共查询到20条相似文献,搜索用时 31 毫秒
1.
Jie Du 《manuscripta mathematica》1992,75(1):411-427
The structure of Schur algebrasS(2,r) over the integral domainZ is intensively studied from the quasi-hereditary algebra point of view. We introduce certain new bases forS(2,r) and show that the Schur algebraS(2,r) modulo any ideal in the defining sequence is still such a Schur algebra of lower degree inr. A Wedderburn-Artin decomposition ofS
K
(2,r) over a fieldK of characteristic 0 is described. Finally, we investigate the extension groups between two Weyl modules and classify the
indecomposable Weyl-filtered modules for the Schur algebrasS
Zp(2,r) withr<p
2
.
Research supported by ARC Large Grant L20.24210 相似文献
2.
This paper studies the state space and feedback aspects of linear system decoupling. Given a minimal realization for a proper transfer function W (s), a general procedure is given for the parametrization of all the minimal decouplings of W (s) into two proper subsystems. This completes and unifies known results on factorization and cascade decomposition. 相似文献
3.
Masatoshi Ito Takeaki Yamazaki Masahiro Yanagida 《Integral Equations and Operator Theory》2004,49(4):461-472
Let T = U|T| and S = V|S| be the polar decompositions. In this
paper, we shall obtain the polar decomposition of TS as TS = UWV|TS|,
where |T||S*| = W||T||S*|| is the polar decomposition.
Next, we shall show that TS = UV|TS| is the polar decomposition if
and only if |T| commutes with |S*|.
Lastly, we shall apply this result to binormal and centered operators.
We shall obtain characterizations of these operator classes from the viewpoint
of the polar decomposition. 相似文献
4.
A decomposition of an ideal as a Galois module in an Abelian p-extension of a complete, discretely valuated field into indecomposable summands is found. Bibliography: 5titles.Translated fromZapiski Nauchnykh Seminarov POMI, Vol. 236, 1997, pp. 23–33. 相似文献
5.
Two theorems about the vertices of indecomposable Specht modules for the
symmetric group, defined over a field of prime characteristic p, are
proved:
1. The indecomposable Specht module $S^\lambda$ has non-trivial cyclic vertex
if and only if $\lambda$ has p-weight 1.
2. If p does not divide n and $S^{(n-r, 1^r)}$ is indecomposable then
its vertex is a p-Sylow subgroup of $S_{n-r-1} \times S_r$.Received: 15 August 2002 相似文献
6.
principally unimodular (PU) if every principal submatrix has determinant 0 or ±1. Let A be a symmetric (0, 1)-matrix, with a zero diagonal. A PU-orientation of A is a skew-symmetric signing of A that is PU. If A′ is a PU-orientation of A, then, by a certain decomposition of A, we can construct every PU-orientation of A from A′. This construction is based on the fact that the PU-orientations of indecomposable matrices are unique up to negation and
multiplication of certain rows and corresponding columns by −1. This generalizes the well-known result of Camion, that if
a (0, 1)-matrix can be signed to be totally unimodular then the signing is unique up to multiplying certain rows and columns
by −1. Camion's result is an easy but crucial step in proving Tutte's famous excluded minor characterization of totally unimodular
matrices.
Received: May 17, 1996 相似文献
7.
8.
V. B. Mnukhin 《Acta Appl Math》1992,29(1-2):83-117
Let (G, W) be a permutation group on a finite set W = {w
1,..., w
n}. We consider the natural action of G on the set of all subsets of W. Let h
0, h
1,..., h
N
be the orbits of this action. For each i, 1 i N, there exists k, 1 k n, such that h
i
is a set of k-element subsets of W. In this case h
i is called a symmetrized k-orbit of the group (G, W) or simply a k-orbit. With a k-orbit h
i
we associate a multiset H(h
i
) = % MathType!MTEF!2!1!+-% feaafeart1ev1aaatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn% hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr% 4rNCHbGeaGGipm0dc9vqaqpepu0xbbG8F4rqqrFfpeea0xe9Lq-Jc9% vqaqpepm0xbba9pwe9Q8fs0-yqaqpepae9pg0FirpepeKkFr0xfr-x% fr-xb9adbaqaaeGaciGaaiaabeqaamaabaabaaGcbaGaeyykJeoaaa!3690!\[\langle \]h
i
(1), h
i
(2),..., h
i
(k)% MathType!MTEF!2!1!+-% feaafeart1ev1aaatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn% hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr% 4rNCHbGeaGGipm0dc9vqaqpepu0xbbG8F4rqqrFfpeea0xe9Lq-Jc9% vqaqpepm0xbba9pwe9Q8fs0-yqaqpepae9pg0FirpepeKkFr0xfr-x% fr-xb9adbaqaaeGaciGaaiaabeqaamaabaabaaGcbaGaeyOkJepaaa!36A1!\[\rangle \] of its (k – 1)-suborbits. Orbits h
i
and h
j
are called equivalent if H(h
i
) = H(h
j
). An orbit is reconstructible if it is equivalent to itself only. The paper concerns the k-orbit reconstruction problem and its connections with different problems in combinatorics. The technique developed is based on the notion of orbit and co-orbit algebras associated with a given permutation group (G, W). 相似文献
9.
Stefan Müller Jeyabal Sivaloganathan Scott J. Spector 《Calculus of Variations and Partial Differential Equations》1999,8(2):159-176
A class of stored energy densities that includes functions of the form with , g and h convex and smooth, and is considered. The main result shows that for each such W in this class there is a such that, if a 3 by 3 matrix satisfies , then W is -quasiconvex at on the restricted set of deformations that satisfy condition (INV) and a.e. (and hence that are one-to-one a.e.). Condition (INV) is (essentially) the requirement that be monotone in the sense of Lebesgue and that holes created in one part of the material not be filled by material from other
parts. The key ingredient in the proof is an isoperimetric estimate that bounds the integral of the difference of the Jacobians
of and by the -norm of the difference of their gradients. These results have application to the determination of lower bounds on critical
cavitation loads in elastic solids.
