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We recently introduced the Alchemical Integral Transform (AIT), enabling the prediction of energy differences, and guessed an ansatz to parameterize space r in some alchemical change λ. Here, we present a rigorous derivation of AIT's kernel K and discuss the parameterization r(λ) in n dimensions, i.e., necessary conditions, mathematical freedoms, and additional constraints when obtaining it. Analytical expressions for changes in energy spectra and densities are given for a number of systems. Examples include homogeneous potentials such as the quantum harmonic oscillator, hydrogen-like atom, and Dirac well, both for one- and multiparticle cases, and a multiparticle system beyond coordinate scaling for harmonic potentials. [ABSTRACT FROM AUTHOR]

Accurate quantum mechanics based predictions of property trends are so important for material design and discovery that even inexpensive approximate methods are valuable. We use the alchemical integral transform to study multi-electron atoms and to gain a better understanding of the approximately quadratic behavior of energy differences between iso-electronic atoms in their nuclear charges. Based on this, we arrive at the following simple analytical estimate of energy differences between any two iso-electronic atoms, Δ E ≈ − (1 + 2 γ N e − 1 ) Δ Z Z ̄ . Here, γ ≈ 0.3766 ± 0.0020 Ha corresponds to an empirical constant, and Ne, ΔZ, and Z ̄ , respectively, to electron number, nuclear charge difference, and average. We compare the formula's predictive accuracy using experimental numbers and non-relativistic, numerical results obtained via density functional theory (pbe0) for the entire periodic table up to Radon. A detailed discussion of the atomic helium-series is included. [ABSTRACT FROM AUTHOR]

In this article, using inverse integral transforms, we derive the exact distribution of the random variable X that is involved in the ratio Z = d X / (X + Y) where X and Y are independent random variables having the same support, and Z and Y have known distributions. We introduce new distributions this way. As an application of the obtained results, several examples are presented. [ABSTRACT FROM AUTHOR]

This manuscript introduces the development of the stochastic Sumudu transform theory of Itô type for stochastic calculus. We employ the stochastic integration by parts method to achieve this. The purpose of the stochastic Sumudu transform is to solve stochastic differential equations and establish a method for solving them using integral transforms. Furthermore, we derive the Sumudu transforms of commonly used functions in stochastic differential equations. These findings will contribute to the enhancement of literature on stochastic differential equations and have practical applications in fields such as applied mathematics and finance. Additionally, we provide several examples to demonstrate the validity of our work. [ABSTRACT FROM AUTHOR]

The presence of multiple nano-cracks and their interactions may lead to damage to the structure and devices of materials. The plane thermoelastic problem of two asymmetric collinear nano-cracks in the aperiodic plane of one-dimensional hexagonal quasicrystals (1DHQs) is studied using the Young–Laplace equation and the classical Kachanov method. The thermal conductivity of the medium inside the crack is considered, and the interaction coefficient between cracks is introduced. The analytical expressions for the temperature, the stress intensity factors (SIFs), and the strain energy density factor (SEDF) are obtained using the Fourier integral transform method. The numerical results discussed the effects of size effects, surface effects, coupling effects and thermal conductivity on temperature, SIFs and SEDF. The results indicated that the temperature difference between the upper and the lower surface increases with the increase of the external loads. The interaction between cracks is more significant when the crack spacing is less than the length of any nano-crack. The surface effects can suppress crack propagation, and the influence of mode I SIFs on crack propagation is more significant than that of mode II thermal stress intensity factors (TSIFs). The results of the thermal fracture mechanism of quasicrystal materials at the micro- and nano-scales will benefit from the main conclusions of this paper. [ABSTRACT FROM AUTHOR]

We introduce new extension of the extended Pochhammer symbol and gamma function by using the extended Mittag-Leffler function. We also present extension of the generalized hypergeometric function as well as some of their special cases by using this extended Pochhammer symbol. Further, we define the extension of the τ-Gauss hypergeometric function. Integral and derivative formulas involving the Mellin transform and fractional calculus techniques associated with this extended τ-Gauss hypergeometric function are also given. Also, new extended τ-Gauss hypergeometric function also provides a few more interesting and well-known results. This enriches the theory of special functions. The obtained results are believed to be newly presented. [ABSTRACT FROM AUTHOR]

