An Almost Sure Result on Sampling of Bandlimited Random Signals

The Shannon-Nyquist sampling theorem for deterministic signals is a fundamental result in the field of telecommunication and signal processing, and many re- sults on this topic have been obtained. However, very few results on random signals have been published, after Kol- mogorov mentioned the importance of Shannon-formula for stochastic signals in 1956. In this paper, following the almost sure result for bandlimited stochastic processes pro- posed by Seip in 1990, we give an almost sure result of the classical sampling theorem for bandlimited random signals with local average sampling.     

UNIQUENESS CONDITIONS OF CL-STRUCTURES IN GL-STRUCTURE EQUIVALENCE CLASSES OF SYSTEM RECONSTRUCTABILITY ANALYSIS

This paper first introduces the basic notions of overall systems with logical relations, their subsystems, structure representation graphs, sets of H-structures and G-structures with logical relations S _H ^L and S _G ^L, immediate refinement and aggregate with logical relations, structure-graph mappings r_V ^L, r_G ^L, etc., and the notions of inclusiveness with logical relations, upper bounding and lower bounding with logical relations. Then it proves the sufficient conditions under which representation graphs R ^L form a lattice. By defining the least upper bound and largest lower bound of (R^L, ) and recommending a lemma on distributivity, this paper proves the sufficient conditions under which G-structures with logical relations form Boolean lattices. Finally after defining the M-structures and C-structures with logical relations, i.e. M-structures and C-structures, this paper proposes the sufficient conditions for the uniqueness of C-structures in G-structure equivalence classes, and proves that the C ^L-structure is the least refined GL-structure in equivalence class S _G ^L/r _G ^L.     

MSVL程序的自动定理证明方法

The MSVL is a temporal logic programming language. It can be used to verify C, Verilog/VHDL programs. To do so, a program written in C or Verilog/VHDL is translated to an MSVL program, and then the task is changed to verify MSVL programs. However, at present, the correctness of MSVL programs can only be proved by hand with deductive approaches. This is tedious and error-prone. To handle this problem, an automatic theorem proving technique for the MSVL based on the interactive theorem prover PVS is proposed. To this end, first the syntax and semantics of the MSVL are described in the specification language of PVS, which enables MSVL programs to be correctly recognized by PVS. Further, an axiomatic system of the MSVL and some theorems are specified. Then the proof commands of PVS are input for invoking the PVS prover to deduce MSVL programs. During verification, simple details can be proved by PVS automatically while complex steps are controlled by human. In this way, MSVL programs can be verified semi-automatically, which facilitates the deduction of MSVL programs. An instance of the bakery algorithm is given to show that our method is feasible.     

Throwing Some Light on the Vast Darkness that is Analysis: Niels Henrik Abel's Critical Revision and the Concept of Absolute Convergence

During the first half of the nineteenth century, mathematical analysis underwent a transition from a predominantly formula-centred practice to a more concept-centred one. Central to this development was the reorientation of analysis originating in A ugustin- L ouis C auchy's (1789–1857) treatment of infinite series in his Cours d'analyse . In this work, C auchy set out to rigorize analysis, thereby critically examining and reproving central analytical results. One of C auchy's first and most ardent followers was the Norwegian N iels H enrik A bel (1802–1829) who vowed to shed some light on the vast darkness in analysis.
This paper investigates some important aspects of A bel's contribution to the reorientation in analysis. In particular, it stresses the role for critical revision in the process of rigorization. By critically examining past practice, the new practice sought to explain the relative success of the previous—now outdated—approach. This is illustrated by discussing a number of issues related to A bel's new proof of the binomial theorem (1826) including his reactions to the exception that he encountered to one of the central theorems of C auchy's theory.
Following this discussion, the formation of new concepts as the result of critical revisions is illustrated by analysing the early history of the concept of absolute convergence. Thereby, it is shown how a new concept was distilled, investigated, put to use and eventually superseded.     

Analysis of thermo-elastic plates based on Reissner’s mixed variational theorem

Analysis of composite/sandwich plates under thermal loads has greater significance due to its extensive application in ocean and aerospace structures. This paper addresses the analysis of composite/sandwich plates under thermal load using layer-wise mixed finite element method. The Reissner mixed variational theorem (RMVT) has been used for the thermal analysis of plates. Transverse stress assumptions are made in the framework of RMVT and the resulting finite element describes a priori inter-laminar continuous transverse shear and normal stresses. This method is equally applicable to the analysis of plates under mechanical and thermal loads. Numerical examples are solved to validate the present formulation using a code developed in C-language and the results obtained with the present model are in good agreement with the analytical solutions available in literature.     

Stochastic analysis of shock process and modeling of condition-based maintenance

The paper presents an analytical formulation for evaluating the maintenance cost of engineering systems that are damaged by shocks arriving randomly in time. The damage process is nonlinear in a sense that damage increments form an increasing sequence (i.e., accelerated damage) or a decreasing sequence (saturated damage) of random increments. Such processes are motivated from damage data collected from nuclear reactor components. To model the nonlinear nature of damage process, the paper proposes the use of non-homogeneous Poisson process for damage increments, which is in contrast with the common use of a renewal process for modeling the damage. The paper presents a conceptually clear and comprehensive derivation of formulas for computing the expected cost rate associated with a periodic inspection and preventive maintenance policy. Distinctions between the analysis of self-announced and latent failures are highlighted. The analytical model presented in this paper is quite generic and versatile, and it can be applied to optimize other types of maintenance policies.     

分形图形在包装设计中的应用研究

从构图独特、神奇美丽又变幻莫测的分形图形出发,首先介绍了分形的概念,然后分析了分形图形对称与均衡、节奏与韵律等的艺术美特征。在此基础上,从包装的促销功能出发,研究了分形图形用于包装设计的可行性。最后通过几款包装设计作品,用实例展示了分形图形用于包装的独特性和促销性。     

几类边值问题的正解

本文利用存在性定理,考察了二阶常微分方程两点、三点以及m-点边值问题正解的存在性.在较弱的条件下,给出了几类边值问题至少有一个正解存在的充分性条件.所得结果改进和推广了文献中的相应结论.     

条形基础荷载对边坡稳定性影响与加固研究

西部山区土地资源贫乏,为了合理地利用土地资源经常在边坡上修筑各类建筑物与构筑物,由于基础荷载会影响边坡的稳定性,荷载过大甚至会引起滑坡,造成生命与财产的重大危害。对此,以坡顶条形基础荷载作用于边坡稳定性为研究模型,应用 M-C 线性破坏准则结合极限分析上限定理,分析附加应力对边坡稳定性的影响。对于稳定性较差的土质边坡,采用抗滑桩进行超前支护,研究地震荷载作用下超前支护桩加固边坡的抗力荷载、临界屈服加速度的影响因素。为坡顶条形基础荷载下边坡稳定性分析与超前支护设计提供一种合理的计算方法。     

用Excel辅助高职数学教学的实践与探索

Excel不仅是一款优秀的办公自动化软件,而且可以较好地辅助于高职数学教学。通过大量实例,以图表的方式列举了Excel在讲解两个重要极限、零点定理、研究函数性态和计算曲边梯形面积时的具体操作。