Wave propagation of a functionally graded plate via integral variables with a hyperbolic arcsine function

Several studies on functionally graded materials(FGMs)have been done by researchers,but few studies have dealt with the impact of the modification of the properties of materials with regard to the functional propagation of the waves in plates.This work aims to explore the effects of changing compositional characteristics and the volume fraction of the constituent of plate materials regarding the wave propagation response of thick plates of FGM.This model is based on a higher-order theory and a new displacement field with four unknowns that introduce indeterminate integral variables with a hyperbolic arcsine function.The FGM plate is assumed to consist of a mixture of metal and ceramic,and its properties change depending on the power functions of the thickness of the plate,such as linear,quadratic,cubic,and inverse quadratic.By utilizing Hamilton’s principle,general formulae of the wave propagation were obtained to establish wave modes and phase velocity curves of the wave propagation in a functionally graded plate,including the effects of changing compositional characteristics of materials.

The Determination Method of Product Engineering Features Based on Linguistic Variables

To overcome the problem of imprecise and unclear information in the development of quality functions,a method for determining the priority of engineering features based on mixed linguistic variables is proposed.First,the evaluation member uses the determined linguistic variable to give the correlation strength evaluation matrix of customer requirements and engineering features.Secondly,the relative importance of the evaluation member and customer requirements are aggregated.Finally,the priority of engineering features is obtained by calculating the deviation.The feasibility and practicability of this method are proven by taking the design of a new product of a long bag low-pressure pulse dust collector as an example.

SOME RESULTS REGARDING PARTIAL DIFFERENTIAL POLYNOMIALS AND THE UNIQUENESS OF MEROMORPHIC FUNCTIONS IN SEVERAL VARIABLES

In this paper,we mainly investigate the value distribution of meromorphic functions in Cmwith its partial differential and uniqueness problem on meromorphic functions in Cmand with its k-th total derivative sharing small functions.As an application of the value distribution result,we study the defect relation of a nonconstant solution to the partial differential equation.In particular,we give a connection between the Picard type theorem of Milliox-Hayman and the characterization of entire solutions of a partial differential equation.

Extended Group Foliation Method and Functional Separation of Variables to Nonlinear Wave Equations

Generalized functional separation of variables to nonlinear evolution equations is studied in terms of the extended group foliation method, which is based on the Lie point symmetry method. The approach is applied to nonlinear wave equations with variable speed and external force. A complete classification for the wave equation which admits functional separable solutions is presented. Some known results can be recovered by this approach.

SPACES OF ANALYTIC FUNCTIONS REPRESENTED BY DIRICHLET SERIES OF TWO COMPLEX VARIABLES

We consider the space X of all analytic functionsof two complex variables s1 and s2, equipping it with the natural locally convex topology and using the growth parameter, the order of f as defined recently by the authors. Under this topology X becomes a Frechet space Apart from finding the characterization of continuous linear functionals, linear transformation on X, we have obtained the necessary and sufficient conditions for a double sequence in X to be a proper bases.

BOUNDARY VALUE PROBLEMS OF CONJUGATE AND GENERALIZED K-HOLOMORPHIC FUNCTIONS IN C^(2)

In this paper,conjugate k-holomorphic functions and generalized k-holomorphic functions are defined in the two-dimensional complex space,and the corresponding Riemann boundary value problems and the inverse problems are discussed on generalized bicylinders.By the characteristics of the corresponding functions and boundary properties of the Cauchy type singular integral operators with conjugate k-holomorphic kernels,the general solutions and special solutions of the corresponding boundary value problems are studied in a detailed fashion,and the integral expressions of the solutions are obtained.

