A matrix version of the Wielandt inequality and its application to statistics

Suppose that A is an n × n positive definite Hemitain matrix. Let X and Y be n × p and n × q matrices (p+ q≤n), such that X* Y = 0. The following inequality is proved X*AY( Y* AY)-Y Y*AX≤( (λ1-λn)/(λ1+λn))2 X*AX, where λ1 and λn are respectively the largest and smallest eigenvalues of A, and M- stands for a generalized inverse of M. This inequality is an extension of the well-known Wielandt inequality in which both X and Y are vectors. The inequality is utilized to obtain some interesting inequalities about covari-ance matrix and various correlation coefficients including the canonical correlation, multiple and simple correlation.     

On the Spectral Moment of Quasi-Unicyclic Graphs

A connected graph G=(V(G),E(G)) is called a quasi-unicyclic graph,if there exists u_0∈V(G) such that G-u_0 is a unicyclic graph.Denote Q(n,d_0)={G:G is a quasi-unicyclic graph of order n with G-u_0 being a unicyclic graph and d_G(u_0)=d_0}.Let A(G) be the adjacency matrix of a graph G,and let λ_1(G),λ_2(G),…,λ_n(G) be the eigenvalues in non-increasing order of A(G).The number■(k=0,1,…,n-1) is called the k-th spectral moment of G,denoted by S_k(G).Let S(G)=(S_0(G),S_1(G),…,S_(n-1)(G)) be the sequence of spectral moments of G.For two graphs G_1,G_2,we have■ if for some k(k=1,2,…,n-1), and we have S_i(G_1)=S_i(G_2)(i=0,1,…,k-1) and S_k(G_1)S_k(G_2).In this paper,we determine the second to the fourth largest quasi-unicyclic graphs,in an S-order,in the set Q(n,d_0),respectively.     

Composition operators between p-Bloch space and q-Bloch space in the unit ball

Let B_n be the unit ball of C~n and φ= (φ_1,…,φ_n) a holomorphic self-map of B_n. The main purpose of this paper is todiscuss the boundedness and compactness of composition operator C_φ between p-Bloch space β~p(B_n) and q-Bloch space β~p(B_n), where p≥0 and q≥0.     

EXISTENCE AND REGULARITY OF POSITIVE SOLUTIONS OF THE ELLIPTIC EQUATIONS INVOLVING CRITICAL NONLINEAR AND SUBLINEAR

0 IntroductionLet Ωbe a smooth bounded domain in R~n with n>3, consider the problem of finding a function u(x)which satisfieswhere 0<α<1, 1 1 there is asolution of (0. 1) for any λ>0.The principal tecncihique of argument in [1] is using positive radial solution (0. 3) of equation -△u=u~2~n-1 in R~*.     

Research on a Class of Equations over Finite Fields

Let F_q stand for the finite field of odd characteristic p with q elements(q=p~n,n∈N)and F_q~* denote the set of all the nonzero elements of F_q.In this paper,by using the augmented degree matrix and the result given by Cao,we obtain a formula for the number of rational points of the following equation over F_q:f(x _1,x _2,...,x _n)=(a_1 x_1 x_2~d+a_2 x_2 x_3~d...+a_(n-1)x_(n-1)x_n~d+a_n x_n x_1~d)~λ-bx_1~(d1)x_2~d2...x_n~(dn),with a_i,b∈F_q~*,n≥2,λ0 being positive integers,and d,d_i being nonnegative integers for 1≤i n.This technique can be applied to the polynomials of the form h_1~λ=h_2 with λ being positive integer and h_1,h_2∈F_q[x _1,x _2,...,x _n].It extends the results of the Markoff-Hurwitz-type equations.     

SOME PROPERTIES OF SUPER-DECOMPOSABLE OPERATORS

In this paper,the following main resvlts have been proved:1.Let T∈B(X) be a super-decomposable operator,then for any hyperinvariant subspace Y of T,the operator T/Y is super-decomposable.2.The operator T∈B(X) is super-decomposable if and only if T/Y is super-decomposable for any hyperinvariant subspace Y of T.3. If T∈B(X) has on open spectral resolvent,then T is superdecomposable.     

A KIND OF BOUNDARY VALUE PROBLEMS FOR THE REGULAR FUNCTIONS WITH VALUES IN A REAL CLIFFORD ALGEBRA

Let A. (R) be a real Clifford algebra and Gan open connected set in R~n . By [1], the function with val-ues in A_n (R) may be written aswhere B ={r_1,r_2,…,r_h} {1,2,…,n}represent that from the sum for'lst and 2nd indi-sates respectively, and we have the following result.Theorem A Function f (x) with values in A. (R) is regular in G if and only ifLet G be the unit hyperball and L the unit hypersphere. Cutting G by the plane: x_3= a_3, …,x_n = a_n(n3) , we obtain a section domain G_a in the x_1x_2 plane. Let L_a be the boundary of G_a, and its center is writ-ten as 0_ = (0,0,α_3,...,α_n) .     

