共查询到20条相似文献,搜索用时 31 毫秒
1.
LiPing Huang 《中国科学A辑(英文版)》2009,52(11):2404-2418
Let D be a division ring with an involution-,H2(D) be the set of 2 × 2 Hermitian matrices over D. Let ad(A,B) = rank(A-B) be the arithmetic distance between A,B ∈ H2(D) . In this paper,the fundamental theorem of the geometry of 2 × 2 Hermitian matrices over D(char(D) = 2) is proved:if :H2(D) → H2(D) is the adjacency preserving bijective map,then is of the form (X) = tP XσP +(0) ,where P ∈ GL2(D) ,σ is a quasi-automorphism of D. The quasi-automorphism of D is studied,and further results are obtained. 相似文献
2.
In this paper we consider the standard Poisson Boolean model of random geometric graphs G(Hλ,s; 1) in Rd and study the properties of the order of the largest component L1 (G(Hλ,s; 1)) . We prove that ElL1 (G(Hλ,s; 1))] is smooth with respect to A, and is derivable with respect to s. Also, we give the expression of these derivatives. These studies provide some new methods for the theory of the largest component of finite random geometric graphs (not asymptotic graphs as s - co) in the high dimensional space (d 〉 2). Moreover, we investigate the convergence rate of E[L1(G(Hλ,s; 1))]. These results have significance for theory development of random geometric graphs and its practical application. Using our theories, we construct and solve a new optimal energy-efficient topology control model of wireless sensor networks, which has the significance of theoretical foundation and guidance for the design of network layout. 相似文献
3.
DingHua Yang 《中国科学A辑(英文版)》2009,52(10):2287-2308
Using the axiomatic method,abstract concepts such as abstract mean, abstract convex function and abstract majorization are proposed. They are the generalizations of concepts of mean, convex function and majorization, respectively. Through the logical deduction, the fundamental theorems about abstract majorization inequalities are established as follows: for arbitrary abstract mean Σ and Σ , and abstract Σ → Σ strict convex function f(x) on the interval I, if xi, yi ∈ I (i = 1, 2, . . . , n) satisfy that (x1... 相似文献
4.
The pressureless Navier-Stokes equations for non-Newtonian fluid are studied. The analytical solutions with arbitrary time blowup, in radial symmetry, are constructed in this paper. With the previous results for the analytical blowup solutions of the N-dimensional (N ≥ 2) Navier-Stokes equations, we extend the similar structure to construct an analytical family of solutions for the pressureless Navier-Stokes equations with a normal viscosity term (μ(ρ)| u|^α u). 相似文献
5.
Jae-Hyun YANG 《数学年刊B辑(英文版)》2010,31(1):85-100
Let Dn be the generalized unit disk of degree n. In this paper, Riemannian metrics on the Siegel-Jacobi disk Dn × C(^m,n) which are invariant under the natural action of the Jacobi group are found explicitly and the Laplacians of these invariant metrics are computed explicitly. These are expressed in terms of the trace form. 相似文献
6.
Yu-shuang Li 《应用数学学报(英文版)》2010,26(1):107-112
A restricted signed r-set is a pair (A, f), where A lohtain in [n] = {1, 2,…, n} is an r-set and f is a map from A to [n] with f(i) ≠ i for all i ∈ A. For two restricted signed sets (A, f) and (B, g), we define an order as (A, f) ≤ (B, g) if A C B and g|A : f A family .A of restricted signed sets on [n] is an intersecting antiehain if for any (A, f), (B, g) ∈ A, they are incomparable and there exists x ∈ A ∩ B such that f(x) = g(x). In this paper, we first give a LYM-type inequality for any intersecting antichain A of restricted signed sets, from which we then obtain |A|≤ (r-1^n-1)(n-1)^r-1 if A. consists of restricted signed r-sets on [n]. Unless r = n = 3, equality holds if and only if A consists of all restricted signed r-sets (A, f) such that x0∈ A and f(x0) =ε0 for some fixed x0 ∈ [n], ε0 ∈ [n] / {x0}. 相似文献
7.
