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.

Convergence Phenomenon with Fourier Series of tg(x2)and Alike

The Fourier series of the 2π-periodic functions tg(x2)and 1sin(x)and some of their relatives (first of their integrals) are investigated and illustrated with respect to their convergence. These functions are Generalized functions and the convergence is weak convergence in the sense of the convergence of continuous linear functionals defining them. The figures show that the approximations of the Fourier series possess oscillations around the function which they represent in a broad band embedding them. This is some analogue to the Gibbs phenomenon. A modification of Fourier series by expansion in powers cosn(x)for the symmetric part of functions and sin(x)cosn−1(x)for the antisymmetric part (analogous to Taylor series) is discussed and illustrated by examples. The Fourier series and their convergence behavior are illustrated also for some 2π-periodic delta-function-like sequences connected with the Poisson theorem showing non-vanishing oscillations around the singularities similar to the Gibbs phenomenon in the neighborhood of discontinuities of functions. .

Characteristics and influencing mechanisms of production-living-ecological space dynamics in the Three Gorges Reservoir Area(TGRA),Chongqing,China

The Three Gorges Reservoir Area(TGRA)is an important ecological barrier in the Yangtze River Basin,China.Therefore,it is of great importance to understand the spatio-temporal variation and the driving factors of production-living-ecological spaces for sustainable and high-quality development in the TGRA.This study investigated the dynamic variation of production-living-ecological spaces in the TGRA by employing land use data in 2000,2005,2010,2015,and 2018,and detected the influencing factors by using the Geographic detector(GeoDetector).Results implied that the structure and dynamic trajectories of production-living-ecological spaces in the TGRA varied in both horizontal and vertical directions,and the study area was dominated by ecological space.A spatial orientation towards the northeast was detected in the evolution of production-living-ecological spaces during 2000-2018.In terms of quantity,the transition from ecological space(grassland and woodland)to agriculture land accounted for the largest proportion from 2000 to 2018.However,the reverse transition from agriculture land to ecological space has increased since 2000 with the efforts of“Grain for Green”.In terms of temporal scale,there was a fluctuating trend in production space with the continuous expansion of living space,while ecological space showed an inverted U-shaped trend during 2000-2018.The dynamic pattern of production-living-ecological spaces in the TGRA was influenced by both physical and socio-economic variables as basic determinants and dominant driving factors,respectively.Finally,the harmonization and protection of production-living-ecological spaces still require policy-makers’efforts.This work may have potential in advancing our understanding about land use conflicts,and provide a reference for rational layout of spatial functions and the realization of sustainable development in the TGRA.

Synchronous measurements of prefrontal activity and pulse rate variability during online video game playing with functional near-infrared spectroscopy

Interactions between the central nervous system(CNS)and autonomic nervous system(ANS)play a crucial role in modulating perception,cognition,and emotion production.Previous studies on CNS–ANS interactions,or heart–brain coupling,have often used heart rate variability(HRV)metrics derived from electrocardiography(ECG)recordings as empirical measurements of sympathetic and parasympathetic activities.Functional near-infrared spectroscopy(fNIRS)is a functional brain imaging modality that is increasingly used in brain and cognition studies.The fNIRS signals contain frequency bands representing both neural activity oscillations and heartbeat rhythms.Therefore,fNIRS data acquired in neuroimaging studies can potentially provide a single-modality approach to measure task-induced responses in the brain and ANS synchronously,allowing analysis of CNS–ANS interactions.In this proof-of-concept study,fNIRS was used to record hemodynamic changes from the foreheads of 20 university students as they each played a round of multiplayer online battle arena(MOBA)game.From the fNIRS recordings,neural and heartbeat frequency bands were extracted to assess prefrontal activities and shortterm pulse rate variability(PRV),an approximation for short-term HRV,respectively.Under the experimental conditions used,fNIRS-derived PRV metrics showed good correlations with ECG-derived HRV golden standards,in terms of absolute measurements and video game playing(VGP)-related changes.It was also observed that,similar to previous studies on physical activity and exercise,the PRV metrics closely related to parasympathetic activities recovered slower than the PRV indicators of sympathetic activities after VGP.It is concluded that it is feasible to use fNIRS to monitor concurrent brain and ANS activations during online VGP,facilitating the understanding of VGP-related heart–brain coupling.