Analytical solution of initial value problem for the fractional oscillation equation with two Caputo fractional derivatives x′′(t)+aDtαx(t)+cx′(t)+bDtβx(t)+kx(t)=q(t)$$ {x}&#x0005E;{\prime \prime }(t)&#x0002B;a{D}_t&#x0005E;{\alpha }x(t)&#x0002B;c{x}&#x0005E;{\prime }(t)&#x0002B;b{D}_t&#x0005E;{\beta }x(t)&#x0002B; kx(t)&#x0003D;q(t) $$, where the coefficients and orders satisfy a,b,c,k>0,1<α≤2$$ a,b,c,k>0,1<\alpha \le 2 $$ and 0<β≤1$$ 0<\beta \le 1 $$, is investigated by using the Laplace transform and complex inverse integral method on the principal Riemann surface. It is proved by using the argument principle that the characteristic equation has a pair of conjugated simple complex roots with a negative real part on the principal Riemann surface under the assumption that α$$ \alpha $$ and β$$ \beta $$ are not both integers. Then three fundamental solutions, the unit impulse response, the unit initial displacement response, and the unit initial rate response, are derived analytically. Each of these solutions is expressed into a superposition of a classical damped oscillation decaying exponentially and a real Laplace integration decaying in a negative power law. Finally, the asymptotic behaviors of these analytical solutions for sufficiently large t$$ t $$ are determined as monotonous decays in a power of negative exponent. [ABSTRACT FROM AUTHOR]

AbstractThe article explores the photothermal interactions occurring in a semiconducting semi-infinite half-space with axisymmetric characteristics. The study is situated within the framework of a fully coupled system of generalized thermoelastic theory for semiconductor media. The bounding surface is traction-free, subjected to a prescribed axisymmetric temperature distribution, and governed by a zero-flux condition. Employing an integral transform technique, the solution is derived, and Laplace transform inversions are carried out using the Gaver-Stehfest numerical scheme. The mathematical model is specifically tailored for Silicon material, and the ensuing numerical results are meticulously discussed and presented graphically. [ABSTRACT FROM AUTHOR]

A switching active disturbance rejection control (SADRC) strategy was proposed to solve the composite disturbance challenge arising from gap, LuGre friction, hydraulic spring force, and external load disturbance in the double closed-loop digital hydraulic cylinder position control system. Firstly, leveraging the established mathematical model of the double closed-loop digital hydraulic cylinder, the high-order state equation was derived. Subsequently, the high-order double closed-loop digital hydraulic cylinder control system was transformed into a second-order integral series control system using ADRC strategy. Given the pronounced nonlinear characteristics of double closed-loop digital hydraulic cylinders, combined with the characteristics of switching control, a SADRC strategy was proposed, and the stability of the closed-loop system was proved based on Lyapunov theory and switching rules. Finally, the effectiveness of the proposed control method was verified through simulation and experiment. Results indicate that the system's response speed employing the SADRC strategy outperforms the PID control strategy by 32.56%, with a 2.0% reduction in error. The average error in the response speed of the digital hydraulic cylinder and the MATLAB simulation value of the tracking error are 9.0% and 1.50% respectively. Notably, the simulation and experimental results exhibit a consistent overall trend, affirming the feasibility and effectiveness of the control strategy. [ABSTRACT FROM AUTHOR]

