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Carbon mitigation and net-zero targets have an important place on the political agenda for all countries. Countries have been seeking to decouple economic growth and carbon emissions to achieve decarbonization. However, there is a cost of the decarbonization of economies, which can be called as Green Sacrifice Ratio (GSR), and this is critical for developing countries because they have been in the growing stage. By considering the critical role of GSR in achieving net-zero emissions by decarbonizing economies, the study comparatively examines how much environmental quality should be sacrificed for per capita economic growth in China and India. In line with this purpose, the study uses the Fourier-Shin cointegration test and various time series estimators with Fourier approximations for the period from 1989/Q1 to 2022/Q4. Estimation results are as follows: (i) all variables follow the non-stationary process, (ii) the long-run relationship exists between variables, and (iii) Estimation results show that GSR is 0.65% for China and 0.78% for India. Therefore, China and India sacrifice a significant amount of environmental quality for a 1% increase in per capita income level. Also, the ecological cost of increasing economic welfare in India is higher with regard to China. Besides, the results are robust according to the alternative method. Thus, the study recommends that both Chinese and Indian policymakers should revise the economic expansion structure with green growth strategies to prevent irreversible environmental degradation due to higher economic growth. [ABSTRACT FROM AUTHOR]

An approach for solving the plane nonaxisymmetric thermoelasticity problems in multilayer cylinders is suggested from the single-solid standpoint, which implies considering a multilayer structure as a single unity with a step-wise variation of material properties. The direct integration method was used to the advantage of our approach by applying toward the compatibility equation in terms of strains instead of the one in terms of stresses. As a result, the governing equation is derived without involving generalized derivatives by the radial coordinate and then reduced to an integral equation of the second kind. Using the resolvent-kernel for solving the latter equation, the thermal stresses are computed as the Fourier series whose constituents are explicitly determined by the corresponding constituents of the thermal loading. [ABSTRACT FROM AUTHOR]

AbstractThe paper investigates the potential of the full-sinusoidal Fourier series as a solution form for the deflection of layered functionally graded beams associated with smart actuators, drawing on the fundamental principles of classical Fourier series theory. The current method simplifies the difficult beam problem to a set of linear algebraic equations by using the Duhamel integration technique and the orthogonality of the trial function. The study takes into account generalized boundary conditions and moving forces, which are seldom discussed in previous research. Under the action of a moving load, the boundary value problem for a functionally graded beam integrated with Terfenol-D is efficiently addressed using the approach of combined differential and integral quadrature. The generalized boundary conditions may be easily achieved by adjusting the stiffness of the restraining springs. The significant agreement between the differential quadrature solution and the Fourier series solution underlines the efficiency and accuracy of both methods. Furthermore, the influences of various crucial physical characteristics on the natural frequencies and the essential flow velocities are explored, including boundary stiffness, foundation parameters, and geometric parameters. [ABSTRACT FROM AUTHOR]

This work attempts to propose a practical methodology for the one-dimensional heat conduction problems with unknown boundary conditions of the first kind at both ends. The methodology can be effectively applied when the remote boundary condition is inaccessible or internal temperature is required, such as a cutting process with cooling lubricant, and ablative thermal protection system. The proposed methodology utilizes the shifting function method in conjunction with the least squares error method to transform the inverse heat conduction problem into an approximate "well-posed" problem. Consequently, the temperature and the heat flux distributions over the entire time and space domains are determined by using half-range Fourier cosine series solutions. Experimental examples of spray cooling problems are provided to illustrate the advantages of the proposed methodology, including fast convergence of the temperature function, fewer discrete measured times in numerical analysis, and regardless of two interior temperature probes positions. [ABSTRACT FROM AUTHOR]

The geometrically nonlinear stability analysis of restrained nanobeams under an elastic medium is considered in the presented manuscript. The investigation is based on the nonlocal strain gradient elasticity theory, Euler-Bernoulli beam theory and geometrical nonlinearity which is a significant change in geometry. To the best of the authors' knowledge, the nonlinear stability response of a nanobeam with elastic boundary conditions and on an elastic foundation has not been presented before via the theory of nonlocal strain gradient. The aim of this paper is to fill this gap in the literature by offering a method that can give a solution under general elastic boundary conditions. Using a Fourier sine series, a Fourier coefficient suitable for constructing an eigenvalue problem is computed. The constructed problem has been treated in the transformed region with the help of the Stokes' transform, then the stability analysis is executed for arbitrary boundary conditions (rigid or restrained) based on the nonlocal strain gradient elasticity. The influences of various nonlinear parameters, deformable boundary conditions, small-scale parameters and elastic foundation parameters on the stability of the constrained nanobeam are studied. It is observed that the investigated variables produce significant changes in buckling loads. [ABSTRACT FROM AUTHOR]

The propagation characteristics of Lamb waves in a functionally graded material (FGM) plate with periodic gratings have been studied. The power series technique is employed to solve the governing differential equations with variable coefficients. In the propagation direction, the displacements of Lamb waves are expanded in the Fourier series due to the periodicity of the structure. The convergences of the power series and Fourier series are proved and the method presented in the article is verified by the finite element method (FEM). The band gaps are obtained by the couplings between the different modes of Lamb waves induced by FGM. The effects of the structural parameters (such as the periodicity, mass, and length of the gratings) and gradient coefficient on band gaps are investigated. Numerical results show that the band gaps shift up as the gradient coefficient increases and the second band gap (SBG) is closed when the gradient coefficient is large enough. The conclusions are of practical significance for designing elastic wave filters with high-performance. [ABSTRACT FROM AUTHOR]

