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1.
本文研究了环Fpm+uFpm+u2Fpm上长度为ps的循环码分类.通过建立环Fpm+uFpm+u2Fpm到环Fpm+uFpm的同态,给出了环Fpm+uFpm+u2Fpm上长度为ps的循环码的新分类方法.应用这种方法,得到了环Fpm+uFpm+u2Fpm长度为ps的循环码的码词数. 相似文献
2.
Els Bergen Esther Ramakers Luc Vrancken 《Abhandlungen aus dem Mathematischen Seminar der Universit?t Hamburg》1999,69(1):139-157
In this paper we prove the Magid-Ryan conjecture for 4-dimensional affine hyperspheres in R5. This conjecture states that every affine hypersphere with non-zero Pick invariant and constant sectional curvature is affinely
equivalent with either (x
1
2
±x
2
2
)(x
3
2
±x
4
2
...(x
2m−1
2
±x
2m
2
) = 1 or (x
1
2
±x
2
2
(x
3
2
±x
4
2
)...(x
2m−1
2
±x
2m
2
)x
2m+1 = 1 where the dimensionn satisfiesn = 2m orn =2m + 1. This conjecture was proved in [11] in case the metric is positive definite and in [2] in case the metric is Lorentzian. 相似文献
3.
The boundary value problem for the stress rates and rates of change fields in the quasi-static motion of a volume V of an elastic-plastic medium [1] consists of finding the pairs σij., ij. related by the governing equations of an appropriate model; here the σij. should be statically admissible i.e. should satisfy the equations and boundary conditions σij=−X/.i; /.σijnj|Sp=pi and ij should be kinematically admissible i.e. 2/.ij = vij + vji, where vi|Su = uio Here Sp and Su are nonintersecting parts of the boundary of the volume V, Xi, pi, ui/.o are specified functions. The question of the existence of a solution of this problem reduces to the question of the functional reaching the lower bound in a set of kinematically admissible /.ijo and statically admissible σij/./*. However, its lower bound may not be reached if in the minimization we limit ourselves only to smooth fields. It is proposed to augment the set of admissible fields σij/./*,ij/.o by closing them in the norm L2 (for vio this corresponds to closure in the norm II1). Some properties of the functional I (σij*,ij/.) are considered in the augmented set of admissible fields. It is shown that the equivalence of the two problems is conserved, where I (σij*,ij0 can be minimized in σij/*,ijo or in σij/*,ij/.o, The lower bound is reached in each of three cases, at a single point. From the fact that uio belongs to the Sobolev space W2(1), there results the absence of surfaces of velocity discontinuity. Variational principles have been used in plasticity theory to construct models [2] and to investigate the existence and properties of solutions [1, 3]. 相似文献
4.
Summary Without using spectral resolution, an elementary proof of convergence of Seidel iteration. The proof is based on the lemma (generalizing a lemma of P. Stein): If (A+A
*)–B
*(A+A
*)B>0, whereB=–(P+L)
–1
R,A=P+L (Lower)+R (upper), then Seidel iteration ofAX=Y
0 converges if and only ifA+A
*>0. This lemma has as corollaries not only the well-known results of E. Reich and Stein, but also applications to a matrix that can be far from symmetric, e.g.M=[A
ij
]
1
2
, whereA
21=–A
12
*
,A
11,A
22 are invertible;A
11
+A
11
*
=A22+A
22
*
; and the proper values ofA
12
–1
A
11,A
12
*–1
A
22 are in the interior of the unit disk.Supported under NSF GP 32527.Supported under NSF GP 8758. 相似文献
5.
Olivier Finkel 《Mathematical Logic Quarterly》2010,56(5):452-460
A dictionary is a set of finite words over some finite alphabet X. The ω ‐power of a dictionary V is the set of infinite words obtained by infinite concatenation of words in V. Lecomte studied in [10] the complexity of the set of dictionaries whose associated ω ‐powers have a given complexity. In particular, he considered the sets ??( Σ 0k) (respectively, ??( Π 0k), ??( Δ 11)) of dictionaries V ? 2* whose ω ‐powers are Σ 0k‐sets (respectively, Π 0k‐sets, Borel sets). In this paper we first establish a new relation between the sets ??( Σ 02) and ??( Δ 11), showing that the set ??( Δ 11) is “more complex” than the set ??( Σ 02). As an application we improve the lower bound on the complexity of ??( Δ 11) given by Lecomte, showing that ??( Δ 11) is in Σ 1 2(22*)\ Π 02. Then we prove that, for every integer k ≥ 2 (respectively, k ≥ 3), the set of dictionaries ??( Π 0k+1) (respectively, ??( Σ 0k +1)) is “more complex” than the set of dictionaries ??( Π 0k) (respectively, ??( Σ 0k)) (© 2010 WILEY‐VCH Verlag GmbH & Co. KGaA, Weinheim) 相似文献
6.
