Amino-functionalized UiO-66-doped mixed matrix membranes with high permeation performance and fouling resistance

For the reduction of bovine serum proteins from wastewater,a novel mixed matrix membrane was prepared by functionalizing the substrate material polyaryletherketone(PAEK),followed by carboxyl groups(C-SPAEKS),and then adding amino-functionalized UiO-66-NH_(2)(Am-UiO-66-NH_(2)).Aminofunctionalization of UiO-66 was accomplished by melamine,followed by an amidation reaction to immobilize Am-UiO-66-NH_(2),which was immobilized on the surface of the membrane as well as in the pore channels,which enhanced the hydrophilicity of the membrane surface while increasing the negative potential of the membrane surface.This nanoparticle-loaded ultrafiltration membrane has good permeation performance,with a pure water flux of up to 482.3 L·m^(-2)·h^(-1) for C-SPAEKS/AmUiO-66-NH_(2) and a retention rate of up to 98.7%for bovine serum albumin(BSA)-contaminated solutions.Meanwhile,after several hydrophilic modifications,the flux recovery of BSA contaminants by this series of membranes increased from 56.2%to 80.55%of pure membranes.The results of ultra-filtration flux time tests performed at room temperature showed that the series of ultrafiltration membranes remained relatively stable over a test time of 300 min.Thus,the newly developed mixed matrix membrane showed potential for high efficiency and stability in wastewater treatment containing bovine serum proteins.

Transfer matrix method for free and forced vibrations of multi-level functionally graded material stepped beams with different boundary conditions

Functionally graded materials(FGMs)are a novel class of composite materials that have attracted significant attention in the field of engineering due to their unique mechanical properties.This study aims to explore the dynamic behaviors of an FGM stepped beam with different boundary conditions based on an efficient solving method.Under the assumptions of the Euler-Bernoulli beam theory,the governing differential equations of an individual FGM beam are derived with Hamilton’s principle and decoupled via the separation-of-variable approach.Then,the free and forced vibrations of the FGM stepped beam are solved with the transfer matrix method(TMM).Two models,i.e.,a three-level FGM stepped beam and a five-level FGM stepped beam,are considered,and their natural frequencies and mode shapes are presented.To demonstrate the validity of the method in this paper,the simulation results by ABAQUS are also given.On this basis,the detailed parametric analyses on the frequencies and dynamic responses of the three-level FGM stepped beam are carried out.The results show the accuracy and efficiency of the TMM.

Dynamic stiffness matrix of a poroelastic multi-layered site and its Green's functions

Few studies of wave propagation in layered saturated soils have been reported in the literature.In this paper,a general solution of the equation of wave motion in saturated soils,based on one kind of practical Blot's equation, was deduced by introducing wave potentials.Then exact dynamic-stiffness matrices for a poroelastic soil layer and half- space were derived,which extended Wolf's theory for an elastic layered site to the case of poroelasticity,thus resolving a fundamental problem in the field of wave propagation and soil-structure interaction in a poroelastic layered soil site.By using the integral transform method,Green's functions of horizontal and vertical uniformly distributed loads in a poroelastic layered soil site were given.Finally,the theory was verified by numerical examples and dynamic responses by comparing three different soil sites.This study has the following advantages:all parameters in the dynamic-stiffness matrices have explicitly physical meanings and the thickness of the sub-layers does not affect the precision of the calculation which is very convenient for engineering applications.The present theory can degenerate into Wolf's theory and yields numerical results approaching those for an ideal elastic layered site when porosity tends to zero.

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.

A Method for Data Classification Based on Discernibility Matrix and Discernibility Function

A method for data classification will influence the efficiency of classification. Attributes reduction based on discernibility matrix and discernibility function in rough sets can use in data classification, so we put forward a method for data classification. Namely, firstly, we use discernibility matrix and discernibility function to delete superfluous attributes in formation system and get a necessary attribute set. Secondly, we delete superfluous attribute values and get decision rules. Finally, we classify data by means of decision rules. The experiments show that data classification using this method is simpler in the structure, and can improve the efficiency of classification.