This paper focuses on the valuation of variable annuities with a guaranteed minimum maturity benefit under a regime-switching Lévy model. The model allows policyholders to surrender their annuities and receive a surrender benefit at predetermined tenor times before maturity. Additionally, we consider a state-dependent periodic fee structure where fees are deducted from the policyholder's account if it exceeds a certain level at discrete time points. Incorporating this fee structure, the Fourier cosine series expansion method based on characteristic functions is employed to determine the values and optimal surrender strategies for variable annuity contracts. Finally, we provide a comprehensive set of numerical examples to demonstrate and assess the effectiveness of our approach thoroughly. [ABSTRACT FROM AUTHOR]

This document deals with the effect of porosity on the buckling of functionally graded sandwich plates under a nonlinear thermal loading using the four-variable refined plate theory. Different types of functionally graded material (FGM) sandwich plates, as well as various boundary conditions were used to highlight the influence of transverse shear, which is composed of two displacement fields, one is related to transverse displacement, and the second is due to the shearing effect. The transverse shear field follows a new warping hyperbolic function. The governing equations were derived from the virtual work principle based on von-Karman nonlinear geometric strains. This study aims to examine a sandwich-type plate, composed of three layers, the core of the plate is entirely made of ceramic material, and the upper and lower faces of the plate are made of functionally graded material. To solve the governing equations, double trigonometric series were used to simplify computations instead of a highly complicated numerical method. While various parameters are considered such as the volume faction index, porosity, and geometrical configurations, the study shows a perfect agreement between the proposed model and those of different works reported in the literature. [ABSTRACT FROM AUTHOR]

This article enlightens the two-dimensional (2D) isotropic micro-polar thermoelastic problem of the three-phase-lag (3PHL) model and heat conduction equation is formulated in the context of memory-dependent derivative (MDD). The equations are converted into the domain of the Laplace transform vector matrix differential equation form and solved by using the eigenvalue technique. To obtain an analytical solution of displacement, temperature, and stress components Silicon material properties are used. Inversion of the Laplace transform with Fourier series expansion technique is used to obtain the numerical solution. For obtaining graphical results Mathematica software is used. For the purpose of exhibiting the beauty of MDD in the present model comparisons are made between the time delay parameters and kernel functions (constant, linear, and non-linear kernels), respectively, over the micro-polar panel. The results obtained have a valuable impact on structural analysis, especially in the design of rotating machinery structures using accurate material properties. [ABSTRACT FROM AUTHOR]

We study the small vibrations of an axially travelling string with a dashpot damping at one end. The string is modelled by a wave equation in a time-dependent interval with two endpoints moving at a constant speed $ \mathbf{v} $ v . For the undamped case, we obtain a conserved functional equivalent to the energy of the solution. We derive precise upper and lower exponentially decaying estimates for the energy with explicit constants. These estimates do not seem to be reported in the literature even for the non-travelling case $ \mathbf{v}=0 $ v = 0. [ABSTRACT FROM AUTHOR]

In this paper, an adaptive tracking control approach is developed for full-state constrained switched nonlinear systems that have actuator saturation, periodic disturbances and unknown control direction. To deal with the full-state constraints, the Barrier Lyapunov functions are introduced to limit the state variables within the corresponding constraint conditions. Meanwhile, the Fourier series expansion technology is employed to deal with unknown periodic disturbances and unknown nonlinear dynamics jointly. Additionally, a Nussbaum-type function is used in the controller design to cope with the and unknown control gain and input saturation. On the basis of the Lyapunov stability theory, it is demonstrated rigorously that all signals of the closed-loop system are uniformly ultimately bounded, and the proposed controller ensures that the tracking error is kept within a compact set close to zero. In the end, the validity of the designed control protocol is verified by a simulation example. [ABSTRACT FROM AUTHOR]

Based on the finite Fourier series and the energy variation principle, an analytical calculation method for the dynamic response of multi-span bridge-track structure systems under the action of moving load series is proposed. The applicability of this method is verified by the comparison of the results with the analytical and numerical approaches. Based on the proposed method, the dynamic response of double-layer and four-layer beam models, commonly used in railway bridge systems is solved, and the calculation formulas of resonance and vibration cancelation velocity of multi-layer beam systems are proposed. The influence of the span number of simply supported beams and the length of subgrade sections on the dynamic response of the four-layer beam system is investigated. The results show that the deflection of the dynamic response of double-layer and four-layer beam systems reaches the maximum value near the mid-span. These two systems have multiple critical speeds under moving loads. When the resonance and vibration cancelation of the multi-beam system occur simultaneously, the vibration cancelation plays a leading role. The span number of simply supported beams and length of subgrade sections influence the dynamic response of the four-layer beam system but have no significant effect on the critical velocity of resonance and vibration cancelation. At present, there is a lack of research on analytical or semi-analytical methods for the dynamic response of multi-span bridge-track structure systems. This research may provide a theoretical basis for the planning, design, operation, and maintenance of bridge-track structure systems to a certain extent. [ABSTRACT FROM AUTHOR]

