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《Mathematical and Computer Modelling》2000,31(10-12):157-163
An auto-sleep system is defined by the following two properties:
- 1.(i) a call for the system occurs randomly and intermittently
- 2.(ii) the system automatically goes to sleep if there occurs no call during a prespecified time T.
- 1.(a) sleep
- 2.(b) warm-up
- 3.(c) nonusage
- 4.(d) usage.
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《Topology and its Applications》1988,28(3):181-193
The following are consequences of the main results in this paper:
- 1.(1) The number of countably compact, completely regular spaces of density κ is 222κ.
- 2.(2) There are 22κ points in U(κ) (= space of uniform ultrafilters on κ), each of which has tightness 2κ in U(κ) and is a limit point of a countable subset of U(κ).
- 3.(3) There are 22κ points in U(κ), each of which has tightness 2κ and is a weak P-point of κ1.
- 4.(4) For each λ ⩽ κ there are at least 22λ · κ points in βκ, each of which has tightness 2λ in β κ and is a weak P-point of κ1. Moreover, under GCH there are at least 22λ · κλ such points.
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《Mathematical and Computer Modelling》1997,25(5):13-58
The overall flotation deinking process can be divided into four basic microprocesses:
- 1.(1) collision or capture of an (ink) particle by an air bubble
- 2.(2) adhesion of an (ink) particle to the air bubble by sliding
- 3.(3) development of a three-phase contact at the air bubble/water/particle interface, and
- 4.(4) bubble/particle stability or instability after an aggregate is formed each of these microprocesses have an associated probability that they will occur successfully in a flotation cell.
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《Topology and its Applications》1988,28(2):141-145
In this paper, we find subspaces of the Pixley-Roy space on the irrationals which are
- 1.(1) a first countable ccc space which does not have a σ-linked base,
- 2.(2) for each n>1, a first countable space which has a σ-n-linked base but which does not have a (σ−n+1)-linked base and
- 3.(3) a first countable space which has, for each n>1, a σ-n-linked base but which does not have a σ-centered base.
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《Mathematical and Computer Modelling》2000,31(10-12):81-88
For second-hand products sold with warranty, the expected warranty cost for an item to the manufacturer, depends on
- 1.(i) the age and/or usage as well as the maintenance history for the item
- 2.(ii) the terms of the warranty policy.
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《Mathematical and Computer Modelling》1997,25(3):81-90
We consider a scheduling problem in which n jobs are grouped into F groups and are to be processed on a single machine. A machine setup time is required when the machine switches from one group of jobs to the other. All jobs have a common due date that needs to be determined. The objective is to find an optimal common due date and an optimal sequence of jobs to minimize the sum of the cost of tardy jobs and the cost related to the common due date. We consider two cases:
- 1.(i) the jobs have to be processed in groups; and
- 2.(ii) the jobs do not have to be processed in groups.
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James R. Clay 《BIT Numerical Mathematics》1970,10(3):249-265
In this paper we wish to show how the computer has played a valuable role in research in the theory of near-rings. Basically, the author has used the computer to generate examples of near-rings to be applied for meaningful conjectures and counter-examples. All the near-rings of order less than eight are listed in [2]. Since there is only one non-abelian group of order less than eight, it is natural to still be curious what happens when one tries to construct a near-ring from a non-abelian group. The methods used by the author to construct near-rings from groups will be illustrated on the two non-abelian groups of order 8. Specifically, for each non-abelian group of order 8, it was decided to construct all near-rings enjoying one of the following four properties:
- near-ring with identity:
- near-rings without two-sided zero;
- near-rings with no zero divisors;
- idempotent near-rings; i.e. near-rings for whichx 2=x for allx.
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《Annals of Pure and Applied Logic》1999,96(1-3):89-105
We consider the common-knowledge paradox raised by Halpern and Moses: common knowledge is necessary for agreement and coordination, but common knowledge is unattainable in the real world because of temporal imprecision. We discuss two solutions to this paradox:
- 1.(1) modeling the world with a coarser granularity, and
- 2.(2) relaxing the requirements for coordination.
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《Mathematical and Computer Modelling》1997,25(7):79-87
Research in graph theory has focused on studying the structure of graphs with the assumption that they are static. However, in many applications, the graphs that arise change with time, i.e., they are dynamic in nature. This is especially true of applications involving graph models in computer science. We present an expository study of dynamic graphs with the main driving force being practical applications. We first develop a formal classification of dynamic graphs. This taxonomy in the form of generalizations and extensions will in turn suggest new areas of application. Next, we discuss areas where dynamic graphs arise in computer science such as compilers, databases, fault-tolerance, artificial intelligence, and computer networks. Finally, we propose approaches that can be used for studying dynamic graphs. The main objective in any study of dynamic graphs should be to
- 1.(i) extend results developed for static graph theory to dynamic graphs,
- 2.(ii) study the properties that describe how a dynamic graph changes,
- 3.(iii) investigate problems and issues in dynamic graph theory that are raised by practical applications of dynamic graphs in computer science.
