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1.
The pre-coloring extension problem consists, given a graph G and a set of nodes to which some colors are already assigned, in finding a coloring of G with the minimum number of colors which respects the pre-coloring assignment. This can be reduced to the usual coloring problem
on a certain contracted graph. We prove that pre-coloring extension is polynomial for complements of Meyniel graphs. We answer
a question of Hujter and Tuza by showing that “PrExt perfect” graphs are exactly the co-Meyniel graphs, which also generalizes
results of Hujter and Tuza and of Hertz. Moreover we show that, given a co-Meyniel graph, the corresponding contracted graph
belongs to a restricted class of perfect graphs (“co-Artemis” graphs, which are “co-perfectly contractile” graphs), whose
perfectness is easier to establish than the strong perfect graph theorem. However, the polynomiality of our algorithm still
depends on the ellipsoid method for coloring perfect graphs.
C.N.R.S.
Final version received: January, 2007 相似文献
2.
Let be a nonisotropic point source of light, and the power intensity of this source in direction . Suppose that the light rays emitted by the source through an aperture fall on a perfectly reflecting surface and reflect off it so that the reflected rays illuminate a closed domain on some plane with intensity . The inverse problem consists of constructing the reflector surface from given position of the source , the input aperture , function , “target” set , and output intensity . For example, the input intensity may have a “bell”-like shape and we may wish to redistribute the energy uniformly over
a prespecified region. The analytical formulation of the described above problem leads to a non-linear partial differential
equation of Monge-Ampère type. In our previous paper we proved existence of weak solutions to this inverse problem and in
this paper we describe and illustrate with examples an algorithm for its numerical solution. The proposed numerical method
can be easily modified for the case when is a closed domain on an arbitrary surface.
Received November 26, 1996 相似文献
3.
A. V. Yakovlev 《Journal of Mathematical Sciences》2012,180(3):360-363
A new general approach to the so-called “matrix problems” is given. With this approach, the “derivative” of a matrix problem
is again a matrix problem of the same type. 相似文献
4.
Shyūichi Izumiya 《manuscripta mathematica》1979,28(4):337-360
In his paper [2], Bierstone proves the equivariant Gromov theorem which is an integrability theorem for “open regularity condition”
of equivariant sections of a smooth G-fibre bundle under the assumption that all orbit bundles of base manifold are non-closed.
Here, we prove the result without his assumption under a nice “open regularity condition” which we call “G-extensible”.
One of the examples of “G-extensible condition” is given by notions of Thom-Boardman singularities. 相似文献
5.
K. S. Banerjee 《Annals of the Institute of Statistical Mathematics》1974,26(1):447-454
Summary Dey [3] has suggested a spring balance weighing design in preference to “repeated designs”, and later, Kulshreshtha and Dey
[5] have suggested yet one more weighing design which, they say, would be preferred to “repeated designs” and to those suggested
in [3], provided one is interested in estimating the weights of some of the objects with increased precision at the cost of
precision for others. It has been shown here that, while the above findings may be true in some situations, one might, in
a given problem, prefer “repeated designs” to those suggested in [3] and [5].
NSF Grant No. GP-28312 and GP-36562. 相似文献
6.
A shape and topology optimization driven solution technique for a class of linear complementarity problems (LCPs) in function
space is considered. The main motivating application is given by obstacle problems. Based on the LCP together with its corresponding
interface conditions on the boundary between the coincidence or active set and the inactive set, the original problem is reformulated
as a shape optimization problem. The topological sensitivity of the new objective functional is used to estimate the “topology”
of the active set. Then, for local correction purposes near the interface, a level set based shape sensitivity technique is
employed. A numerical algorithm is devised, and a report on numerical test runs ends the paper. 相似文献
7.
This paper presents a computationally effective heuristic method which produces good-quality solutions for large-scale set
covering problems with thousands of constraints and about one million variables. The need to solve such large-scale problems
arises from a crew scheduling problem of mass transit agencies where the number of work shifts required has to be minimized.
This problem may be formulated as a large-scale non-unicost set covering problem whose rows are trips to be performed while
columns stand for round trips. The proposed method is mainly based on lagragian relaxation and sub-gradient optimization.
After the reduction of the number of rows and columns by the logical tests, “greedy” heuristic algorithms provide upper and
lower bounds which are continuously improved to produce goodquality solutions. Computational results, regarding randomly generated
problems and real life problems concerning crew scheduling at Italian Railways Company, show that good-quality solutions can
be obtained at an acceptable computational cost.
This work was supported by the project “Progetto Finalizzato Transporti 2” of National Research Council of Italy (C.N.R.)
contract No. 94.01436PF74 and by “Ferrovie dello Stato S.p.A.” 相似文献
8.
