共查询到10条相似文献,搜索用时 140 毫秒
1.
Summary For P∈ F2[z] with P(0)=1 and deg(P)≧ 1, let A =A(P) be the unique subset of N (cf. [9]) such that Σn≧0 p(A,n)zn ≡ P(z) mod 2, where p(A,n) is the number of partitions of n with parts in A. To determine the elements of the set A, it is important to consider the sequence σ(A,n) = Σ d|n, d∈A d, namely, the periodicity of the sequences (σ(A,2kn) mod 2k+1)n≧1 for all k ≧ 0 which was proved in [3]. In this paper, the values of such sequences will be given in terms of orbits. Moreover, a formula
to σ(A,2kn) mod 2k+1 will be established, from which it will be shown that the weight σ(A1,2kzi) mod 2k+1 on the orbit <InlineEquation ID=IE"1"><EquationSource Format="TEX"><![CDATA[<InlineEquation ID=IE"2"><EquationSource Format="TEX"><![CDATA[$]]></EquationSource></InlineEquation>]]></EquationSource></InlineEquation>z_i$
is moved on some other orbit zj when A1 is replaced by A2 with A1= A(P1) and A2= A(P2) P1 and P2 being irreducible in F2[z] of the same odd order. 相似文献
2.
LICHANGPIN YANGZHONGHUA 《高校应用数学学报(英文版)》1998,13(3):263-270
This paper deals with the steady state bifurcation of the K-S equation in two spatial dimensions with periodic boundary value condition and of zero mean. With the increase of parameter a, the steady state bifurcation behaviour can be very complicated. For convenience, only the cases a=2 and a=5 witl be discussed. The asymptotic expressions of the steady state solutions bifurcated from the trivial solution near a=2 and a=5 are given. And the stability of thenontriviat sotutions bifurcated from a=2 is studied. Of course, the cases a=n^2 m^2,n,m∈N(a≠2,5) can be similarly discussed by the same method which is used to discussing the cases a=2 and a= 5. 相似文献
3.
Cédric Rousseau 《Bulletin of the Brazilian Mathematical Society》2005,36(3):379-391
Let A be a symmetric hyperbolic matrix in SL(2, ℤ) and Γ the subgroup of SL(2, ℤ) generated by A. We aim to study the infinitesimal rigidity of the standard action of Γ on the torus
. More precisely, we will consider the Sobolev Ws–infinitesimal rigidity of this action (that is to determine if the cohomology space H1(Γ,Ws (T M)) is trivial or not), and show that it is Ws–infinitesimally rigid only if 0 ≤ s < 1. A consequence will be that this action is not C∞–infinitesimally rigid.
*I would like to thank A. El Kacimi for introducing me this problem about which we had many fruitful discussions. 相似文献
4.
The main goal of this paper is to extend the approximation theorem of contiuous functions by Haar polynomials (see Theorem
A) to infinite matrices (see Theorem C). The extension to the matricial framework will be based on the one hand on the remark
that periodic functions which belong toL
∞ (T) may be one-to-one identified with Toeplitz matrices fromB(l
2) (see Theorem 0) and on the other hand on some notions given in the paper. We mention for instance:ms—a unital commutative subalgebra ofl
∞,C(l
2) the matricial analogue of the space of all continuous periodic functionsC(T), the matricial Haar polynomials, etc.
In Section 1 we present some results concerning the spacems—a concept important for this generalization, the proof of the main theorem being given in the second section.
Partially supported by EUROMMAT ICA1-CT-2000-70022.
Partially supported by V-Stabi-RUM/1022123.
Partially supported by EUROMMAT ICA1-CT-2000-70022 and V-Stabi-RUM/1022123. 相似文献
5.
Summary LetR be a Cohen-Macaulay ring andI an unmixed ideal of heightg which is generically a complete intersection and satisfiesI
(n)=In for alln≥1. Under what conditions will the Rees algebra be Cohen-Macaulay or have good depth? A series of partial answers to this
question is given, relating the Serre condition (S
r
) of the associated graded ring to the depth of the Rees algebra. A useful device in arguments of this nature is the canonical
module of the Rees algebra. By making use of the technique of the fundamental divisor, it is shown that the canonical module
has the expected form: ω
R[It]
≅(t(1−t)
g−2).
