共查询到20条相似文献,搜索用时 125 毫秒
1.
Karl Jakob Dienst 《Monatshefte für Mathematik》1977,84(3):197-208
The miquelian Minkowski-planes can be characterized by cycle-reflections. More exactly: If is a non degenerate quadric of index 2 in a 3-dimensional pappian projective space, and if is the set of plane intersections of, which don't contain a line of (the elements of are called cycles), then the incidence-structure is a miquelian Minkowski-plane. In these hold:(*) there exists a reflection on every cycle (i. e. a non-identical automorphism of the Minkowski-plane, which fixes the points of the cycle) and(**) the product of three reflections on cycles through two fixed points fixes the points of a cycle.It is shown, that the properties (*) and (**) characterize the miquelian Minkowski-planes under the Minkowski-planes (i. e. incidence-structures, which are generalizations of intersection-geometries of quadrics mentioned above). Counter-examples show, that miquelian Minkowski-planes could not be characterized only by property (*). 相似文献
2.
Various kinds of semicontinuity and the solution sets of parametric multivalued symmetric vector quasiequilibrium problems 总被引:2,自引:1,他引:1
We introduce some definitions related to semicontinuity of multivalued mappings and discuss various kinds of semicontinuity-related
properties. Sufficient conditions for the solution sets of parametric multivalued symmetric vector quasiequilibrium problems
to have these properties are established. Comparisons of the solution sets of our two problems are also provided. As an example
of applications of our main results, the mentioned semicontinuity-related properties of the solution sets to a lower and upper
bounded quasiequilibrium problem are obtained as consequences. 相似文献
3.
Levent Tunçel 《Foundations of Computational Mathematics》2001,1(3):229-254
We generalize primal—dual interior-point methods for linear programming (LP) problems to the convex optimization problems
in conic form. Previously, the most comprehensive theory of symmetric primal—dual interior-point algorithms was given by Nesterov
and Todd for feasible regions expressed as the intersection of a symmetric cone with an affine subspace. In our setting, we
allow an arbitrary convex cone in place of the symmetric cone. Even though some of the impressive properties attained by Nesterov—Todd
algorithms are impossible in this general setting of convex optimization problems, we show that essentially all primal—dual
interior-point algorithms for LP can be extended easily to the general setting. We provide three frameworks for primal—dual
algorithms, each framework corresponding to a different level of sophistication in the algorithms. As the level of sophistication
increases, we demand better formulations of the feasible solution sets. Our algorithms, in return, attain provably better
theoretical properties. We also make a very strong connection to quasi-Newton methods by expressing the square of the symmetric
primal—dual linear transformation (the so-called scaling) as a quasi-Newton update in the case of the least sophisticated
framework.
August 25, 1999. Final version received: March 7, 2001. 相似文献
4.
Louis Aimé Fono Henri Gwet Bernadette Bouchon-Meunier 《European Journal of Operational Research》2007
In this paper, we determine by means of fuzzy implication operators, two classes of difference operations for fuzzy sets and two classes of symmetric difference operations for fuzzy sets which preserve properties of the classical difference operation for crisp sets and the classical symmetric difference operation for crisp sets respectively. The obtained operations allow us to construct as in [B. De Baets, H. De Meyer, Transitivity-preserving fuzzification schemes for cardinality-based similarity measures, European Journal of Operational Research 160 (2005) 726–740], cardinality-based similarity measures which are reflexive, symmetric and transitive fuzzy relations and, to propose two classes of distances (metrics) which are fuzzy versions of the well-known distance of cardinality of the symmetric difference of crisp sets. 相似文献
5.
Cristina Draghici 《Journal of Mathematical Analysis and Applications》2006,324(1):543-554
We prove that the integral of n functions over a symmetric set L in Rn, with additional properties, increases when the functions are replaced by their symmetric decreasing rearrangements. The result is known when L is a centrally symmetric convex set, and our result extends it to nonconvex sets. We deduce as consequences, inequalities for the average of a function whose level sets are of the same type as L, over measurable sets in Rn. The average of such a function on E is maximized by the average over the symmetric set E*. 相似文献
6.
集合的对称差及其测度 总被引:1,自引:0,他引:1
集合的对称差是集合的基本运算之一,它在测度论及其应用中扮演着一个重要的角度,本文深入地对集合的对称差进行讨论,研究了它的性质,通过集合的不交分解揭示了若干个集合的对称差的本质,给出了关于集合的对称差的测度计算公式。 相似文献
7.
Eva Vandersmissen 《Applied Categorical Structures》2007,15(5-6):633-645
In this paper we will study completeness in symmetric metrically generated constructs via nearness spaces. Our approach consists
in associating an appropriate regular nearness space with a given symmetric metered space. The completion theory known for
regular nearness space has some convenient properties on which our completion of symmetric metered spaces will be based. This
technique appears to be suitable for most symmetric metrically generated constructs and leads to a firm completion theory.
相似文献
8.
CHU YuMing XIA WeiFeng & ZHAO TieHong Department of Mathematics Huzhou Teachers College Huzhou China Institut de Mathmatiques Universit Pierre et Marie Curie Paris F- France 《中国科学 数学(英文版)》2010,(2)
The Schur convexity and concavity of a class of symmetric functions are discussed, and an open problem proposed by Guan in Some properties of a class of symmetric functions is answered. As consequences, some inequalities are established by use of the theory of majorization. 相似文献
9.
