共查询到20条相似文献,搜索用时 15 毫秒
1.
《Quaestiones Mathematicae》2013,36(2):105-140
ABSTRACT This article is concerned with variational problems whose field variables are functions on a product manifold M x G of two manifolds M and G. These field variables are denoted by ψhαj in local coordinates (h, j = 1,…,n = dim M, α = 1,…,r = dim G), and it is supposed that they behave as type (0,2) tensor fields under coordinate transformations on M. The dependance of ψhαj on the coordinates of G is specified by a generalized gauge transformation that depends on a map h: M → G. The requirement that the action integral be independent of the choice of this map imposes conditions on the matrices that define the gauge transformation in a manner that gives rise to a Lie algebra, which in turn imposes a Lie group structure on the manifold G. As in the case of standard gauge theories (whose gauge potentials consist of r type (0,1) vector fields on M) certain combinations of the first derivatives of the field variations ψhαj give rise to a set of r tensors on M, the so-called field strengths, that can be regarded as special representations of G. These may be used to construct appropriate connection and curvature forms of M. The Euler-Lagrange equations of the variational problem, when expressed in terms of such connections, admit a particularly simple representation and give rise a set of n conservation laws in terms of type (1,1) tensor fields. 相似文献
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《Quaestiones Mathematicae》2013,36(1-2):259-274
Abstract This paper brings together the theory of observational cosmology and the null-cone characteristic initial value problem (CIVP) of numerical relativity. A computer code is constructed which calculates the past behaviour of the Universe from input data that is, in principle, measurable. For practical reasons the code is limited to the case of axisymmetry without rotation. The construction of the code brings to light an interesting general point about observational cosmology. In a big-bang universe it is impossible, even in principle, to determine the state of the universe at early times. For the Einstein-de Sitter model this limit is t 0/27, where t 0 means now. 相似文献
4.
《Quaestiones Mathematicae》2013,36(1-2):89-99
Abstract We show that the Tarski-Kantorovitch Principle for continuous maps on a partially ordered set yields some fixed point theorems for contractive maps on a uniform space. Our proofs do not depend on the Axiom of Choice. 相似文献
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Shin-ya Matsushita Wataru Takahashi 《Nonlinear Analysis: Theory, Methods & Applications》2010,73(6):1466-6030
Let C be a nonempty, closed and convex subset of a uniformly convex and smooth Banach space and let {Tn} be a family of mappings of C into itself such that the set of all common fixed points of {Tn} is nonempty. We consider a sequence {xn} generated by the hybrid method by generalized projection in mathematical programming. We give conditions on {Tn} under which {xn} converges strongly to a common fixed point of {Tn} and generalize the results given in [12], [14], [13] and [11]. 相似文献
7.
In 1943, Hadwiger made the conjecture that every k-chromatic graph has a K
k
-minor. This conjecture is, perhaps, the most interesting conjecture of all graph theory. It is well known that the case k=5 is equivalent to the Four Colour Theorem, as proved by Wagner [39] in 1937. About 60 years later, Robertson, Seymour and Thomas [29] proved that the case k=6 is also equivalent to the Four Colour Theorem. So far, the cases k7 are still open and we have little hope to verify even the case k=7 up to now. In fact, there are only a few theorems concerning 7-chromatic graphs, e. g. [17].In this paper, we prove the deep result stated in the title, without using the Four Colour Theorem [1,2,28]. This result verifies the first unsettled case m=6 of the (m,1)-Minor Conjecture which is a weaker form of Hadwigers Conjecture and a special case of a more general conjecture of Chartrand et al. [8] in 1971 and Woodall [42] in 1990.The proof is somewhat long and uses earlier deep results and methods of Jørgensen [20], Mader [23], and Robertson, Seymour and Thomas [29].* Research partly supported by the Japan Society for the Promotion of Science for Young Scientists. Research partly supported by the Danish Natural Science Research Council.Dedicated to Professor Mike Plummer on the occasion of his sixty-fifth birthday. 相似文献
8.
Sheng Bau 《Quaestiones Mathematicae》2018,41(4):541-548
We show that if G is a 3-connected graph of minimum degree at least 4 and with |V (G)| ≥ 7 then one of the following is true: (1) G has an edge e such that G/e is a 3-connected graph of minimum degree at least 4; (2) G has two edges uv and xy with ux, vy, vx ∈ E(G) such that the graph G/uv/xy obtained by contraction of edges uv and xy in G is a 3-connected graph of minimum degree at least 4; (3) G has a vertex x with N(x) = {x1, x2, x3, x4} and x1x2, x3x4 ∈ E(G) such that the graph (G ? x)/x1x2/x3x4 obtained by contraction of edges x1x2 and x3x4 in G – x is a 3-connected graph of minimum degree at least 4.Each of the three reductions is necessary: there exists an infinite family of 3- connected graphs of minimum degree not less than 4 such that only one of the three reductions may be performed for the members of the family and not the two other reductions. 相似文献
9.
《数学物理学报(B辑英文版)》2001,(1)
10.
We prove that for a fixed integer s2 every K
s,s
-free graph of average degree at least r contains a K
p
minor where
. A well-known conjecture on the existence of dense K
s,s
-free graphs would imply that the value of the exponent is best possible. Our result implies Hadwigers conjecture for K
s,s
-free graphs whose chromatic number is sufficiently large compared with s. 相似文献
11.
