ON HERMITE MATRIX POLYNOMIALS AND HERMITE MATRIX FUNCTIONS

In this paper properties of Hermite matrix polynomials and Hermite matrix functions are studied. The concept ot total set with respect to a matrix functional is introduced and the total property of the Hermite matrix polynomials is proved. Asymptotic behaviour of Hermite matrix polynomials is studied and the relationship of Hermite matrix functions with certain matrix differential equations is developed. A new expression of the matrix exponential for a wide class of matrices in terms of Hermite matrix polynomials is proposed.

SZEG KERNEL FOR HARDY SPACE OF MATRIX FUNCTIONS

By the characterization of the matrix Hilbert transform in the Hermitian Clifford analysis, we introduce the matrix Szeg5 projection operator for the Hardy space of Hermitean monogenic functions defined on a bounded sub-domain of even dimensional Euclidean space, establish the Kerzman-Stein formula which closely connects the matrix Szego projection operator with the Hardy projection operator onto the Hardy space, and get the matrix Szego projection operator in terms of the Hardy projection operator and its adjoint. Furthermore, we construct the explicit matrix Szego kernel function for the Hardy space on the sphere as an example, and get the solution to a boundary value problem for matrix functions.

Positivity of Matrices with Generalized Matrix Functions

Using an elementary fact on matrices we show by a unified approach the positivity of a partitioned positive semidefinite matrix with each square block replaced by a compound matrix, an elementary symmetric function or a generalized matrix function. In addition, we present a refined version of the Thompson determinant compression theorem.

ORTHOGONAL MATRIX POLYNOMIALS WITH RESPECT TO LINEAR MATRIX MOMENT FUNCTION ALS:THEORY AND APPLICATIONS

In this paper orthogonal matrix polynomials with respect to a right matrix moment functional an introduced. Basic results, important examples and applications to the approximation of matrix integrals are studied. Error bounds for the proposed matrix quadrature rules are given.

Precise integration method without inverse matrix calculation for structural dynamic equations

The precise integration method proposed for linear time-invariant homogeneous dynamic systems can provide accurate numerical results that approach an exact solution at integration points. However, difficulties arise when the algorithm is used for non-homogeneous dynamic systems due to the inverse matrix calculation required. In this paper, the structural dynamic equalibrium equations are converted into a special form, the inverse matrix calculation is replaced by the Crout decomposition method to solve the dynamic equilibrium equations, and the precise integration method without the inverse matrix calculation is obtained. The new algorithm enhances the present precise integration method by improving both the computational accuracy and efficiency. Two numerical examples are given to demonstrate the validity and efficiency of the proposed algorithm.

Neurodegenerative diseases are a function of matrix breakdown:how to rebuild extracellular matrix and intracellular matrix

Matrix within cells,the cytoskeleton,and that which surrounds cells,the extracellular matrix（ECM）,are connected to one another through a number of receptors including those in primary cilia,serving as an important chemical and physical signaling system：Mechanical forces generated through the matrix play a critical role in determining the form and function of tissues（Hughes et al.,2018）.

ORTHOGONAL MATRIX POLYNOMIALS WITH RESPECT TO A CONJUGATE BILINEAR MATRIX MOMENT FUNCTIONAL: BASIC THEORY

In this paper basic results for a theory of orthogonal matrix polynomials with respect to a conjugate bilinear matrix moment functional are proposed. Properties of orthogonal matrix polynomial sequences including a three term matrix relationship are given. Positive definite conjugate bilinear matrix moment functionals are introduced and a characterization of positive definiteness in terms of a block Haenkel moment matrix is established. For each positive definite conjugate bilinear matrix moment functional an associated matrix inner product is defined.

A NOTE ON SOBOLEV ORTHOGONALITY FOR LAGUERRE MATRIX POLYNOMIALS

Abstract. Let {L（Ln^（A,λ）（x）}n≥0 be the sequence of monic Laguerre matrix polynomials defined on [0,∞） byLn^（A,λ）（x）=n!/（-λ）^n ∑nk-0（-λ）^k/k!（n-k）!（A＋I）n[（A＋I）k]^-1x^k,where A ∈ C^r×r. It is known that {Ln^（A,λ）（x）}n≥0 is orthogonal with respect to a matrix moment functional when A satisfies the spectral condition that Re（z） 〉 -1 for every z E or（a）. In this note we show that forA such that σ（A） does not contain negative integers, the Laguerre matrix polynomials Ln^（A,λ）（x） are orthogonal with respect to a non-diagonal SobolevLaguerre matrix moment functional, which extends two cases： the above matrix case and the known scalar case.