Background: The Expanded Special Project for the Elimination of Neglected Tropical Diseases (ESPEN) was launched in 2019 by the World Health Organization and African nations to combat Neglected Tropical Diseases (NTDs), including Soil-transmitted helminths (STH), which still affect over 1.5 billion people globally. In this study, we present a comprehensive geostatistical analysis of publicly available STH survey data from ESPEN to delineate inter-country disparities in STH prevalence and its environmental drivers while highlighting the strengths and limitations that arise from the use of the ESPEN data. To achieve this, we also propose the use of calibration validation methods to assess the suitability of geostatistical models for disease mapping at the national scale. Methods: We analysed the most recent survey data with at least 50 geo-referenced observations, and modelled each STH species data (hookworm, roundworm, whipworm) separately. Binomial geostatistical models were developed for each country, exploring associations between STH and environmental covariates, and were validated using the non-randomized probability integral transform. We produced pixel-, subnational-, and country-level prevalence maps for successfully calibrated countries. All the results were made publicly available through an R Shiny application. Results: Among 35 countries with STH data that met our inclusion criteria, the reported data years ranged from 2004 to 2018. Models from 25 countries were found to be well-calibrated. Spatial patterns exhibited significant variation in STH species distribution and heterogeneity in spatial correlation scale (1.14 km to 3,027.44 km) and residual spatial variation variance across countries. Conclusion: This study highlights the utility of ESPEN data in assessing spatial variations in STH prevalence across countries using model-based geostatistics. Despite the challenges posed by data sparsity which limit the application of geostatistical models, the insights gained remain crucial for directing focused interventions and shaping future STH assessment strategies within national control programs. Author summary: The Expanded Special Project for the Elimination of Neglected Tropical Diseases (NTDs, ESPEN) was established in 2019 to help monitor and control NTDs such as Soil-transmitted helminths (STH) in African countries. We carried out a geostatistical analysis of STH data for 35 countries from the ESPEN database. Separate geostatistical models were developed for each country to tailor the selection of spatial covariates and estimation of covariance parameters to the unique spatial patterns across countries. Moreover, it was observed that the geostatistical models exhibited inadequate calibration in some countries, and thus carrying out spatial predictions at unsampled locations was not possible. These findings urge caution in developing an Africa-wide model based solely on ESPEN data, given the observed heterogeneity in the model parameter estimates and the challenges encountered in model calibration across different species and countries. Despite challenges posed by data sparsity, the insights gained remain crucial for directing focused interventions and shaping future STH assessment strategies within national control programs. [ABSTRACT FROM AUTHOR]

We solve the nonstationary problem of heat conduction for two contacting thermosensitive layers under the conditions of complex heat exchange with ambient media. The solution is obtained by using the analytical-numerical approach based on the application of a version of the methods of successive approximations, linearizing parameters, Laplace integral transform, and its numerical inversion with the help of the Prudnikov formula adapted to the problems of heat conduction. We investigate the thermal state of the outlined thermosensitive piecewise-homogeneous structure for different combinations of boundary conditions on its surfaces. [ABSTRACT FROM AUTHOR]

Two half-spaces and a layer of finite height of linear elastic orthotropic medium containing a penny-shaped crack and a circular rigid disk are considered such that the crack surface is parallel to the rigid disk, where both are situated at two different interfaces of layer and half-space and perpendicular to the axis of symmetry. The rigid disk is agitated by an axisymmetric torsion. The equations of equilibrium are solved with the use of Hankel's integral transform method. Then, the tangential displacement components and shear stress components are determined. With the help of mixed-type boundary conditions, a system of integral equations is derived. After that, by utilizing a trial solution, these integral equations are transformed into a pair of simultaneous Fredholm integral equations of the second kind. The numerical results of the Fredholm integral equations are evaluated by converting it into a system of algebraic equations to interpret the physical quantity, like the stress intensity factor (SIF), which is demonstrated graphically. The obtained results are compared to the previously published article to ensure its accuracy. [ABSTRACT FROM AUTHOR]

In this research, we investigate the propagation characteristics of Laguerre-Whittaker-Gaussian beams (LWGBs) through a paraxial ABCD optical system. We get the analytical expression for LWGBs using the Huygens-Fresnel integral. We then use this formula to study the propagation properties of a fractional Fourier transform (FRFT) optical system. Numerous aspects influencing the evolution of LWGBs in FRFT are investigated in detail, and their characteristics are illustrated graphically with numerical examples. The findings show that the initial LWGBs parameters (m, l, and n), fractional order p, and focal length f all impact the intensity and phase distributions of LWGBs, which vary regularly throughout propagation. These results might find applications in optical micromanipulation, remote sensing, and free-space optical communications. [ABSTRACT FROM AUTHOR]

The present article aims to manifest a two-dimensional dynamical problem based on a unified way of dual-phase lags generalized thermoelasticity. The problem deals with finite mode-I crack due to tensile force in an unbounded linear thermoelastic space under a specified stress distribution and temperature. Here the governing equations are constructed for a homogenous and isotropic medium. Boundary conditions convert the problem into four dual integral equations, whose solution corresponds to the solution of Fredholm's integral equation of first order. The integral transform methods are applied to obtain the solution to a problem. An inversion of the Laplace transform using the Bellman method is applied to determine the numerical value of the components of temperature, stress, and displacement for copper material, which are interpreted graphically. Moreover, the stress intensity factor (SIF) near the crack center is calculated and shown graphically. [ABSTRACT FROM AUTHOR]