10.
M. A. Sevodin 《Russian Mathematics (Iz VUZ)》2013,57(10):62-64
We consider sets which are convex in directions from some cone K. We generalize some well-known properties of ordinary convex sets for the case of K-convex sets and give some applications in optimization theory. 相似文献
11.
For an irreducible symmetric Markov process on a (not necessarily compact) state space associated with a symmetric Dirichlet
form, we give Poincaré-type inequalities. As an application of the inequalities, we consider a time-inhomogeneous diffusion
process obtained by a time-dependent drift transformation from a diffusion process and give general conditions for the transience
or recurrence of some sets. As a particular case, the diffusion process appearing in the theory of simulated annealing is
considered. 相似文献
12.
S. Muto 《International Journal of Game Theory》1982,11(3-4):195-201
Symmetric solutions (or symmetric stable sets) and their uniqueness are investigated for some classes of symmetric,n-person, cooperative games in characteristic function form known as (n, k) games. 相似文献
13.
J. Howard Redfield 《Journal of Graph Theory》1984,8(2):205-223
Wider extension is here given to the theory developed in an earlier paper, in which the enumeration of certain configurations or combinatorial entities was made to depend on two or more groups (range groups). The present paper recognizes for the first time the essential part played by an additional group, the frame group, which includes all the range groups as subgroups, and which was implicit in the earlier theory as the symmetric group of the degree of the range groups. The use of frame groups which are not symmetric greatly extends the range of application of the theory, and allows its development in terms of abstract groups. By the use of the conjugate sets of the subgroups (both cyclic and noncyclic) of the frame group, instead of merely the conjugate sets of its operations, a complete solution is obtained for the problem (solved only for special cases in the earlier paper) of determining the invariance groups admitted by the various configurations enumerated. 相似文献
14.
15.
Patrick Desrosiers Luc Lapointe Pierre Mathieu 《Journal of Algebraic Combinatorics》2006,24(2):209-238
We present the basic elements of a generalization of symmetric function theory involving functions of commuting and anticommuting (Grassmannian) variables. These new functions, called symmetric functions in superspace, are invariant under the diagonal action of the symmetric group on the sets of commuting and anticommuting variables. In this work, we present the superspace extension of the classical bases, namely, the monomial symmetric functions, the elementary symmetric functions, the completely symmetric functions, and the power sums. Various basic results, such as the generating functions for the multiplicative bases, Cauchy formulas, involution operations as well as the combinatorial scalar product are also generalized. 相似文献
16.
17.
Molodtsov initiated the concept of soft set theory, which can be used as a generic mathematical tool for dealing with uncertainty. There has been some progress concerning practical applications of soft set theory, especially the use of soft sets in decision making. In this paper we generalize the adjustable approach to fuzzy soft sets based decision making. Concretely, we present an adjustable approach to intuitionistic fuzzy soft sets based decision making by using level soft sets of intuitionistic fuzzy soft sets and give some illustrative examples. The properties of level soft sets are presented and discussed. Moreover, we also introduce the weighted intuitionistic fuzzy soft sets and investigate its application to decision making. 相似文献
18.
We attempt a broad exploration of properties and connections between the symmetry function of a convex set S ${S \subset\mathbb{R}^n}We attempt a broad exploration of properties and connections between the symmetry function of a convex set S
and other arenas of convexity including convex functions, convex geometry, probability theory on convex sets, and computational
complexity. Given a point , let sym(x,S) denote the symmetry value of x in S:
, which essentially measures how symmetric S is about the point x, and define
x
* is called a symmetry point of S if x
* achieves the above maximum. The set S is a symmetric set if sym
(S)=1. There are many important properties of symmetric convex sets; herein we explore how these properties extend as a function
of sym
(S) and/or sym
(x,S). By accounting for the role of the symmetry function, we reduce the dependence of many mathematical results on the strong
assumption that S is symmetric, and we are able to capture and otherwise quantify many of the ways that the symmetry function influences properties
of convex sets and functions. The results in this paper include functional properties of sym
(x,S), relations with several convex geometry quantities such as volume, distance, and cross-ratio distance, as well as set approximation
results, including a refinement of the L?wner-John rounding theorems, and applications of symmetry to probability theory on
convex sets. We provide a characterization of symmetry points x
* for general convex sets. Finally, in the polyhedral case, we show how to efficiently compute sym(S) and a symmetry point x
* using linear programming. The paper also contains discussions of open questions as well as unproved conjectures regarding
the symmetry function and its connection to other areas of convexity theory.
Dedicated to Clovis Gonzaga on the occasion of his 60th birthday. 相似文献
19.
In this paper we introduce the middle-parametric representation of a fuzzy number presenting some of the advantages in the use of this representation. A special attention is focused on the subset of symmetric fuzzy numbers presenting the special properties of their arithmetic. The approach on symmetric fuzzy numbers is sustained by the applications of these kinds of fuzzy numbers in fuzzy linear programming and by the presence of the symmetric Gaussian type fuzzy numbers in the theory of errors. As potential applications of the middle-parametric representation, some fuzzy interpolation problems are considered. 相似文献