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1.
《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.
2.
《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.
3.
《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.
4.
5.
《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.
6.
7.
《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.
8.
Moti Gitik 《Israel Journal of Mathematics》1995,92(1-3):61-112
The strength of precipitousness, presaturatedness and saturatedness of NSκ and NS κ λ is studied. In particular, it is shown that:
- The exact strength of “ $NS_{\mu ^ + }^\lambda $ for a regularμ > max(λ, ?1)” is a (ω,μ)-repeat point.
- The exact strength of “NSκ is presaturated over inaccessible κ” is an up-repeat point.
- “NSκ is saturated over inaccessible κ” implies an inner model with ?αo(α) =α ++.
9.
《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.
10.
《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.
11.
《Discrete Applied Mathematics》1987,16(1):11-15
The vertices of a threshold graph G are partitioned into a clique K and an independent set I so that the neighborhoods of the vertices of I are totally ordered by inclusion. The question of whether G is hamiltonian is reduced to the case that K and I have the same size, say r, in which case the edges of K do not affect the answer and may be dropped from G, yielding a bipartite graph B. Let d1≤d2≤…≤dr and e1≤e2≤…≤er be the degrees in B of the vertices of I and K, respectively. For each q = 0, 1,…,r−1, denote by Sq the following system of inequalities: dj⩾j + 1, j = 1,2,…,q, ej⩾j + 1, j = 1, 2,…, r−1−1. Then the following conditions are equivalent:
- 1.(1) B is hamiltonian,
- 2.(2) Sq holds for some q = 0, 1,…, r−1,
- 3.(3) Sq holds for each q = 0, 1,…, r−1.
12.
《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.
13.
《European Journal of Operational Research》1997,96(1):1-35
This paper surveys the current state of the literature in management science/operations research approaches to air pollution management. After introducing suitable background we provide some of the institutional and legal framework needed to understand the continuing regulatory efforts in United States. Attention is then turned to mathematical programming models ranging from fairly simple deterministic linear programs to quite sophisticated stochastic models which have appeared in the literature dealing with these topics. This is followed by extensions reflecting some of the work we have undertaken in association with the Texas Natural Resource Conservation Commission, a regulatory agency in Texas. Application and potential use of models is the central theme of this survey. Issues for future research are presented at the end and an extensive list of publications is provided in the references at the end of the article.Principal air quality issues of local, national, and international concern are listed below in increasing order of difficulty based on the number of different types of pollutants and problems in quantification of the risks the pollutants pose:
- 1.1. Stratospheric ozone depletion: one relatively easily controllable class of trace gases - ozone depleting chemicals, or ODCs, principally chloroflurocarbons (CFCs) — with relatively well quantified risks;
- 2.2. Criteria pollutants: six common pollutants — ozone (O3), carbon monoxide (CO), sulfur dioxide (SO2), nitrogen dioxide (NO2), lead (Pb), and particulate matter less than 10 microns in size (PM10) — regulated since 1970 in the U.S. and presenting relatively well quantified risks;
- 3.3. Acid precipitation: two relatively easily controllable classes of trace gases — oxides of nitrogen (NOx) and oxides of sulfur (SOx) with relatively well quantified risks;
- 4.4. Global warming/climate change: a few difficult to control trace gases — principally carbon dioxide (CO2), methane (CH4), nitrous oxide (N2O), and CFCs — with highly uncertain risks;
- 5.5. Toxics or HAPS (hazardous air pollutants): hundreds of types of gaseous chemicals and particles with uncertain risks;
- 6.6. Somewhat dated, but nevertheless useful, is the following reference: Glossary on Air Pollution (Copenhagen, World Health Organization, 1980).
14.
《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.
15.
《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.
16.
《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.
17.
《Mathematical and Computer Modelling》1997,25(2):109-116
This work deals with the guidance and control of a system which is composed of a rolling cylinder and a controlled slender rod that is pivoted, through its center of mass, about the cylinder's center. Given a finite time interval [0, tf], and let P1 and P2 be two points in the (X, Y)-plane. The problem dealt with here is to find a closed-loop control law for the cylinder-rod system such that:
- 1.(i) the cylinder center will move from P1 to P2 during [0, tf] and will come to rest at P2, and
- 2.(ii) the rod will rotate from an angle ψ21 to ψ22 during [0, tf] and will stop to rotate at t = tf.
18.
《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.
19.
Ramanujan graphs 总被引:2,自引:0,他引:2
A large family of explicitk-regular Cayley graphsX is presented. These graphs satisfy a number of extremal combinatorial properties.
- For eigenvaluesλ ofX eitherλ=±k or ¦λ¦≦2 √k?1. This property is optimal and leads to the best known explicit expander graphs.
- The girth ofX is asymptotically ≧4/3 log k?1 ¦X¦ which gives larger girth than was previously known by explicit or non-explicit constructions.
20.
Given a tree, T, consider one of its longest paths, PT, not necessarily unique. We define T to be m–distant if no vertices of T are a distance greater than m away from PT. We will show that all 3–distant graphs are graceful, providing they satisfy the following properties.
- 1.They have perfect matchings.
- 2.They can be constructed by attaching paths of length 2 to the vertices of a 1–distant tree (caterpillar), by the identification of their end vertices.