The mathematical theory of elasticity helps in the study of physical quantities in the problem of structures. The structures face the problem of crack's presence, which makes the problem difficult but not impossible to deal. Integral equations are useful in a variety of problems. Integral equations are used to solve problems like fracture mechanics or fracture design. The physical interest in the fracture design criterion is due to stress and crack opening displacement components. We have an accurate form of stress and displacement components for a pair of longitudinal crack propagations in the bone fracture of the human body at the interface of an isotropic and orthotropic half-space that are bounded together in the proposed study. The expression was calculated using the Fourier transform approach near the crack tips, but these components were evaluated using Fredholm integral equations and subsequently reduced to coupled Fredholm integral equations. We employ the Lowengrub and Sneddon problem in this research and reduce it to triple integral equations. The Srivastava and Lowengrub method reduces the solution of these equations to a coupled Fredholm integral equation. The problem is further reduced to a decoupled Fredholm integral equation of the second kind. Triple integral equations are solved, and the problem is reduced to a coupled Fredholm integral equation. The Fredholm integral equation is solved and reduced to a decoupled Fredholm integral equation of the second kind. Stress and crack opening displacement components drive physical interest in fracture design criteria. Finally, the stress and displacement components may be simply calculated in their exact form. [ABSTRACT FROM AUTHOR]

ABSTRACT Based on the fractional‐order (FO) characteristics of inductors and capacitors, many basic PWM DC–DC converters are defined and modeled by FO calculus in previous studies, but the research of FO resonant dc converters is still in its early stage. Therefore, this paper adopts FO calculus and Laplace transform to model and analyze a ZCS boost converter with an LC resonant tank, which mainly focuses on the influence of the FO component on the soft switching characteristics, converter efficiency, and output voltage gain of this isolated dc converter. This paper extends the topology to the fractional order domain and conducts FO modeling. The order of the resonant inductor and capacitor will affect the amplitude/phase of the resonant current and then affect the converter ZCS characteristic. The analysis demonstrates that the reduction of FOI and FOC order is not conducive to the ZCS of switching devices and converter efficiency. Based on the voltage and current relationship of the FO LC resonant tank, a parameter design guideline is presented. Numerical tools are used to solve the FO output voltage gain and draw the gain curve. And the order of FOI and FOC provides new flexibility for the converter output gain and soft switching design. Finally, simulations and a 360 W hardware experimental prototype are conducted to verify the accuracy and effectiveness of theoretical analysis. [ABSTRACT FROM AUTHOR]

The accuracy in evaluating conductive layer coating thicknesses over conductive materials has recently been advanced with the potential application of apparent eddy current conductivity (AECC) spectroscopy. This approach minimises the sensitivity to variation in lift-off distance between the used eddy current coils and tested samples while capturing the actual conductivity profile with accuracy. This investigation further explores the potential integration of AECC spectroscopy with emerging machine learning (ML) capabilities in a theoretical-based supervised learning approach using artificial neural networks (ANNs). The complex spatial integral transform of the eddy current signal effectively filters out the information related to abrupt changes in the conductivity profile of step-like multi-layer structures, which renders the application of ANNs unfeasible for such structures. However, in the case of rectangular conductivity profiles covered in this study, it not only demonstrates the accuracy in estimating AECC spectrums over a range of different coating and substrate conductivity combinations and their associated coating thicknesses but also the retrieval of these unknown input parameters from measured AECC spectrums. The implementation of the ANN inverse model to experimentally measured AECC spectrums resulted in a maximum uncertainty of 3.37% in the conductive layer thickness estimation within a practical lift-off range. [ABSTRACT FROM AUTHOR]

In this paper, an axisymmetric deformation problem of a circular plate of double-porous medium with fractional order thermoelastic dual-phase-lag has been discussed by taking a mathematical model. The solution of the problem is obtained in the transformed field of Laplace and Hankel transforms using eigen value approach in dimensionless form. The solution in the transformed form is inverted numerically for a specific model using a numerical inversion technique for integral transforms through a programme code in MATLAB. The numerical results are discussed graphically, and the impact of the fractional order parameter on various field quantities (normal stress, shear stress, equilibrated stresses and temperature distribution) is observed. Particular cases are discussed by (i) neglecting the porous parameters and (ii) taking different combinations of phase-lag parameters and fractional order parameter, to describe the generalized nature of the problem and the validity of the problem considered. [ABSTRACT FROM AUTHOR]