This paper aims to develop a novel approach to determining the fiber/matrix interfacial shear strength (IFSS) due to both carbon fiber roughness and the presence of carbon nanotubes (CNTs) in the matrix of a polymer composite in the form of a fiber overwrap. Under an atomic force microscope (AFM), the carbon fiber surface exhibits multi-scale asperities extending from a nanometer to several microns, likely caused by shrinkage during the graphitization process. Therefore, a Fourier series decomposition of the surface asperity data is performed to model these asperities present at various wavelengths on the fiber resulting in an amplitude and wavelength corresponding to each Fourier series term, effectively capturing the surface roughness over the entire spectrum of wavelengths. Furthermore, Molecular Dynamics (MD) simulations were performed to determine the interfacial shear strength of any subcomponent asperity of a specific amplitude and wavelength. Using MD data, governing equations were developed to compute the length-scale-averaged shear strength for a carbon fiber with any given surface asperities from the interfacial shear force for each of these subcomponent wavelengths. The results show that the presence of CNTs enhanced the IFSS by about 19% overall for a given surface asperity profile compared with the case without CNTs. [ABSTRACT FROM AUTHOR]

Currently, there is no regulation on the settlement threshold of continuous beam bridge pier of high-speed railway (HSR), a method is proposed in the present study to calculate the settlement threshold of continuous beam pier based on the analytic mapping relationship. First, the dynamic model of the train-track-continuous beam bridge was established. Then, the mapping rail irregularities caused by pier settlement obtained from the analytic mapping relationship superimposed with the initial rail irregularities converted from the Chinese track irregularities spectrum by using the trigonometric series method. Furthermore, the proposed method was verified by comparative analysis with the measured data and the existing results. Finally, the types and thresholds of uneven settlement of continuous beam bridge pier were revealed based on the parameter discussion method. It was found that the influence of pier settlement on the train dynamic performance index had a strong correlation with the train running direction. The settlement threshold of long-span continuous beam pier was looser than that of simply supported beams with a 32 m span. The settlement threshold of continuous beam piers can be appropriately relaxed in design. [ABSTRACT FROM AUTHOR]

Abstract– In this paper, we have generalized two known theorems dealing with the absolute weighted arithmetic mean summability factors of infinite series and Fourier series to the absolute matrix summability methods. Some new and known results have also been obtained. [ABSTRACT FROM AUTHOR]

In this paper, we show a complete characterization of the uniform boundedness of the partial sum operator in a discrete Sobolev space with Jacobi measure. As a consequence, we obtain the convergence of the Fourier series. Moreover it is showed that this Sobolev space is the first category which implies that it is not possible to apply the Banach–Steinhaus theorem. [ABSTRACT FROM AUTHOR]

A bootstrap procedure for constructing prediction bands for a stationary functional time series is proposed. The procedure exploits a general vector autoregressive representation of the time-reversed series of Fourier coefficients appearing in the Karhunen–Loève representation of the functional process. It generates backward-in-time functional replicates that adequately mimic the dependence structure of the underlying process in a model-free way and have the same conditionally fixed curves at the end of each functional pseudo-time series. The bootstrap prediction error distribution is then calculated as the difference between the model-free, bootstrap-generated future functional observations and the functional forecasts obtained from the model used for prediction. This allows the estimated prediction error distribution to account for the innovation and estimation errors associated with prediction and the possible errors due to model misspecification. We establish the asymptotic validity of the bootstrap procedure in estimating the conditional prediction error distribution of interest, and we also show that the procedure enables the construction of prediction bands that achieve (asymptotically) the desired coverage. Prediction bands based on a consistent estimation of the conditional distribution of the studentized prediction error process also are introduced. Such bands allow for taking more appropriately into account the local uncertainty of the prediction. Through a simulation study and the analysis of two datasets, we demonstrate the capabilities and the good finite-sample performance of the proposed method. [ABSTRACT FROM AUTHOR]

This paper proposes a series solution for studying the ground motion of twin-peaks hill, double triangular hills, and hill-canyon composite topography. The propagation medium of SH wave is linearly elastic, isotropic, and homogeneous. A flexible multi-region-matching technique (MRMT) and complex function method are adopted to construct the wave field expression in each sub-region. To solve the unknown coefficients in the wave field expressions, Fourier series expansion method in the complex domain is adopted. Finally, some typical numerical examples are calculated to analyse the influence of the topography shape parameters, wave number, and the incident angle on ground motion. [ABSTRACT FROM AUTHOR]

Monitoring of high-density images from video sequences provides an important potential for crowd detection and classification. In fact, shadow presence from video sequences causes detection failures of results or mistakes in interpretation. In this contribution, we present an automatic system to deal with shadow elimination based on extracting the vector size of the movement and detection of occlusion management with the Fourier series approach because of the position and orientation of the camera, speed magnitude and visual tracking of crowd scenes, and mathematical morphology of discrete data in a non-linear approach. The model consists of distinctive real objects from fused data and crowded scene caused by shades, which often has consequence such as the failure counting and grading of vehicle and people, while dealing with traditional methods. As we reveal, our technique is principally appropriate for UMN and PETS data to eliminate shadow nuisance and detection occlusion with quite good performance. For classification, we use two classes in each image, for each category of events detected by fuzzy logic. Although this comes down to easy system modeling, as it relates to the use of fuzzy rules. The provided results advocate in favor of our method in terms of effectiveness and precision. Indeed, the proposed approach provides the ability to segment more specific objects, such as people and vehicles in real-time space. The results were compared to other methods, namely Covariance Matrices for Crowd Behavior, Social Force Method, and Ground Truth Technique. [ABSTRACT FROM AUTHOR]

