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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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《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》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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《Annals of Pure and Applied Logic》1988,37(3):205-248
We develop a series of Ehrenfeucht games and prove the following results:
- 1.(i) The first order theory of the divisible and indecomposable p-group, the first order theory of the group of rational numbers with denominators prime to p and the first order theory of a cyclic group of prime power order can be decided in 22cn log n Turing time.
- 2.(ii) The first order theory of the direct sum of countably many infinite cyclic groups, the first order theory of finite Abelian groups and the first order theory of all Abelian groups can be decided in 22dn Turing space.
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LetX be an Hausdorff space. We say thatX is a CO space, ifX is compact and every closed subspace ofX is homeomorphic to a clopen subspace ofX, andX is a hereditarily CO space (HCO space), if every closed subspace is a CO space. It is well-known that every well-ordered chain with a last element, endowed with the interval topology, is an HCO space, and every HCO space is scattered. In this paper, we show the following theorems: Theorem (R. Bonnet):
- Every HCO space which is a continuous image of a compact totally disconnected interval space is homeomorphic to β+1 for some ordinal β.
- Every HCO space of countable Cantor-Bendixson rank is homeomorphic to α+1 for some countable ordinal α.
- X has only countably many isolated points,
- Every closed subset of X is countable or co-countable,
- Every countable closed subspace of X is homeomorphic to a clopen subspace, and every uncountable closed subspace of X is homeomorphic to X, and
- X is retractive.
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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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Yan-Kui Song 《Czechoslovak Mathematical Journal》2013,63(2):451-460
In this paper, we prove the following statements:
- There exists a Tychonoff star countable discrete closed, pseudocompact space having a regular-closed subspace which is not star countable.
- Every separable space can be embedded into an absolutely star countable discrete closed space as a closed subspace.
- Assuming $2^{\aleph _0 } = 2^{\aleph _1 } $ , there exists a normal absolutely star countable discrete closed space having a regular-closed subspace which is not star countable.
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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(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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《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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Prof. Dr. J. Pfanzagl 《Probability Theory and Related Fields》1968,10(1):43-62
The paper concerns estimates of probability measures (=p-measures) determined from a countable number of independent realizations. The main results are:
- For suitable topologies, the existence of a consistent sequence of estimates implies the existence of a sequence of estimates which is strongly consistent a. e. with respect to an arbitrary finite prior measure. In the case of a measurable parameter the existence of a consistent sequence of estimates implies strong consistency of the Bayes estimates for the quadratic loss function.
- If a family ofp-measures is separable with respect to the supremum metric, there exists a sequence of strict estimates which is uniformly consistent with respect to the supremum metric on any totally bounded subset ofp-measures.
- IfB is totally σ-bounded with respect to the supremum metric there exists a density-consistent sequence of estimates. IfB is separable with respect to the supremum metric there exists a sequence of estimates which is density consistent a. e. with respect to an arbitrary finite prior measure.
- A sequence of uniformly consistent tests exists for all compact hypotheses in the case of an abstract sample space and for all weakly closed hypotheses in the case of a separable metric sample space.
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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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《European Journal of Operational Research》1986,23(2):236-245
Consider a set of trips where each trip is specified a priori by a place of origin, a destination, a duration, a cost and a time interval within which the trip must begin. The trips may include visits to one or more specific points. Our problem is to determine the number of vehicles required together with their routes and schedules, so that each trip begins within his given time interval, while the fixed costs related to the number of vehicles, and the travel costs between trips are minimized. The problem is a generalization of the m-travelling salesman problem.We compare numerical results for 3 algorithms developed by our research team:
- 1.(1) Column generation on a set partitioning problem solved by simplex and branch-and-bound; columns are generated by a shortest path algorithm with time constraints on the nodes.
- 2.(2) Adaptation of the Carpaneto-Toth algorithm for the asymmetric travelling salesman problem: solution of network problems by relaxing scheduling constraints, and branch-and-bound on flow variables.
- 3.(3) Solution of network problems by relaxing scheduling constraints and branch-and-bound based on dividing the time windows.
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《Comptes Rendus de l'Academie des Sciences Series IIA Earth and Planetary Science》1997,324(6):659-663
We prove the following theorems:
- 1)Any surgery of index one on u tight contact manifold (of dimension three) gives rise to a manifold which carries a natural tight contact structure.
- 2)In a tight contact manifold, any two isotopic spheres which carry the same characteristic foliation are isotopic through a contact isolopy.
- 3)In a tight contact manifold, any two isotopic spheres have isomorphic complements.
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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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《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.
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Bidirected graphs generalize directed and undirected graphs in that edges are oriented locally at every node. The natural notion of the degree of a node that takes into account (local) orientations is that of net-degree. In this paper, we extend the following four topics from (un)directed graphs to bidirected graphs:
- –Erdős–Gallai-type results: characterization of net-degree sequences,
- –Havel–Hakimi-type results: complete sets of degree-preserving operations,
- –Extremal degree sequences: characterization of uniquely realizable sequences, and
- –Enumerative aspects: counting formulas for net-degree sequences.