共查询到20条相似文献,搜索用时 0 毫秒
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Consider a convex polygon V
n
with n sides, perimeter P
n
, diameter D
n
, area A
n
, sum of distances between vertices S
n
and width W
n
. Minimizing or maximizing any of these quantities while fixing another defines 10 pairs of extremal polygon problems (one
of which usually has a trivial solution or no solution at all). We survey research on these problems, which uses geometrical
reasoning increasingly complemented by global optimization methods. Numerous open problems are mentioned, as well as series
of test problems for global optimization and non-linear programming codes. 相似文献
3.
In this article Turán-type problems for several triple systems arising from (k, k ? 2)-configurations [i.e. (k ? 2) triples on k vertices] are considered. It will be shown that every Steiner triple system contains a (k, k ? 2)-configuration for some k < c log n/ log log n. Moreover, the Turán numbers of (k, k ? 2)-trees are determined asymptotically to be ((k ? 3)/3).(n2) (1?o(1)). Finally, anti-Pasch hypergraphs avoiding (5, 3) -and (6, 4)-Configurations are considered. © 1993 John Wiley & Sons, Inc. 相似文献
4.
A. I. Stepanets 《Mathematical Notes》2007,82(5-6):660-676
In this paper, we consider extremal problems for numerical positive series. The terms of these series are pairwise products of the elements of two sequences, one of which is fixed and the other varies within a given set of sequences. We obtain exact solutions for a number of such problems. As one of the possible applications of the results obtained, we find solutions of some extremal problems related to best n-term approximations of periodic functions. 相似文献
5.
Samuel Krushkal 《Israel Journal of Mathematics》2009,172(1):279-307
The study of extremal problems for Fredholm eigenvalues was initiated by Schiffer in the context of the existence of conformal
maps onto canonical domains.
We present a different approach to solving rather general extremal problems for Fredholm eigenvalues related to appropriate
univalent functions with quasiconformal extensions. It involves the complex geometry of the universal Teichmüller space. 相似文献
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In this article, we consider the following problem. Given four distinct vertices v1,v2,v3,v4. How many edges guarantee the existence of seven connected disjoint subgraphs Xi for i = 1,…, 7 such that Xj contains vj for j = 1, 2, 3, 4 and for j = 1, 2, 3, 4, Xj has a neighbor to each Xk with k = 5, 6, 7. This is the so called “rooted K3, 4‐minor problem.” There are only few known results on rooted minor problems, for example, [15,6]. In this article, we prove that a 4‐connected graph with n vertices and at least 5n ? 14 edges has a rooted K3,4‐minor. In the proof we use a lemma on graphs with 9 vertices, proved by computer search. We also consider the similar problems concerning rooted K3,3‐minor problem, and rooted K3,2‐minor problem. More precisely, the first theorem says that if G is 3‐connected and e(G) ≥ 4|G| ? 9 then G has a rooted K3,3‐minor, and the second theorem says that if G is 2‐connected and e(G) ≥ 13/5|G| ? 17/5 then G has a rooted K3,2‐minor. In the second case, the extremal function for the number of edges is best possible. These results are then used in the proof of our forthcoming articles 7 , 8 . © 2007 Wiley Periodicals, Inc. J Graph Theory 55: 191–207, 2007 相似文献
8.
The chromatic neighborhood sequence of a graph G is the list of the chromatic numbers of the subgraphs induced by the neighborhoods of the vertices. We study the maximum multiplicity of this sequence, proving, amongst other things, that if a chromatic neighborhood sequence has t distinct values, the largest value being dt, then there is a value with multiplicity at least . This bound is asymptotically tight. © 2002 Wiley Periodicals, Inc. J Graph Theory 40: 68–74, 2002 相似文献
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S. Thiry 《Numerical Algorithms》1993,5(4):215-225
The problem of finding a Chebyshev solution of the real matrix equationAX+YB=C, whereC is anm×n matrix, is considered. This equation is equivalent to a linear system [I
n
A,B
T
I
m
]z=d. The characterization and the computation of best linear Chebyshev approximations are connected with the notion of extremal signature. The purpose of this paper is to analyze the extremal signatures of this problem. 相似文献
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V. B. Demidovich G. G. Magaril-Ilyaev V. M. Tikhomirov 《Journal of Mathematical Sciences》2007,142(2):1923-1932
The study of Tchebycheff spaces (generalizing the space of algebraic polynomials) and extremal problems related to them began
one and a half centuries ago. Recently, many facts of approximation theory have been understood and reinterpreted from the
point of view of general principles of the theory of extremum and convex duality. This approach not only allowed one to prove
the previously known results for algebraic polynomials and generalized polynomials in a unified way, but also enabled one
to obtain new results. In this paper, we work out this direction with special attention to the optimal recovery problems.