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）.

On <i>p</i>and <i>q</i>-Horn’s Matrix Function of Two Complex Variables

The main aim of this paper is to define and study of a new Horn’s matrix function, say, the p and q-Horn’s matrix function of two complex variables. The radius of regularity on this function is given when the positive integers p and q are greater than one, an integral representation of pHq 2 is obtained, recurrence relations are established. Finally, we obtain a higher order partial differential equation satisfied by the p and q-Horn’s matrix function.

A New Extension of Humbert Matrix Function and Their Properties

This paper deals with the study of the composite Humbert matrix function with matrix arguments . The convergence and integral form this function is established. An operational relation between a Humbert matrix function and Kummer matrix function is studied. Also, integral expressions of this relation are deduced. Finally, we define and study of the composite Humbert Kummer matrix functions.

Generalized Form of Hermite Matrix Polynomials via the Hypergeometric Matrix Function

The object of this paper is to present a new generalization of the Hermite matrix polynomials by means of the hypergeometric matrix function. An integral representation, differential recurrence relation and some other properties of these generalized forms are established here. Moreover, some new properties of the Hermite and Chebyshev matrix polynomials are obtained. In particular, the two-variable and two-index Chebyshev matrix polynomials of two matrices are presented.

Changes of renal function impairment, extracellular matrix regulation, renal fibrosis and inflammation in patients with chronic glomerulonephritis

Objective: To investigate the changes and clinical significance of renal function impairment, extracellular matrix regulation, renal fibrosis and inflammation in patients with chronic glomerulonephritis. Methods: A total of 50 patients with chronic glomerulonephritis admitted to our hospital from May 2016 to February 2018 were selected as observation group and 50 healthy people as control group.The expression levels and related inflammatory markers of renal dysfunction [including Uric acid (UA), retinol binding protein (RBP) and type IV collagen (Col-IV)], extracellular matrix modulation [including tissue inhibitor of metalloproteinase -1 (TIMP-1) and matrix metalloproteinase-9 (MMP-9)], renal fibrosis [including transforming growth factor β1 (TGF-β1), laminin (LN) and hyaluronic acid (HA).] and degree of inflammation [including leukocyte stimulating hormone-1 (Lkn-1) and tumor necrosis factor-α (TNF-α)] were observed and compared between the two groups. Results:The changes of renal function impairment, extracellular matrix regulation, renal fibrosis and inflammation were significant in both groups. Compared with healthy controls in the control group, UA[(352.49±26.57) μmol/L], RBP[(98.75±26.91) mg/L], Col-IV[(224.77±72.32) ng/L], TIMP-1[(145.79±49.67) ng/mL], MMP-9[(177.71±52.35) ng/mL], TGF-β1[(15.23±7.61) ng/mL], LN[(153.82±23.01) μg/L], HA[(366.80±77.98) μg/L], Lkn-1[(82.71±20.64) pmol/L] and TNF-α[(138.01±45.26) pg/mL] levels were significantly elevated. The differences were statistically significant. Conclusions: Chronic glomerulonephritis patients with renal dysfunction and abnormal regulation of extracellular matrix, and severe renal fibrosis, the body is at a higher level of inflammation, clinical indicators should be strengthened to detect the early diagnosis of the disease and treatment basis.

