混合序列的若干收敛性质

给出一类较广泛的 混合序列基本不等式 ,讨论了  混合序列的收敛性质 ,获得了几乎与独立情形完全一样的Baun和Katz定理 ,Marcinkiewicz强大数律 。

Generally Unitary Solution to a System of Matrix Equations over the Quaternion Field

Generally unitary solution to the system of martix equations over the quaternion field [X mA ns =B ns ,X nn C nt =D nt ] is considered. A necessary and sufficient condition for the existence of and the expression for the generally unitary solution of the system are derived.

Rings satisfying UR-stable range

A ring R is said to be satisfying P-stable range provided that whenever aR ＋ bR = R, there exists y ∈ P（R） such that a ＋ by is a unit of R, where P（R） is the subset of R which satisfies the property that up, pu∈ P（R） for every unit u of R and p ∈P（R）. By studying this ring, some known results of rings satisfying unit-1 stable range, （ S, 2） -stable range, weakly unit 1- stable range and stable range one are unified. An element of a ring is said to be UR if it is the sum of a unit and a regular dement and a ring is said to be satisfying UR-stable range if R has P-stable range and P（R） is the set of all UR-elements of R, Some properties of this ring are studied and it is proven that if R satisfies UR-stahle range then so does any n × n matrix ring over R.

The Necessary and Sufficient Conditions for Two Kinds of Matrix Equtions Having Semipositive Subdefinite Solutions

Finding solutions of matrix equations in given set SR n×n is an active research field. Lots of investigation have done for these cases, where S are the sets of general or symmetric matrices and symmetric positive definite or sysmmetric semiposite definite matrices respectively . Recently, however, attentions are been paying to the situation for S to be the set of general(semi) positive definite matrices(called as semipositive subdefinite matrices below) . In this paper the necessary and sufficient conditions for the following two kinds of matrix equations having semipositive, subdefinite solutions are obtained. General solutions and symmetric solutions of the equations (Ⅰ) and (Ⅱ) have been considered in in detail.

Quasi-χ~2 Distribution and the Independence of Wishart Distribution

In this paper, the authors generalize the definition of χ 2 distribution and introduce a quasi χ 2 distribution, and then prove several properties of it, find the necessary and sufficient conditions of independence about multivariate normal distributions, matrix normal distributions and two parts of the Wishart distribution.

Criteria Conditions for Generalized Diagonally Dominant Matrices

In this paper, some new sufficient conditions for generalized dominant matrices are given, and some results in [1] are generalized and improved.

Necessary and Sufficient Condition for Generalized Diagonal Dominance Matrices

In the paper,a necessary and sufficeent condition for generalized diagonal domiance matrices is given.Further, the relations among all generalized positive definite matrices are shown, also,some flaws and mistakes in the references are corrected.

E-matrices and Several Necessary and Sufficient Conditions

In this paper,we define a kind of sguare matrices which is called E-matrices,and give several necessary and sufficient conditions for E-matrices.

The Least Square Solutions to the Quaternion Matrix Equation AX=B

A norm of a quaternion matrix is defined. The expressions of the least square solutions of the quaternion matrix equation AX = B and the equation with the constraint condition DX = E are given.

Some Remarks On E＇-matrices

The class of E＇-matrices introduced in [4] is a subclass of Q0-matrices whose proper principal submatrices are Q--matrices. In this paper, we investigate the relation of the class E＇ to other known matrix classes and obtain a series of necessary and sufficient conditions for E＇-matrices.

Criteria Conditions for Generalized Diagonally Dominant Matrices

In this paper, we provide some new criteria conditions for generalized strictly diagonally dominant matrices, such that the corresponding results in [1] are generalized and improved.

3D Se-doped NiCoP nanoarrays on carbon cloth for efficient alkaline hydrogen evolution

The exploration of stable and highly efficient alkaline hydrogen evolution reaction(HER)electrocatalysts is imperative for alkaline water splitting.Herein,Se-doped NiCoP with hierarchical nanoarray structures directly grown on carbon cloth(Se-NiCoP/CC)was prepared by hydrothermal reaction and phosphorization/selenization process.The experimental results reveal that Se doping could increase the electrochemical active sites and alter the electronic structure of NiCoP.The optimized Se-NiCoP/CC electrode exhibits outstanding HER activity in alkaline electrolyte,which only needs a low overpotential of 79 mV at the current density of 10 mA/cm^(2).When serving as anode and cathode electrode simultaneously,the Se-NiCoP/CC electrodes achieve current density of 50 mA/cm^(2) at a low voltage of only 1.62 V.This work provides a feasible way to rationally design high active HER electrocatalysts.

