell system $\left\{\begin{array}{c}-△u+V\left(x\right)u-(2\omega +\varphi )\varphi u=f(x,u),x\in {\mathbb{R}}^3,\hfill \\ △\varphi =(\omega +\varphi )u^2,x\in {\mathbb{R}}^3,\hfill \end{array}\right.$where $\omega >0$ is a constant, $V$ and $f$ are periodic with respect to $x$. By combining deformation type arguments, Lusternik–Schnirelmann theory and some new tricks, we prove that the above system admits infinitely many geometrically distinct solutions under weaker superlinear conditions instead of the common super-cubic conditions on $f$. Our result seems new and extends the previous results in the literature.     

An evaluation method for measuring SPL and mode shape of tire cavity resonance by using multi-microphone system

This paper presents an evaluation method for measuring the sound pressure level and mode shapes of tire cavity resonance by using a multi-microphone system. Two commercial tires were evaluated to compare abilities of noise suppression by means of this method in the range of the first resonance from 200 to 260 Hz. One tire was a special tire that suppresses tire cavity resonance with polyurethane foam mounted on the tire’s inner liner. The other tire was a normal tire with no polyurethane foam. The mode shape change from vertical to horizontal direction in both tires. However, the sound pressure level of the special tire was lower than the normal tire at all frequencies.     

A variational approach for a generalized emden-fowler equation

Existence of positive solutions of singular boundary value problems related to Emden-Fowler equation is proved. A general minimization theorem in Sobolev spaces is applied.     

Dynamics of the rotational degrees of freedom in an undercooled crystal of cyanoadamantane

Results of molecular dynamics are presented for a simple model of cyanoadamantane crystal. Rotator cubic phase was simulated over a wide range of temperatures. In this system, glass formation is not induced by quenched diluted disorder, but it occurs similarly to conventional glasses. Simulations have shown that the system evolves from free small-step rotational diffusion to jump like motion. The results obtained with this model are used to discuss the validity of the Mode Coupling Theory (MCT) predictions.     

广义Ekeland变分原理的推广

给出了经典Ekeland变分原理的一个推广,完善并改进了已有文献的证明,并把它推广到了拟度量空间上.     

服装工程师人才培养模式的研究与构建

本文分析国家对工程人才培养的标准和要求,考虑企业对服装人才的需求,体现"突出基础,加强实践,注重创新,持续发展,提倡科技,重视生态,多样优化,国际视野"的学生培养指导思想,结合学校以工科为背景,以纺织服装为特色,及为纺织服装行业培养高级应用型专门人才进行定位,对服装专业的应用型工程师培养模式进行分析和研究,提出"3+1四模块"服装人才培养体系,完成课程体系、实践教学体系、企业培养方案构建,为全面提高服装人才的工程化培养提供了可行的实施办法.