共查询到20条相似文献，搜索用时 31 毫秒
1.
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!. |
2.
3.
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). |
4.
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. |
5.
Reuben Hersh 《Mathematical Intelligencer》2001,23(3):52-60
Summary The responses were very varied. But these five statements would be generally accepted:
Until we find a consensus about which advances are “major,” we can’t refute Hardy’s claim that no major advance has been made
by a mathematician over 50. But his slogan, “Mathematics is a young man’s game,” is misleading, even harmful. So far as it
may discourage people from mathematics when they’re no longer young, it’s unjustified and destructive. 相似文献
| 1. | There’s tremendous variation in how mathematicians age. No one pattern describes everybody. |
| 2. | Many mathematicians have been productive in advanced age. |
| 3. | To most (not all!) mathematicians, aging brings losses in memory and computing ability. These may be compensated by broader perspective and mature judgment. Possibly more serious is slowness or difficulty in learning new material. Some responses were more specific. |
| 4. | Live healthy and follow your own bent, not the pressures of others. |
| 5. | Older and retired mathematicians are an under-utilized resource for the mathematics community. |
6.
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. |
7.
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. |
8.
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) |
9.
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. |
10.
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. |
11.
The paper deals with three related issues.
This work was done while this author was visiting at the Department of Managerial Economics and Decision Sciences, J. L. Kellogg Graduate School of Management, Northwestern University. 相似文献
| 1. | It introduces a measure of partial subgame perfection for equilibria of repeated games. |
| 2. | It illustrates that the folk-theorem discontinuity generated by small complexity costs, as exhibited by Abreu and Rubinstein, does not exist in the presence of any level of perfection. |
| 3. | It shows that reactive strategy equilibria, such as tit-for-tat, cannot be subgame perfect, even partially so. As a corollary, this shows a need to use full automata rather than exact automata when studying complexity and perfection in repeated games. |
12.
We construct a self-avoiding process taking values in the finite Sierpinski gasket, and study its properties. We then study continuum limit processes that are suggested by the statistical mechanics of self-avoiding paths on the pre-Sierpinski gasket. We prove that there are three types of continuum limit processes according to the parameters defining the statistical mechanics of self-avoiding paths:
相似文献
| (i) | the self-avoiding process we construct in this paper; |
| (ii) | a deterministic motion along a Peano curve on the finite Sierpinski gasket; |
| (iii) | a deterministic motion along a line segment. |
13.
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. |
14.
Birge Zimmermann Huisgen 《manuscripta mathematica》1991,70(1):157-182
We show that all projective resolutions over a monomial relations algebra Λ simplify drastically at the stage of the second
syzygy; more precisely, we show that the kernel of any homomorphism between two projective left Λ-modules is isomorphic to
a direct sum of principal left ideals generated by paths. As consequences, we obtain:
This research was partially supported by a grant from the National Science Foundation. 相似文献
| (a) | a tight approximation of the finitistic dimensions of Λ in terms of the (very accessible) projective dimensions of the principal left ideals generated by paths; |
| (b) | a basis for comparison of the ‘big’ and ‘little’ finitistic dimensions of Λ, yielding in particular that these two invariants cannot differ by more than 1 and that they are equal in ‘most’ cases; |
| (c) | manageable algorithms for computation of finitistic dimensions. |
15.
Following our approach to metric Lie algebras developed in a previous paper we propose a way of understanding pseudo-Riemannian
symmetric spaces which are not semisimple. We introduce cohomology sets (called quadratic cohomology) associated with orthogonal
modules of Lie algebras with involution. Then we construct a functorial assignment which sends a pseudo-Riemannian symmetric
space M to a triple consisting of:
That leads to a classification scheme of indecomposable nonsimple pseudo-Riemannian symmetric spaces. In addition, we obtain
a full classification of symmetric spaces of index 2 (thereby completing and correcting in part earlier classification results
due to Cahen and Parker and to Neukirchner). 相似文献
| (i) a Lie algebra with involution (of dimension much smaller than the dimension of the transvection group of M); | |
| (ii) a semisimple orthogonal module of the Lie algebra with involution; and | |
| (iii) a quadratic cohomology class of this module. |
16.
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. |
17.
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. |
18.
19.
In the framework of dynamic programming we provide two results:
This research was supported by the fund for the promotion of research in the technion. 相似文献
| – | An example where uniform convergence of theT-stage value does not imply equality of the limit and the lower infinite value. |
| – | Generalized Tauberian theorems, that relate uniform convergence of theT-stage value to uniform convergence of values associated with a general distribution on stages. |
20.
Let (G, τ) be a commutative Hausdorff locally solid lattice group. In this paper we prove the following:
As an application, a version of the Nikodym boundedness theorem for set functions with values in a class of locally solid
topological groups is established. 相似文献
| (1) | If (G, τ) has the A(iii)-property, then its completion is an order-complete locally solid lattice group. |
| (2) | If G is order-complete and τ has the Fatou property, then the order intervals of G are τ-complete. |
| (3) | If (G, τ) has the Fatou property, then G is order-dense in Ĝ and has the Fatou property. |
| (4) | The order-bound topology on any commutative lattice group is the finest locally solid topology on it. |