Disparities in tree mortality among plant functional types(PFTs)in a temperate forest:Insights into size-dependent and PFT-specific patterns

Tree mortality significantly influences forest structure and function,yet our understanding of its dynamic patterns among a range of tree sizes and among different plant functional types(PFTs)remains incomplete.This study analysed size-dependent tree mortality in a temperate forest,encompassing 46 tree species and 32,565 individuals across different PFTs(i.e.,evergreen conifer vs.deciduous broadleaf species,shade-tolerant vs.shade-intolerant species).By employing all-subset regression procedures and logistic generalized linear mixed-effects models,we identified distinct mortality patterns influenced by biotic and abiotic factors.Our results showed a stable mortality patte rn in eve rgreen conifer species,contrasted by a declining pattern in deciduous broadleaf and shadetolerant,as well as shade-intolerant species,across size classes.The contribution to tree mortality of evergreen conifer species shifted from abiotic to biotic factors with increasing size,while the mortality of deciduous broadleaf species was mainly influenced by biotic factors,such as initial diameter at breast height(DBH)and conspecific negative density.For shade-tolerant species,the mortality of small individuals was mainly determined by initial DBH and conspecific negative density dependence,whereas the mortality of large individuals was subjected to the combined effect of biotic(competition from neighbours)and abiotic factors(i.e.,convexity and pH).As for shade-intolerant species,competition from neighbours was found to be the main driver of tree mortality throughout their growth stages.Thus,these insights enhance our understanding of forest dynamics by revealing the size-dependent and PFT-specific tree mortality patterns,which may inform strategies for maintaining forest diversity and resilience in temperate forest ecosystems.

EFFICIENT ESTIMATION OF FUNCTIONAL-COEFFICIENT REGRESSION MODELS WITH DIFFERENT SMOOTHING VARIABLES

In this article,a procedure for estimating the coefficient functions on the functional-coefficient regression models with different smoothing variables in different coefficient functions is defined.First step,by the local linear technique and the averaged method,the initial estimates of the coefficient functions are given.Second step,based on the initial estimates,the efficient estimates of the coefficient functions are proposed by a one-step back-fitting procedure.The efficient estimators share the same asymptotic normalities as the local linear estimators for the functional-coefficient models with a single smoothing variable in different functions.Two simulated examples show that the procedure is effective.

FRACTIONAL INTEGRALS OF PERIODIC FUNCTIONS OF SEVERAL VARIABLES

In this paper it has been systematically studied the imbedding properties o f fractional integral operators of periodic functions of several variables,and isomorphic properties of fractional intregral operators in the spaces of Lipschitz continuous functions. It has also been proved that the space of fractional integration,the space of Lipschitz continuous functions and the Sobolev space are identical in L^2-norm.Results obtainedhere are not true for fractional integrals(or Riesz potentials)in R^n.

A Radial Basis Function Method with Improved Accuracy for Fourth Order Boundary Value Problems

Accurately approximating higher order derivatives is an inherently difficult problem. It is shown that a random variable shape parameter strategy can improve the accuracy of approximating higher order derivatives with Radial Basis Function methods. The method is used to solve fourth order boundary value problems. The use and location of ghost points are examined in order to enforce the extra boundary conditions that are necessary to make a fourth-order problem well posed. The use of ghost points versus solving an overdetermined linear system via least squares is studied. For a general fourth-order boundary value problem, the recommended approach is to either use one of two novel sets of ghost centers introduced here or else to use a least squares approach. When using either ghost centers or least squares, the random variable shape parameter strategy results in significantly better accuracy than when a constant shape parameter is used.

Construction of crash prediction model of freeway basic segment based on interactive influence of explanatory variables

In order to improve the prediction precision of the safety performance function （SPF） of freeway basic segments, design and crash data of 640 segments are collected from different institutions. Three negative binomial （NB） regression models and three generalized negative binomial （GNB） regression models are built to prove that the interactive influence of explanatory variables plays an important role in fitting goodness. The effective use of the GNB model in analyzing the interactive influence of explanatory variables and predicting freeway basic segments is demonstrated. Among six models, the two models （one is the NB model and the other is the GNB model. ） which consider the interactive influence of the annual average daily traffic （AADT） and length are more reasonable for predicting results. Furthermore, a comprehensive study is carried out to prove that when considering the interactive influence, the NB and GNB models have almost the same fitting performance in estimating the crashes, among which the GNB model is slightly better for prediction performance.

