AN EQUIVALENCE BETWEEN RING F AND INFINITE MATRIX SUBRING OVER F

In 1974 Fuller characterized the equivalences between certain subcategories of thecategory of modules over a ring and the category of unital modules over a ring with iden-tity.In this paperthe author uses this equivalence to extend the well-known theorem:F≈M_n(F),where F is a ring with identity and M_n(F)is the ring of matrices over F.     

NECESSARY AND SUFFICIENT CONDITIONS FOR THE EXISTENCE OF PERIODIC SOLUTIONS OF RICCATI'S EQUATION WITH PERIODIC COEFFICIENTS

In this paper, the concept of generalized ω-periodic solution is given for Riccati's equationy'=a(t)y~2 b(t)y c(t)with perriodic coefficients, the relation between generalized ω-periodicsolutions and the characteristic numbers of system x'_1=c(t)x_2, x'_2=-a(t)x_1-b(t)x_2 is indicated, andseveral necessary and sufficient conditions are given using the coefficients. Moreover, in the case of a(t)without zero, the relation between the number of continuous ω-periodic solutions of y'=a(t)y~2 b(t)y c(t) δand the parameter δ is given; thus the problem on the existence of continuous ω-periodic.solutions is basically solved.     

On Some Classes of Interpolating Splines

In this article, we consider some classes of interpolating spline with difference. derivative and integral interpolating conditions respectively. Let Δ_π:a=x_o相似文献   

MEAN SQUARE ERROR FOR UNIFORMKERNEL ESTIMATE AND NEAREST NEIGHBOR ESTIMATE OF NONPARAMETRIC REGRESSION FUNCTIONS

Let (X_(?), Y_(?)), i=1, …, n be R~d×R~1-valued iid. samples taken from (X, Y). We denote the regression function by m(x)=E(Y|X=x). In this paper we consider the Mean Square Error (MSE) of two usual estimates of m(x_0) based on (X_(?), Y_(?)), i=1,…, n at a point x_0, the Uniform-Kernel Estimate m_n(x_0) and NN-Estimate (x_0). We prove that under some reasonable conditions the lowest asymptotic MSE attained for these two estimates have the same form: where C(x_0) is a constant depending on x_0. Hence from the point of view of MSE, one has no reason to claim superiority of m_m(x_0)to (x_0) or vice versa.     

ON THE METHOD OF SOLUTION FOR A KIND OFNONLINEAR SINGULAR INTEGRAL EQUATION

The solutions of the nonlinear singular integral equation ψo(t)2 2b/πi ∫L ψ(τ)/T-t dr =f(t), t ∈ L, are considered, where L is a closed contour in the complex plane, b ≠- 0 is a constant and f(t) is a polynomial. It is an extension of the results obtained in [1] when f(t) is a constant. Certain special cases are illustrated.     

COMPLETELY POSITIVE MAPS AND-ISOMORPHISM OF C-ALGEBRAS

Let A,B be unital C~*-algebras.X_A={|are all completely positive linear maps from M_n(C)to A with ‖a‖≤1}.(a=((e_(11))…(e_(1n)……(e_(n1))…(e_(nn))),where{e_(iy)}is the matrix unit of M_n(C).)Let a be the natural action of SU(n)on M_n(C).For n≥3,if Φis an a-invariant affine isomorphism between X_A and X_B,Φ(0)=0,then A and B are~*-isomorphic.In this paper a counter example is given for the case n=2.     

ASYMPTOTICALLY OPTIMAL EMPIRICAL BAYES ESTIMATION FOR PARAMETERS OF TWO-SIDED TRUNCATION DISTRIBUTION FAMILIES

Consider the two-sided truncation distrbution families written in the formf(x,θ)dx=w(θ_1, θ_2)h(x)I_([θ_1,θ_2])(x)dx, where θ=(θ_1,θ_2).T(x)=(t_1(x), t_2(x))=(min(x_1,…,x_m), max(x_1, …,x_m))is a sufficient statistic and its marginal density is denoted by f(t)dμ~T. The prior distribution of θ belongs to the familyF={G:∫‖θ‖~2dG(θ)<∞}.In this paper, the author constructs the empirical Bayes estimator (EBE) of θ, φ_n (t), by using the kernel estimation of f(t). Under a quite general assumption imposed upon f(t) and h(x), it is shown that φ_n(t) is an asymptotically optimal EBE of θ.     

THE CONVERGENCE RATES OF EMPIRICAL BAYES ESTIMATION FOR PARAMETERS OF TWO-SIDED TRUNCATION DISTRIBUTION FAMILIES

Consider the two-sided truncation distribution families written in the form f(x,θ)=w(θ_1, θ_2)·h(x)I_([θ_1,θ_2])(x)dx, where θ=(θ_1,θ_2). T(X)=(t_1(X), t_2(X))=(min(X_1, …, X_m), max(X_1, …, X_m)) is a sufficient statistic and we denote its marginal density by f(t)dμ~T. The prior distribution of θ belong to the famlly. In this paper, we have constructed the empirical Bayes (EB) estimator of θ, φ_n(t), by using the kernel estimation of f(t) and established its convergence rates. Under suitable conditions it is shown that the rates of convergenc of EB estimator are O(N~-((λ中-1)(k 1))/(2(k 2)k)), where the neural number k>1 and 1/2<λ<1-1/2k. Finally an example about this result is given.     

