共查询到20条相似文献,搜索用时 78 毫秒
1.
Let Λ be a finitely generated associative k-algebra where k is an algebraically closed field. For each natural number d, we have the variety of d-dimensional module structures on kd given by the multiplication of the elements from a generating set of Λ. The general linear group Gld(k) acts on this variety by conjugation and the orbits under this action correspond to isomorphism classes of d-dimensional Λ-modules. For two d-dimensional Λ-modules M and N one says that M degenerates to N if the orbit corresponding to N is in the Zariski-closure of the orbit corresponding to M. Now in this situation the stabilizers of the elements in the orbit corresponding to N acts on the orbit corresponding to M.
In this paper we characterize degenerations of k[t]/(tr)-modules with the property that for each y in the orbit corresponding to N, there is an xy in the orbit corresponding to M such that the orbit corresponding to M is the disjoint union of orbits of the xy’s under the action of the stabilizer of y where y runs through the orbit corresponding to N.
Presented by Idun ReitenMathematics Subject Classifications (2000) 14L30, 16G10. 相似文献
2.
Let R be a local ring and let (x
1, …, x
r) be part of a system of parameters of a finitely generated R-module M, where r < dimR
M. We will show that if (y
1, …, y
r) is part of a reducing system of parameters of M with (y
1, …, y
r) M = (x
1, …, x
r) M then (x
1, …, x
r) is already reducing. Moreover, there is such a part of a reducing system of parameters of M iff for all primes P ε Supp M ∩ V
R(x
1, …, x
r) with dimR
R/P = dimR
M − r the localization M
P of M at P is an r-dimensional Cohen-Macaulay module over R
P.
Furthermore, we will show that M is a Cohen-Macaulay module iff y
d is a non zero divisor on M/(y
1, …, y
d−1) M, where (y
1, …, y
d) is a reducing system of parameters of M (d:= dimR
M). 相似文献
3.
William J. Martin 《Designs, Codes and Cryptography》2000,21(1-3):181-187
A code C F
n is s-regular provided, forevery vertex x F
n, if x is atdistance at most s from C then thenumber of codewords y C at distance ifrom x depends only on i and the distancefrom x to C. If denotesthe covering radius of C and C is -regular,then C is said to be completely regular. SupposeC is a code with minimum distance d,strength t as an orthogonal array, and dual degrees
*. We prove that d 2t + 1 whenC is completely regular (with the exception of binaryrepetition codes). The same bound holds when C is(t + 1)-regular. For unrestricted codes, we show thatd s
* + t unless C is a binary repetitioncode. 相似文献
4.
P. M. Gruber 《Discrete and Computational Geometry》1995,13(1):517-527
A closed convex surfaceS in
withd odd, is an ellipsoid if and only if it has the following property: for any pair of pointsx, y inS there is an affine transformation which mapsx ontoy and a suitable neighborhood ofx inS onto a neighborhood ofy inS. 相似文献
5.
This paper considers the solution of the problem: inff[y, x(y)] s.t.y
[y, x(y)] E
k
, wherex(y) solves: minF(x, y) s.t.x R(x, y) E
n
. In order to obtain local solutions, a first-order algorithm, which uses {dx(y)/dy} for solving a special case of the implicitly definedy-problem, is given. The derivative is obtained from {dx(y, r)/dy}, wherer is a penalty function parameter and {x(y, r)} are approximations to the solution of thex-problem given by a sequential minimization algorithm. Conditions are stated under whichx(y, r) and {dx(y, r)/dy} exist. The computation of {dx(y, r)/dy} requires the availability of
y
F(x, y) and the partial derivatives of the other functions defining the setR(x, y) with respect to the parametersy.Research sponsored by National Science Foundation Grant ECS-8709795 and Office of Naval Research Contract N00014-89-J-1537. We thank the referees for constructive comments on an earlier version of this paper. 相似文献
6.
Alan P Sprague 《Journal of Combinatorial Theory, Series B》1978,24(3):294-300
We denote the distance between vertices x and y of a graph by d(x, y), and pij(x, y) = ∥ {z : d(x, z) = i, d(y, z) = j} ∥. The (s, q, d)-projective graph is the graph having the s-dimensional subspaces of a d-dimensional vector space over GF(q) as vertex set, and two vertices x, y adjacent iff . These graphs are regular graphs. Also, there exist integers λ and μ > 4 so that μ is a perfect square, p11(x, y) = λ whenever d(x, y) = 1, and p11(x, y) = μ whenever d(x, y) = 2. The (s, q, d)-projective graphs where and , are characterized by the above conditions together with the property that there exists an integer r satisfying certain inequalities. 相似文献
7.
