The Topological Structure of Subseries Convergence

Let E be an abstract set, G be an Abelian topological group, FEG and be afamily of subsets of F. Let the sequence {xj}E be subseries aF convergent. In this paper,we present a sufficient and necessary condition for {xj} to be also subseries convergent in thetopology of uniform convergence on the sets in ,     

Planning the Restoration of an Open-cast Coal Site

This paper describes an operational research approach to planning the restoration of an open-cast coal site.No established operational research technique exactly fitted the problem, which was one of planning a large-scale earth-moving operation, where the quantities to be moved were not specified, but had to be planned to conform with stringent restrictions on gradients, continuity, drainage and total volume. A numerical technique was developed, used in conjunction with the dual solutions of successive transportation programmes to reach progressively an optimum solution.The nature of the problem allowed an unusually clear-cut comparison to be made between the previous conventional plan and the operational-research-based plan; the latter showed considerable savings and was put into practice.There would appear to be many other situations where the approach could be applied.     

Artinian ring and amalgamated algebra along an ideal

Let R and S be two commutative rings with unity, let I be an ideal of S and $$\varphi : R \longrightarrow S$$ be a ring homomorphism. In this paper, we give a characterization for the the amalgamated algebra $$R \bowtie ^\varphi I$$ to be an Artinian ring.     

任意角可以m等分的条件

设 p是任意奇素数 ,证明了任意角不能通过圆规直尺作图 p等分 .进而证明了任意角可以 m等分的充要条件是 m是 2的方幂     

Einstein 4-manifolds and nonpositive isotropic curvature

We give conditions for the linear span of the positive L-weakly compact (resp. M-weakly compact) operators to be a Banach lattice under the regular norm, for that Banach lattice to have an order continuous norm, to be an AL-space or an AM-space.     

ON THE SPECTRAL PROPERTIES OF M-MATRICES AND ITS APPLICATIONS

1.IntroductionAndPreliminariesThespectralpropertiesofM-matricesplayanimportantroleinnonnegativemainstheory,andhavebeenappliedtostudythenumericalsolutionoflinearsystems.Recentlylmanyarticleshavediscussedwiththistopics(see[l--5]).ThepurposeofthispaperistoestablishthespectralinequalitiesofsingularM-matrices.ByapplyingthesepropertiesweanswerpartiallyanopenproblemandsolveanopenproblemposedbySchneiderin[4,5],somerecelltresultI2'4'6]onsplittingsofanM-matrixarealsoimproved.Allnotationsanddefinitio…     

ESS,NIS and GIS for matrix games in n‐species systems

In this paper, we discuss the concepts of evolutionarily stable strategy (ESS), neighborhood invader strategy (NIS) and global invader strategy (GIS) in n‐species systems. We give their definitions both on system level and species level. Although the definition on system level and that on species level are apparently different, it is found that they are equivalent to one another. About the relationships among an ESS, an NIS and a GIS for n‐species systems, we obtain the results similar to the ones for single species models: a GIS must be an NIS; an NIS must be an ESS; an ESS may not be a GIS; a GIS must be unique. The stability in the frequency dynamics with two phenotypes is also considered and the global stability of a GIS is shown. Copyright © 2010 John Wiley & Sons, Ltd.     

Practically Equal: An Analysis of the Practical Nature of Equality and Incomparability

There exists an ongoing debate about the nature of incomparability. In this paper, I argue that incomparability is most usefully seen as a practical, rather than a metaphysical, issue. When confronted with an important choice between two options, an agent often will be at a loss as to how to decide between them. A common response to this problem is to assert that the options must therefore be equal, and that it is perfectly rational to be indifferent and decide between them in some arbitrary fashion. Contrary to this common view, this paper shows that equality should be seen as the result of indifference and not the cause of it. I will show that the judgment between whether options are either equal or incomparable is actually a decision, made by an agent, that can in turn be judged as more or less rational.     

用最少的虚工序构建等效多阶段工序网络

运用网络计划可以直观地表示项目管理中的诸多疑难问题, 便于分析和求解. 但是它也存在明显的缺点, 如, (1) 工序网络的有向无回路性表明很多时候适合运用动态规划法, 但它在通常情况下的无阶段性使得该方法无法直接应用; (2) 任意构建的工序网络容易表现得错综复杂, 不利于研究; (3) 用最少的虚工序表示双代号网络是NP-难问题, 因此对一个工序系统可能构建出多个差别迥异的工序网络, 有碍于进度计划管理研究, 等等. 如果能将工序网络构建成等效的多阶段网络, 各工序分别表示在相应的阶段中, 无疑有助于上述问题的解决. 构建等效多阶段工序网络需要添加虚工序. 通过添加最少的虚工序将工序网络构建成等效多阶段网络, 从而有助于建立更合理的工序网络表示法.     

SOME THEOREMS ON CONVEX HYPERSURFACES IN AN AFFINE SPACE

Let M and M~* be hypersurfaces in an affine space A~(n+1) of dimension n+1. The main results of this paper are the following:(1) Two types of integral formulas for M and M~*.(2) Some conditions for an affine convex hypersurface to be an affine sphere.(3) Some conditions for M and M~* to be different only by an affine transformation or a translation.     

A Note on S-Nakayama’s Lemma

Ukrainian Mathematical Journal - We propose an S-version of Nakayama’s lemma. Let R be a commutative ring, let S be a multiplicative subset of R, and let M be an S-finite R-module. Also let I...     

