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1.
A conjecture of Regev and Vishik on the equality of two multisets of hook numbers is proved.
Supported in part by N.S.F. Grant No. DMS-94-01197.
Supported in part by N.S.F. Grant No. DMS-95-00646. 相似文献
2.
Medieval algebra is distinguished from other arithmetical problem-solving techniques by its structure and technical vocabulary. In an algebraic solution one or several unknowns are named, and via operations on the unknowns the problem is transferred to the artificial setting of an equation expressed in terms of the named powers, which is then simplified and solved. In this article we examine Diophantus? Arithmetica from this perspective. We find that indeed Diophantus? method matches medieval algebra in both vocabulary and structure. Just as we see in medieval Arabic and Italian algebra, Diophantus worked out the operations expressed in the enunciation of a problem prior to setting up a polynomial equation. Further, his polynomials were regarded as aggregations with no operations present. 相似文献
3.
It is known that non-symmetric convex bodies generally cannot be characterized by the volumes of hyperplane sections through
one interior point. Falconer and Gardner, however, independently proved that volumes of hyperplane sections through two different
interior points determine the body uniquely. We prove that if −1 < q < n − 1 is not an integer, then the derivatives of the order q at zero of parallel section functions at one interior point completely characterize convex bodies in
. If 0 ≤ q < n − 1 is an integer then one needs the derivatives of order q at two different interior points (except for the case where q = n − 2, q odd), generalizing the results of Falconer and Gardner.
The first named author was partially supported by the NSF grant DMS 0455696.
Received: 31 January 2006 相似文献
4.
In the introduction of the Arithmetica Diophantus says that in order to solve arithmetical problems one has to “follow the way he (Diophantus) will show.” The present paper has a threefold objective. Firstly, the meaning of this sentence is discussed, the conclusion being that Diophantus had elaborated a program for handling various arithmetical problems. Secondly, it is claimed that what is analyzed in the introduction is definitions of several terms, the exhibition of their symbolism, the way one may operate with them, but, most significantly, the main stages of the program itself. And thirdly, it is argued that Diophantus' intention in the Arithmetica is to show the way the stages of his program should be practically applied in various arithmetical problems. 相似文献
5.
Luigi Borzacchini 《Mediterranean Journal of Mathematics》2006,3(3-4):433-448
The method of exhaustion is one of the greatest achievements of Greek mathematics, but the history of its development is not
clear. First and foremost Archimedes’ role has been keenly debated, by and large undermined, so that even his name seems condemned
to disappear in the name of the Eudoxus-Archimedes Lemma. In this paper we try to revaluate his role by a new interpretation
(or, more precisely, by the refinement of an old one) of the historical development of the theory, underlining the theoretical
relevance of the problem of addition/subtraction and comparison between curves.
Dedicated to the memory of Professor Aldo Cossu 相似文献
6.
Martin C. Olsson 《Advances in Mathematics》2005,198(1):93-106
We prove that every separated Artin stack of finite type over a noetherian base scheme admits a proper covering by a quasi-projective scheme. An application of this result is a version of the Grothendieck existence theorem for Artin stacks. 相似文献
7.
For a convex body M
n
byb(M) the least integerp is denoted, such that there are bodiesM
1, ...,M
p
each of which is homothetic toM with a positive ratiok<1 andM
1...M
p
M. H. Martini has proved [7] thatb(M)<-3·2
n–2 for every zonotope M
n
, which is not a parallelotope.In the paper this Martini's result is extended to zonoids. In the proof some notions and facts of real functions theory are used (points of density, approximative continuity). 相似文献
8.
In a finite group G every element can be factorized in such a way that there is one factor for each prime divisor p of | G |, and the order of this factor is pα for some integer α ≧ 0. We define g ∈G to be uniquely factorizable if it has just one such factorization (whose factors must be pairwise commuting). We consider the existence of uniquely factorizable
elements and its relation to the solvability of the group. We prove that G is solvable if and only if the set of all uniquely factorizable elements of G is the Fitting subgroup of G. We also prove various sufficient conditions for the non-existence of uniquely factorizable elements in non-solvable groups.
Received: 9 June 2005 相似文献
9.
Valeriu Soltan 《Journal of Geometry》2006,84(1-2):152-163
For a pair of convex bodies K1 and K2 in Euclidean space
, n ≥ 3, possibly unbounded, we show that K1 is a translate of K2 if either of the following conditions holds: (i) the orthogonal projections of K1 on 2-dimensional planes are translates of the respective orthogonal projections of K2, (ii) there are points p1 ∈K1 and p2 ∈K2 such that for every pair of parallel 2-dimensional planesL1and L2 through p1 and p2, respectively, the section K1 ∩ L1is a translate of K2 ∩ L2. 相似文献
10.
