共查询到20条相似文献，搜索用时 46 毫秒
1.
José Rodríguez 《Archiv der Mathematik》2007,88(1):62-70
Let X be a weakly Lindel?f determined Banach space. We prove that the following two statements are equivalent:
Some applications and related examples are given.
Received: 11 January 2006; Revised: 24 May 2006 相似文献
| (i) | Every Radon probability measure on (BX*, w*) has separable support. |
| (ii) | Every countably additive X*-valued measure with σ-finite variation has norm separable range. |
2.
3.
P. Moszkowski 《Periodica Mathematica Hungarica》1989,20(2):147-154
The major sequences of lengthn are defined as the words withn letters taken from the integers 1, 2, ,n and containing at least
相似文献
| 1. | letter equal ton |
| 2. | letters equal or more thann – 1,n – 1 letters equal or more than 2. |
4.
We present a new pivot-based algorithm which can be used with minor modification for the enumeration of the facets of the
convex hull of a set of points, or for the enumeration of the vertices of an arrangement or of a convex polyhedron, in arbitrary
dimension. The algorithm has the following properties:
For example, the algorithm finds thev vertices of a polyhedron inR
d defined by a nondegenerate system ofn inequalities (or, dually, thev facets of the convex hull ofn points inR
d, where each facet contains exactlyd given points) in timeO(ndv) andO(nd) space. Thev vertices in a simple arrangement ofn hyperplanes inR
d can be found inO(n
2
dv) time andO(nd) space complexity. The algorithm is based on inverting finite pivot algorithms for linear programming. 相似文献
| (a) | Virtually no additional storage is required beyond the input data. |
| (b) | The output list produced is free of duplicates. |
| (c) | The algorithm is extremely simple, requires no data structures, and handles all degenerate cases. |
| (d) | The running time is output sensitive for nondegenerate inputs. |
| (e) | The algorithm is easy to parallelize efficiently. |
5.
T. E. Armstrong 《International Journal of Game Theory》1991,20(1):65-90
We consider games in coalition function form on a, generally infinite, algebra of coalitions. For finite algebras the additive part mappingv E(v ¦) is the usual. The concern here is the analogue for infinite algebras. The useful construction is the finitely additive stochastic process of additive parts of the game on the filtration
f
of finite subalgebras of.It is shown that
is an isomorphism between:
相似文献
| a) | Additive games and martingales |
| b) | Superadditive games and supermartingales |
| c) | Shapley's games of bounded deviationBD() in his (1953) dissertation and bounded F-processes of Armstrong (1983) |
| d) | Gilboa's spaceBS() (1989) and bounded processes of Armstrong (1983) |
6.
The star unfolding of a convex polytope with respect to a pointx on its surface is obtained by cutting the surface along the shortest paths fromx to every vertex, and flattening the surface on the plane. We establish two main properties of the star unfolding:
These two properties permit conceptual simplification of several algorithms concerned with shortest paths on polytopes, and
sometimes a worst-case complexity improvement as well:
相似文献
| 1. | It does not self-overlap: it is a simple polygon. |
| 2. | The ridge tree in the unfolding, which is the locus of points with more than one shortest path fromx, is precisely the Voronoi diagram of the images ofx, restricted to the unfolding. |
| • | The construction of the ridge tree (in preparation for shortest-path queries, for instance) can be achieved by an especially simpleO(n 2) algorithm. This is no worst-case complexity improvement, but a considerable simplification nonetheless. |
| • | The exact set of all shortest-path “edge sequences” on a polytope can be found by an algorithm considerably simpler than was known previously, with a time improvement of roughly a factor ofn over the old bound ofO(n 7 logn). |
| • | The geodesic diameter of a polygon can be found inO(n 9 logn) time, an improvement of the previous bestO(n 10) algorithm. |
7.
Marcel Erné 《Algebra Universalis》1993,30(4):538-580
We study several kinds of distributivity for concept lattices of contexts. In particular, we find necessary and sufficient conditions for a concept lattice to be
In cases (2), (4) and (5), our criteria are first order statements on objects and attributes of the given context. Several applications are obtained by considering the completion by cuts and the completion by lower ends of a quasiordered set as special types of concept lattices. Various degrees of distributivity for concept lattices are expressed by certain separation axioms for the underlying contexts. Passing to complementary contexts makes some statements and proofs more elegant. For example, it leads to a one-to-one correspondence between completely distributive lattices and so-called Cantor lattices, and it establishes an equivalence between partially ordered sets and doubly founded reduced contexts with distributive concept lattices. 相似文献
| (1) | distributive, |
| (2) | a frame (locale, complete Heyting algebra), |
| (3) | isomorphic to a topology, |
| (4) | completely distributive, |
| (5) | superalgebraic (i.e., algebraic and completely distributive). |
8.