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《Mathematical and Computer Modelling》2000,31(4-5):17-26
In the modelisation of the dynamics of a sole population, an interesting issue is the influence of daily vertical migrations of the larvae on the whole dynamical process. As a first step towards getting some insight on that issue, we propose a model that describes the dynamics of an age-structured population living in an environment divided into N different spatial patches. We distinguish two time scales: at the fast time scale, we have migration dynamics and at the slow time scale, the demographic dynamics. The demographic process is described using the classical McKendrick model for each patch, and a simple matrix model including the transfer rates between patches depicts the migration process. Assuming that the migration process is conservative with respect to the total population and some additional technical assumptions, we proved in a previous work that the semigroup associated to our problem has the property of positive asynchronous exponential growth and that the characteristic elements of that asymptotic behaviour can be approximated by those of a scalar classical McKendrick model. In the present work, we develop the study of the nature of the convergence of the solutions of our problem to the solutions of the associated scalar one when the ratio between the time scales is ε (0 < ε ⪡ 1). The main result decomposes the action of the semigroup associated to our problem into three parts:
- 1.(1) the semigroup associated to a demographic scalar problem times the vector of the equilibrium distribution of the migration process;
- 2.(2) the semigroup associated to the transitory process which leads to the first part; and
- 3.(3) an operator, bounded in norm, of order ε.
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《Mathematical and Computer Modelling》1998,27(9-11):27-49
This paper formulates the Dynamic Traffic Routing (DTR) problem as a real-time feedback control problem. Three different forms of the formulation are presented:
- 1.(1) distributed parameter system form derived from the conservation law;
- 2.(2) space discretized continuous lumped parameter form;
- 3.(3) space and time discretized lumped parameter form.
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《Mathematical and Computer Modelling》1997,25(1):93-105
A procedure of the dynamic programming (DP) for the discrete-continuous problem of a route optimization is considered. It is possible to consider this procedure as a dynamic method of optimization of the towns choice in the well-known traveling salesman problem. In the considered version of DP, elements of a dynamic optimization are used. Two variants of the function of the aggregations of losses are investigated:
- 1.(1) the additive functions;
- 2.(2) the function characterizing the aggregation of losses in the bottle-neck problem.
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Alexander Pott 《Geometriae Dedicata》1994,52(2):181-193
We consider projective planes Π of ordern with abelian collineation group Γ of ordern(n?1) which is generated by (A, m)-elations and (B, l)-homologies wherem =AB andA εl. We prove
- Ifn is even thenn=2e and the Sylow 2-subgroup of Γ is elementary abelian.
- Ifn is odd then the Sylow 2-subgroup of Γ is cyclic.
- Ifn is a prime then Π is Desarguesian.
- Ifn is not a square thenn is a prime power.
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《Topology and its Applications》1988,29(3):245-265
Given a Tychonoff space X and classes U and V of topological groups, we say that a topological group G = G(X, U, V) is a free (U,V)-group over X if (a) X is a subspace of G, (b) G ϵ U, and (c) every continuous f: X → H with H ϵ V extends uniquely to a continuous homomorphism f̄: G→H. For certain classes U and V, we consider the question of the existence of free (U,V)- groups. Our principal results are the following. Let PA and CA denote, respectively, the class ofpseudocompact Abelian groups and the class of compact Abelian groups. Then
- 1.(a) there is a free (PA,PA)-group over X iff; X=Ø and
- 2.(b) there is for each X a free (PA,CA)-group over X in which X is closed.
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In my talk, I will present some works done in the nineties on Laplacians on graphs: from eigenvalue problems to inverse problem for resistor networks. I will focus on the motivations and the main results as well as on the main ideas:
- •A differential topology point of view on the minor relation: a nice stratification associated to a finite graph Γ whose strata are associated to the minors of Γ
- •“Discrete” (graphs) versus “continuous” (Riemannian manifolds)
- •Stability of spectra with respect to singular limits: a finite dimensional theory of operators with domains (Von Neumann theory).
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《Historia Mathematica》2002,29(2):193-198
Analysis of the errors in two Old Babylonian “algebraic” problems shows
- •that the computations were performed on a device where additive contributions were no longer identifiable once they had entered the computation;
- •that this device must have been some kind of counting board or abacus where numbers were represented as collections of calculi;
- •that units and tens were represented in distinct ways, perhaps by means of different calculi.
- •Additive Beiträge waren nach ihrer Eintragung in die Rechnung nicht länger identifizierbar.
- •Das Gerät war eine Art Rechenbrett, auf welchem Zahlen als Haufen von Rechensteinen erschienen.
- •Einer und Zehner wurden in verschiedener Weise, evtl. mittels verschiedener Rechensteine repräsentiert.