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1.
We explore two necessary and sufficient conditions for the singleton core in college admissions problems. One is a condition on the colleges’ preference profiles, called acyclicity, and the other is a condition on their capacity vectors. We also study the implications of our acyclicity condition. The student-optimal stable matching is strongly efficient for the students, given an acyclic profile of the colleges’ preference relations. Even when the colleges’ true preference profile is acyclic, a college may be better off by misreporting its preference when the college-optimal stable mechanism is used. 相似文献
2.
Exceptional Family of Elements for a Variational Inequality Problem and its Applications 总被引:1,自引:0,他引:1
This paper introduces a new concept of exceptional family of elements (abbreviated, exceptional family) for a finite-dimensional nonlinear variational inequality problem. By using this new concept, we establish a general sufficient condition for the existence of a solution to the problem. Such a condition is used to develop several new existence theorems. Among other things, a sufficient and necessary condition for the solvability of pseudo-monotone variational inequality problem is proved. The notion of coercivity of a function and related classical existence theorems for variational inequality are also generalized. Finally, a solution condition for a class of nonlinear complementarity problems with so-called P
* -mappings is also obtained. 相似文献
3.
In this paper, we establish the necessary and sufficient conditions of existence for a positive solution to a class of non-variational
quasilinear elliptic systems in R
N
. The sufficient condition of existence result bases on the Mountain Pass Lemma and the sub-super solution methods, and the
necessary condition is a consequence of a Picone’s identity. The system models some phenomena in different physical and other
natural sciences: non-Newtonian mechanics, nonlinear elasticity and glaciology, combustion theory, population biology and
so on. 相似文献
4.
Frank Niedermeyer Saharon Shelah Karsten Steffens 《Archive for Mathematical Logic》2006,45(6):665-672
If P is a hereditary property then we show that, for the existence of a perfect f-factor, P is a sufficient condition for countable graphs and yields a sufficient condition for graphs of size ℵ1. Further we give two examples of a hereditary property which is even necessary for the existence of a perfect f-factor. We also discuss the ℵ2-case.This paper was supported by the Volkswagen Stiftung 相似文献
5.
Let G be a Lie group, H ≤ G a closed subgroup and M ≈ G/H. In [14] André Weil gave a necessary and sufficient condition for the existence of invariant measures on homogeneous spaces of arbitrary locally compact groups. For Lie groups using the structure theory we give a neater necessary and sufficient condition for the existence of a G-invariant measure on M, cf. Theorems (2.1) and (3.2) in the introduction. 相似文献
6.
Eric Bahel 《International Journal of Game Theory》2011,40(3):551-589
In this paper, we study the Ranking property for discrete cost sharing methods. In the two-agent model, we characterize the
set of methods satisfying this axiom: the symmetry of the flow representing the method is necessary and sufficient for Ranking.
In higher dimensions (n ≥ 3), we identify strong implications of the axiom; however, we prove that these conditions are not sufficient to characterize
Ranking. For the so-called elementary fixed flows, we derive a necessary and sufficient condition. 相似文献
7.
Georges Haddad 《Israel Journal of Mathematics》1981,39(1-2):83-100
The paper gives a necessary and sufficient condition for the existence of monotone trajectories to differential inclusionsdx/dt ∈S[x(t)] defined on a locally compact subsetX ofR
p, the monotonicity being related to a given preorder onX. This result is then extended to functional differential inclusions with memory which are the multivalued case to retarded
functional differential equations. We give a similar necessary and sufficient condition for the existence of trajectories
which reach a given closed set at timet=0 and stay in it with the monotonicity property fort≧0. 相似文献
8.
In this paper we discuss continuation properties and asymptotic behavior of -regular solutions to abstract semilinear parabolic problems in case when the nonlinear term satisfies critical growth conditions. A necessary and sufficient condition for global in time existence of -regular solutions is given. We also formulate sufficient conditions to construct a piecewise -regular solutions (continuation beyond maximal time of existence for -regular solutions). Applications to strongly damped wave equations and to higher order semilinear parabolic equations are finally discussed. In particular global solvability and the existence of a global attractor for in is achieved in case when a nonlinear term f satisfies a critical growth condition and a dissipativeness condition. Similar result is obtained for a 2mth order semilinear parabolic initial boundary value problem in a Hilbert space . 相似文献
9.