In this paper, we study asymptotic properties of the maximum likelihood estimator (MLE) for the speed of a stochastic wave equation. We follow a well-known spectral approach to write the solution as a Fourier series, then we project the solution to a N-finite dimensional space and find the estimator as a function of the time and N. We then show consistency of the MLE using classical stochastic analysis. Afterward, we prove the asymptotic normality using the Malliavin–Stein method. We also study asymptotic properties of a discretized version of the MLE for the parameter. We provide this asymptotic analysis of the proposed estimator as the number of Fourier modes, N, used in the estimation and the observation time go to infinity. Finally, we illustrate the theoretical results with some numerical experiments. [ABSTRACT FROM AUTHOR]

Taylor series play a ubiquitous role in calculus courses, and their applications as approximants to functions are widely taught and used everywhere. However, it is not common to present the students with other types of approximations besides Taylor polynomials. These notes show that polynomials construed to satisfy certain boundary conditions at an interval of definition can be represented by rapidly converging Fourier series. These polynomials are shifted and re-scaled versions of the Bernoulli polynomials. From this construction, an argument to 'invert' the Fourier series to obtain an approximation to sines and cosines in terms of the Bernoulli polynomials is presented. We then show that approximating sines and cosines by the Bernoulli polynomials might be much better than using the truncated Taylor series, especially in problems where global proprieties are desired. These contents can be taught in advanced Calculus classes approaching series of functions and their applications. [ABSTRACT FROM AUTHOR]

Variable annuities with complex surrender features are nowadays increasingly popular for managing longevity risks. The study of their accurate pricing and sensitivity analysis is one of the main actuarial research topics. This paper studies the valuation problem of variable annuity contracts with guaranteed minimum maturity benefits on a set of predetermined discrete tenor dates under regime-switching Lévy models. Extending from existing vanilla payoffs, we consider the guaranteed minimum maturity benefits with lookback and geometric average features. We customise the dynamic programming principle to solve the corresponding optimal stopping problem, relying on some semi-analytical valuation formulae resulting from an acute Fourier cosine series expansion. Finally, numerical illustrations are provided to show the accuracy and efficiency of the proposed method. We also demonstrate the use of our proposed method in a range of sensitivity analysis exercises, which shed light on the pricing and risk management of complex variable annuity products. [ABSTRACT FROM AUTHOR]

The generalized thermo-viscoelastic theory without energy dissipation is used in this work to investigate the transfer of bioheat and the mechanical heat-induced response in a human skin plane tissue with variable thermal and rheological properties. Integral transformations are used for Laplace and Fourier. In the scheme of two-dimensional equations, the exponential matrix procedure, which forms the basis of the state-space approach of modern control theory, is applied. The resulting formulation is applied to a thermal shock half-space problem. The inversion process for Fourier and Laplace transforms is carried out using a numerical method based on Fourier series expansions. Comparisons between computational measurements and Penne's experimental verification indicate that the Green–Naghdi (II) bioheat mathematical model is an effective method for estimating the transition of bioheat to viscoelastic skin tissue. The influences of variable thermal conductivity and volume materials properties on all fields are examined. [ABSTRACT FROM AUTHOR]

In this article, the dynamic instability of the hybrid fiber/nanocomposite-reinforced toroidal shells is investigated. By using the approximation of Fourier series and applying the Galerkin method, a semi-analytical solution is achieved. The proposed method provides an accurate assessment of the dynamic stability of the shell with no computational costs in comparison to the numerical methods. By comparing the obtained results for some examples with those available in the present literature, the accuracy of present formulation is approved. In order to evaluate the effects of geometrical and mechanical specifications on the dynamic instability of the proposed shells, a comprehensive parametric study is performed, as well. [ABSTRACT FROM AUTHOR]

To prove the existence of piecewise continuous solutions to a logistic quasi-periodic differential system with impulses (whose coefficients have rationally independent periods), this system is divided into a differential equation and a difference equation. The quasi-periodicity of a function is proved by showing that this function is the uniform limit of a series of trigonometric polynomials with a finite total number of frequencies. The asymptotically stable quasi-periodic positive and piecewise continuous solution is proved to exist and to be unique. Quasi-periodic variation of the environment leads to a quasi-periodic growth of the population size in the sense that the rationally independent frequencies of the system are also frequencies of the quasi-periodic solution. The positive solutions have a repeated behavior similar to that of the quasi-periodic solution for a sufficiently long time due to asymptotical stability. The separation of the continuous-discrete system into a differential equation and a difference equation is a method of proving the existence of a quasi-periodic solution with perturbed coefficients of the impulsive system. [ABSTRACT FROM AUTHOR]