ON α-CONVEX FUNCTIONS WITH MISSING COEFFICIENTS

Let J_n (a,A,B), α≥0, -1≤B相似文献   

Study of operator reliability in nuclear power plants

The study of the reliability of operator's diagnosis and decision-making during abnormal events with HCR model has been introduced. A new approach has been proposed by the authors to deal with the classification of HIs. The modification of T0.5 by PSFs coefficients has been discussed. In addition, it is emphasized that T0. 5 and SD(σ) of response times can be used as a scale to predict and evaluate the reliability of crew/operator behavior. These processings provide improvement and refinement to HCR model and its practical application. The experiment for operator response time of Chinese NPP using a lull-scale simulator has proved the above-mentioned processings and presented the quantitative results of operator reliability in Chinese NPP.     

一个人员指派问题(英文)

Let T be a set of personnel.Suppose that“≤”is a partial ordering relationon T(which expresses,for example,the seniority of the perssonnel)such that(T,≤)is a rooted tree.Let U be a subset of T.If U can be partitioned into groups eachconsisting of one leader,say t,and k ordinary members,say t_1,t_2,…,t_k,with theproperty that the leader must have higher seniority than the k ordinary members,     

ON DIRICHLET''''S DIVISOR PROBLEM

Let d(n) denote tho number of divisors of n and . It is well-known that as x≡θ, Dirichlet proved thatΔ(x)≡D(x) -xlogx- (2r-l)x= O(x1/2)where r is Euler's constant. Actually Δ (x) =O(xz), for some a loss than1/2. Let θ be tho greatest lowor bound of α, tho best result hither-to obtained is that θ≤15/46 which belongs to T. T. Chin and was obtained and published in 1953 by Richert independently. Tho main object of this paper is to prove thatθ≤13/40.     

THE CONTINUITY OF THE CARATHEODORY OPERATOR

Let X be a set of points on which a completely additive measure is given. Lot F(x.y) be a real-valued function which is defined for every point xeX and for every real number y and satisfies the Caratheodory conditions: F(x, y) is continuous in y for almost every x, and measurable in x for every y. It was proved by B. B. that the operator F defined by the equationis continuous in the space of the measurable functions on X. It was recently proved by M. A. that, if the given measure is continuous, the operator F, whenever it transforms the whole space If into Lq(1≤p,q<+∞) is continuous and baunded.     

A note on a conjecture of Graffiti

In this paper,we will give a very simpleproof of a conjecture of Graffiti. （WOW Conjecture 584） ：Let T be a tree of order n with independence number a , thenA λ1≤ 2 ＋ a , where A t is the Laplacian spectralradius. （ Xiao - dong Zhang , On the two conjectures of Graffiti, Linear Algebra and its Applications , described all extremal treesthat attain the maximal Laplacian spectral radius and used theresults to show conjectures.     

Binding number,minimum degree and bipancyclism in bipartite graphs

Let G =(V_1,V_2,E) be a balanced bipartite graph with2 n vertices.The bipartite binding number of G,denoted by B(G),is defined to be n if G =K_n and min i∈{1,2}|N(S)|n min |N(S)|/|S|otherwise.We call G bipancyclic if it contains a cycle of every even length m for 4 ≤ m ≤ 2n.A theorem showed that if G is a balanced bipartite graph with 2n vertices,B(G) 3 / 2 and n 139,then G is bipancyclic.This paper generalizes the conclusion as follows:Let 0 c 3 / 2 and G be a 2-colmected balanced bipartite graph with 2n(n is large enough) vertices such that B(G) c and δ(G)(2-c)n/(3-c)+2/3.Then G is bipancyclic.     

Recurrent sequences in median filters (II)

1 Introduction Throughout this note k denotes a fixed integer and k>1. Let x={x(n)}_n=0, ±, ±2,… be a real sequence. For each integer n, we denote by x(n) the median value of the following 2k+1 numbers: x(n-k), x(n-k+1), …, x(n),…, x(n+k-1), x(n+k). By this permuting operation, the sequence x={x(n)} is transformed in     

Multipliers on weighted Hardy spaces over locally compact Vilenkin groups

A weighted Hpω(G) multiplier theorem on the multiplier operator T associated with a function m∈ L∞ (Γ) is shown and the atomic decomposition of functions fin Hp*(G) is obtained, where G is a Vilenkin group, r its dual, 0 < p≤1 and ω is a weight on G which is more general than that proposed by C. W. Onneweer et al.     

Perturbations of the radical of nest algebras

Let R N and K-N be the radical ideal and the compact operator ideal of nest algebra T(N) respectively. It is proved thatR-N+K-N=span{T∈T(N)∶TT(N)NCT}=span{T∈T(N): #σ′(ST)≤1, S∈T(N)}.     

B-Valued Dyadic Derivative

The principles of the new maximal operator H＊ we defined are discussed. We prove that it is bounded from martingale Hardy-Lorentz L^Xp.q[0,1） to the Lorentz L^Xp.q[0,1） for 1/2〈 p〈∞, 0〈~ q ≤ ∞, where X is any Banach space. When the Banach space X has the RN property, the sequence dnHnf converges to f a.e. Meanwhile the convergence in L^Xp norm for 1≤p〈∞ is a consequence of that the family functions K （n∈N） is an approximate identity.     

Finite groups whose element orders do not exceed twenty

Let h(T) denote the number of distinct finite groups G such that 7re( G) = P. Here P is a set of positive integers, and 7r,(G) is the set of element orders of G. It is proved that /i(r)6l0, 1,2, oo| for Tell, 2, 3,"-, 20|.