A family of projective splitting methods for the sum of two maximal monotone operators 总被引:1,自引:0,他引:1
A splitting method for two monotone operators A and B is an algorithm that attempts to converge to a zero of the sum A + B by solving a sequence of subproblems, each of which involves only the operator A, or only the operator B. Prior algorithms of this type can all in essence be categorized into three main classes, the Douglas/Peaceman-Rachford class, the forward-backward class, and the little-used double-backward class. Through a certain “extended” solution set in a product space, we construct a fundamentally new class of splitting methods for pairs of general maximal monotone operators in Hilbert space. Our algorithms are essentially standard projection methods, using splitting decomposition to construct separators. We prove convergence through Fejér monotonicity techniques, but showing Fejér convergence of a different sequence to a different set than in earlier splitting methods. Our projective algorithms converge under more general conditions than prior splitting methods, allowing the proximal parameter to vary from iteration to iteration, and even from operator to operator, while retaining convergence for essentially arbitrary pairs of operators. The new projective splitting class also contains noteworthy preexisting methods either as conventional special cases or excluded boundary cases. Dedicated to Clovis Gonzaga on the occassion of his 60th birthday. 相似文献
12.
《Quaestiones Mathematicae》2013,36(3):333-350
Abstract During my long life I published many papers with related titles. To keep this paper short I will not give proofs and will restrict myself to problems in graph theory, but I will try to give references and make these as complete as possible. I will start with Turk type problems in extremal graph theory. 相似文献
13.
In this paper we consider an optimal control problem for a nonlinear second order ordinary differential equation with integral constraints. A necessary optimality condition in form of the Pontryagin minimum principle is derived. The proof is based on McShane-variations of the optimal control, a thorough study of their behaviour in dependence of some denning parameters, a generalized Green formula for second order ordinary differential equations with measurable coefficients and certain tools of convex analysis.Dedicated to Lothar von Wolfersdorf on the occasion of his 60th birthday 相似文献
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15.
The local tree-width of
a graph G=(V,E) is the function
ltwG : that associates
with every r the maximal
tree-width of an r-neighborhood in
G. Our main grapht heoretic
result is a decomposition theorem for graphs with excluded
minors, which says that such graphs can be decomposed into trees
of graphs of almost bounded local tree-width.As an application of this theorem, we show that a number
of combinatorial optimization problems, suchas
Minimum Vertex Cover,
Minimum Dominating Set,
and Maximum Independent
Set have a polynomial time approximation scheme when
restricted to a class of graphs with an excluded minor. 相似文献
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17.
Chaichana Jaiboon 《Nonlinear Analysis: Theory, Methods & Applications》2010,73(5):1180-1202
In this paper, we introduce a new general iterative method for finding a common element of the set of solutions of a mixed equilibrium problem (MEP), the set of fixed points of an infinite family of nonexpansive mappings and the set of solutions of variational inequalities for a ξ-inverse-strongly monotone mapping in Hilbert spaces. Furthermore, we establish the strong convergence theorem for the iterative sequence generated by the proposed iterative algorithm under some suitable conditions, which solves some optimization problems. Our results extend and improve the recent results of Yao et al. [Y. Yao, M.A. Noor, S. Zainab, Y.C. Liou, Mixed equilibrium problems and optimization problems, J. Math. Anal. Appl. 354 (2009) 319-329; Y. Yao, M. A. Noor, Y.C. Liou, On iterative methods for equilibrium problems, Nonlinear Anal. 70 (1) (2009) 479-509] and many others. 相似文献
18.
Stable monotone variational inequalities 总被引:3,自引:0,他引:3
L. McLinden 《Mathematical Programming》1990,48(1-3):303-338
Variational inequalities associated with monotone operators (possibly nonlinear and multivalued) and convex sets (possibly unbounded) are studied in reflexive Banach spaces. A variety of results are given which relate to a stability concept involving a natural parameter. These include characterizations useful as criteria for stable existence of solutions and also several characterizations of surjectivity. The monotone complementarity problem is covered as a special case, and the results are sharpened for linear monotone complementarity and for generalized linear programming.Sponsored by the United States Army under Contract No. DAAG29-80-C-0041 at the University of Wisconsin - Madison and by the National Science Foundation under Grant No. DMS-8405179 at the University of Illinois at Urbana-Champaign. 相似文献
19.
Sisir Roy 《Acta Appl Math》1992,26(3):209-218
The random zero point field induces the probabilistic aspect in the geometry of background spacetime. The corrections to the metric tensor for Riemannian or pseudo-Euclidean spaces are calculated by averaging over the ensemble of random A
(x). This provides a cut-off procedure which yields a finite energy density for the vacuum state. 相似文献
20.
A. D. Ioffe R. T. Rockafellar 《Calculus of Variations and Partial Differential Equations》1996,4(1):59-87
Necessary conditions are developed for a general problem in the calculus of variations in which the Lagrangian function, although finite, need not be Lipschitz continuous or convex in the velocity argument. For the first time in such a broadly nonsmooth, nonconvex setting, a full subgradient version of Euler's equation is derived for an arc that furnishes a local minimum in the classical weak sense, and the Weierstrass inequality is shown to accompany it when the arc gives a local minimum in the strong sense. The results are achieved through new techniques in nonsmooth analysis.This research was supported in part by funds from the U.S.-Israel Science Foundation under grant 90-00455, and also by the Fund for the Promotion of Research at the Technion under grant 100-954 and by the U.S. National Science Foundation under grant DMS-9200303.This article was processed by the author using the
style filepljourlm from Springer-Verlag. 相似文献