__________
Translated from Fundamentalnaya i Prikladnaya Matematika, Vol. 11, No. 2, pp. 87–100, 2005. 相似文献
14.
Bla Bollobs 《Journal of Graph Theory》1977,1(2):117-123
The aim of this note is to give an account of some recent results and state a number of conjectures concerning extremal properties of graphs. 相似文献
15.
Ralph J. Faudree Ronald J. Gould Michael S. Jacobson Richard H. Schelp 《Journal of Graph Theory》1987,11(4):555-564
We examine several extremal problems for graphs satisfying the property |N(x) ∪ N(y)| ? s for every pair of nonadjacent vertices x, y ? V(G). In particular, values for s are found that ensure that the graph contains an s-matching, a 1-factor, a path of a specific length, or a cycle of a specific length. 相似文献
16.
For a family $\boldmath{F}(k) = \{{\mathcal F}_1^{(k)}, {\mathcal F}_2^{(k)},\ldots,{\mathcal F}_t^{(k)}\}$ of k‐uniform hypergraphs let ex (n, F (k)) denote the maximum number of k‐tuples which a k‐uniform hypergraph on n vertices may have, while not containing any member of F (k). Let rk(n) denote the maximum cardinality of a set of integers Z?[n], where Z contains no arithmetic progression of length k. For any k≥3 we introduce families $\boldmath{F}(k) = \{{\mathcal F}_1^{(k)},{\mathcal F}_2^{(k)}\}$ and prove that nk?2rk(n)≤ex (nk2, F (k))≤cknk?1 holds. We conjecture that ex(n, F (k))=o(nk?1) holds. If true, this would imply a celebrated result of Szemerédi stating that rk(n)=o(n). By an earlier result o Ruzsa and Szemerédi, our conjecture is known to be true for k=3. The main objective of this article is to verify the conjecture for k=4. We also consider some related problems. © 2002 Wiley Periodicals, Inc. Random Struct. Alg. 20: 131–164, 2002. 相似文献
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M. P. Savelov 《Mathematical Methods of Statistics》2016,25(1):67-77
We consider a class of extremal problems for multiple hypothesis testing with set-valued decisions and given total variation distances between hypotheses. The quality of a test is measured by an arbitrary piecewise linear continuous function of the error probabilities. We show that the extremal value of the test quality may be found as a solution of some linear programming problem, so the original infinite-dimensional problem is reduced to a certain finite-dimensional one. 相似文献
19.
Given an open bounded connected set R
N
and a prescribed amount of two homogeneous materials of different density, for smallk we characterize the distribution of the two materials in that extremizes thekth eigenvalue of the resulting clamped membrane. We show that these extremizers vary continuously with the proportion of the two constituents. The characterization of the extremizers in terms of level sets of associated eigenfunctions provides geometric information on their respective interfaces. Each of these results generalizes toN dimensions the now classical one-dimensional work of M. G. Krein.The work of the first author was supported in part by NSF Grant DMS-8201719 (A. Manitius, P. I.), an IBM fellowship, a GE teaching incentive, and DARPA Contract F49620-87-C-0065. That of the second author was supported in part by ONR Grant N00014-84-5-516, AFOSR Grant AFOSR-86-0180, and NSF Grant DMS-8713722. 相似文献
20.
Given an open bounded connected set R
N
and a prescribed amount of two homogeneous materials of different density, for smallk we characterize the distribution of the two materials in that extremizes thekth eigenvalue of the resulting clamped membrane. We show that these extremizers vary continuously with the proportion of the two constituents. The characterization of the extremizers in terms of level sets of associated eigenfunctions provides geometric information on their respective interfaces. Each of these results generalizes toN dimensions the now classical one-dimensional work of M. G. Krein.The work of the first author was supported in part by NSF Grant DMS-8201719 (A. Manitius, P. I.), an IBM fellowship, a GE teaching incentive, and DARPA Contract F49620-87-C-0065. That of the second author was supported in part by ONR Grant N00014-84-5-516, AFOSR Grant AFOSR-86-0180, and NSF Grant DMS-8713722. 相似文献