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.

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.

Two kinds of contact problems in three-dimensional icosahedral quasicrystals

Two kinds of contact problems, i.e., the frictional contact problem and the adhesive contact problem, in three-dimensional （3D） icosahedral quasicrystals are dis- cussed by a complex variable function method. For the frictional contact problem, the contact stress exhibits power singularities at the edge of the contact zone. For the adhe- sive contact problem, the contact stress exhibits oscillatory singularities at the edge of the contact zone. The numerical examples show that for the two kinds of contact problems, the contact stress exhibits singularities, and reaches the maximum value at the edge of the contact zone. The phonon-phason coupling constant has a significant effect on the contact stress intensity, while has little impact on the contact stress distribution regu- lation. The results are consistent with those of the classical elastic materials when the phonon-phason coupling constant is 0. For the adhesive contact problem, the indentation force has positive correlation with the contact displacement, but the phonon-phason cou- pling constant impact is barely perceptible. The validity of the conclusions is verified.

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.

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.

On the Extension of the Three-Term Recurrence Relation to Probabilities Distributions without Moments

In this paper, we extend the three-term recurrence relation for orthogonal polynomials associated with a probability distribution having a finite moment of all orders to a class of orthogonal functions associated with an infinitely divisible probability distribution µ?having a finite moments of order less or equal to four. An explicit expression of these functions will be given in term of the Lévy-Khintchine function of the measure?µ.

On the Evaluation of Oscillatory Kind with Cauchy Principal Value

In this paper, we discuss the integrals of oscillatory kind function with Cauchy principal value in point zero which have the form like , where f (x) is smooth function and r is odd integer. In this integral, xr has several stationary points , and the Cauchy principal value . We use some integral technique to transform it into the form like so that we can calculate it. At the end, we give some numerical examples to prove the accuracy of this method.

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.

The Interannual Variability of Summer Rainfall in the Arid and Semiarid Regions of Northern China and Its Association with the Northern Hemisphere Circumglobal Teleconnection

Using the latest daily observational rainfall datasets for the period 1961–2008, the present study investigates the interannual variability of June–September （JJAS） mean rainfall in northern China. The regional characteristics of JJAS mean rainfall are revealed by a rotated empirical orthogonal function （REOF） analysis. The analysis identifies three regions of large interannual variability of JJAS rainfall： North China （NC）, Northeast China （NEC）, and the Taklimakan Desert in Northwest China （TDNWC）. Summer rainfall over NC is shown to have displayed a remarkable dry period from the late 1990s; while over NEC, decadal-scale variation with a significant decreasing trend in the last two decades is found, and over TDNWC, evidence of large interannual variability is revealed. Results also show that the interannual variability of JJAS rainfall in northern China is closely associated with the Northern Hemisphere circumglobal teleconnection （CGT）. Correlation coefficients between the CGT index and regional-averaged JJAS mean rainfall over NC and NEC were calculated, revealing values of up to 0.50 and 0.53, respectively, both of which exceeded the 99% confidence level.

ON THE COEFFICIENTS OF DIFFERENTIATED EXPANSIONS AND DERIVATIVES OF CHEBYSHEV POLYNOMIALS OF THE THIRD AND FOURTH KINDS

Two new analytical formulae expressing explicitly the derivatives of Chebyshev polynomials of the third and fourth kinds of any degree and of any order in terms of Chebyshev polynomials of the third and fourth kinds themselves are proved. Two other explicit formulae which express the third and fourth kinds Chebyshev expansion coefficients of a general-order derivative of an infinitely differentiable function in terms of their original expansion coefficients are also given. Two new reduction formulae for summing some terminating hypergeometric functions of unit argument are deduced. As an application of how to use Chebyshev polynomials of the third and fourth kinds for solving high-order boundary value problems, two spectral Galerkin numerical solutions of a special linear twelfth-order boundary value problem are given.

