Empirical Likelihood Statistical Inference for Compound Poisson Vector Processes under Infinite Covariance Matrix

The paper discusses the statistical inference problem of the compound Poisson vector process(CPVP)in the domain of attraction of normal law but with infinite covariance matrix.The empirical likelihood(EL)method to construct confidence regions for the mean vector has been proposed.It is a generalization from the finite second-order moments to the infinite second-order moments in the domain of attraction of normal law.The log-empirical likelihood ratio statistic for the average number of the CPVP converges to F distribution in distribution when the population is in the domain of attraction of normal law but has infinite covariance matrix.Some simulation results are proposed to illustrate the method of the paper.

The Sequential Continuity of Multiplication on a Class of Infinite Matrix Algebras

Let λ and μ are sequence spaces and have both the signed_weak gliding hump property, (λ,μ) be the algebra of the infinite matrix operators which transform λ into μ, in this paper, we study the strong? Mackey? weak multiplier sequentially continuous problem of infinite matrix algebras (λ,μ).

Infinite Matrix Rings on Spaces with Signed-Weakly Gliding Hump Property

In this paper, several elementary properties of infinite matrix rings on spaces with the singed weakly gliding hump property are obtained.

A CLASS OF INFINITE MATRIX TOPOLOGICAL ALGEBRAS

Let λ and μ be sequence spaces and have both the signed weak gliding hump property, (λ,μ) the algebra of the infinite matrix operators which transform λ into μ . In this paper, it is proved that if λ and μ are β spaces and λ β and μ β have also the signed weak gliding hump property, then for any polar topology τ, ((λ,μ),τ) is always sequentially complete locally convex topological algebra.

THE SCHUR TEST OF COMPACT OPERATORS

Infinite matrix theory is an important branch of function analysis.Every linear operator on a complex separable infinite dimensional Hilbert space corresponds to an infinite matrix with respect a orthonormal base of the space,but not every infinite matrix corresponds to an operator.The classical Schur test provides an elegant and useful criterion for the boundedness of linear operators,which is considered a respectable mathematical accomplishment.In this paper,we prove the compact version of the Schur test.Moreover,we provide the Schur test for the Schatten class S_(2).It is worth noting that our main results can be applicable to the general matrix without limitation on non-negative numbers.We finally provide the Schur test for compact operators from l_(p) into l_(q).

ENUMERATIONS OF ONE-VERTEX MAPS WITH FACE PARTITION ON THE PLANE

In addition to the known method given in [1], authors provide other three methods to the enumeration of one-vertex maps with face partition on the plane. Correspondingly, there are four functional equations in the enufuntion. It is shown that the four equations are equivalent. Moreover, an explicit expression of the solution is found by expanding the powers of the matrix of infinite order directly. This is a new complement of what appeared in [1].

Direction of arrival estimation method based on quantum electromagnetic field optimization in the impulse noise

In order to resolve direction finding problems in the impulse noise,a direction of arrival(DOA)estimation method is proposed.The proposed DOA estimation method can restrain the impulse noise by using infinite norm exponential kernel covariance matrix and obtain excellent performance via the maximumlikelihood(ML)algorithm.In order to obtain the global optimal solutions of this method,a quantum electromagnetic field optimization(QEFO)algorithm is designed.In view of the QEFO algorithm,the proposed method can resolve the difficulties of DOA estimation in the impulse noise.Comparing with some traditional DOA estimation methods,the proposed DOA estimation method shows high superiority and robustness for determining the DOA of independent and coherent sources,which has been verified via the Monte-Carlo experiments of different schemes,especially in the case of snapshot deficiency,low generalized signal to noise ratio(GSNR)and strong impulse noise.Beyond that,the Cramer-Rao bound(CRB)of angle estimation in the impulse noise and the proof of the convergence of the QEFO algorithm are provided in this paper.

THE EXPONENTIAL OF QUASI BLOCK-TOEPLITZ MATRICES

The matrix Wiener algebra,W_(N):=M_(N)(W)of order N>0,is the matrix algebra formed by N×N matrices whose entries belong to the classical Wiener algebraWof functions with absolutely convergent Fourier series.A block-Toeplitz matrix T(a)=[A_(i,j)]i,j≥0is a block semi-infinite matrix such that its blocks A_(i,j) are finite matrices of order N,A_(i,j)=A^(r,s) whenever i-j=r-s and its entries are the coefficients of the Fourier expansion of the generator a:T→M_(N)(C).Such a matrix can be regarded as a bounded linear operator acting on the direct sum of N copies of L^(2)(T).We show that exp(T(a))differes from T(exp(a))only in a compact operator with a known bound on its norm.In fact,we prove a slightly more general result:for every entire function f and for every compact operator E,there exists a compact operator F such that f(T(a)+E)=T(f(a))+F.We call these T(a)+E′s matrices,the quasi block-Toeplitz matrices,and we show that via a computation-friendly norm,they form a Banach algebra.Our results generalize and are motivated by some recent results of Dario Andrea Bini,Stefano Massei and Beatrice Meini.

Wiener's lemma:localization and various approaches

Matrices and integral operators with off-diagonal decay appear in numerous areas of mathematics including numerical analysis and harmonic analysis, and they also play impor-tant roles in engineering science including signal processing and communication engineering. Wiener’s lemma states that the localization of matrices and integral operators are preserved un-der inversion. In this introductory note, we re-examine several approaches to Wiener’s lemma for matrices. We also review briefly some recent advances on localization preservation of operations including nonlinear inversion, matrix factorization and optimization.

SYSTEMATIC ERROR FROM Th/U RATIO IN LUMINESCENCE AND ESR DATING

In luminescence and ESR dating methods,total count rate from thick source alpha counting is commonly used fox estimating annual dose with assumption of equal activities for both uranium and thorium decay chains.This is equal to a Th/U weight ratio of 3.2.The systematic error in total dose rate due to uncertainty of the ratio is calculated.It is found that the error is insignificant for uniformly distributed samples such as sediment,but can be significant for some extreme circumstances.

A separation form of unified convergence theorem

In this paper, by introducing isometrically Pc0 property a separation form of convergence theorem is presented and the results generalize and unify several interesting conclusions in recent years.

A Unified Convergence Theorem

We prove a unified convergence theorem, which presents, in four equivalentforms, the famous Antosik-Mikusinski theorems. In particular, we show that Swartz' three uniformconvergence principles are all equivalent to the Antosik-Mikusinski theorems.