共查询到20条相似文献，搜索用时 15 毫秒
1.
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. |
2.
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. |
3.
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. |
4.
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. |
5.
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. |
6.
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!. |
7.
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. |
8.
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. |
9.
We consider actions of non-compact simple Lie groups preserving an analytic rigid geometric structure of algebraic type on
a compact manifold. The structure is not assumed to be unimodular, so an invariant measure may not exist. Ergodic stationary
measures always exist, and when such a measure has full support, we show the following:
An important ingredient in the proofs is a generalization of Gromov’s centralizer theorem beyond the case of invariant measures. 相似文献
| 1. | Either the manifold admits a smooth equivariant map onto a homogeneous projective variety, defined on an open dense conull invariant set, or the Lie algebra of the Zariski closure of the Gromov representation of the fundamental group contains a Lie subalgebra isomorphic to the Lie algebra of the acting group. As a corollary, a smooth non-trivial homogeneous projective factor does exist whenever the fundamental group of M admits only virtually solvable linear representations, and thus in particular when M is simply connected, regardless of the real rank. |
| 2. | There exist explicit examples showing that analytic rigid actions of certain simple real rank one groups may indeed fail to have a smooth projective factor. |
| 3. | It is possible to generalize Gromov’s theorem on the algebraic hull of the representation of the fundamental group of the manifold to the case of rigid non-unimodular structures, again for actions of groups of any real rank. |
10.
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. |
11.
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). |
12.
Giuseppe Pellegrino 《Rendiconti del Circolo Matematico di Palermo》1998,47(1):141-168
| 1. | Letm be the greatest integer such that . ThenPG(3,q) contains complete caps of sizek=(m+1)(q+1)+ω, with ω=0, 1, 2. | |
| 2. |
PG(3,q),q≥5, contains complete caps of size |
|
| 3. | InPG(3,q) complete caps different from ovaloids have some external planes. |
13.
LetG be a finite nonsolvable group andH a proper subgroup ofG. In this paper we determine the structure ofG ifG satisfies one of the following conditions:
相似文献
| (1) | Every solvable subgroupK(K⊉H) is eitherp-decomposable or a Schmidt group,p being the smallest odd prime factor of |G|. |
| (2) | |G∶H| is divisible by an odd prime and every solvable subgroupK(K⊉H) is either 2′-closed or a Schmidt group. |
| (3) | |G∶H| is even and every solvable subgroupK(K⊉H) is either 2-closed or a Schmidt group. |
14.
A. S. Sivatski 《Journal of Mathematical Sciences》2007,145(1):4823-4830
The main purpose of the paper is to strengthen previous author’s results. Let k be a field of characteristic ≠ 2, n ≥ 2. Suppose
that elements
are linearly independent over ℤ/2ℤ. We construct a field extension K/k and a quaternion algebra D = (u, v) over K such that
In particular, the algebra A provides an example of an indecomposable algebra of index 2n+1 over a field, the u-invariant and the 2-cohomological dimension of which equal 2n+3 and n + 3, respectively. Bibliography: 10 titles.
__________
Translated from Zapiski Nauchnykh Seminarov POMI, Vol. 338, 2006, pp. 227–241. 相似文献
| (1) | the field K has no proper extension of odd degree |
| (2) | the u-invariant of K equals 4 |
| (3) | the multiquadratic extension is not 4-excellent, and the quadratic form 〈uv,-u,-v, a〉 provides a relevant counterexample |
| (4) | the central division algebra A = D ⊗E (a, t0) ⊗E (b1, t1) ⋯ ⊗E (bn, tn) does not decompose into a tensor product of two nontrivial central simple algebras over E, where E = K ((t0))((t1)) … ((tn)) is the Laurent series field in the variables t0, t1, …, tn |
| (5) | ind A = 2n+1. |
15.
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. |
16.
Abstract This paper develops the model theory of ordered structures that satisfy Keisler’s regularity scheme and its strengthening REF
(the reflection scheme) which is an analogue of the reflection principle of Zermelo-Fraenkel set theory. Here is a language with a distinguished linear order <, and REF
consists of formulas of the form
where φ is an -formula, φ
<x
is the -formula obtained by restricting all the quantifiers of φ to the initial segment determined by x, and x is a variable that does not appear in φ. Our results include:
Theorem
The following five conditions are equivalent for a complete first order theory T in a countable language
with a distinguished linear order:
Moreover, if κ is a regular cardinal satisfying κ = κ
<κ
, then each of the above conditions is equivalent to:
相似文献
| (1) | Some model of T has an elementary end extension with a first new element. |
| (2) | T ⊢ REF . |
| (3) | T has an ω 1-like model that continuously embeds ω 1. |
| (4) | For some regular uncountable cardinal κ, T has a κ-like model that continuously embeds a stationary subset of κ. |
| (5) | For some regular uncountable cardinal κ, T has a κ-like model that has an elementary extension in which the supremum of M exists. |
| (6) | T has a κ + -like model that continuously embeds a stationary subset of κ. |
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.
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. |
19.
For the Azimi-Hagler spaces more geometric and topological properties are investigated. Any constructed space is denoted by
X
α,p
. We show
相似文献
| (i) | The subspace [(e nk )] generated by a subsequence (e nk ) of (e n ) is complemented. |
| (ii) | The identity operator from X α,p to X α,p when p > q is unbounded. |
| (iii) | Every bounded linear operator on some subspace of X α,p is compact. It is known that if any X α,p is a dual space, then |
| (iv) | duals of X α,1 spaces contain isometric copies of ℓ ∞ and their preduals contain asymptotically isometric copies of c 0. |
| (v) | We investigate the properties of the operators from X α,p spaces to their predual. |
20.
Eric Schmutz 《Central European Journal of Mathematics》2008,6(3):482-487
It is known that the unit sphere, centered at the origin in ℝ
n
, has a dense set of points with rational coordinates. We give an elementary proof of this fact that includes explicit bounds
on the complexity of the coordinates: for every point ν on the unit sphere in ℝ
n
, and every ν > 0; there is a point r = (r
1; r
2;…;r
n) such that:
One consequence of this result is a relatively simple and quantitative proof of the fact that the rational orthogonal group
O(n;ℚ) is dense in O(n;ℝ) with the topology induced by Frobenius’ matrix norm. Unitary matrices in U(n;ℂ) can likewise be approximated by matrices in U(n;ℚ(i))
相似文献
| – | ⊎ ‖r-v‖∞ < ε. |
| – | ⊎ r is also a point on the unit sphere; Σ r i 2 = 1. |
| – | ⊎ r has rational coordinates; for some integers a i , b i . |
| – | ⊎ for all . |