Let U = ℂ2, Γ = ℤ2, and let ℂ[x
1±1, x
2±1] be the ring of Laurent polynomials. The Witt algebra L is the Lie algebra of derivations over ℂ[x
1±1, x
2±1], which is spanned by elements of the form D(u, r) = x
r
(u
1
d
1 + u
2
d
2), u = (u
1, u
2) ∈ U, r ∈ Γ, where d
1 and d
2 are the degree derivations of ℂ[x
1±1, x
2±1]. The image of gl
2-module V under Larsson functor F
α
, denoted by W = F
α
(V), gives a class of L-modules, often called the Larsson-modules of L. In this paper, we study the derivations from the Witt algebra L to its Larsson-modules W, and we determine the first cohomology group H
1(L,W). 相似文献
7.
WangShiying ZhangYuren LiuYan 《高校应用数学学报(英文版)》1999,14(4):492-494
Abstract. Let Sn be the symmetric group 相似文献
8.
Bronislaw Wajnryb 《Israel Journal of Mathematics》1991,76(3):265-288
Forn even andp an odd prime a symplectic group Sp(n, p) is a quotient of the Artin braid groupB
n+1. Ifs
1, …,s
n
are standard generators ofB
n+1 then the kernel of the corresponding epimorphism is the normal closure of just four elements:s
1
p
,(s
1
s
2)6,s
1
(p+1)/2
s
2
4
s
1
(p−1)/2
s
2
−2
s
1
−1
s
2
2
and (s
1
s
2
s
3)4
A
−1
s
1
−2
A, whereA=s
2
s
3
−1
s
2
(p−1)/2
s
4
s
3
2
s
4, all of them lying in the subgroupB
5. Sp(n, p) acts on a vector space and the image of the subgroupB
n
ofB
n+1 in Sp(n, p), denoted Sp(n−1,p), is a stabilizer of one vector. A sequence of inclusions …B
k+1·B
k
… induces a sequence of inclusions …Sp(k,p)·Sp(k−1,p)…, which can be used to study some finite-valued invariants of knots and links in the 3-sphere via the Markov theorem.
Partially supported by the Technion VPR-Fund. 相似文献
9.
An SOLS (self-orthogonal latin square) of order v with ni missing sub-SOLS (holes) of order hi (1ik), which are disjoint and spanning (i.e. ∑i=1k nihi=v), is called a frame SOLS and denoted by FSOLS(h1n1h2n2 hknk). It has been proved that for b2 and n odd, an FSOLS(anb1) exists if and only if n4 and n1+2b/a. In this paper, we show the existence of FSOLS(anb1) for n even and FSOLS(an11) for n odd. 相似文献
10.
Marcus Waurick 《PAMM》2016,16(1):883-884
We show that a bounded sequence (an)n of symmetric d × d-matrix valued functions is G-convergent if and only if ((ι∗︁anι)−1 )n converges in the weak operator topology. Here ι: R(grad0) ↪ L2(Ω)d denotes the (canonical) embedding from the range of the weak gradient grad0 defined on H10(Ω) into L2(Ω)d, where Ω ⊆ ℝd is open and bounded. (© 2016 Wiley-VCH Verlag GmbH & Co. KGaA, Weinheim) 相似文献
11.
Kizmaz [13] studied the difference sequence spaces e∞(△), c(△), and c0(△).Several article dealt with the sets of sequences of m-th order difference of which are bounded, convergent, or convergent to zero. Altay and Basar [5] and Altay, Basar, and Mursaleen [7] introduced the Euler sequence spaces eτ0, eτ0, andeτ∞, respectively. The main purpose of this article is to introduce the spaces eτ0(△(m)), eτc(△(m)), and eτ∞(△(m)) consisting of all sequences whose mth order differences are in the Euler spaces eτ0, eτc, and eτ∞, respectively. Moreover, the authors give some topological properties and inclusion relations, and determine the α-, β-, and γ-duals of the spaces eτ0(△(m)), eτc(△(m)), and eτ∞(△(m)), and the Schauder basis of the spaces eτ0(△(m)), eτc(△(m)). The last section of the article is devoted to the characterization of some matrix mappings on the sequence space eτc(△(m)). 相似文献
12.
For any n-dimensional compact Riemannian manifold (M,g) without boundary and another compact Riemannian manifold (N,h), the authors establish the uniqueness of the heat flow of harmonic maps from M to N in the class C([0,T),W1,n). For the hydrodynamic flow (u,d) of nematic liquid crystals in dimensions n = 2 or 3, it is shown that the uniqueness holds for the class of weak solutions provided either (i) for n = 2, u ∈ Lt∞ L2x∩L2tHx1, ▽P∈ Lt4/3 Lx4/3 , and ▽d∈ L∞t Lx2∩Lt2Hx2; or (ii) for n = 3, u ∈ Lt∞ Lx2∩L2tHx1∩ C([0,T),Ln), P ∈ Ltn/2 Lxn/2 , and ▽d∈ L2tLx2 ∩ C([0,T),Ln). This answers affirmatively the uniqueness question posed by Lin-Lin-Wang. The proofs are very elementary. 相似文献
13.