The third author was partially supported by the NSF
This article was processed by the author using theLaTex style filecljour1 from Springer-Verlag. 相似文献
6.
Ming-Jun Lai 《Advances in Computational Mathematics》2006,25(1-3):41-56
We propose a constructive method to find compactly supported orthonormal wavelets for any given compactly supported scaling
function φ in the multivariate setting. For simplicity, we start with a standard dilation matrix 2I2×2 in the bivariate setting and show how to construct compactly supported functions ψ1,. . .,ψn with n>3 such that {2kψj(2kx−ℓ,2ky−m), k,ℓ,m∈Z, j=1,. . .,n} is an orthonormal basis for L2(ℝ2). Here, n is dependent on the size of the support of φ. With parallel processes in modern computer, it is possible to use these orthonormal
wavelets for applications. Furthermore, the constructive method can be extended to construct compactly supported multi-wavelets
for any given compactly supported orthonormal multi-scaling vector. Finally, we mention that the constructions can be generalized
to the multivariate setting.
Dedicated to Professor Charles A. Micchelli on the occasion of his 60th birthday
Mathematics subject classifications (2000) 42C15, 42C30. 相似文献
7.
B. Ruf 《Proceedings of the Steklov Institute of Mathematics》2006,255(1):234-243
We consider nonlinear elliptic equations of the form −Δu = g(u) in Ω, u = 0 on ∂Ω, and Hamiltonian-type systems of the form −Δu = g(v) in Ω, −Δv = f(u) in Ω, u = 0 and v = 0 on ∂Ω, where Ω is a bounded domain in ℝ2 and f, g ∈ C(ℝ) are superlinear nonlinearities. In two dimensions the maximal growth (= critical growth) of f and g (such that the problem can be treated variationally) is of exponential type, given by Pohozaev-Trudinger-type inequalities.
We discuss existence and nonexistence results related to the critical growth for the equation and the system. A natural framework
for such equations and systems is given by Sobolev spaces, which provide in most cases an adequate answer concerning the maximal
growth involved. However, we will see that for the system in dimension 2, the Sobolev embeddings are not sufficiently fine
to capture the true maximal growths. We will show that working in Lorentz spaces gives better results.
Dedicated to Professor S. Nikol’skii on the occasion of his 100th birthday 相似文献
8.
B. R. Seth 《Annali di Matematica Pura ed Applicata》1960,50(1):119-125
Summary The use of finite components of strain and a linear stress-strain relation shows that a plate can be bent into a cylindrical
shell whose section is given by rn
cos nθ=an, where n=(3−2σ)−1, σ being the Poisson’s ratio. The case (σ=1/2) and the one given by r2/5 cos2/5 θ=a2/5, (σ=1/4) are discussed in detail.
To Antonio Signorini on his 70th birth day. 相似文献
9.
Bin Han 《Advances in Computational Mathematics》2006,24(1-4):375-403
In this paper, we present a necessary and sufficient condition for the existence of solutions in a Sobolev space Wpk(ℝs) (1≤p≤∞) to a vector refinement equation with a general dilation matrix. The criterion is constructive and can be implemented.
Rate of convergence of vector cascade algorithms in a Sobolev space Wpk(ℝs) will be investigated. When the dilation matrix is isotropic, a characterization will be given for the Lp (1≤p≤∞) critical smoothness exponent of a refinable function vector without the assumption of stability on the refinable function
vector. As a consequence, we show that if a compactly supported function vector φ∈Lp(ℝs) (φ∈C(ℝs) when p=∞) satisfies a refinement equation with a finitely supported matrix mask, then all the components of φ must belong to a Lipschitz
space Lip(ν,Lp(ℝs)) for some ν>0. This paper generalizes the results in R.Q. Jia, K.S. Lau and D.X. Zhou (J. Fourier Anal. Appl. 7 (2001) 143–167)
in the univariate setting to the multivariate setting.
Dedicated to Professor Charles A. Micchelli on the occasion of his 60th birthday
Mathematics subject classifications (2000) 42C20, 41A25, 39B12.
Research was supported in part by the Natural Sciences and Engineering Research Council of Canada (NSERC Canada) under Grant
G121210654. 相似文献