This paper studies the problem of the constant pressure control for high pressure tubing. The main factors affecting the pressure change in high pressure oil pipe are the opening time of check valve and the cam angular velocity. Based on the theory of fluid mechanics, ordinary differential equation and Fourier series, the flow-pressure model and pressure-cam angular velocity model are established, respectively. Furthermore, the above model is extended to the case of multiple nozzles. These three models accurately express the functional relationship between the fuel flow rate, the pressure in the tubing and the cam angular velocity. According to the established models, the pressure in the high-pressure oil pipe can be accurately controlled by adjusting some parameters. Finally, a simulation example is given to verify the effectiveness of the proposed method. [ABSTRACT FROM AUTHOR]

Seasonal variations in age class sizes involve those of births and those of mortality across ages. They affect censuses and, consequently, rates involving numbers by age. As their analytical expression becomes inextricable, a simulation of aging cohorts by months of age shows that mortality oscillations for human populations are not sufficient to prevent age classes from oscillating approximately like associated births, contrary to what previous literature suggests. The amplification converges after damping, and the level reached depends on the amplification of mortality oscillations relative to births between 0 and 6 months of age. The damping rate depends mainly on the amplification of the mortality of 0–5 months compared to births. The application to 1896 South Russian data shows that age class sizes vary during the year like the births of the associated cohorts and that the numbers counted at the census vary strongly according to the month of the census. [ABSTRACT FROM AUTHOR]

In this article, the problem of a salient with complex boundary conditions in a piezoelectric strip is studied by Fourier series expansion method, and SH guided wave is considered as an external load acting on piezoelectric strip. First, on the basis of repeated image superposition, the analytical expression of scattering wave is conducted, which satisfies the stress free and electric insulation conditions on the upper and lower horizontal boundaries of the strip. Next, with the aid of boundary condition, integral equations are setup and solved by applying orthogonal function expansion technique and effective truncation. Results clarified the influence on the dynamic stress concentration factor and electric field intensity concentration factor under proper conditions. Besides, the analytical solutions are compared with the finite element solutions to verify the accuracy of the conclusions in this article. [ABSTRACT FROM AUTHOR]

This manuscript aims to research the thermal buckling of saturated thick (Timoshenko) nanobeams under different boundary conditions using Fourier sine and cosine series for the first time. The equation of motion and related boundary conditions are derived by using the kinematic relations of shear deformation (Timoshenko beam) theory to contain the shear effect. Consequently, the rotary inertia and transverse shear strain are considered through the mathematical analysis. Fourier sine and cosine series are used to compute the critical buckling temperature of the thick saturated nanobeam with deformable boundaries. To check the validity of the presented method, the developed Fourier series method with Stokes' transformation is applied to validate the thermal buckling of rigidly supported thick nanobeam by giving the proper values to spring parameters. In particular, the presented analytical procedure can also be degenerated to the thin Euler-Bernoulli nanobeam by assigning proper value to shear correction factor. Influence of the deformable boundary conditions, small scale parameter and the saturated parameter (porosity coefficient) on the thermal buckling temperature are discussed in detail. The theoretical models and eigen-value formulation presented herein should also be served to solve the thermal stability response of different micro sized-structures with various temperature effects and supporting conditions. [ABSTRACT FROM AUTHOR]

The problems of an elliptical arc crack lying along the interface of an anisotropic inclusion are considered in this article. By means of the complex series expansion of the stress functions, the related coefficients in the stress functions are obtained using the continuity condition for the stresses at the imperfect interface and using equilibrium condition based on relationships of stresses and displacements at the imperfect interface between matrix and inclusion. The displacements and stresses at the interface in the matrix and in the inclusion can be calculated. The imperfection at the interface between matrix and inclusion is expressed by the Fourier series, which can be used to represent the crack lying along the interface and the perfect interface. The method presented in this article can be used to analyze the problems of crack, inclusion, and hole in the anisotropic materials due to separate or combined effect of eigenstrains and far-field tension. [ABSTRACT FROM AUTHOR]

This paper presents an analytical solution for free-vibration and stability analyses of hybrid-composite toroidal shells. The considered hybrid material incorporates the composition of fibers and nanocomposite-reinforced matrix (NCRM) such as carbon nanotubes (CNTs) and graphene nanoplatelets (GPLs). The governing differential equations are extended based on the first-order transverse shear deformation theory (FSDT) and are solved by employing the approximation of Fourier series and Galerkin method. The considered hybrid composite material in the parametric studies are consisted of three layers in which the polymeric matrix are reinforced by CNTs in some layers and reinforced by GPLs in the other layers. [ABSTRACT FROM AUTHOR]

Dynamic incident anti-plane shearing (SH guided wave) is considered to calculate dynamic stress in an infinite strip region with a semi-salient. With the aid of series expansion method, the expression of SH guided wave is established, which satisfies the stress free condition on the upper and lower horizontal boundaries of the strip. The expression of standing wave is constructed by the means of Fourier series expansion. The expression of scattering wave is conducted based on repeated image superposition. Boundary conditions are solved by applying orthogonal function expansion technique. Results clarified the influence on the dynamic stress concentration factor under proper conditions. [ABSTRACT FROM AUTHOR]

A semi-analytical model is proposed in this study to investigate the in-plane vibration behavior of porous annular plate with porosity distributions in the thickness and radial directions. A variational method combined with a multi-segment technique is employed to establish the theoretical model of elastic restrained porous annular plate. Admissible functions of each plate segment are expanded in the mixed series form, that is, the Jacobian orthogonal polynomial for radial variables and Fourier series for circumferential variables. The boundary penalty parameters are introduced to implement different boundary restrictions and the coupling penalty parameters are employed for ensuring the continuity conditions between segments. A series of numerical examples are given to discuss the convergence characteristics and numerical stability of the current model. The comparison between modal tests and numerical predictions shows that good prediction capabilities with acceptable errors are achieved by the proposed method. The influences of geometrical and material parameters on the in-plane vibration characteristics of porous annular plate are also discussed in detail. [ABSTRACT FROM AUTHOR]