INTEGRAL EQUATION METHOD'S APPLICATION IN HOLE-EDGE STRESS OF COMPOSITE MATERIAL PLATE WITH DIFFERENT SHAPED HOLES

The strength of composite plate with different hole-shapes is always one of the most important but complicated issues in the application of the composite material. The holes will lead to mutations and discontinuity to the structure. So the hole-edge stress concentration is always a serious phenomenon. And the phenomenon makes the structure strength decrease very quickly to form dangerous weak points. Most partial damage begins from these weak points. According to the complex variable functions theory, the accurate boundary condition of composite plate with different hole-shapes is founded by conformal mapping method to settle the boundary condition problem of complex hole-shapes. Composite plate with commonly hole-shapes in engineering is studied by several complex variable stress fimction. The boundary integral equations are founded based on exact boundary conditions. Then the exact hole-edge stress analytic solution of composite plate with rectangle holes and wing manholes is resolved. Both of offset axis loadings and its influences on the stress concentration coefficient of the hole-edge are discussed. And comparisons of different loads along various offset axis on the hole-edge stress distribution of orthotropic plate with rectangle hole or wing manhole are made. It can be concluded that hole-edge with continuous variable curvatures might help to decrease the stress concentration coefficient; and smaller angle of outer load and fiber can decrease the stress peak value.

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.

Cubic Spline Solutions of Nonlinear Bending and Buckling of Circular Plates with Arbitrarily Variable Thickness

The cubic B-splines taken as trial function, the large deflection of a circular plate with arbitrarily variable thickness,as well as the buckling load, have been calculated by the method of point collocation. The support can be elastic. Loads imposed can be polynomial distributed loads, uniformly distributed radial forces or moments along the edge respectively or their combinations. Convergent solutions can still be obtained by this method under the load whose value is in great excess of normal one. Under the action of the uniformly distributed loads, linear solutions of circular plates with linearly or quadratically variable thickness are compared with those obtained by the parameter method. Buckling of a circular plate with identical thickness beyond critical thrust is compared with those obtained by the power series method.

Detection Performance Analysis of Spectrum Sensing in Cognitive Radio Networks with Mobile Secondary Users

The majority of existing papers about spectrum sensing have the assumption that secondary users(SUs) are stationary. However,mobility is an essential feature of mobile communications networks. In this paper,the detection performance of spectrum sensing by mobile SUs was analyzed. Three performance metrics,i.e.,detection probability,miss detection probability and false alarm probability,were thoroughly investigated. In our analysis,a critical variable was the real-time received primary user signal power by a mobile SU. Its probability distribution and mathematical expectation were analytically derived. Moreover,the three performance metrics in single-node spectrum sensing and multi-node collaborative spectrum sensing systems were also derived. Extensive simulations were performed. The results are consistent with the theoretical analysis. And it is concluded that SU mobility has a significant impact on the detection probability and the miss detection probability,but not on the false alarm probability.

DAMAGE THEORY OF MATERIALS WITH MICROSTRUCTURE

A new form of damage theory of materials is proposed,that is valid for the case of nonconservative stresses.The partial entropy,strain and microstructure parameters are taken as the state variables.Without assuming the free energy to be a state function,the basic governing equations are derived.According to the balance of released and dissipated energy,the general form of damage evolution equation is obtained.Further,assuming the existence of independent damage mechanisms, the normality of damage evolution equation is proven.The generalized damage variables are dis- cussed.Finally,some examples are given to show the applications of the theory.