Development of quality function development matrix to measure the quality management performance of contractor

Quality function development (QFD) matrix was introduced as a tool to measure the quality management performance of contractors. Engineering quality, quality management system components, and their relationship were defined. An integrated engineering quality system was decomposed into seven factors and the quality management system was composed of eight factors. Importance weights of all factors and their relationship point were acquired by questionnaires and interviews. Then, QFD matrix was formulated and the calculating process was proposed. This model was verified on a case study. The result shows that it is useful for contractor in benchmarking themselves and invaluable for owners in the process of deciding contractor.

An Efficient Numerical Scheme for Biological Models in the Frame of Bernoulli Wavelets

This article considers three types of biological systems:the dengue fever disease model,the COVID-19 virus model,and the transmission of Tuberculosis model.The new technique of creating the integration matrix for the Bernoulli wavelets is applied.Also,the novel method proposed in this paper is called the Bernoulli wavelet collocation scheme(BWCM).All three models are in the form system of coupled ordinary differential equations without an exact solution.These systems are converted into a system of algebraic equations using the Bernoulli wavelet collocation scheme.The numerical wave distributions of these governing models are obtained by solving the algebraic equations via the Newton-Raphson method.The results obtained from the developed strategy are compared to several schemes such as the Runge Kutta method,and ND solver in mathematical software.The convergence analyses are discussed through theorems.The newly implemented Bernoulli wavelet method improves the accuracy and converges when it is compared with the existing methods in the literature.

Exact Solutions and Finite Time Stability of Linear Conformable Fractional Systems with Pure Delay

We study nonhomogeneous systems of linear conformable fractional differential equations with pure delay.By using new conformable delayed matrix functions and the method of variation,we obtain a representation of their solutions.As an application,we derive a finite time stability result using the representation of solutions and a norm estimation of the conformable delayedmatrix functions.The obtained results are new,and they extend and improve some existing ones.Finally,an example is presented to illustrate the validity of our theoretical results.

Adaptive Shape Control for Thermal Deformation of Membrane Mirror with In-plane PVDF Actuators

Optical membrane mirrors are promising key components for future space telescopes. Due to their ultra-thin and high flexible properties, the surfaces of these membrane mirrors are susceptible to temperature variations. Therefore adaptive shape control of the mirror is essential to maintain the surface precision and to ensure its working performance. However, researches on modeling and control of membrane mirrors under thermal loads are sparse in open literatures. A 0.2 m diameter scale model of a polyimide membrane mirror is developed in this study. Three Polyvinylidene fluoride(PVDF) patches are laminated on the non-reflective side of the membrane mirror to serve as in-plane actuators. A new mathematical model of the piezoelectric actuated membrane mirror in multiple fields,(i.e., thermal,mechanical, and electrical field) is established, with which dynamic and static behaviors of the mirror can be analyzed.A closed-loop membrane mirror shape control system is set up and a surface shape control method based on an influence function matrix of the mirror is then investigated. Several experiments including surface displacement tracking and thermal deformation alleviation are performed. The deviations range from 15 μm to 20 μm are eliminated within 0.1 s and the residual deformation is controlled to micron level, which demonstrates the effectiveness of the proposed membrane shape control strategy and shows a satisfactory real-time performance. The proposed research provides a technological support and instruction for shape control of optical membrane mirrors.

Network-Based H_∞ Filtering for Linear Systems with Randomly Varying Sensor Delay

An H∞ filter design for linear time delay system with randomly varying sensor delay is investigated.The delay considered here is assumed to satisfy a certain stochastic characteristic.A stochastic variable satisfying Bernoulli random binary distribution is introduced and a new system model is established by employing the measurements with random delay.By using the linear matrix inequality(LMI) technique,sufficient conditions are derived for ensuring the mean-square stochastic stability of the filtering error systems and guaranteeing a prescribed H∞ filtering performance.Finally,a numerical example is given to demonstrate the effectiveness of the proposed approach.