Geometric parameters of equilibrium configurations of trans- and cis-conformers of HSOSH molecule, their dipole moments, rotational constants in the ground electronic and vibrational states, and kinetic parameters corresponding to two torsional coordinates γ 1 and γ 2 were calculated at CCSD(T)-F12/cc-pVDZ-F12 level of theory. In the latter case, at each node of the two-dimensional grid γ 1 and γ 2 all other geometric parameters of the molecule were optimized. The obtained configurations were used for calculation of 2D potential energy surface at CCSD(T)-F12/cc-pVTZ-F12 level without additional optimization. The energies of a number of excited torsional states were determined by numerically solving the vibrational Schrödinger equation of restricted dimensionality using two-dimensional complex Fourier series. The obtained data on the frequencies of torsional vibrations of S-H groups in the two conformers and the frequencies of tunneling in the ground and excited torsional states are compared with the results obtained earlier at MP2/CBS(T,Q) level of theory. [ABSTRACT FROM AUTHOR]

Size-dependent stability analysis of nanobeams under axial loading is investigated by strain gradient elasticity. An effective general model is proposed for different deformable boundary conditions by combining Fourier sine series and Stokes' transformation. The theoretical model presented here bridges the gap between clamped and pinned-pinned supporting conditions, which is of great significance for the application of the strain gradient small scale effects to nanobeam. Analytical solutions are obtained and comparisons with results obtained by the researchers for rigid boundary conditions are carried out. The outcomes can be useful for the optimization and design of nano-sized beams and provide new benchmarks for nanomechanical analyses. [ABSTRACT FROM AUTHOR]

The influence of laser short-pulse heating is utilized to investigate an elastic-mechanical-thermodiffusion (EMTD) model. The model is studied when the holes/electrons interaction of semiconductor medium is occurred with a fractional derivative of the heat equation. The governing equations describing this model are very complex, so they are studied in one dimension (1D) when the considered physical quantities are in a non-dimensional. In this case, the thermoelastic deformation (TD) due to the electronic deformation (ED) with some initial conditions is considered. Laplace transforms are used to analyze the governing equations mathematically when the thermal conductivity is variable. To obtain the complete solutions, the inverse Laplace transforms are used numerically based on the Fourier series with the application of some boundary conditions. Several comparisons of the wave propagation distribution of the fundamental fields are presented graphically according to different values of the fractional parameter, memories parameters, and thermal conductivity with discussion. [ABSTRACT FROM AUTHOR]

Abstract The appropriate control of maintenance effort in the edge computing based on open-source software (OSS) relates to stable and reliable operation, because the fault detection phenomenon depends on the effort expenditure. Actually, several software reliability growth models with testing-effort have been proposed in the past. In this paper, we propose cyclic Wiener process models to consider the network environment under the edge OSS operation. Then, we assume that the sawtooth wave and square one as the cyclic noises. Thereby, the proposed models will be able to comprehend two characteristics of OSS and network environment. Then, it will be useful to assess the operation effort expenditures with network environment of edge OSS service. Moreover, actual effort data sets are analyzed to show numerical examples of the proposed model considering the network environment under the edge OSS operation. [ABSTRACT FROM AUTHOR]

Enlightened by the Caputo fractional derivative, the present study deals with a novel mathematical model of elasto-thermodiffusion to investigate the transient phenomena for an isotropic three-dimensional thermoelastic medium subjected to permeating gas induced by a rectangular thermal pulse, where the heat conduction equation is defined in an integral form of a common derivative on a slipping interval by incorporating the memory-dependent heat transfer. The chemical potential is also assumed to be known on the bounding plane. Employing the Laplace transform and double-Fourier transform techniques, the problem has been solved analytically in the transformed domain. Numerical inversion of the Laplace transform and double-Fourier transforms are carried out using a Fourier series expansion technique. According to the graphical representations corresponding to the numerical results, conclusions about the new theory is constructed. Excellent predictive capability is demonstrated due to the presence of memory-dependent derivative, the effect of delay time and thermodiffusion also. [ABSTRACT FROM AUTHOR]

Thermoelastic damping (TED) has been confirmed as an intrinsic energy loss and determines the upper limit of the quality factor of micro/nanoelectromechanical system (M/NEMS) resonators. A framework for determining the TED in the full clamped (C-C-C-C), clamped-free-clamped-free (C-F-C-F), and cantilever (C-F-F-F) rectangular microplate resonators operating in the fundamental mode by considering three-dimensional heat conduction in conjunction with modified couple stress theory (MCST) is proposed in this article. Then by using Rayleigh's method, three analytical models expressed by Fourier series for TED are derived, respectively. The difference between the present TED model and the previous one-dimensional (1-D) MCST model and 3-D classical model are comprehensively investigated. The comparison results indicate that the size effect on TED decreases to be ignorable as the thickness increases to h/l ≥ 50. In the case of h/l ≤ 50, the size effect cannot be ignored. The corresponding critical thicknesses for TED peaks are independent of the size effect. TED behaviors vary significantly under different structural support types. [ABSTRACT FROM AUTHOR]

