Mn(C)中的不可约性

对于M_n(C)(所有n×n矩阵的全体)中的不可约矩阵得到以下结果:对于任意A∈M_n(C),设λ₁, λ₂,…,λ_m为A的所有特征值,这里m≤n而且当i≠j时,λ_i≠λ_j.则A是不可约的当且仅当任意P∈A′(A),P^*=P=P²,有σ(P|ker(A-λ₁))=σ(P|ker(A-λ₂))=…=σ(P|ker(A-λ_m))为单点集.     

Heisenberg群上一类左不变LPDO的局部基本解及局部可解性

In this paper it is proved that local fundamental solution exists in some space W^m(H_n) (m∈Z), if the left invariant differential operator on the Heisenberg group H_n satisfies certain condition. The main results are:l.Let L be a left invariant differential operator on H_n. If there exist R≥0, r,s∈R and operators {B_λ|λ∈Γ_R} ∈V^s(Γ_R, M^r) such that, for almost all λ∈Γ_R, B_λ is the right inverse of Ⅱ_λ(L), then there exists E∈W^m(H_n) (when m≥0 or m even) or E∈W^m-1(H_n) (when m<0 and odd) such that LE =δ(near the origie) Where m=min([r],-[2s]-n-2); 2. Let L(W,T) be of the form (3.1). If there exist R≥0 and r,s∈R such that when |λ|≥R,(?) and C_λ≥ C|λ|^x(C>0), then the same conclusion as above holds with m=min(-[2r]-n-2,[-2s]-n-2).     

四元数矩阵的特征值与奇异值估计

In this paper, we give accurate estimation of eigenvalues and singular values of A + B,C^*AC and AB, where A, B and C are quaternions matrices. These results improve and generalze the results in [4] and [5]. We also obtainsum (?),for k=1,…,n. Where A and B are self-conjugate quaternions matrices of order n, and λ₁≥…≥λ_n,μ₁≥μ_n,λ₁,(A + B)≥…≥λ_n(A+B) be the eigenvalues of A,B and A + B, respectively.     

三角域上Bernstein多项式的Lipschitz常数

设T是平面上以T₁,T₂,T₃为顶点的三角形,f(p)为定义在T上的函数,称Bⁿ(f,P):=(?)f(i/n,j/n,k/n)B_i,j,kⁿ(P),为f的n次Bernstein多项式,这儿B_i,j,kⁿ(P):(n!)/(i!j!k!)uⁱv^jω^k是Bernstein基函数,(u,v,w)是P关于T的重心坐标。 B.M.Brown等人对单变量的Bernstein多项式证明了如果f∈Lip_Aλ,0<λ≤1,则对所有的n,都有B^α(f,x)∈Lip_Aλ。本文的目的是对定义在三角域T:{(x,y):x≥0,y≥0,x+y≤1}上的Bernstein多项式证明了类似的结果: 设f(P)∈Lip_Aλ,0<λ≤1,则对所有的n,Bⁿ(f,P)∈Lip_(2^1/2λA)λ,并且,在一定意义上,常数2^1/2λA是最好的。 上述结果对于任意的锐角或直角三角形T,也是成立的。 最后还指出,当T可为钝角三角形时,则不存在同一常数C,使对所有的n和任意三角形T,有Bⁿ(f,P)∈Lip_cλ。     

右半平面内解析函数的准确零(R)级

Let f(s)=(?)a_ne^-λ_m3(s=σ+it),0<λ_n↑+∞), where (?)(n/logU(λ_n))=E<+∞,(?)(log|α_n|/λ_n)=0.     

关于覆盖同余式组的一个注记

In this paper, it is shown that., if x≡α_i(mod n_i)(i=1,…,k),112<…k,0≤α_ii is a covering sets of residue classes, there exist two distinct pairs of integer number n_i,n_j(is,n_t(si,n_j)>1, (n_s,n_t)>1, where (a,b) is the greatest common divisor of a,b.     

矩阵指数的偏迹不等式

In this paper it is shown that if C is an n×n complex matrix and C^(k) is the k-th compound of C, 1≤k≤n, N = (n k) and if the eigenvalues of C^(k) are labeled inorder of decreasing magnitude |λ₁(C^(k))|≥λ₂(C^(k))|≥…≥λ_N(C^(k))|define the partial trace tr_i^(k)(C) by (?) Then for two n×n Hermrtian matrices A, B,with equality holds if A, B are commutative or k = n.     

关于控制算子的若干注记

Let B(H) be the set of all bounded linear operators on a Hilbert space H. An operator T∈B(H) is called dominant if (T-λ)(T-λ)^*≤M_λ²(T-λ)^*(T-λ),?λ∈C.The numerical range of T is difined by W (T) = {(Tx, x): ‖x‖ = 1, x∈H}. In Section 1 some new characteristic of dominant operators are given. If C = AB - BA, we prove that O∈W(C)^- then A is a dominart or φ-quasihy ponor-mal. In Section 2 we prove that O∈σ_e(△_A^σ) if A is a dominant, where(?), we also prove that if A∈B(H) is a norm attaining Ф-quasihyponormal, then A has a non-trivial invariant subspace. In Section 3 we discuss the closeness of the range of bounded linear operator F_AB:X→AX-XB, and prove that R(δ_A)∩{A}′∩{Aⁿ}′=0, where δ_A:X→AX-XA.     