The matrix least squares (LS) problem minx ||AXB^T--T||F is trivial and its solution can be simply formulated in terms of the generalized inverse of A and B. Its generalized problem minx1,x2 ||A1X1B1^T + A2X2B2^T - T||F can also be regarded as the constrained LS problem minx=diag(x1,x2) ||AXB^T -T||F with A = [A1, A2] and B = [B1, B2]. The authors transform T to T such that min x1,x2 ||A1X1B1^T+A2X2B2^T -T||F is equivalent to min x=diag(x1 ,x2) ||AXB^T - T||F whose solutions are included in the solution set of unconstrained problem minx ||AXB^T - T||F. So the general solutions of min x1,x2 ||A1X1B^T + A2X2B2^T -T||F are reconstructed by selecting the parameter matrix in that of minx ||AXB^T - T||F. 相似文献
8.
Let α∈ (0,∞), p, q ∈ [1,∞), s be a nonnegative integer, and ω∈ A1(Rn) (the class of Muckenhoupt's weights). In this paper, we introduce the generalized weighted Morrey-Campanato space L(α, p, q, s, ω; Rn) and obtain its equivalence on different p ∈ [1,β) and integers s ≥ nα (the integer part of nα), where β = (1q - α)-1 when α 1q or β = ∞ when α≥ 1q. We then introduce the generalized weighted Lipschitz space ∧(α, q, ω; Rn) and prove that L(α, p, q, s, ω; Rn) ∧(α, q, ω; Rn) when α∈ (0,∞), s ≥ nα , and p ∈ [1,β). 相似文献
9.
Da Chun YANG 《数学学报(英文版)》2005,21(5):1209-1218
Let F be a compact d-set in R^n with 0 〈 d ≤ n, which includes various kinds of fractals. The author establishes an embedding theorem for the Besov spaces Bpq^s(F) of Triebel and the Sobolev spaces W^1,P(F,d,μ) of Hajtasz when s 〉 1, 1 〈 p 〈∞ and 0 〈 q ≤ ∞. The author also gives some applications of the estimates of the entropy numbers in the estimates of the eigenvalues of some fractal pseudodifferential operators in the spaces Bpq^0(F) and Fpq^0(F). 相似文献
10.
The paper proves that, if f(x) ∈ L^p[-1,1],1≤p〈∞ ,changes sign I times in (-1, 1),then there exists a real rational function r(x) ∈ Rn^(2μ-1)l which is eopositive with f(x), such that the following Jackson type estimate ||f-r||p≤Cδl^2μωφ(f,1/n)p holds, where μ is a natural number ≥3/2+1/p, and Cδ is a positive constant depending only on δ. 相似文献
11.
Zhanying Yang 《Acta Appl Math》2011,114(3):193-205
In this paper, we are concerned with the boundedness of convolution-type Calderón-Zygmund operators on some endpoint Triebel-Lizorkin
spaces. We establish the boundedness on [(F)\dot]10,q\dot{F}_{1}^{0,q} (2<q<∞) under a very weak pointwise regularity condition. The boundedness is established by the Daubechies wavelets and the atomic-molecular
approach. 相似文献
12.
Let (L,⊕,0,1) be an effect algebra and let X be a Banach space. A function μ : L → X is called a vector measure if μ(a ⊕ b) = μ(a) + μ(b) whenever a⊥b in L. The function μ is said to be s-bounded if lim n→∞μ(a n ) = 0 in X for any orthogonal sequence (a n ) n∈N in L. In this paper, we introduce two properties of sequence of s-bounded vector measures and give some results on these properties. 相似文献
13.
Let G be a graph of order n and let λ1,λ2,...,λn be its eigenvalues. The Estrada index[2] of G is defined as EE = EE(G) =∑n i=1 eλi. In this paper, new bounds for EE are established, as well as some relations between EE and graph energy E. 相似文献
14.