The problem of computing the distribution of quadratic forms in normal variables has a long tradition in the statistical literature. Well-established numerical algorithms that deal with this task rely on the inversion of Fourier transforms or series representations. In this article, the Mellin transform is proposed as a tool to compute both the density and the cumulative distribution functions of a positive definite quadratic form: an outline of the numerical algorithm is presented, providing details on the error analysis. The algorithm's characteristics allow us to propose an efficient way to compute the random variables' quantiles. From the theoretical point of view, the analytic properties of the Mellin transform are exploited to provide a novel representation of the distribution of the ratio of independent quadratic forms as a mixture of beta random variables of the second kind. Moreover, algorithms are proposed for computations related to ratios of both independent and dependent quadratic forms. The methods are tested and compared to popular numerical algorithms in terms of computational times and accuracy. The R package QF implementing all the proposed algorithms is also made available. for this article are available online. [ABSTRACT FROM AUTHOR]

The Cauchy problem for the heat equation is a model of situation where one seeks to compute the temperature, or heat-flux, at the surface of a body by using interior measurements. The problem is well-known to be ill-posed, in the sense that measurement errors can be magnified and destroy the solution, and thus regularization is needed. In previous work it has been found that a method based on approximating the time derivative by a Fourier series works well [Berntsson F. A spectral method for solving the sideways heat equation. Inverse Probl. 1999;15:891–906; Eldén L, Berntsson F, Regińska T. Wavelet and Fourier methods for solving the sideways heat equation. SIAM J Sci Comput. 2000;21(6):2187–2205]. However, in our situation it is not resonable to assume that the temperature is periodic which means that additional techniques are needed to reduce the errors introduced by implicitly making the assumption that the solution is periodic in time. Thus, as an alternative approach, we instead approximate the time derivative by using a cubic smoothing spline. This means avoiding a periodicity assumption which leads to slightly smaller errors at the end points of the measurement interval. The spline method is also shown to satisfy similar stability estimates as the Fourier series method. Numerical simulations shows that both methods work well, and provide comparable accuracy, and also that the spline method gives slightly better results at the ends of the measurement interval. [ABSTRACT FROM AUTHOR]

High-accuracy seabed surface modelling provides multi-source high-precision fundamental geographic datasets for marine visual computing, seabed topography detection, marine biology, marine engineering and other fields. Proposed in this paper is a high-precision seabed surface model, which combines B-spline functions and Fourier-series, referred to as the Spline-Fourier-series (S-FS) method. Firstly, the mathematical relationship between the B-spline functions and Fourier-series in the modelling process is explored in depth, deducing the non-recursive basis functions of the p t h Spline-Fourier-series model and the specific representation of the two dimensional p t h Spline-Fourier-series model. Furthermore, using a publicly available Large-area bathymetric dataset, extensive experiments are conducted for comparisons with traditional methods (nearest-neighbor, bilinear, bicubic) and traditional Fourier-series, which generally shows the S-FS method has higher accuracy, better convergence and stronger robustness. Finally, based on its mathematically theoretical model, three characteristics (dimensionality reduction, multi-resolution expression and multi-scale visualization) of the S-FS method for constructing high-precision seabed surface are analyzed visually and deeply. Compared with B-spline function, the basic functions of the S-FS method inherit its prioritized compactly-supported performance and do not need to be recursively calculated anymore, thereby further showing its feasibility and extensibility in the field of high-precision seabed surface modelling. [ABSTRACT FROM AUTHOR]

The objective of this paper is to predict the fiber/matrix interfacial debond strength in composites. Atomic force microscopy (AFM) images of the surface topography of a de-sized carbon fiber reveal that there are surface asperities present at various length scales ranging from a nanometer to several microns. These asperities are likely caused by shrinkage of the polyacrylonitrile (PAN) precursor during the graphitization process. In order to bridge the length scales, a Fourier series-decomposition covering a range of asperity wavelengths and amplitudes is necessary to effectively capture the roughness of the fiber surface at different length scales. Further, once a surface asperity profile has been resolved into individual subcomponents using Fourier-decomposition, MD simulations can then be employed to obtain the interfacial shear strength of the subcomponent asperity of a given amplitude and wavelength. Finally, by recombining the peak interfacial shear force obtained from each of these subcomponents into the overall shear force for the fiber surface profile, the length-scale-averaged shear strength can be obtained for any given asperity. The objective of this paper is to use this novel approach to determine the interfacial shear strength of de-sized carbon fiber embedded in an epoxy matrix and compare predicted results with experimental data. [ABSTRACT FROM AUTHOR]

The plate problem has been investigated for centuries while exact solutions for anisotropic plates are still hard to obtain. In this paper, we aim to get exact solutions for rectangular anisotropic plates with four clamped edges through the state space method. A state space equation for the anisotropic elasticity is derived from the linear elasticity theory for the first time. The Fourier series in exponential form are adopted in the current work. This can transform the transfer matrix with differential operators in state space into a constant matrix. After superposition and differential treatments, the equations for the boundary conditions of four clamped edges are then combined with the state space equation for the anisotropic elasticity, forming a new compound state space which represents the 3 D anisotropic plate problem to be solved. By use of the state space method, a solvable linear equation system under the compound state space is formed. Example solution cases for both orthotropic and monoclinic plates with different thicknesses are provided. For comparison purpose, numerical results from the finite element method are also given to indicate the reliability and accuracy of the current state space method. [ABSTRACT FROM AUTHOR]