Through the notion of projective center of symmetry of a convex body we will give a quick proof and clarify the ideas surrounding Höbinger's problem, originally proved by Burton and Larman in [1]. 相似文献
11.
Let v1,…,vm be a finite set of unit vectors in Rn. Suppose that an infinite sequence of Steiner symmetrizations are applied to a compact convex set K in Rn, where each of the symmetrizations is taken with respect to a direction from among the vi. Then the resulting sequence of Steiner symmetrals always converges, and the limiting body is symmetric under reflection in any of the directions vi that appear infinitely often in the sequence. In particular, an infinite periodic sequence of Steiner symmetrizations always converges, and the set functional determined by this infinite process is always idempotent. 相似文献
12.
XuYINFENG 《高校应用数学学报(英文版)》1996,11(2):235-238
Abstract. Let S be a set of finite plauar points. A llne segment L(p, q) with p, q E Sis called a stable line segment of S, if there is no Line segment with two endpoints in S intersecting L(p, q). In this paper, some geometric properties of the set of all stable line segments 相似文献
13.
Amos J. Carpenter 《Numerische Mathematik》1992,62(1):465-482
Summary We investigate the location of the zeros of the normalized generalized Bessel polynomials and the normalized reversed generalized Bessel polynomials. Also, the rate at which these zeros approach certain well-defined curves is investigated. On the basis of numerical computations and graphs, four new conjectures are proposed.Dedicated to Richard S. Varga on the occasion of his sixtieth birthday (October 9, 1988)This research was made possible and supported by a Butler University Fellowship Award 相似文献
14.
New notions of amenability and contractability are introduced. Examples are given to show that for most of the new notions, the corresponding class of Banach algebras is larger than that for the classical amenable algebras introduced by Johnson. General theory is developed for these notions, and studied for several concrete classes of Banach algebras; special consideration is given to Banach algebras defined on locally compact groups. 相似文献
15.
Yannis Thomaidis Author Vitae 《Historia Mathematica》2011,38(1):28-41
Diophantos in Arithmetica, without having defined previously any concept of “equality” or “equation,” employs a concept of the unknown number as a tool for solving problems and finds its value from an equality ad hoc created. In this paper we analyze Diophantos’s practices in the creation and simplification of such equalities, aiming to adduce more evidence on certain issues arising in recent historical research on the meaning of the “equation” in Diophantos’s work. 相似文献
16.
L.E. Bazylevych 《Topology and its Applications》2006,153(11):1699-1704
We present an alternative proof of the following fact: the hyperspace of compact closed subsets of constant width in Rn is a contractible Hilbert cube manifold. The proof also works for certain subspaces of compact convex sets of constant width as well as for the pairs of compact convex sets of constant relative width. Besides, it is proved that the projection map of compact closed subsets of constant width is not 0-soft in the sense of Shchepin, in particular, is not open. 相似文献
17.
In this paper we discuss necessary conditions and sufficient conditions for the compression of an analytic Toeplitz operator onto a shift coinvariant subspace to have nontrivial reducing subspaces. We give necessary and sufficient conditions for the kernel of a Toeplitz operator whose symbol is the quotient of two inner functions to be nontrivial and obtain examples of reducing subspaces from these kernels. Motivated by this result we give necessary conditions and sufficient conditions for the kernel of a Toeplitz operator whose symbol is the quotient of two inner functions to be nontrivial in terms of the supports of the two inner functions. By studying the commutant of a compression, we are able to give a necessary condition for the existence of reducing subspaces on certain shift coinvariant subspaces. 相似文献
18.
The classification of simple biset functors is known, but the evaluation of a simple biset functor at a finite group G may be zero. We investigate various situations where this happens, as well as cases where this does not occur. We also prove a closed formula for such an evaluation under some restrictive conditions on G. 相似文献
19.
O. E. Barndorff-Nielsen P. Blæsild A. L. Carey P. E. Jupp M. Mora M. K. Murray 《Acta Appl Math》1992,28(3):219-252
The concept of phylon is introduced as a generalisation of derivative strings, differential strings and new tensors. The behaviour of phyla under change of coordinates is given by finite-dimensional algebraic representations of a very large group, the infinite phylon group. These representations are studied from both the general and the matrix points of view. Various examples of phyla are given, mainly from a statistical context. The basic structure of these representations is given. 相似文献
20.
Ralf Kemper 《Applied Categorical Structures》1995,3(4):363-370
We give characterizations of the epimorphisms in the categories of open and separated totally convex and (pre)separated absolutely convex spaces. 相似文献