关于α阶星像函数类的一个子类

设f(z)=z+…在单位圆|z|<1内解析.给定λ(0≤λ<1),我们定义线性算子Ω^λ Ω^λf=Γ(2-λ)z^λD_z^λf(z);和Ω^n+λf=Ωⁿ(Ω^λf),n∈N∪{0}.其中D_z^λf(z)表示f(z)的分数阶导数且Ω¹ f(z)=zf′(z).用A_{n相似文献}   

二阶抛物方程组解的Lp-正则性和Hölder连续性

在可控和自然增长条件下,非线性抛物组 u''_t-D_aA_i^a(x,t,u,Du)= B_i(x,t,u,Du),i=1,…,N,(x,t)∈Q之解。u∈L²(0,T;H¹(Ω,R^N))∩L^∞(0,T;L²(Ω,R^N))(或∩L^∞(Q,R^N))的空间导数D_au事实上属于L_loc^p(Q,R^N),p>2;拟线性抛物组 u''_t-Dα[A_ij^αβ(x,t,u)D_βu^j+a_j^a(x,t,u)]=B_i(x,t,u,Du),i=1,…,N的每一个解都在一开集 Q₁?Q上 Holder连续,且H^n+2-p(Q\Q₁)=0;若当j>i时A_ij^αβ=0,且B_i(x,t,u,p)关于|p|的增长阶小于2,则Q₁=Q;若A_ij^αβ和a_i^a都Holder连续,则D_au也在Q₁上 Holdler连续.     

Estimates of stability of characterization of additive types of distributions

An estimate of stability of characterization of distribution types is obtained for the case of additive types. Under some conditions, the estimate has the order ε^1/3L(ε), where L(ε) is a slowly varying function. Proceedings of the Seminar on Stability Problems for Stochastic Models, Moscow, Russia, 1996, Part I.     

一类完全正则半群簇子簇格的性质

本文研究了完全正则半群簇的子簇格［Ｖ＋∩ＰＶ，Ｖ＋∩ＰＶ］的某些格运算性质，我们证明了簇Ｖ＋∩ＰＶ可分解为Ｖ与Ｖ＋∩ＰＶ的并；对任意完全正则半群簇Ｗ，有Ｗ∩（Ｖ∨Ｖ＋∩ＰＶ）＝（Ｗ∩Ｖ）∨（Ｗ∩Ｖ＋∩ＰＶ）．特别地，我们得到了等式Ｖ＋∩ＰＶ＝Ｖ成立的若干条件．     

Study of the blow-up of solutions of systems of equations of hydrodynamic type

Mathematical Notes - We study the initial boundary-value problem for three-dimensional systems of equations of pseudoparabolic type. The system is similar to the Oskolkov system, but differs from...     

Characterization of types of asymptotic discernibility of families of hypotheses

We give a characterization of the types of asymptotic discernibility of families of hypotheses in the case of hypothetical measures that are not, in general, mutually absolutely continuous. The case when the logarithm of the likelihood ratio admits an asymptotic expansion of the type of an expansion with local asymptotic normality is examined in detail. Examples are studied.Translated fromTeoriya Sluchainykh Protsessov, Vol. 15, pp. 64–71, 1987.     

Distribution of types of symmetry of tensors of high degree

The asymptotic distribution of tensors of degree N in symmetry types is studied in this paper.Translated from Zapiski Nauchnykh Seminarov Leningradskogo Otdeleniya Matematicheskogo Instituta im. V. A. Steklova AN SSSR, Vol. 155, pp. 181–186, 1986.     

Preservation of equivalence of derivations under reduction of depth of formulas

In this paper we consider derivations in the (&, )-fragment of the intuitionistic propositional calculus. As is known, replacement of any occurrence of a formula [F] in a sequent S by an occurrence of the formula [p], where p is a new propositional variable, with the simultaneous addition to the antecedent of the formula F p or p F depending on the sign of the occurrence of F in S, leaves the derivability unchanged. We give a proof of the fact that the natural extension of this transformation to derivations preserves the relation of equivalence of derivations, i.e., transformed derivations are equivalent if and only if the originals are equivalent. (Derivations are considered equivalent if certain of their normal forms coincide, or, what is the same, if their deductive terms coincide.) It is proved that by the iteration of this transformation, each derivation of an arbitrary sequent S can be transformed into a derivation of a sequent S, depending only on S, whose succedent is a variable, and in the antecedent there occur only formulas of the form a,a & b, a b,,(a b) c, a & b c, a (b & c), wherea, b, c are variables. Here if S is balanced, then S is also balanced. (A sequent is called balanced if each variable occurs in it no more than twice.) The familiar correspondence between certain concepts of the theory of categories and concepts of the theory of proofs allows one to assert that there has been constructed a univalent functor, mapping a free Cartesian closed category into itself.Translated from Zapiski Nauchnykh Seminarov Leningradskogo Otdeleniya Matematicheskogo Instituta im. V. A. Steklova AN SSSR, Vol. 88, pp. 197–207, 1979.     

Estimate of growth of Lebesgue functions of linear methods of summation

Sufficient conditions are obtained in terms of matrix elements for the boundedness of Lebesgue functions of linear methods of summation of expansions in orthogonal systems of polynomial type.Translated from Matematicheskie Zametki, Vol. 6, No. 3, pp. 277–286, September, 1969.