Let A be a function with derivatives of order m and D γ A ∈■β (0 < β < 1, |γ| = m). The authors in the paper prove that if Ω(x, z) ∈ L ∞ (R n ) × L s (S n 1 ) (s ≥ n/(n β)) is homogenous of degree zero and satisfies the mean value zero condition about the variable z, then both the generalized commutator for Marcinkiewicz type integral μ A Ω and its variation μ A Ω are bounded from L p (R n ) to L q (R n ), where 1 < p < n/β and 1/q = 1/p β/n. The authors also consider the boundedness of μ A Ω and its variation μ A Ω on Hardy spaces. 相似文献
15.
Let Ω be a bounded domain with a smooth C2 boundary in RN(N ≥ 3), 0 ∈Ω, and n denote the unit outward normal to ЭΩ.We are concerned with the Neumann boundary problems: -div(|x|α|△u|p-2△u)=|x|βup(α,β)-1-λ|x|γup-1,u(x)〉0,x∈Ω,Эu/Эn=0 on ЭΩ,where 1〈p〈N and α〈0,β〈0 such that p(α,β)△=p(N+β)/N-p+α〉p,y〉α-p.For various parameters α,βorγ,we establish certain existence results of the solutions in the case 0∈Ω or 0∈ЭΩ. 相似文献
16.
In this paper,we obtain the boundedness of the parabolic singular integral operator T with kernel in L(logL)1/γ(Sn-1) on Triebel-Lizorkin spaces.Moreover,we prove the boundedness of a class of Marcinkiewicz integrals μΩ,q(f) from ∥f∥ F˙p0,q(Rn) into Lp(Rn). 相似文献
17.
Guan-zhen Zhou 《高校应用数学学报(英文版)》2010,25(1):43-47
The inequality plays an important role in Fourier analysis and approximation theory. It has recently been generalized by Telyakovskii and Leindler. This paper further generalizes and improves their results by introducing a new class of sequences called γ-piecewise bounded variation sequence (γ-PBVS). 相似文献
18.
Wei HUANG Ye JIANG Li Xin ZHANG 《数学学报(英文版)》2005,21(5):1057-1070
Let {X,Xn;n ≥ 1} be a strictly stationary sequence of ρ-mixing random variables with mean zeros and finite variances. Set Sn =∑k=1^n Xk, Mn=maxk≤n|Sk|,n≥1.Suppose limn→∞ESn^2/n=:σ^2〉0 and ∑n^∞=1 ρ^2/d(2^n)〈∞,where d=2 if 1≤r〈2 and d〉r if r≥2.We prove that if E|X|^r 〈∞,for 1≤p〈2 and r〉p,then limε→0ε^2(r-p)/2-p ∑∞n=1 n^r/p-2 P{Mn≥εn^1/p}=2p/r-p ∑∞k=1(-1)^k/(2k+1)^2(r-p)/(2-p)E|Z|^2(r-p)/2-p,where Z has a normal distribution with mean 0 and variance σ^2. 相似文献
19.
In this paper, we discuss the boundedness of Marcinkiewicz integral μΩ with homogeneous kernel on the weighted Herz-type Hardy spaces, and prove that μΩ is bounded from H K αq ,p ( w1 ; w2 ) into Kαq ,p (w 1; w2). 相似文献
20.
M. S. Sarsak 《Acta Mathematica Hungarica》2011,132(3):244-252
We introduce and study new separation axioms in generalized topological spaces, namely,
m-T\frac14\mu\mbox{-}T_{\frac{1}{4}},
m-T\frac38\mu \mbox{-}T_{\frac{3}{8}} and
m-T\frac12\mu\mbox{-}T_{\frac{1}{2}}.
m-T\frac14\mu\mbox{-}T_{\frac{1}{4}} spaces are strictly placed between μ-T
0 spaces and
m-T\frac38\mu\mbox{-}T_{\frac{3}{8}},
m-T\frac38\mu\mbox{-}T_{\frac{3}{8}} spaces are strictly placed between
m-T\frac14\mu\mbox{-}T_{\frac{1}{4}} spaces and
m-T\frac12\mu \mbox{-}T_{\frac{1}{2}} spaces, and
m-T\frac12\mu\mbox{-}T_{\frac{1}{2}} spaces are strictly placed between
m-T\frac38\mu\mbox{-}T_{\frac{3}{8}} spaces and μ-T
1 spaces. 相似文献