The present analysis reports the Kelvin–Voigt-type magneto-thermo-viscoelastic interactions in a thermally conducting unbounded half-space whose surface is subjected to time-harmonic thermal source in the context of micropolar thermoelasticity, being enlightened by memory-dependent derivative (MDD) in the context of three-phase (3P) lag model. The bounding plane of the half-space is stress-free and is subjected to a prescribed temperature distribution. Employing the Laplace transform and Fourier transforms, analytical results for the distributions of the thermophysical quantities have been derived in the transformed domain. The numerical inversions of the respective transforms have been carried out using a suitable numerical scheme based on Fourier series expansion technique. Numerical computations for the stresses, displacement and temperature within the medium have been carried out and also have been demonstrated graphically. Since, micropolar elasticity allows better results to be obtained for microstructural and singular domains as compared to the classical theory of elasticity, therefore, the investigations outline how the micropolarity, magnetic field and viscoelastic parameters influence the thermophysical quantities of the half-space to determine the microstructural changes within the body. Moreover, significant differences on the thermophysical quantities are revealed due to the influence of memory effect and time-delay also, which helps to determine the past effects to the present. [ABSTRACT FROM AUTHOR]

This present work is devoted to investigate the transient phenomena for a novel mathematical model of elasto-thermodiffusion in an isotropic three-dimensional thermoelastic medium subjected to permeating gas induced by a rectangular thermal pulse, where the heat conduction equation is defined in an integral form of a common derivative involving a nonsingular kernel interval by incorporating the Caputo-Fabrizio (CF) heat transfer law. The time-dependent chemical potential is also assumed to be known on the bounding plane. Employing the Laplace transform and double-Fourier transform techniques, the problem has been solved analytically in the transformed domain. Numerical inversion of the Laplace transform and double-Fourier transforms are carried out using a Fourier series expansion technique. According to the graphical representations corresponding to the numerical results, conclusions about the new theory is constructed. Excellent predictive capability is demonstrated due to the presence of the CF parameter and thermodiffusion also. [ABSTRACT FROM AUTHOR]

A magnetic-yielding zone model for an infinitely long piezo-electro-magnetic strip weakened by two mode-III semi-permeable collinear cracks is proposed. Fourier series method and integral equation technique are adopted to solve the problem. The closed-form analytical expressions are obtained for several fracture parameters, namely crack opening potential drop, crack-sliding displacement, crack opening induction drop, intensity factors, and energy release rates. Also, the explicit analytical expressions are derived for developed magnetic-yielding zones. An illustrative numerical study is presented for poled BaTiO3-CoFe2O4 material to observe the impact of inter-crack distance, volume fraction, prescribed loadings, electro-magnetic crack-face boundary conditions on fracture parameters. [ABSTRACT FROM AUTHOR]

A new algorithm for the approximation and simulation of twofold iterated stochastic integrals together with the corresponding Lévy areas driven by a multidimensional Brownian motion is proposed. The algorithm is based on a truncated Fourier series approach. However, the approximation of the remainder terms differs from the approach considered by Wiktorsson (2001). As the main advantage, the presented algorithm makes use of a diagonal covariance matrix for the approximation of one part of the remainder term and has a higher accuracy due to an exact approximation of the other part of the remainder. This results in a significant reduction of the computational cost compared to, e.g., the algorithm introduced by Wiktorsson. Convergence in L p (Ω) -norm with p ≥ 2 for the approximations calculated with the new algorithm as well as for approximations calculated by the basic truncated Fourier series algorithm is proved and the efficiency of the new algorithm is analyzed. [ABSTRACT FROM AUTHOR]

Based on classical laminated plate theory, the free vibration of arbitrary straight-sided quadrilateral laminates with variable angle tows (VAT) is studied. It is assumed that the fiber orientation angle in each ply of VAT laminate varies linearly along x direction. The laminates have elastic restraints on the boundaries to simulate arbitrary boundary conditions. A four-node coordinate transformation is used to transform the arbitrary quadrilateral plate in physical domain into a square one. The complex Fourier series is employed to denote the transverse vibration mode of VAT laminates. The natural frequency and mode shape are obtained. Convergence and accuracy of the present method are verified through the comparison with those existing results. The influence of fiber path, boundary stiffness and boundary conditions on the natural frequency of VAT laminate is investigated in detail. The results presented here may be helpful for the design of VAT composite laminates. [ABSTRACT FROM AUTHOR]

This paper presents an analytical solution to the ground motion of an isosceles hill with slope change under incident SH waves. A new partitioning method, multi-region-matching technique (MRMT), is proposed in this paper to establish an accurate analytical solution model. Based on the complex function method and multipolar coordinate transformation, the infinite algebraic equations are established according to the continuity conditions at the two auxiliary boundaries. Fourier series expansion method in complex-domain is adopted to solve the unknown coefficients in wave field expressions. Numerical results demonstrate the slope of the hill is an important parameter affecting the anti-plane response. [ABSTRACT FROM AUTHOR]