H. Edelsbrunner 《Combinatorica》1990,10(3):251-260
LetC be a cell complex ind-dimensional Euclidean space whose faces are obtained by orthogonal projection of the faces of a convex polytope ind+ 1 dimensions. For example, the Delaunay triangulation of a finite point set is such a cell complex. This paper shows that the in_front/behind relation defined for the faces ofC with respect to any fixed viewpointx is acyclic. This result has applications to hidden line/surface removal and other problems in computational geometry.Research reported in this paper was supported by the National Science Foundation under grant CCR-8714565 相似文献
8.
Marek Biskup 《Random Structures and Algorithms》2011,39(2):210-227
We study the asymptotic growth of the diameter of a graph obtained by adding sparse “long” edges to a square box in ${\mathbb Z}^dWe study the asymptotic growth of the diameter of a graph obtained by adding sparse “long” edges to a square box in ${\mathbb Z}^d$. We focus on the cases when an edge between x and y is added with probability decaying with the Euclidean distance as |x ? y|?s+o(1) when |x ? y| → ∞. For s ∈ (d, 2d) we show that the graph diameter for the graph reduced to a box of side L scales like (log L)Δ+o(1) where Δ?1 := log2(2d/s). In particular, the diameter grows about as fast as the typical graph distance between two vertices at distance L. We also show that a ball of radius r in the intrinsic metric on the (infinite) graph will roughly coincide with a ball of radius exp{r1/Δ+o(1)} in the Euclidean metric. © 2010 Wiley Periodicals, Inc. Random Struct. Alg., 39, 210‐227, 2011 相似文献
9.
《代数通讯》2013,41(5):2053-2065
Abstract We consider the group G of C-automorphisms of C(x, y) (resp. C[x, y]) generated by s, t such that t(x) = y, t(y) = x and s(x) = x, s(y) = ? y + u(x) where u ∈ C[x] is of degree k ≥ 2. Using Galois's theory, we show that the invariant field and the invariant algebra of G are equal to C. 相似文献
10.
Pierre Fraisse 《Journal of Graph Theory》1986,10(4):553-557
Let G = (V, E) be a digraph of order n, satisfying Woodall's condition ? x, y ∈ V, if (x, y) ? E, then d+(x) + d?(y) ≥ n. Let S be a subset of V of cardinality s. Then there exists a circuit including S and of length at most Min(n, 2s). In the case of oriented graphs we obtain the same result under the weaker condition d+(x) + d?(y) ≥ n – 2 (which implies hamiltonism). 相似文献
11.
Xavier Tolsa 《Journal of Geometric Analysis》2011,21(1):195-223
We show that, for some Cantor sets in ℝ
d
, the capacity γ
s
associated with the s-dimensional Riesz kernel x/|x|
s+1 is comparable to the capacity
[(C)\dot]\frac23(d-s),\frac32\dot{C}_{\frac{2}{3}(d-s),\frac{3}{2}} from non-linear potential theory. It is an open problem to show that, when s is positive and non-integer, they are comparable for all compact sets in ℝ
d
. We also discuss other open questions in the area. 相似文献
12.
A NEW PROPERTY OF BINARY UNDIRECTED de BRUIJN GRAPHS 总被引:2,自引:0,他引:2
XU Junming 《数学年刊B辑(英文版)》2000,21(1):39-42
1.IntroductionThen-dimensionalbinarydirecteddeBruijngraph,denotedbyB(n),hasthevertex-set{xlxz'xu:xiE{0,1}}.TherearetwoarcsfromavertexxlxZ'xutothevenicesxzxa'x.-lx.0andxZx3'x.-l-c.1.Then-dimensionalbinaryundirecteddeBruijngraph,denotedbyUB(n),isobtainedfromB(n)bydeletingtheorientationofthearcsandthenomittingmultipleedgesandloops.ItiswellknownthatUB(n)hasdiameternandconnectivitytwo.ThedeBruijngraphshavebeenwidelyusedincodingtheory[6].Theyhavebeenalsoproposedasapossiblegoodcomputeri… 相似文献
13.