OPTIMIZATION OF TETRANDRINE TREATMENT IN RAT HEPATIC FIBROSIS MODEL

Objective To optimize the therapeutic dosage of tetrandrine （Tet） in rat hepatic fibrosis roodel. Methods 50 Wistar rats were divided into 5 groups at random including normal control, model control, Tettreated model groups of 10mg· kg^ - 1· d^ - 1, 5mg· kg^ - 1· d^ - 1 and 2.5mg· kg^ - 1· d^ - 1（ n = 10 in each group ）. All rats, except for the normal controls, were injected with axenic porcine serum （0. 5ml each time, twice a week） intraperitoneally for 8 weeks to establish hepatic fibrosis. After the 8th week, rats of Tet-treated model groups were given by gavage once a day with different doses of Tet for another 8 weeks. Then the liver function, serum levels of hyaluronic acid （ HA ）, laminin （ LM）, and procollagen type Ⅲ （PCⅢ） were tested. Collagen type 1 and Ⅲ, pathological changes in liver tissue were also assessed. Results Most indices of liver function including alanine minotransferase （ALT）, aspartate aminotransferase （AST）, albumin （ ALB）, albumin/globulin ratio （ A/G） and alkaline phosphatase （ALP） improved significantly in Tet-treated groups with the exception of γ-glutamyl transpeptidase （γ- GT） and total bilirubin （TBIL）. Secondly, markedly lowered levels of HA, LM and collagen type I, III were also detected by radioimmunology and immunohistochemistry in the 5 mg· kg^ - 1· d^ - 1 Tet-treated model group. Moreover, pathologi- cal findings confirmed the statistically significant improvement in hepatofibrotic degree resulted from the treatment of 5mg· kg^ - 1· d^ - 1 rather than other doses of Tet. Conclusion For experimental Wistar rats, Tet exhibited an anti-hepatofibrotic action in doses within the range of 2.5mg· kg^ - 1· d^ - 1 to 10mg· kg^ - 1· d^ - 1 and 5mg· kg^ - 1· d^ - 1 may be the optimum one among all doses.

Co/Zn-metal organic frameworks derived functional matrix for highly active amorphous Se stabilization and advanced lithium storage

Lithium-selenium batteries,as an advanced rechargeable battery system,have attracted wide attention.However,its application is hurdled by the ambiguous underlying mechanism such as the unclear active phase and the key role of the host materials.Herein,a three-dimensional(3D) functional matrix derived from the Co/Znmetal organic framework is synthesized to unravel the questions raised.It reveals that the strong interaction and voids in the 3D matrix serve to anchor the amorphous Se with high electrochemical properties.The obtained 3DC/Se exhibits 544.2 and 273.2 mAh·g^(-1) t current densities of 0.1C and 2.0C,respectively,with a diffusion-controlled mechanism.The excessive amount of Se beyond the loading capacity of the matrix leads to the formation of trigonal phase Se,which shows an unsatisfying electrochemical property.

EQUISTABILITY OF THE MATRIX DIFFERENTIAL EQUATIONS

In this paper the problem about equistability of the matrix equistability of the matrix differential equations have been discussed, and some criteria for equistability have been given.

Construction of periodic wavelet frames with dilation matrix

An important tool for the construction of periodic wavelet frame with the help of extension principles was presented in the Fourier domain by Zhang and Saito [Appl. Comput. Harmon. Anal., 2008, 125： 68-186]. We extend their results to the dilation matrix cases in two aspects. We first show that the periodization of any wavelet frame constructed by the unitary extension principle formulated by Ron and Shen is still a periodic wavelet frame under weaker conditions than that given by Zhang and Saito, and then prove that the periodization of those generated by the mixed extension principle is also a periodic wavelet frame if the scaling functions have compact supports.

Regulation of ovarian function by the matrix metalloproteinase system

In most organs of mammals, cyclic remodelling of tissues after morphogenesis is minimal; however, reproductive tissues of female animals including endometrium, mammary gland, ovarian follicle and corpus luteum undergo growth, maturation and involution at various stages in the reproductive cycle or lifespan of the animal. Reconstruction of the extracellular matrix (ECM) is required for the dynamic tissue reorganization characteristic of these tissues. The ECM consists of proteinaceous and nonproteinaceous molecules that provide the tissue-specific, extracellular architecture to which cells attach. Furthermore, interaction of cellular receptors with proteins of the ECM can regulate cellular structure, second messenger generation and gene expression. Mainte-

Explicit Factorization of Pascal Matrices

In this paper, two kinds of generalized Pascal matrices Pn,k and Qn,k, and two kinds of generalized Pascal functional matrices On,k[x,y] and Qn,k[x,y] are introduced and studied. Factorization of Pascal matrices into products of (0,1) Jordan matrices is established. Factorization of Pascal functional matrices into products of bidiagonal matrices is obtained.

Modeling and Analysis of Interstand Tension Control in 6-high Tandem Cold Rolling Mill

The interstand tension control is one of the most important ways to meet tight tolerances for strip product quality during tandem cold rolling process. Using coordinate analysis and parabolic approximation for the mass flow balance principle, the strip velocities eliminating the use of forward slips and backward slips were calculated. In order to reduce the effect of roll eccentricity on the tension measurement, a filter based on bilinear transformation was de- signed. Applying a first-order Taylor series approximation, the transfer function matrix model of interstand tension stress was derived. The actual measurements on-site and the final calculation results showed that the established model had high calculation accuracy and was beneficial for interstand tension control of random cold rolling process.