A Method of Gene-Function Annotation Based on Variable Precision Rough Sets

It is very important in the field of bioinformatics to apply computer to perform the function annotation for new sequenced bio-sequences. Based on GO database and BLAST program, a novel method for the function annotation of new biological sequences is presented by using the variable-precision rough set theory. The proposed method is applied to the real data in GO database to examine its effectiveness. Numerical results show that the proposed method has better precision, recall-rate and harmonic mean value compared with existing methods.

The derivative-dependent functional variable separation for the evolution equations

This paper studies variable separation of the evolution equations via the generalized conditional symmetry. To illustrate, we classify the extended nonlinear wave equation utt = A（u, ux）uxx＋B（u, ux, ut） which admits the derivative- dependent functional separable solutions （DDFSSs）. We also extend the concept of the DDFSS to cover other variable separation approaches.

Functional Variable Separation for Extended Nonlinear Elliptic Equations

This paper is devoted to the study of functional variable separation for extended nonlinear elliptic equations. By applying the functional variable separation approach to extended nonlinear elliptic equations via the generalized conditional symmetry, we obtain complete classification of those equations which admit functional separable solutions （FSSs） and construct some exact FSSs to the resulting equations.

Variable Separation and Derivative-Dependent Functional Separable Solutions to Generalized Nonlinear Wave Equations

Using the generalized conditional symmetry approach, we obtain a number of new generalized (1+1)-dimensional nonlinear wave equations that admit derivative-dependent functional separable solutions.

A numerical method based on boundary integral equations and radial basis functions for plane anisotropic thermoelastostatic equations with general variable coefficients

A boundary integral method with radial basis function approximation is proposed for numerically solving an important class of boundary value problems governed by a system of thermoelastostatic equations with variable coe?cients. The equations describe the thermoelastic behaviors of nonhomogeneous anisotropic materials with properties that vary smoothly from point to point in space. No restriction is imposed on the spatial variations of the thermoelastic coe?cients as long as all the requirements of the laws of physics are satis?ed. To check the validity and accuracy of the proposed numerical method, some speci?c test problems with known solutions are solved.

Multi-attribute group decision making method under 2-dimension uncertain linguistic variables

A method is proposed to deal with the uncertain multiple attribute group decision making problems,where 2-dimension uncertain linguistic variables(2DULVs)are used as the reliable way for the experts to express their fuzzy subjective evaluation information.Firstly,in order to measure the 2DULVs more accurately,a new method is proposed to compare two 2DULVs,called a score function,while a new function is defined to measure the distance between two 2DULVs.Secondly,two optimization models are established to determine the weight of experts and attributes based on the new distance formula and a weighted average operator is used to determine the comprehensive evaluation value of each alternative.Then,a score function is used to determine the ranking of the alternatives.Finally,the effectiveness of the proposed method is proved by an illustrated example.

The Jacobi elliptic function-like exact solutions to two kinds of KdV equations with variable coefficients and KdV equation with forcible term

By use of an auxiliary equation and through a function transformation, the Jacobi elliptic function wave-like solutions, the degenerated soliton-like solutions and the triangle function wave solutions to two kinds of Korteweg de Vries （KdV） equations with variable coefficients and a KdV equation with a forcible term are constructed with the help of symbolic computation system Mathematica, where the new solutions are also constructed.

A NEW METHOD FOR STRUCTURAL TOPOLOGICAL OPTIMIZATION BASED ON THE CONCEPT OF INDEPENDENT CONTINUOUS VARIABLES AND SMOOTH MODEL

A concept of the independent-continuous topological variable is proposed to establish its corresponding smooth model of structural topological optimization. The method can overcome difficulties that are encountered in conventional models and algorithms for the optimization of the structural topology. Its application to truss topological optimization with stress and displacement constraints is satisfactory, with convergence faster than that of sectional optimizations.

On Humbert Matrix Polynomials of Two Variables

In this paper we introduce Humbert matrix polynomials of two variables. Some hypergeometric matrix representations of the Humbert matrix polynomials of two variables, the double generating matrix functions and expansions of the Humbert matrix polynomials of two variables in series of Hermite polynomials are given. Results of Gegenbauer ma-trix polynomials of two variables follow as particular cases of Humbert matrix polynomials of two variables.