Nikola Kompa 《Acta Analytica》2005,20(1):16-28
The basic idea of conversational contextualism is that knowledge attributions are context sensitive in that a given knowledge
attribution may be true if made in one context but false if made in another, owing to differences in the attributors’ conversational
contexts. Moreover, the context sensitivity involved is traced back to the context sensitivity of the word “know,” which,
in turn, is commonly modelled on the case either of genuine indexicals such as “I” or “here” or of comparative adjectives
such as “tall” or “rich.” But contextualism faces various problems. I argue that in order to solve these problems we need
to look for another account of the context sensitivity involved in knowledge attributions and I sketch an alternative proposal. 相似文献
9.
D. -F. Li 《Fuzzy Optimization and Decision Making》2007,6(3):237-254
The aim of this paper is to develop a new fuzzy closeness (FC) methodology for multi-attribute decision making (MADM) in fuzzy
environments, which is an important research field in decision science and operations research. The TOPSIS method based on
an aggregating function representing “closeness to the ideal solution” is one of the well-known MADM methods. However, while
the highest ranked alternative by the TOPSIS method is the best in terms of its ranking index, this does not mean that it
is always the closest to the ideal solution. Furthermore, the TOPSIS method presumes crisp data while fuzziness is inherent
in decision data and decision making processes, so that fuzzy ratings using linguistic variables are better suited for assessing
decision alternatives. In this paper, a new FC method for MADM under fuzzy environments is developed by introducing a multi-attribute
ranking index based on the particular measure of closeness to the ideal solution, which is developed from the fuzzy weighted
Minkowski distance used as an aggregating function in a compromise programming method. The FC method of compromise ranking
determines a compromise solution, providing a maximum “group utility” for the “majority” and a minimum individual regret for
the “opponent”. A real example of a personnel selection problem is examined to demonstrate the implementation process of the
method proposed in this paper. 相似文献
10.
S. A. Nazarov 《Journal of Mathematical Sciences》1996,80(5):1989-2034
The asymptotic series for solutions of the mixed boundary-value problem for the Poisson equation in a domain, which is a junction
of singularly degenerating domains, are constructed. In this paper, which is the first part of the publication, the three-dimensional
problem (“wheel hub with spokes”) and the analogous two-dimensional problems are considered. The methods of matched and compound
asymptotic expansions are used. It is shown that a special self-adjoint extension of the operator of the limit problem in
the “hub” supplied by the straight-line segments (“limits of spokes”) can be chosen as an asymptotical model of the problem
in question; the extension parameters are to be some integral characteristics of the boundary-layer problems. Bibliography:
39 titles.
Translated from Trudy Seminara imeni I. G. Petrovskogo. No. 18, pp. 3–78, 1995. 相似文献
11.
We consider the problem of controlling a linear system of ordinary differential equations with a linear observable output.
The system contains uncertain items (disturbances), for which we know only “hard” pointwise constraints. The problem of synthesizing
a control that brings the trajectories of the system into a given target set in finite time is solved under weakened conditions
without assuming that the control and the disturbance are of the same type. To this end, we suggest an approach that amounts
to constructing an information set and a weakly invariant set with subsequent “aiming” of the first set at the second. Both
stages are carried out in a finite-dimensional space, which permits one to use an efficient algorithm for solving the synthesis
problem approximately on the basis of the ellipsoidal calculus technique. The results are illustrated by an example in which
the control of a linear oscillation system is constructed. 相似文献
12.
The linear search problem concerns a search on the real line for a point selected at random according to a given probability
distribution. The search begins at zero and is made by a continuous motion with constant speed, first in one direction and
then the other. The problem is to determine when it is possible to devise a “best” search plan. In former papers the best
plan has been selected according to the criterion of minimum expected path length. In this paper we consider a more general,
nonlinear criterion for a “best” plan and show that the substantive requirements of the earlier results are not affected by
these changes. 相似文献
13.
T. V. Panchapagesan 《Rendiconti del Circolo Matematico di Palermo》1995,44(3):417-440
The concept of an orthogonal spectral representation (OTSR) of a Hilbert spaceH relative to a spectral measureE(.) is introduced and it is shown that every Hilbert space admits an OTSR relative to a given spectral measure. Apart from
the various results obtained about OTSRs, the principal result of Allan Brown (1974) is deduced as an easy consequence of
this study. A new complete system of unitary invariants called the “equivalence of OTSRs”, is given for spectral measures.
Two special types of OTSRs called “BOTSR” and “COBOTSR” are introduced and characterized respectively in terms of the “GCGS-property”
and “CGS-property” of the associated spectral measure. Various complete systems of unitary invariants are given for spectral
measures with the GCGS-property. Finally, the Wecken-Plesner-Rohlin theorem on hermitian operators with simple spectra is
generalized to arbitrary spectral measures. 相似文献
14.