9.
Laurent Bartholdi 《Israel Journal of Mathematics》2006,154(1):93-139
We develop the theory of “branch algebras”, which are infinite-dimensional associative algebras that are isomorphic, up to
taking subrings of finite codimension, to a matrix ring over themselves. The main examples come from groups acting on trees.
In particular, for every field
% MathType!End!2!1! we contruct a
% MathType!End!2!1! which
The author acknowledges support from TU Graz and UC Berkeley, where part of this research was conducted. 相似文献
| – | • is finitely generated and infinite-dimensional, but has only finitedimensional quotients; |
| – | • has a subalgebra of finite codimension, isomorphic toM 2(k); |
| – | • is prime; |
| – | • has quadratic growth, and therefore Gelfand-Kirillov dimension 2; |
| – | • is recursively presented; |
| – | • satisfies no identity; |
| – | • contains a transcendental, invertible element; |
| – | • is semiprimitive if % MathType!End!2!1! has characteristic ≠2; |
| – | • is graded if % MathType!End!2!1! has characteristic 2; |
| – | • is primitive if % MathType!End!2!1! is a non-algebraic extension of % MathType!End!2!1!; |
| – | • is graded nil and Jacobson radical if % MathType!End!2!1! is an algebraic extension of % MathType!End!2!1!. |
10.
Ronen Peretz 《Israel Journal of Mathematics》1999,109(1):181-187
LetF(X, Y) be a two dimensional polynomial map overC. We show how to use the notion of induced resultants in order to give short and elementary proofs to the following three
theorems:
相似文献
| 1. | If the Jacobian of F is a non-zero constant, then the image of F contains all of C2 except for a finite set. |
| 2. | If F is invertible, then the inverse map is determined by the free terms of the induced resultants. |
| 3. | If F is invertible, then the degree of F equals the degree of its inverse. |
11.
Yuji Kobayashi 《Archiv der Mathematik》2005,85(3):227-232
Let k ≧ 3 be an integer or k = ∞ and let K be a field. There is a recursive family
of finitely presented groups Gn over a fixed finite alphabet with solvable word problem such that
Received: 22 July 2004 相似文献
| (1) | the center of Gn is trivial for every |
| (2) | the dimension d(n) of the center of the group algebra K · Gn over K is either 1 or k, and |
| (3) | it is undecidable given n whether d(n) = 1 or d(n) = k. |
12.
Graham Everest 《Mathematical Intelligencer》1998,20(3):9-16
Conclusions Mahler’s measure is alive and well in several quite diverse contexts. The differing points of view seem to generate a healthy
friction. If the general level of health is measured by the quantity and quality of unsolved problems, then it may help to
list these.
相似文献
| 1. | Lehmer’s Problem. |
| 2. | The elliptic analogue of Lehmer, at least in tractable special cases. |
| 3. | An explanation of Boyd’s remarkable formulae. It seems thatK-theory should provide the conceptual framework. More generally, perhaps values of the elliptic Mahler measure will arise as values of L-functions of higher-dimensional varieties. |
| 4. | It looks almost certain that the elliptic Mahler measure should arise as an entropy. This would form a fascinating bridge between two large areas of interest. Ward and I have begun to write about this [10]. At the very least, this would show that the global canonical height of an algebraic point on an elliptic curve arises as an entropy. But of what, and what does this mean? |
| 5. | There are many other pretty results about the classical Mahler measure which could be lifted to the elliptic setting. |
13.
14.
G. Forst 《Inventiones Mathematicae》1976,34(2):135-150
Continuing earlier work on construction of harmonic spaces from translation invariant Dirichlet spaces defined on locally compact abelian groups, it is shown that the potential kernel for a non-symmetric translation invariant Dirichlet form on a locally compact abelian group under the extra assumptions that
相似文献
| (i) | the potential kernel is absolutely continuous and the canonical l.s.c. density is continuous in the complement of the neutral element. |
| (ii) | the theory is of local type. |
| (iii) | the underlying group is not discrete, can be interpreted as the potential kernel for a translation invariant axiomatic theory of harmonic functions, in which (among other properties) the domination axiom is fulfilled. |
15.
Given a connected graph G, a vertex v of G is said to be a branch vertex if its degree is greater than 2. We consider two problems arising in the context of optical networks:
For these NP-hard problems, heuristics, that give good quality solutions, do not exist in the literature. In this paper we
analyze the relation between the problems, provide a single commodity flow formulation to solve the problems by means of a
solver and develop different heuristic strategies to compute feasible solutions that are compared with the exact ones. Our
extensive computational results show the algorithms to be very fast and effective. 相似文献
| (i) | Finding a spanning tree of G with the minimum number of branch vertices and |
| (ii) | Finding a spanning tree of G such that the degree sum of the branch vertices is minimized. |
16.