Davar Khoshnevisan 《Probability Theory and Related Fields》2008,140(1-2):169-193
Häggström et al. (Ann Inst H Poincaré Probab Stat 33(4):497–528, 1997) have introduced a dynamical version of percolation on a graph G. When G is a tree they derived a necessary and sufficient condition for percolation to exist at some time t. In the case that G is a spherically symmetric tree (Peres and Steif in Probab Theory Relat Fields 111(1):141–165, 1998), derived a necessary and sufficient condition for percolation to exist at some time t in a given target set D. The main result of the present paper is a necessary and sufficient condition for the existence of percolation, at some time ${t\in D}H?ggstr?m et al. (Ann Inst H Poincaré Probab Stat 33(4):497–528, 1997) have introduced a dynamical version of percolation
on a graph G. When G is a tree they derived a necessary and sufficient condition for percolation to exist at some time t. In the case that G is a spherically symmetric tree (Peres and Steif in Probab Theory Relat Fields 111(1):141–165, 1998), derived a necessary
and sufficient condition for percolation to exist at some time t in a given target set D. The main result of the present paper is a necessary and sufficient condition for the existence of percolation, at some time
, in the case that the underlying tree is not necessary spherically symmetric. This answers a question of Yuval Peres (personal
communication). We present also a formula for the Hausdorff dimension of the set of exceptional times of percolation.
Research supported in part by a grant from the National Science Foundation. 相似文献
10.
Magic squares have been extremely useful and popular in combinatorics and statistics. One generalization of magic squares is magic rectangles which are useful for designing experiments in statistics. A necessary and sufficient condition for the existence of magic rectangles restricts the number of rows and columns to be either both odd or both even. In this paper, we generalize magic rectangles to even by odd nearly magic rectangles. We also prove necessary and sufficient conditions for the existence of a nearly magic rectangle, and construct one for each parameter set for which they exist. 相似文献
11.
S. Miyoshi 《Commentarii Mathematici Helvetici》1997,72(3):400-410
We show that there exists a family of smooth orientable circle bundles over closed orientable 3-manifolds each of which has
a codimension-one foliation transverse to the fibres of class C
0
but has none of class C
3
. There arises a necessary condition induced from the Milnor-Wood inequality for the existence of a foliation transverse to
the fibres of an orientable circle bundle over a closed orientable 3-manifold. We show that with some exceptions this necessary
condition is also sufficient for the existence of a smooth transverse foliation if the base space is a closed Seifert fibred
manifold.
Received: May 13, 1996 相似文献
12.
I. V. Potapenko 《Ukrainian Mathematical Journal》2010,62(2):222-226
We establish a condition for two symmetric tensor fields that is necessary and sufficient for the existence of a displacement
vector in the case of infinitesimal deformation of a surface in the Euclidean space E
3. 相似文献
13.
14.
S. K. Kaushik 《Journal of Contemporary Mathematical Analysis (Armenian Academy of Sciences)》2009,44(4):212-218
Fusion Banach frames satisfying property S have been studied. A sufficient condition for the existence of a fusion Banach frame satisfying property S in weakly compactly generated Banach spaces has been given. Also, a necessary and sufficient condition for a fusion Banach
frame to satisfy property S has been given. Finally, fusion Banach frames satisfying property S have been characterized in terms of closedness of certain subspaces of the dual spaces in the weak*-topology. 相似文献
15.