Received January 5, 1998 / Accepted March 13, 1998 相似文献
10.
Loyiso G. Nongxa 《manuscripta mathematica》1999,100(2):159-171
A necessary and sufficient condition is derived for an arbitrary cyclic regulating almost completely decomposable group to
belong to a K(n)-class, n≥ 0. This allows one to formulate a Structure Theorem for clipped p-primary cyclic regulating groups in each K(n)-class. Using the Indecomposability Criterion we construct an example of an indecomposable balanced Butler group which does
not have a unique regulating subgroup.
Received: 3 November 1998 相似文献
11.
Let denote a 2ν-dimensional vector space over a finite field Fq with a non-degenerate form of Witt index ν, and G denote the corresponding isometry group. Let W be a fixed maximal flat, and Θ be the set of all the minimal flats not contained in W. The set-wise stabilizer of W in G acts transitively on Θ and thus this action determines an association scheme. In this paper, we compute the intersection numbers and character tables for these schemes. 相似文献
12.
A Cartesian decomposition of a coherent configuration is defined as a special set of its parabolics that form a Cartesian decomposition of the underlying set. It turns out that every tensor decomposition of comes from a certain Cartesian decomposition. It is proved that if the coherent configuration is thick, then there is a unique maximal Cartesian decomposition of ; i.e., there is exactly one internal tensor decomposition of into indecomposable components. In particular, this implies an analog of the Krull–Schmidt theorem for the thick coherent configurations. A polynomial-time algorithm for finding the maximal Cartesian decomposition of a thick coherent configuration is constructed. 相似文献
13.
14.
M. É. Mikhailov 《Mathematical Notes》1998,63(3):370-373
We continue the study of indecomposable finite (consisting of a finite number of points) pseudometric spaces (i.e., spaces
whose only decomposition into a sum is the division of all distances in equal proportion). We prove that the indecomposability
property is invariant under the following operation: connect two disjoint points by an additional simple chain, which is the
inverted copy of the shortest path connecting these points. The indecomposability of the spaces presented by the graphsK
m,n
(m ≥ 2,n ≥ 3) with edges of equal length is also proved.
Translated fromMatematicheskie Zametki, Vol. 63, No. 3, pp. 421–424, March, 1998. 相似文献
15.
In [1, 3] it was shown: Theorem A. If G is the fundamental group of a finite graph of λ-dimensional duality groups with |G
o(e) : G
e
| < ∞ and |G
τ(e) : G
e
| < ∞ for every edge e of the corresponding G-tree, then G is an (λ + 1)-dimensional duality group.
Here we use the methods of Brown and Geoghegan in [3] to obtain examples of duality groups under weaker conditions than those
of Theorem A.
Received: 5 June 2007 相似文献
16.
M. J. Dunwoody 《Combinatorica》1982,2(1):15-23
LetΓ be infinite connected graph with more than one end. It is shown that there is a subsetd ⊂V Γ which has the following properties. (i) Bothd andd*=VΓ\d are infinite. (ii) there are only finitely many edges joiningd andd*. (iii) For eachgε AutΓ at least one ofd⊂dg, d*⊂dg, d⊂d* g, d*⊂d* g holds. Any group acting on Γ has a decomposition as a free product with amalgamation or as an HNN-group. 相似文献
17.
Summary Letv andK be positive integers. A (v, k, 1)-Mendelsohn design (briefly (v, k, 1)-MD) is a pair (X,B) whereX is av-set (ofpoints) andB is a collection of cyclically orderedk-subsets ofX (calledblocks) such that every ordered pair of points ofX are consecutive in exactly one block ofB. A necessary condition for the existence of a (v, k, 1)-MD isv(v–1) 0 (modk). If the blocks of a (v, k, 1)-MD can be partitioned into parallel classes each containingv/k blocks wherev ) (modk) or (v – 1)/k blocks wherev 1 (modk), then the design is calledresolvable and denoted briefly by (v, k, 1)-RMD. It is known that a (v, 3,1)-RMD exists if and only ifv 0 or 1 (mod 3) andv 6. In this paper, it is shown that the necessary condition for the existence of a (v, 4, 1)-RMD, namelyv 0 or 1 (mod 4), is also sufficient, except forv = 4 and possibly exceptingv = 12. These constructions are equivalent to a resolvable decomposition of the complete symmetric directed graphK
v
*
onv vertices into 4-circuits.Research supported by the Natural Sciences and Engineering Research Council of Canada under Grant A-5320. 相似文献
18.
Given a rational surface singularity (S,P), we relate S-isomorphism classes of normal blowing-ups of S and properties of semifactorization for complete ideals in . This relation is understood via the natural cell decomposition of the characteristic cone P˜(X/S), where X is a desingularization of S.
Received: 1 April 1998 / Revised version: 2 July 1998 相似文献
19.
Michael J. J. Barry 《代数通讯》2017,45(4):1819-1824
If K is a field of finite characteristic p, G is a cyclic group of order q = pα, U and W are indecomposable KG-modules with dim U = m and dim W = n, and λ(m,n,p) is a standard Jordan partition of mn, we describe how to find a generator for each of the indecomposable components of the KG-module U ? W. 相似文献
20.
It is proved that for every positive integer k, every n-connected graph G of sufficiently large order contains a set W of k vertices such that G—W is (n-2)-connected. It is shown that this does not remain true if we add the condition that G(W) is connected. 相似文献