Effects of intensive insulin therapy on immune function, inflammatory markers, matrix metalloproteinase and stress response in patients with severe pneumonia

Objective:To explore the effects of intensive insulin therapy on immune function, inflammatory markers, matrix metalloproteinase and stress response in patients with severe pneumonia.Methods: From January 2016 to December 2017, 80 cases of severe pneumonia in ICU of our hospital were selected as the subjects of this study, according to the principle of randomization, they were divided into control group (40 cases) and observation group (40 cases). The control group was given routine insulin + routine treatment, and the observation group was given insulin intensification + routine treatment. The changes of immune function, inflammation index, matrix metalloproteinase and stress level were compared between the two groups before and after treatment.Results: After treatment, the levels of IgA, IgG and IgM in the two groups were significantly higher than those before treatment, and the levels of IgA, IgG and IgM in the observation group were significantly higher than those in the control group;the levels of TNF-α, sTREM1 and CRP in the two groups were significantly lower than those before treatment, and the levels of TNF-α, sTREM1 and CRP in the observation group were significantly lower than those in the control group;the levels of TIMP-1, MMP-9 and MMP-9/TIMP-1 in the two groups were significantly lower than those before treatment, and the levels of TIMP-1, MMP-9 and MMP-9/TIMP-1 in the observation group were significantly lower than those in the control group;the levels of SF and LPO in the two groups were significantly lower than those before treatment, while the levels of SOD in the observation group were significantly higher than those before treatment, and the levels of SF and LPO in the observation group were significantly lower than those in the control group, while the levels of SOD in the observation group were significantly higher than those in the control group. Conclusions:Intensive insulin therapy can effectively improve the immune function of severe pneumonia patients, reduce their inflammatory reaction, matrix metalloproteinase levels and oxidative stress injury.

Effect of S-1 combined with oxaliplatin on serum tumor markers,matrix metalloproteinase and immune function in elderly patients with gastric cancer

Objective: To investigate the effect of Compound Tegafur and Oteracil Potassium Sustained Capsules (S-1) combined with oxaliplatin chemotherapy on serum tumor marker matrix metalloproteinase and immune function in elderly patients with gastric cancer. Methods:According to the random data table, 80 cases of elderly patients with gastric cancer were divided into control group and observation group (n=40), patients in the control group were treated with oxaliplatin combined with Capecitabine Tablets, and the observation group patients were treated with S-1 combined with oxaliplatin, all treated for 6 cycles, before and after treatment, levels of serum tumor markers, matrix metalloproteinase and immune function were compared between the two groups. Results: Before treatment, there was no significant difference in the levels of CEA, CA125, CA19-9, MMP-2, MMP-9, CD3+, CD4+, CD8+and CD4+/CD8+between the two groups;After treatment, the levels of CEA, CA125, CA19-9, MMP-2, MMP-9 and CD8+in the two groups were significantly lower than those in the same group before treatment, and the levels of the observation group[(7.79±2.78) ng/mL, (22.56±7.31) U/mL, (13.48±3.05) U/mL, (57.84±8.93) ng/mL, (199.14±67.39) ng/mL and (26.21±4.18)%] were significantly lower than those in the control group;Compared with the group before treatment, the levels of CD3+, CD4+and CD4+/CD8+in the two groups were significantly increased, and the observation group [(66.89±5.84)%, (41.63±5.24)% and (1.37±0.29)] was significantly higher than the control group. Conclusion: S-1 combined with oxaliplatin chemotherapy can effectively reduce serum tumor markers and matrix metalloproteinase levels, improve immune function, has an important clinical value.

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.

Kernel matrix learning with a general regularized risk functional criterion

Kernel-based methods work by embedding the data into a feature space and then searching linear hypothesis among the embedding data points. The performance is mostly affected by which kernel is used. A promising way is to learn the kernel from the data automatically. A general regularized risk functional （RRF） criterion for kernel matrix learning is proposed. Compared with the RRF criterion, general RRF criterion takes into account the geometric distributions of the embedding data points. It is proven that the distance between different geometric distdbutions can be estimated by their centroid distance in the reproducing kernel Hilbert space. Using this criterion for kernel matrix learning leads to a convex quadratically constrained quadratic programming （QCQP） problem. For several commonly used loss functions, their mathematical formulations are given. Experiment results on a collection of benchmark data sets demonstrate the effectiveness of the proposed method.