M. M. Cropper J. L. Goldwasser A. J. W. Hilton D. G. Hoffman P. D. Johnson 《Journal of Graph Theory》2000,33(4):199-219
Philip Hall's famous theorem on systems of distinct representatives and its not‐so‐famous improvement by Halmos and Vaughan (1950) can be regarded as statements about the existence of proper list‐colorings or list‐multicolorings of complete graphs. The necessary and sufficient condition for a proper “coloring” in these theorems has a rather natural generalization to a condition we call Hall's condition on a simple graph G, a vertex list assignment to G, and an assignment of nonnegative integers to the vertices of G. Hall's condition turns out to be necessary for the existence of a proper multicoloring of G under these assignments. The Hall‐Halmos‐Vaughan theorem may be stated: when G is a clique, Hall's condition is sufficient for the existence of a proper multicoloring. In this article, we undertake the study of the class HHV of simple graphs G for which Hall's condition is sufficient for the existence of a proper multicoloring. It is shown that HHV is contained in the class ℋ︁0 of graphs in which every block is a clique and each cut‐vertex lies in exactly two blocks. On the other hand, besides cliques, the only connected graphs we know to be in HHV are (i) any two cliques joined at a cut‐vertex, (ii) paths, and (iii) the two connected graphs of order 5 in ℋ︁0, which are neither cliques, paths, nor two cliques stuck together. In case (ii), we address the constructive aspect, the problem of deciding if there is a proper coloring and, if there is, of finding one. © 2000 John Wiley & Sons, Inc. J Graph Theory 33: 199–219, 2000 相似文献
16.
Let G = (V, E) be a graph and x, y, z ∈ V be three designated vertices. We give a necessary and sufficient condition for the existence of a rigid two-dimensional framework
(G, p), in which x, y, z are collinear. This result extends a classical result of Laman on the existence of a rigid framework on G. Our proof leads to an efficient algorithm which can test whether G satisfies the condition.
Supported by the MTA-ELTE Egerváry Research Group on Combinatorial Optimization, and the Hungarian Scientific Research Fund
grant no. F034930, T037547, and FKFP grant no. 0143/2001. 相似文献
17.
Maria Charina Mihai Putinar Claus Scheiderer Joachim Stöckler 《Constructive Approximation》2013,38(2):253-276
Recent advances in real algebraic geometry and in the theory of polynomial optimization are applied to answer some open questions in the theory of multivariate tight wavelet frames whose generators have at least one vanishing moment. Namely, several equivalent formulations of the so-called Unitary Extension Principle (UEP) are given in terms of Hermitian sums of squares of certain nonnegative Laurent polynomials and in terms of semidefinite programming. These formulations merge recent advances in real algebraic geometry and wavelet frame theory and lead to an affirmative answer to the long-standing open question of the existence of tight wavelet frames in dimension d=2. They also provide, for every d, efficient numerical methods for checking the existence of tight wavelet frames and for their construction. A class of counterexamples in dimension d=3 show that, in general, the so-called sub-QMF condition is not sufficient for the existence of tight wavelet frames. Stronger sufficient conditions for determining the existence of tight wavelet frames in dimension d≥3 are derived. The results are illustrated on several examples. 相似文献
18.
We give a necessary and sufficient condition for the existence of a tree of order n with a given degree set. We relate this to a well-known linear Diophantine problem of Frobenius. 相似文献
19.
A pitch tournament is a resolvable or near resolvable(ν,8,7) BIBD that satisfies certain criteria in addition to theusual condition that ν ≡ 0 or 1 (mod 8). Here we establish that for the case ν = 8n the necessary condition forpitch tournaments is sufficient for all n > 1615, with at most 187 smaller exceptions. This complements our earlier study of the ν = 8n + 1 case, where we established sufficiency for all n > 224, with at most 28 smaller exceptions. The four missing cases for (ν,8,7) BIBDs are provided, namely ν∈{48,56,96,448}, thereby establishing that the necessary existence conditions are sufficient without exception. Some constructions for resolvable designs are also provided, reducing the existence question for (ν,8,7) RBIBDs to 21 possible exceptions. © 2001 John Wiley & Sons, Inc. J Combin Designs 9: 334–356, 2001 相似文献
20.
We obtain a priori estimates for solutions to the prescribed scalar curvature equation on S
3. The usual non-degeneracy assumption on the curvature function is replaced by a new condition, which is necessary and sufficient
for the existence of a priori estimates, when the curvature function is a positive Morse function. 相似文献