On imaging obstacles inside inhomogeneous media

We show that an obstacle inside a known inhomogeneous medium can be determined from measurements of the scattering amplitude at one frequency, without a priori knowledge of the boundary condition. We also show that an obstacle inside a known inhomogeneous anisotropic conducting medium can be determined from electrostatic current and voltage measurements on the boundary of a domain containing the obstacle. Moreover, two obstacles with boundary measurements which are merely comparable as operators must be identical. The first part of the paper gives an extension of the factorization method which may be of independent interest and also yields a new reconstruction procedure.     

Using origami boxes to explore concepts of geometry and calculus

The purpose of this classroom note is to provide an example of how a simple origami box can be used to explore important concepts of geometry and calculus. This article describes how an origami box can be folded, then it goes on to describe how its volume and surface area can be calculated. Finally, it describes how the box could be folded to maximize the surface area and the volume.     

关于Sigma-Pi神经网络中的逼近问题

研究Ｒ上不连续函数可作为Ｓｉｇｍａ－Ｐｉ神经网络激励函数的条件,给出了Ｒ一局部黎曼可积函数可作为Ｓｉｇｍａ－Ｐｉ神经网络激励函数的特征条件,本文的结果表明：局部黎曼可积函数作为Ｓｉｇｍａ－Ｐｉ神经网络激励函数的特征条件与连续函数时的情形是一致的。     

New results on the parametric stability of nonlinear systems

In this paper, we derive some new results on the parametric stability of nonlinear systems. Explicitly, we derive a necessary and sufficient condition for a nonlinear system to be locally parametrically exponentially stable at an equilibrium point. We also derive a necessary condition for the nonlinear system to be locally parametrically asymptotically stable at an equilibrium point. Next, we derive some new results on the parametric stability of discrete-time nonlinear systems. As in the continuous case, we derive a necessary and sufficient condition for a discrete-time nonlinear system to be locally parametrically exponentially stable at an equilibrium point. We also derive a necessary condition for the discrete-time nonlinear system to be locally parametrically asymptotically stable at an equilibrium point. We illustrate our results with some classical examples from the bifurcation theory.     

Appropriate use of a CAS in the teaching and learning of mathematics

If the use of a computer algebra system (CAS) is to be meaningful and have an impact on students, then it must be grounded in good pedagogy and have some clearly defined goals. It is the authors' belief that an important goal for teaching mathematics with the CAS is that courses be designed so that students can become active participants in their learning experience, planning the problem-solving strategies and carrying them out. The CAS becomes an important tool and a partner in this learning process. To this end, here the authors' have linked the use of the CAS to an existing classification scheme for Mathematical Tasks, called the MATH Taxonomy, and illustrated, through concrete examples, how the goals of teaching and learning of mathematics can be set using this classification together with the CAS.     

A transport model for the evolution of urban systems

When comparing an urban system to an elasto-plastic lattice, an analogy to the solid state of matter can be exploited using the concepts of the band theory similarly. Thereafter, the population dynamics – in a region of certain stability in the state space and within appropriate energy bands – can be described in terms of Cellular Automata, with two mobile agents or pseudo particles: the inhabitant (representative of an average individual) and the recurson (representative of its multidimensional resources). As in the solid state, transition rules take the form of two coupled transport equations, comprising the terms equivalent to the generation-recombination and circulation processes. The first process can be compared to a predator–prey growth model, typical of Ecology; whereas the circulation process – composed of a drift component and a diffusion component – should be compared to the concentration-sprawl demographic balance seen in urban occupation and dynamics. Thus, it needs to be defined and determined an urban potential function, an equivalent population charge, mobility and diffusion parameters, as well as net growth factors. This analogy, discussed within the context of a case study for Great Mendoza, plausibly explains the varied growth rates of the political departments, as well as the principal urban trends for spatial occupation.     

On the representation of localized functions in ℝ2 by the Maslov canonical operator

We prove that localized functions can be represented in the form of an integral over a parameter, the integrand being the Maslov canonical operator applied to an amplitude obtained from the Fourier transform of the function to be represented. This representation generalizes an earlier one obtained by Dobrokhotov, Tirozzi, and Shafarevich and permits representing localized initial data for wave type equations with the use of an invariant Lagrangian manifold, which simplifies the asymptotic solution formulas dramatically in many cases.     

Estimation for a marginal generalized single-index longitudinal model

In this paper, we suggest an estimating equations based approach to study a general single-index model with a given out-layer link for longitudinal data and treat the classical one as its special case. Within a wide range of bandwidths which is for estimating the inner-layer nonparametric link, the root-n consistency of the estimator of the index can be proved. The estimation efficiency can be achieved even when there is an infinite-dimensional nuisance parameter to be estimated. The performance of the new method is assessed through the comparison with other existing methods and through an application to an epileptic seizure study.     

The plane wave expansion, infinite integrals and identities involving spherical Bessel functions

This paper shows that the plane wave expansion can be a useful tool in obtaining analytical solutions to infinite integrals over spherical Bessel functions and the derivation of identities for these functions. The integrals are often used in nuclear scattering calculations, where an analytical result can provide an insight into the reaction mechanism. A technique is developed whereby an integral over several special functions which cannot be found in any standard integral table can be broken down into integrals that have existing analytical solutions.