D. S. Filippychev 《Computational Mathematics and Modeling》1999,10(1):61-73
We study the problem of the behavior of a plasma bounded longitudinally by an absorbing sheath. This model contains charged
particles (electrons and ions) moving subject to a self-consistent electrostatic field. New particle pairs are generated in
the region of a distributed source. As a numerical model we used the electrostatic “particle-in-cell” method supplemented
by the Emmert model for a bulk source and the algorithm of binary Coulomb collisions using the Monte Carlo method. We give
a mathematical statement of the problem. The computations were carried out using the direct implicit method with the “explicit
limit” time step. The results of numerical simulation of this system are given. We consider the formation and evoluiton of
potential structures (multiple weak nonmonotonic double layers). Five figures. Bibliography: 35 titles.
Translated fromProblemy Matematicheskoi Fiziki, 1998, pp. 75–89. 相似文献
15.
Alessandra Celletti Luigi Chierchia 《Zeitschrift für Angewandte Mathematik und Physik (ZAMP)》2005,57(1):33-41
A new (iso-energetic) KAM method is tested on a specific three-body problem “extracted” from the Solar system (Sun-Jupiter
+ asteroid 12 Victoria). Analytical results in agreement with the observed data are established. This paper is a concise presentation
of [2].
Supported by the MIUR projects: “Dynamical Systems: Classical, Quantum, Stochastic” and “Variational Methods and Nonlinear
Differential Equations”
Received: February 3, 2004 相似文献
16.
Classification is concerned with the development of rules for the allocation of observations to groups, and is a fundamental
problem in machine learning. Much of previous work on classification models investigates two-group discrimination. Multi-category
classification is less-often considered due to the tendency of generalizations of two-group models to produce misclassification
rates that are higher than desirable. Indeed, producing “good” two-group classification rules is a challenging task for some
applications, and producing good multi-category rules is generally more difficult. Additionally, even when the “optimal” classification
rule is known, inter-group misclassification rates may be higher than tolerable for a given classification model. We investigate
properties of a mixed-integer programming based multi-category classification model that allows for the pre-specification
of limits on inter-group misclassification rates. The mechanism by which the limits are satisfied is the use of a reserved
judgment region, an artificial category into which observations are placed whose attributes do not sufficiently indicate membership
to any particular group. The method is shown to be a consistent estimator of a classification rule with misclassification
limits, and performance on simulated and real-world data is demonstrated. 相似文献
17.
A method is developed for calculating the electromagnetic field of a magnetic dipole in a quasilayered two-dimensional medium.
The quasi-three-dimensional problem is reduced to a two-dimensional problem for the Fourier-transformed electromagnetic field.
An equivalent system of integral equations on the layer boundaries is obtained.
This research was partially supported by the State Scientific-Technical Program “Future Information Technologies” (grant No.
0201.06.010) and the Interuniversity Scientific Program “Russian Universities: Basic Research.”
Translated from Chislennye Metody v Matematicheskoi Fizike, Moscow State University, pp. 94–110, 1998. 相似文献
18.
In order to solve a quadratic 0/1 problem, some techniques, consisting in deriving a linear integer formulation, are used.
Those techniques, called “linearization”, usually involve a huge number of additional variables. As a consequence, the exact
resolution of the linear model is, in general, very difficult.
Our aim, in this paper, is to propose “economical” linear models. Starting from an existing linearization (typically the so-called
“classical linearization”), we find a new linearization with fewer variables. The resulting model is called “Miniaturized”
linearization. Based on this approach, we propose a new linearization scheme for which numerical tests have been performed. 相似文献
19.
This paper is aimed at introducing an algebraic model for physical scales and units of measurement. This goal is achieved
by means of the concept of “positive space” and its rational powers. Positive spaces are “semi-vector spaces” on which the
group of positive real numbers acts freely and transitively through the scalar multiplication. Their tensor multiplication
with vector spaces yields “scaled spaces” that are suitable to describe spaces with physical dimensions mathematically. We
also deal with scales regarded as fields over a given background (e.g., spacetime). 相似文献
20.
Typically local search methods for solving constraint satisfaction problems such as GSAT, WalkSAT, DLM, and ESG treat the
problem as an optimisation problem. Each constraint contributes part of a penalty function in assessing trial valuations.
Local search examines the neighbours of the current valuation, using the penalty function to determine a “better” neighbour
valuation to move to, until finally a solution which satisfies all the constraints is found. In this paper we investigate
using some of the constraints as “hard” constraints, that are always satisfied by every trial valuation visited, rather than
as part of a penalty function. In this way these constraints reduce the possible neighbours in each move and also the overall
search space. The treating of some constraints as hard requires that the space of valuations that are satisfied is “connected”
in order to guarantee that a solution can be found from any starting position within the region; thus the concept of islands
and the name “island confinement method” arises. Treating some constraints as hard provides new difficulties for the search
mechanism since the search space becomes more jagged, and there are more deep local minima. A new escape strategy is needed.
To demonstrate the feasibility and generality of our approach, we show how the island confinement method can be incorporated
in, and significantly improve, the search performance of two successful local search procedures, DLM and ESG, on SAT problems
arising from binary CSPs.
A preliminary version of this paper appeared in AAAI’2002. 相似文献