Generation of Complex Matrices Belonging to Matrix Groups with Controlled Condition Number

The authors study the generation of matrices with complex entries belonging to some matrix groups, mainly those that are defined by a scalar product space. These matrices have useful applications in quantum mechanical problems and complex control problems. In this work, the authors try to generate matrices such that： （1） the condition number of these types of matrices is controlled and （2） The algorithm used to generate these matrices preserves their structure.

A Necessary and Sufficient Condition for Solvability of the Matrix Equation AXB＋CYD＝E Over an Arbitrary Skew Field

A necessary and sufficient condition for the consisteney of the matrix equation AXB+CYD=E over an arbitrary skew field is given. Thus Roth's equivalence theorem is generalized.

Density Matrix for Mesoscopic Distributed Parameter Circuits

Under the Born-von-Karmann periodic boundary condition, we propose a quantization scheme for non-dissipative distributed parameter circuits (i.e. a uniform periodic transmission line). We find the unitary operator for diagonalizing the Hamiltonian of the uniform periodic transmission line. The unitary operator is expressed in a coordinate representation that brings convenience to deriving the density matrix rho(q,q',beta). The quantum fluctuations of charge and current at a definite temperature have been studied. It is shown that quantum fluctuations of distributed parameter circuits, which also have distributed properties, are related to both the circuit parameters and the positions and the mode of signals and temperature T. The higher the temperature is, the stronger quantum noise the circuit exhibits.

Preparation and photoelectric effect of Zn^(2+)-TiO_2 nanotube arrays

Zn 2+-TiO2 nanotube arrays were prepared by anodic oxidation method.The current-time curves were used to investigate their growth mechanism.Scanning electron microscopy and X-ray diffractometry were applied to characterizing their structures and properties.The photoelectrochemical properties were studied by electrochemical impedance spectrum(EIS).The optimised working conditions for TiO2 nanotube arrays were found to be pH 1,0.5%HF(mass fraction),20 V oxidation voltage and for 2 h.The produced sample was in anatase form,with length of 70-100 nm,thickness of 10 nm,uniform diameter and structure that does not collapse under the preparation conditions.The EIS results show that TiO2 nanotube arrays prepared with 0.5%HF(mass fraction) present a low impedance and TiO2 nanotube arrays loaded by Zn 2+could have a decreased resistance.This decrease could likely accelerate the transfer of carriers and even increase photoelectric conversion.

Robust synchronization of uncertain complex systems with time-varying delays

Synchronization analysis and design problems for uncertain time-delayed high-order complex systems with dynamic output feedback synchronization protocols are investigated. By stating projection on the synchronization subspace and the complement synchronization subspace, synchronization problems are transformed into simultaneous stabilization problems of multiple subsystems related to eigenvalues of the Laplacian matrix of the interaction topology of a complex system. In terms of linear matrix inequalities(LMIs), sufficient conditions for robust synchronization are presented, which include only five LMI constraints.By the changing variable method, sufficient conditions for robust synchronization in terms of LMIs and matrix equalities are given,which can be checked by the cone complementarily linearization approach. The effectiveness of theoretical results is shown by numerical examples.

On Zero One Symmetric and Normal Matrices

We present additional equivalent conditions on the existence of a 0 1 symmetric matrix with given row sum vector. The case of a 0 1 normal matrix is also considered.

Some Equivalent Conditions for Block Independence of Reflexive Inner Inverse of Block Matrix

The definition of block independence in generalized inverse of block matrix was introduced in [1]. In this paper, we give some equivalent conditions for two m × n matrices being block independent in reflexive inner inverse .

UNCONDITIONAL CAUCHY SERIES AND UNIFORM CONVERGENCE ON MATRICES

The authors obtain new characterizations of unconditional Cauchy series in terms of separation properties of subfamilies of p(N), and a generalization of the Orlicz-Pettis Theorem is also obtained. New results on the uniform convergence on matrices and a new version of the Hahn-Schur summation theorem are proved. For matrices whose rows define unconditional Cauchy series, a better sufficient condition for the basic Matrix Theorem of Antosik and Swartz, new necessary conditions and a new proof of that theorem are given.