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1.
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. |
2.
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!. |
3.
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. |
4.
A nearlattice S is a meet semilattice together with the property that any two elements possessing a common upper bound have a supremum. Here the authors have introduced the notion of sectionally semicomplemented distributive nearlattices and given several characterizations of them. The skeleton SCon(S) of Con(S), the congruence lattice, consists of all those nearlattice congruences which are the pseudocomplements of members of Con(S). The relationship between skeletal congruences and kernel of skeletal congruences leads to numerous characterizations of sectionally semicomplemented distributive nearlattices and semiboolean algebras. For example we prove, for a distributive nearlattice S with 0, the following conditions are equivalent:
AMS Subject Classifications (1991): 06A12, 06A99, 06B10. 相似文献
| (i) | S is sectionally semicomplemented |
| (ii) | The map Θ Θ ̸ker Θ of SCon(S) onto KSCon(S) is one-to-one. |
| (iii) | The map Θ Θ ̸ker Θ of SCon(S) onto KSCon(S) preserves finite joins. |
| (iv) | The map Θ Θ ker ̸Θ is a lattice isomorphism of SCon(S) onto KSCon(S), whose inverse is the map J ̸ Θ(J)**. |
5.
John W. Snow 《Algebra Universalis》2005,54(1):65-71
A congruence lattice L of an algebra A is called power-hereditary if every 0-1 sublattice of Ln is the congruence lattice of an algebra on An for all positive integers n. Let A and B be finite algebras. We prove
Received November 11, 2004; accepted in final form November 23, 2004. 相似文献
| • | If ConA is distributive, then every subdirect product of ConA and ConB is a congruence lattice on A × B. |
| • | If ConA is distributive and ConB is power-hereditary, then (ConA) × (ConB) is powerhereditary. |
| • | If ConA ≅ N5 and ConB is modular, then every subdirect product of ConA and ConB is a congruence lattice. |
| • | Every congruence lattice representation of N5 is power-hereditary. |
6.
Marie-Claude Arnaud 《Annales Henri Poincare》2008,9(5):881-926
In this article, we prove different results concerning the regularity of the C
0-Lagrangian invariant graphs of the Tonelli flows. For example :
Submitted: July 23, 2007. Accepted: February 14, 2008. 相似文献
| • | in dimension 2 and in the autonomous generic case, we prove that such a graph is in fact C 1 on some set with (Lebesgue) full measure; |
| • | under certain dynamical additional hypothesis, we prove that these graphs are C 1. |
Résumé. Dans cet article, on démontre différents résultats concernant la régularité des graphes C 0-lagrangiens invariants par des flots de Tonelli. Par exemple :
• en dimension 2, dans le cas autonome et générique, on montre que ces graphes sont de classe C 1 sur un ensemble de mesure (de Lebesque) pleine; • sous certaines hypothèses concernant la dynamique restreinte, on montre que ces graphes sont de classe C 1.
Submitted: July 23, 2007. Accepted: February 14, 2008. 相似文献
7.
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. |
8.
In this paper, we discuss the representation-finite selfinjective artin algebras of classB
n andC
n and obtain the following main results:
For any fieldk, let Λ be a representation-finite selfinjective artin algebras of classB
n orC
n overk.
相似文献
| (a) | We give the configuration ofZB n andZC n. |
| (b) | We show that Λ is standard. |
| (c) | Under the condition ofk being a perfect field, we describe Λ by boundenk-species and show that Λ is a finite covering of the trivial extension of some tilted algebra of typeB n orC n. |
9.
We consider smooth non-degenerate surfaces in ℙ4, and prove that there is a finite number of such surfaces which are:
A complete list is given in both cases. 相似文献
| (a) | sectionally non-special, i.e.h1(O C(1))=0, where C is a general hyperplane section of S; or |
| (b) | not of general type and non-special (i.e. h1(O C(1))=0. |
10.
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) |
11.
We show that the following two problems are polynomially equivalent:
As a consequence, an optimality testing oracle may be used to design a polynomial time algorithm for approximately solving the (weighted) Max-Cut Problem. 相似文献
| 1) | Given a (weighted) graphG, and a cutC ofG, decide whetherC is maximal or not. |
| 2) | Given a (weighted) graphG, and a cutC ofG, decide whetherC is maximal or not, and in case it is not, find a better solutionC. |
12.
13.
GuangYan Jia 《中国科学A辑(英文版)》2009,52(4):785-793
In this paper, we prove that for a sublinear expectation ɛ[·] defined on L
2(Ω,), the following statements are equivalent:
Furthermore, we prove a sandwich theorem for subadditive expectation and superadditive expectation.
This work was supported by National Basic Research Program of China (973 Program) (Grant No. 2007CB814901) (Financial Risk)
and National Natural Science Foundation of China (Grant No. 10671111) 相似文献
| (i) | ɛ is a minimal member of the set of all sublinear expectations defined on L 2(Ω,) |
| (ii) | ɛ is linear |
| (iii) | the two-dimensional Jensen’s inequality for ɛ holds. |
14.
LetK be a class of spaces which are eigher a pseudo-opens-image of a metric space or ak-space having a compact-countable closedk-network. LetK′ be a class of spaces which are either a Fréchet space with a point-countablek-network or a point-G
δ
k-space having a compact-countablek-network. In this paper, we obtain some sufficient and necessary conditions that the products of finitely or countably many
spaces in the classK orK′ are ak-space. The main results are that
Project supported by the Mathematical Tianyuan Foundation of China 相似文献
| Theorem A | If X, Y∈K. Then X x Y is a k-space if and only if (X, Y) has the Tanaka's condition. |
| Theorem B | The following are equivalent: |
| (a) | BF(ω 2)is false. |
| (b) | For each X, Y ∈ K′, X x Y is a k-space if and only if (X,Y) has the Tanaka's condition. |
15.
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. |
16.
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. |
17.
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). |
18.
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. |
19.
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. |
20.
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. |