Hamza A. S. Abujabal 《Georgian Mathematical Journal》1996,3(1):1-10
We discuss the commutativity of certain rings with unity 1 and one-sideds-unital rings under each of the following conditions:x
r
[x
s
,y]=±[x,y
t
]x
n
x
r
[x
s
,y]=±x
n
[x,y
t
]x
r
[x
s
,y]=±[x,y
t
]y
m
, andx
r
[x
s
,y]=±y
m
[x,y
t
], wherer, n, andm are non-negative integers andt>1,s are positive integers such that eithers, t are relatively prime ors[x,y]=0 implies [x,y]=0. Further, we improve the result of [6, Theorem 3] and reprove several recent results. 相似文献
14.
If k is a field of characteristic zero, c ∈ k?0, and 1 ≤ s ≤ r are integers such that either r ? s + 1 divides s or s divides r ? s + 1, then it is shown that the derivation y r ? x + (xy s + c)? y of the polynomial ring k[x, y] is simple. 相似文献
15.
Reinhard Wolf 《Arkiv f?r Matematik》1997,35(2):387-400
One of our main results is the following: LetX be a compact connected subset of the Euclidean spaceR
n
andr(X, d
2) the rendezvous number ofX, whered
2 denotes the Euclidean distance inR
n
. (The rendezvous numberr(X, d
2) is the unique positive real number with the property that for each positive integern and for all (not necessarily distinct)x
1,x
2,...,x
n
inX, there exists somex inX such that
.) Then there exists some regular Borel probability measure μ0 onX such that the value of ∫
X
d
2(x, y)dμ0 (y) is independent of the choicex inX, if and only ifr(X, d
2) = supμ ∫
X
∫
X
d
2(x, y)dμ(x)dμ(y), where the supremum is taken over all regular Borel probability measures μ onX. 相似文献
16.
Finite Projective Geometries and Classification of the Weight Hierarchies of Codes (Ⅰ) 总被引:1,自引:0,他引:1
WenDeCHEN TorleivKLφVE 《数学学报(英文版)》2004,20(2):333-348
The weight hierarchy of a binary linear [n,κ] code C is the sequence (d1,d2,...,dκ), where dr is the smallest support of an r-dimensional subcode of C. The codes of dimension 4 are collected in classes and the possible weight hierarchies in each class is determined by finite projective geometries.The possible weight hierarchies in class A, B, C, D are determined in Part (Ⅰ). The possible weight hierarchies in class E, F, G, H, I are determined in Part (Ⅱ). 相似文献
17.
Surjeet Kour 《代数通讯》2013,41(11):4100-4110
It is shown that the derivation y r ? x + (xy s + g)? y , where 0 ≤ r < s are integers, is a simple derivation of k[x, y], the polynomial ring in two variables over a field k of characteristic zero. 相似文献
18.
A graph G is bridged if every cycle C of length at least 4 has vertices x,y such that dG(x,y) < dC(x,y). A cycle C is isometric if dG(x,y) = dC(x,y) for all x,y ∈ V(C). We show that every graph contractible to a graph with girth g has an isometric cycle of length at least g. We use this to show that every minimal cutset S in a bridged graph G induces a connected subgraph. We introduce a “crowning” construction to enlarge bridged graphs. We use this to construct examples showing that for every connected simple graph H with girth at least 6 (including trees), there exists a bridged graph G such that G has a unique minimum cutset S and that G[S] = H. This provides counterexamples to Hahn's conjecture that dG(u,v) ≤ 2 when u and v lie in a minimum cutset in a bridged graph G. We also study the convexity of cutsets in bridged graphs. © 2003 Wiley Periodicals, Inc. J Graph Theory 43: 161–170, 2003 相似文献
19.
It is shown that if there exists a binary code C of length d and covering radius k then a zonotope in the d-dimensional Euclidean space can be illuminated by |C| affine subspaces of dimension k. Applying results from coding theory, the exact value of the illumination numbers of d-dimensional parallelotopes is determined in some special cases.
This revised version was published online in August 2006 with corrections to the Cover Date. 相似文献
20.
G. L. O’brien 《Israel Journal of Mathematics》1981,39(1-2):145-154
LetG be a finite directed graph which is irreducible and aperiodic. Assume each vertex ofG leads to at least two other vertices, and assumeG has a cycle of prime length which is a proper subset ofG. Then there exist two functionsr:G →G andb:G →G such that ifr(x)=y andb(x)=z thenx →y andx →z inG andy ≠z and such that some composition ofr’s andb’s is a constant function.
This work was supported in part by the Natural Sciences and Engineering Research Council of Canada. I am grateful to Cornell
University whose kind hospitality I enjoyed while working on this problem. 相似文献