Walter Gómez Bofill 《Mathematical Methods of Operations Research》1998,47(3):473-497
We discuss three scalarizations of the multiobjectie optimization from the point of view of the parametric optimization. We analyze three important aspects:
This paper is a short version of the thesis of the author at the University of Havanna, Department of Mathematics Havanna, Cuba. 相似文献
| i) | What kind of singularities may appear in the different parametrizations |
| ii) | Regularizations in the sense of Jongen, Jonker and Twilt, and in the sense of Kojima and Hirabayashi. |
| iii) | The Mangasarian-Fromovitz Constraint Qualification for the first parametrization. |
17.
Yōhei Yamasaki 《Graphs and Combinatorics》1989,5(1):275-282
We have generalized the theory of Shannon's games in [10]. In this paper, we treat a game on a graph with an action of elementary abelian group but our decision of the winner is more general. Our theory can be applied for non-negative integersn andr, to the two games on a graph withn + 1 distinguished terminals whose rules are as follows:
Dedicated to Professor Sin Hitotumatu for his 60'th birthday 相似文献
| (1) | the players Short and Cut play alternately to choose an edge, |
| (2) | the former contracts it and the later deletes it |
| (3) | the former if and only if he connects the terminals into at mostn – r + 1 ones. |
18.
Belmesnaoui Aqzzouz 《Rendiconti del Circolo Matematico di Palermo》2006,55(2):147-162
We show that if (K,L) is a semi-abelian category, there exists an abelian categoryK
x with the followings properties:
相似文献
| 1 | The categoryK is a full subcategory ofK x. |
| 2 | The free objects ofK are projectives inK x. |
| 3 | A sequence ofK-morphismes isK-exact if, and only if, it isK x-exact. |
| 4 | To each objectU ofK x we can associate a surjections:X→U whereX is an object ofK. |
19.
A. A. Tuganbaev 《Mathematical Notes》1998,64(1):116-120
Rings over which every nonzero right module has a maximal submodule are calledright Bass rings. For a ringA module-finite over its centerC, the equivalence of the following conditions is proved:
Translated fromMatematicheskie Zametki, Vol. 64, No. 1, pp. 136–142, July, 1998.This research was partially supported by the Russian Foundation for Basic Research under grant No. 96-01-00627. 相似文献
| (1) | A is a tight Bass ring; |
| (2) | A is a left Bass ring; |
| (3) | A/J(A) is a regular ring, andJ(A) is a right and leftt-nilpotent ideal. |
20.
A graph G is a {d, d+k}-graph, if one vertex has degree d+k and the remaining vertices of G have degree d. In the special case of k = 0, the graph G is d-regular. Let k, p ⩾ 0 and d, n ⩾ 1 be integers such that n and p are of the same parity. If G is a connected {d, d+k{-graph of order n without a matching M of size 2|M| = n − p, then we show in this paper the following: If d = 2, then k ⩾ 2(p + 2) and
If d ⩾ 3 is odd and t an integer with 1 ⩽ t ⩽ p + 2, then
If d ⩾ 4 is even, then
The special case k = p = 0 of this result was done by Wallis [6] in 1981, and the case p = 0 was proved by Caccetta and Mardiyono [2] in 1994. Examples show that the given bounds (i)–(viii) are best possible. 相似文献
| (i) | n ⩾ k + p + 6. |
| (ii) | n ⩾ d + k + 1 for k ⩾ d(p + 2) |
| (iii) | n ⩾ d(p + 3) + 2t + 1 for d(p + 2 −t) + t ⩽ k ⩽ d(p + 3 −t) + t − 3 |
| (iv) | n ⩾ d(p + 3) + 2p + 7 for k ⩽ p. |
| (v) | n ⩾ d + k + 2 − η for k ⩾ d(p + 3) + p + 4 + η |
| (vi) | n ⩾ d + k + p + 2 − 2t = d(p + 4) + p + 6 for k = d(p + 3) + 4 + 2t and p ⩾ 1 |
| (vii) | n ⩾ d + k + p + 4 for d(p + 2) ⩽ k ⩽ d(p + 3) + 2 |
| (viii) | n ⩾ d(p + 3) + p + 4 for k ⩽ d(p + 2) − 2, where 0 ⩽ t ⩽ 1/2p − 1 and η = 0 for even p and 0 ⩽ t ⩽ 1/2(p − 1) and η = 1 for odd p. |