PARAMETER ESTIMATION OF SPATIAL AR MODEL

Consider a stable AR model of two parameter spatial series {X_t, t∈N~2}, i. e. {X_(t)t∈N~2} is homogeneous and satisfies the following difference equationX_t-sum from n=s∈相似文献   

Maximum likelihood character of distributions

In this paper,some distributions in the family of those with invariance under orthogonaltransformations within an s-dimensional linear subspace are characterized by maximun likelihoodcriteria.Specially,the main result is:suppose P_v is a projection matrix of a given s-dimensionalsubspace V,and x_1,…,x_n are i.i.d.samples drawn from a population with a pdf f(x′P_vx),wheref(·) is a positive and continuously differentiable function.Then P_v(M_n) is the maximum likelihoodestimator of P_v ifff(x)=c_kexp(kx) (k>0),where M_n=sum from i=1 to n x_ix′_i,P_v(M_n)=sum from i=1 to (?) (?)_i(?)′_t,λ_1,…,λ_(?) are the first s largest eigenvalues of matrix M_n,and(?)_1,…,(?)_(?) are their associated eigenvectors.     

NECESSARY CONDITION FOR THE STRONG UNIFORM CONVERGENCE OF THE NEAREST NEIGHBOUR DENSITY ESTIMATE

Let X_1,X_2,...,X_n be iid. Sample drawn from a population with distribution F, if F have a density, denote it by f. Various methods of estimating f by x_1,X_2,...,X_n, have proposed in the literatures, for example, the kernel estimate and nearest neighhour estimate. The later was introduced by Loftsgarden and Quesenberry[1]. The method is as follows:     

On the Approximation of Continuous Functions by Pal-Type Interpolation Polynomials

Let us denote by -1=x_n相似文献   

Elements of Small Orders in K2F Ⅱ

In "Elements of small orders in K2(F)" (Algebraic K-Theory, Lecture Notes in Math., 966, 1982, 1-6.), the author investigates elements of the form {a, Φn(a)} in the Milnor group K2F of a field F, where Φn(x) is the n-th cyclotomic polynomial. In this paper, these elements are generalized. Applying the explicit formulas of Rosset and Tate for the transfer homomorphism for K2, the author proves some new results on elements of small orders in K2F.     

Matrix Algebra Motivated by Essentially Stochastic Matrices

A matrix of order n whose row sums are all equal to 1 is called an essentially stochastic matrix (see Johnsen [4]). We extend this notion as the following. Let F be a field of characteristic 0 or a prime greater than n. M_n(F) denotes the set of all n×n matrices over F. Let t be an elernent of F. A matrix A=(a_(ij)) in M_n(F) is called essentially t-stochastic' provided its row sums are each equal to t. We denote by R_n(t) the set of all essentially t-stochastic matrices over F. We shall mainly study R_n(0) and. Our main references are Johnson [2,4] and Kim [5].     

HAUSDORFF DIMENSION OF THE DOUBLE POINT SET OF THE WESTWATER PROCESS

Let X={X_i}_(t∈[0,1])be the Westwater process which is the coordinate process under3-dimensional polymer measure v(g)constructed by J.Westwater.In this paper,theHausdorff dimension problem for the double point set of X is investigated.As a result,it is proved thatdim D_2=1,v(g)-a.e.,where D_2={x∈R~3:X=X_(?)=x for some s相似文献   

ON PRIMALITY OF THE COMBINATION OF EXPONENTIAL FUNCTIONS

The author discusses in this paper the transcendental unsolvability of the functionalequation F(z)=fog(z) with f being meromorphic and g entire,for the function of theformwhere Q_j's are rational,P_j's are polynomials. The main results are:a) F(z) is pseudo-prime, i. e. F=fog has no transcendental solutions f and g;b)If 0≤n_1相似文献   

GLOBAL EXISTENCE OF SOLUTIONS TO INITIAL BOUNDARY VALUE PROBLEM FOR NONLINEAR PARABOLIC EQUATIONS

§1. Introduction In this paper we are concerned with the following initial boundary value problem for nonlinear parabolic equations: where Γ is the smooth boundary of a bounded domain Ω∈R~n, x=(x_1,…x_n), D_xu=(u_(x_1),… u_(x_n)), D_x~2=(u_(x_ix_j)), (i, j=1, …,n). What we want do do in this paper is to consider the global existence of smooth solutions for (1.1) under the assumption of small initial data.     

车多项式对Ferrers矩阵的刻画

In this paper,we show that there exist precisely W(A) Ferrers matrices F(C1,C2,…,cm)such that the rook polynomials is equal to the rook polynomial of Ferrers matrix F(b1,b2,…,bm), where A={b1,b2-1,…,bm-m 1} is a repeated set,W(A) is weight of A.     

高阶Hermite-Fejer型插值的渐近估计

1. Introduction Let f∈C[-1,1] and X_k=X_(kn)=COSθ_k=COS(2k-1)π/(2n)(k=1,…,n) be the zeros of the Chebyshev polynomial T_n(x)=cosnθ(x=cosθ). Let ω(t) be a given modulus of continuity and H_ω={f;ω(f,t)≤ω(t),for all.t≥0}. In this paper, c will always denote different constant independent of x, n and f and the sign"A～B" means that there exist two positive constants c_1相似文献   

Elements of Small Orders in K_2FⅡ

In"Elements of small orders in K_2(F)"(Algebraic K-Theory,Lecture Notes in Math.,966,1982,1-6.),the author investigates elements of the form {a,Φ_n(a)} in the Milnor group K_2F of a field F,whereΦ_n(x)is the n-th cyclotomic polynomial.In this paper,these elements are generalized.Applying the explicit formulas of Rosset and Tate for the transfer homomorphism for K_2,the author proves some new results on elements of small orders in K_2F.