On Polynomial Functions over Finite Commutative Rings

Let R be an arbitrary finite commutative local ring. In this paper, we obtain a necessary and sufficient condition for a function over R to be a polynomial function. Before this paper, necessary and sufficient conditions for a function to be a polynomial function over some special finite commutative local rings were obtained.     

Hyers–Ulam–Rassias stability of Cauchy equation in the space of Schwartz distributions

We reformulate and prove the Hyers–Ulam–Rassias stability of Cauchy equation in the space of Schwartz tempered distributions and Fourier hyperfunctions.     

The Computational Complexity of the Chow Form

We present a bounded probability algorithm for the computation of the Chowforms of the equidimensional components of an algebraic variety. In particular, this gives an alternative procedure for the effective equidimensional decomposition of the variety, since each equidimensional component is characterized by its Chow form. The expected complexity of the algorithm is polynomial in the size and the geometric degree of the input equation system defining the variety. Hence it improves (or meets in some special cases) the complexity of all previous algorithms for computing Chow forms. In addition to this, we clarify the probability and uniformity aspects, which constitutes a further contribution of the paper. The algorithm is based on elimination theory techniques, in line with the geometric resolution algorithm due to M. Giusti, J. Heintz, L. M. Pardo, and their collaborators. In fact, ours can be considered as an extension of their algorithm for zero-dimensional systems to the case of positive-dimensional varieties. The key element for dealing with positive-dimensional varieties is a new Poisson-type product formula. This formula allows us to compute the Chow form of an equidimensional variety from a suitable zero-dimensional fiber. As an application, we obtain an algorithm to compute a subclass of sparse resultants, whose complexity is polynomial in the dimension and the volume of the input set of exponents. As another application, we derive an algorithm for the computation of the (unique) solution of a generic overdetermined polynomial equation system.     

On the Global Stability of Solutions of Moment Systems in Nonequilibrium Thermodynamics

In this paper, we study the linearization of the Cauchy problem and the mixed problem for the system of Grad--Hermite moments in nonequilibrium thermodynamics in the neighborhood of the equilibrium state. Stability conditions for solutions of the Cauchy problem are proved as a generalization of the classical Hermite--Biller theorem on stable polynomials. For the mixed problem, we prove an analog of the Vishik--Lyusternik theorem on small singular perturbations of general elliptic problems. The last observation allows us to introduce the Shapiro--Lopatinskii condition, which implies the well-posedness of the mixed problem.     

Essential domains and two conjectures in dimension theory

This note investigates two long-standing conjectures on the Krull dimension of integer-valued polynomial rings and of polynomial rings in the context of (locally) essential domains.

     

Quadratic Integrals of Motion for the Systems of Identical Particles

The dynamical systems of identical particles admitting quadratic integrals of motion are classified. The relevant integrals are explicitly constructed and their relation to separation of variables in Hamilton-Jacobi equation is clarified.     

Layout-Specific Circuit Evaluation in 3-D Integrated Circuits

In this paper, we describe a comprehensive layout methodology for bonded three-dimensional integrated circuits (3D ICs). In bonded 3D integration technology, parts of a circuit are fabricated on different wafers, and then, the wafers are bonded with a glue layer of Cu or polymer based adhesive. Using our layout methodology, designers can layout such 3D circuits with necessary information on inter-wafer via/contact and orientation of each wafer embedded in the layout. We have implemented the layout methodology in 3DMagic. Availability of 3DMagic has led to interesting research with a wide range of layout-specific circuit evaluation, from performance comparison of 2D and 3D circuits to layout-specific reliability analyses in 3D circuits. Using 3DMagic, researchers have designed and simulated an 8-bit encryption processor mapped into 2D and 3D FPGA layouts. Moreover, the layout methodology is an essential element of our ongoing research for the framework of a novel Reliability Computer Aided Design tool, ERNI-3D.     

如何提高电子产品的可靠性

主要介绍了电子产品在研制、生产、试验中的可靠性工作。     

高入纤功率光纤通信系统的可靠性研究

掺铒光纤放大器(EDFA)和拉曼放大器(FRA)的使用,使得光纤通信系统中的入纤功率有了很大的提高.较高的入纤功率不仅会在光纤中引起各种非线性效应,对光脉冲的传输产生影响,也会对光纤本身的可靠性产生影响,为此介绍了高入纤功率对光纤系统的影响,分析了其产生的机理,并提出了应对措施.     

电力调度自动化系统实用化应用

介绍了县级电网调度自动化系统的实用化应用，包括系统结构，功能特点以及保证系统安全运行的技术经验．