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1.
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. |
2.
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. |
3.
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. |
4.
Non-singular solutions to the normalized Ricci flow equation 总被引：2，自引：0，他引：2
In this paper, we study non-singular solutions to Ricci flow on a closed manifold of dimension at least 4. Amongst other things
we prove that, if M is a closed 4-manifold on which the normalized Ricci flow exists for all time t > 0 with uniformly bounded sectional curvature, then the Euler characteristic . Moreover, the 4-manifold satisfies one of the followings
where (resp. ) is the Euler characteristic (resp. signature) of M.
The first author was supported by a NSF Grant of China and the Capital Normal University. 相似文献
| (i) | M is a shrinking Ricci soliton; |
| (ii) | M admits a positive rank F-structure; |
| (iii) | the Hitchin–Thorpe type inequality holds |
5.
6.
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. |
7.
Hans Munthe-Kaas 《BIT Numerical Mathematics》1998,38(1):92-111
We construct generalized Runge-Kutta methods for integration of differential equations evolving on a Lie group. The methods
are using intrinsic operations on the group, and we are hence guaranteed that the numerical solution will evolve on the correct
manifold. Our methods must satisfy two different criteria to achieve a given order.
These tasks are completely independent, so once correction functions are found to the given order, we can turn any classical
RK scheme into an RK method of the same order on any Lie group.
The theory in this paper shows the tight connections between the algebraic structure of the order conditions of RK methods
and the algebraic structure of the so called ‘universal enveloping algebra’ of Lie algebras. This may give important insight
also into the classical RK theory.
This work is sponsored by NFR under contract no. 111038/410, through the SYNODE project. WWW:http://www.math.ntnu.no/num/synode. 相似文献
| – | • CoefficientsA i,j andb j must satisfy the classical order conditions. This is done by picking the coefficients of any classical RK scheme of the given order. |
| – | • We must construct functions to correct for certain non-commutative effects to the given order. |
8.
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). |
9.
Joshua E. S. Socolar 《Mathematical Intelligencer》2007,29(2):33-38
I have exhibited several types of monotiles with matching rules that force the construction of a hexagonal parquet. The isohedral
number of the resulting tiling can be made as large as desired by increasing the aspect ratio of the monotile. Aside from
illustrating some elegant peculiarities of the hexagonal parquet tiling, the constructions demonstrate three points.
相似文献
| 1. | Monotiles with arbitrarily large isohedral number do exist; |
| 2. | The additional topological possibilities afforded in 3D allow construction of a simply connected monotile with a rule enforced by shape only, which is impossible for the hexagonal parquet in 2D; |
| 3. | The precise statement of the tiling problem matters— whether color matching rules are allowed; whether multiply connected shapes are allowed; whether spacefilling is required as opposed to just maximum density. So what about the quest for thek = ∞ monotile? Schmitt. |
10.
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. |
11.
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. |
12.
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. |
13.
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!. |
14.
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. |
15.
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. |
16.
In this paper, we show that algebraic extensions of semi-hyponormal operators (defined below) are subscalar. As corollaries we get the following:
From these results and [Es] it is known that such operators with rich spectra have nontrivial invariant subspaces.The second author was supported by the grant for the promotion of scientic research in women's universities. 相似文献
| (1) | Everyk-quasihyponormal operator is subscalar. |
| (2) | Every algebraic extension of Aluthge transforms ofp-hyponormal operators is subscalar. |
17.
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) |
18.
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
19.
This paper introduces the concept of orthogonal vector measures, and gives the Yosida-Hewittdecomposition theorem for this kind of vector measures. The major results are(a) Any orthogonal vector measure can gain it countable additivity by enlarging its domain;(b) Every orthogonal vector measure can be represented as the sum of two orthogonal vectormeasures, one of which is countably additive, and the other is purely finitely additive. Furthermore,these vector measures are completely perpendicular to each other. 相似文献
20.
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. |