Solution of Matrix Game with Triangular Intuitionistic Fuzzy Pay-Off Using Score Function

Using score function in a matrix game is very rare. In the proposed paper we have considered a matrix game with pay-off as triangular intuitionistic fuzzy number and a new ranking order has been proposed using value judgement index, available definitions and operations. A new concept of score function has been developed to defuzzify the pay-off matrix and solution of the matrix game has been obtained. A numerical example has been given in support of the proposed method.

PET image reconstruction with a system matrix containing point spread function derived from single photon incidence response

A point spread function（PSF） for the blurring component in positron emission tomography（PET） is studied. The PSF matrix is derived from the single photon incidence response function. A statistical iterative reconstruction（IR） method based on the system matrix containing the PSF is developed. More specifically, the gamma photon incidence upon a crystal array is simulated by Monte Carlo（MC） simulation, and then the single photon incidence response functions are calculated. Subsequently, the single photon incidence response functions are used to compute the coincidence blurring factor according to the physical process of PET coincidence detection. Through weighting the ordinary system matrix response by the coincidence blurring factors, the IR system matrix containing the PSF is finally established. By using this system matrix, the image is reconstructed by an ordered subset expectation maximization（OSEM） algorithm. The experimental results show that the proposed system matrix can substantially improve the image radial resolution, contrast,and noise property. Furthermore, the simulated single gamma-ray incidence response function depends only on the crystal configuration, so the method could be extended to any PET scanner with the same detector crystal configuration.

Design of Luenberger function observer with disturbance decoupling for matrix second-order linear systems-a parametric approach

A simple method for disturbance decoupling for matrix second-order linear systems is proposed directly in matrix second-order framework via Luenberger function observers based on complete parametric eigenstructure assignment. By introducing the H2 norm of the transfer function from disturbance to estimation error, sufficient and necessary conditions for disturbance decoupling in matrix second-order linear systems are established and are arranged into constraints on the design parameters via Luenberger function observers in terms of the closed-loop eigenvalues and the group of design parameters provided by the eigenstructure assignment approach. Therefore, the disturbance decoupling problem is converted into an eigenstructure assignment problem with extra parameter constraints. A simple example is investigated to show the effect and simplicity of the approach.

Extracting Sub-Networks from Brain Functional Network Using Graph Regularized Nonnegative Matrix Factorization

Currently,functional connectomes constructed from neuroimaging data have emerged as a powerful tool in identifying brain disorders.If one brain disease just manifests as some cognitive dysfunction,it means that the disease may affect some local connectivity in the brain functional network.That is,there are functional abnormalities in the sub-network.Therefore,it is crucial to accurately identify them in pathological diagnosis.To solve these problems,we proposed a sub-network extraction method based on graph regularization nonnegative matrix factorization(GNMF).The dynamic functional networks of normal subjects and early mild cognitive impairment(eMCI)subjects were vectorized and the functional connection vectors(FCV)were assembled to aggregation matrices.Then GNMF was applied to factorize the aggregation matrix to get the base matrix,in which the column vectors were restored to a common sub-network and a distinctive sub-network,and visualization and statistical analysis were conducted on the two sub-networks,respectively.Experimental results demonstrated that,compared with other matrix factorization methods,the proposed method can more obviously reflect the similarity between the common subnetwork of eMCI subjects and normal subjects,as well as the difference between the distinctive sub-network of eMCI subjects and normal subjects,Therefore,the high-dimensional features in brain functional networks can be best represented locally in the lowdimensional space,which provides a new idea for studying brain functional connectomes.

Wigner Function：from Ensemble Average of Density Operator to Its Matrix Element in Entangled Pure States

We show that the Wigner function W=Tr(Δρ)( an ensemble average of the density operator ρ，Δis the Wigner operator) can be expressed as a matrix element of ρ in the entangled pure states.In doing so,converting from quantum master equations to time-evolution equation of the Wigner functions seems direct and concise,The entangled states are defined in the enlarged Fock space with a fictitious freedom.

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.