LetB1:
n×
N1→
m1,B2:
n×
N2→
m2andQ:
m2→
m1be bilinear forms which are related as follows: ifμandνsatisfyB1(ξ, μ)=0 andB2(ξ, ν)=0 for someξ≠0, thenμτQν=0. Supposep−1+q−1=1. Coifman, Lions, Meyer and Semmes proved that, ifuLp(
n) andvLq(
n), and the first order systemsB1(D, u)=0,B2(D, v)=0 hold, thenuτQvbelongs to the Hardy spaceH1(
n), provided that both (i)p=q=2, and (ii) the ranks of the linear mapsBj(ξ, ·) :
Nj→
m1are constant. We apply the theory of paracommutators to show that this result remains valid when only one of the hypotheses (i), (ii) is postulated. The removal of the constant-rank condition whenp=q=2 involves the use of a deep result of Lojasiewicz from singularity theory. 相似文献
14.
15.
Let
d−1{(x1,…,xd)
d:x21+···+x2d=1} be the unit sphere of the d-dimensional Euclidean space
d. For r>0, we denote by Brp (1p∞) the class of functions f on
d−1 representable in the formwhere dσ(y) denotes the usual Lebesgue measure on
d−1,
and Pλk(t) is the ultraspherical polynomial.For 1p,q∞, the Kolmogorov N-width of Brp in Lq(
d−1) is given bythe left-most infimum being taken over all N-dimensional subspaces XN of Lq(
d−1).The main result in this paper is that for r2(d−1)2,where ANBN means that there exists a positive constant C, independent of N, such that C−1ANBNCAN.This extends the well-known Kashin theorem on the asymptotic order of the Kolmogorov widths of the Sobolev class of the periodic functions. 相似文献
16.
Fangwei Chen Congli Yang 《Journal of Contemporary Mathematical Analysis (Armenian Academy of Sciences)》2011,46(5):273-279
Under the assumptions that E
λ
n
is an n-dimensional, simply connected Riemannian manifold of constant sectional curvature λ and L
λ
r
is an r-dimensional, totally geodesic submanifold of E
λ
n
, the paper investigates the q-th integral of the mean curvature M
q
n
of a convex body K
r
in E
λ
n
and gives the expression of M
q
n
in the terms of M
p
r
, where M
p
r
is the p-th integral of the mean curvature of K
r
> in L
λ
r
. A result of L. A. Santaló [2] holds in particular. 相似文献
17.
Jouko Tervo 《Israel Journal of Mathematics》1988,63(1):41-66
The paper considers a boundary value problem with the help of the smallest closed extensionL
∼ :H
k →H
k
0×B
h
1×...×B
h
N
of a linear operatorL :C
(0)
∞
(R
+
n
) →L(R
+
n
)×L(R
n−1)×...×L(R
n−1). Here the spacesH
k (the spaces ℬ
h
) are appropriate subspaces ofD′(R
+
n
) (ofD′(R
n−1), resp.),L(R
+
n
) andC
(0)
∞
(R
+
n
)) denotes the linear space of smooth functionsR
n
→C, which are restrictions onR
+
n
of a function from the Schwartz classL (fromC
0
∞
, resp.),L(R
n−1) is the Schwartz class of functionsR
n−1 →C andL is constructed by pseudo-differential operators. Criteria for the closedness of the rangeR(L
∼) and for the uniqueness of solutionsL
∼
U=F are expressed. In addition, ana priori estimate for the corresponding boundary value problem is established. 相似文献
18.
E. V. Derets 《Ukrainian Mathematical Journal》2000,52(3):368-378
We establish lower bounds for the Kolmogorov widths d
2n-1(W
r
H
1ω.L
p
) and Gel’fand widths d
2n-1(W
r
H
1ω.L
p
) of the classes of functions W
r
H
1ω with a convex integral modulus of continuity ω(t). 相似文献
19.
We study the families of lines on the quintic threefolds of the pencilx
0
5
+x
1
5
+x
2
5
+x
3
5
+x
4
5
-5tx
0
x
1
x
2
x
3
x
4=0. We show that on the generic threefold of the pencil there exists a 1-dimensional family of lines that is not a cone.
Partially supported by funds M.P.I. 相似文献
20.
Edoardo Ballico 《Rendiconti del Circolo Matematico di Palermo》2001,50(1):209-212
Let X be a smooth curve of genus g with two pencils, sayg
k
1
andg
m
1
. Here we show that, in general, dim|rg
k
1
+ug
m
1
| has the expected dimension and construct examples in which dim |rg
k
1
+ug
m
1
| has a prescribed value. 相似文献