An approximate algorithm for calculating integral convolution operators that arise when estimating barrier options in Lévy models using the Wiener–Hopf method is constructed. Additionally, the possibility of applying machine learning methods (artificial neural networks) to approximating a special type of integrals, which are a key element in the construction of approximate formulas for the considered Wiener–Hopf integral operators, is studied. The main idea is to expand the price function in the Fourier series and transform the integration contour for each term of the Fourier series. As a result, we obtain a set of typical integrals that depend on the Wiener–Hopf factors but are independent of the price function; then, the most computationally expensive part of the numerical method is reduced to calculating these integrals. Since they only need to be calculated once, rather than at each iteration as was the case in standard implementations of the Wiener–Hopf method, this will significantly speed up the calculations. Moreover, a neural network can be trained to calculate typical integrals. The proposed approach is especially efficient for spectrally one-sided Lévy processes for which explicit Wiener–Hopf factorization formulas are known. In this case, we obtain formulas convenient for calculations by integrating along the cut. The main advantage of including neural networks in the computational scheme is the ability to perform calculations on a nonuniform grid. Such a hybrid numerical method can successfully compete with classical methods for calculating convolutions in similar problems using the fast Fourier transform. Computational experiments show that neural networks with one hidden layer of 20 neurons are able to efficiently cope with the problems of approximating the auxiliary integrals under consideration. [ABSTRACT FROM AUTHOR]

Many properties of special polynomials, such as recurrence relations, sum formulas, integral transforms and symmetric identities, have been studied in the literature with the help of generating functions and their functional equations. In this paper, we introduce hybrid forms of q-Mittag-Leffler functions. The q-Mittag-Leffler–Bessel and q-Mittag-Leffler–Tricomi functions are constructed using a q-symbolic operator. The generating functions, series definitions, q-derivative formulas and q-recurrence formulas for q-Mittag-Leffler–Bessel and q-Mittag-Leffler–Tricomi functions are obtained. The N q -transforms and N q -transforms of q-Mittag-Leffler–Bessel and q-Mittag-Leffler–Tricomi functions are obtained. These hybrid q-special functions are also studied by plotting their graphs for specific values of the indices and parameters. [ABSTRACT FROM AUTHOR]

The paper studies integral operators on the interval of real line which naturally arise in some problems in the theory of integral equations and mathematical physics. We study boundedness in weighted Lebesgue spaces: Sufficient and necessary conditions for boundedness are given. Also, special important particular cases of operators and spaces are considered as examples. We construct identity approximation within the framework of the class of operators under study, and two different approaches are given. [ABSTRACT FROM AUTHOR]

A mathematical model has been developed to investigate the SIF (stress intensity factor) and COD (crack opening displacement) for the propagation of mode-III fracture influenced by propagating SH-wave in a pre-stressed dry sandy elastic continuum. The Wiener-Hopf mathematical method along with the Fourier integral transform (FIT) technique have been successively implemented to obtain the solution of the boundary value problem associated with the mathematical model. Furthermore, the closed form solutions of SIF and COD for non-static and static conditions of mode-III fracture have been obtained, and are found to be in well agreement with the existing results present in the literature. The sound effects of various affecting parameters viz. horizontal and vertical (compressive/tensile) pre-stresses, crack depth, and crack velocity on SIF and COD have been explored. In order to delineate the influences of these aforementioned parameters on SIF and COD graphically, numerical simulation has been accomplished. [ABSTRACT FROM AUTHOR]

In this article, a new approach to study the fractionalized second grade fluid flow is described by the different fractional derivative operators near an exponentially accelerated vertical plate together with exponentially variable velocity, energy and mass diffusion through a porous media is critically examined. The phenomenon has been expressed in terms of partial differential equations, then transformed the governing equations in non-dimentional form. For the sake of better rheology of second grade fluid, developed a fractional model by applying the new definition of Constant Proportional-Caputo hybrid derivative (CPC), Atangana Baleanu in Caputo sense (ABC) and Caputo Fabrizio (CF) fractional derivative operators that describe the generalized memory effects. For seeking exact solutions in terms of Mittag-Leffler and G-functions for velocity, temperature and concentration equations, Laplace integral transformation technique is applied. For physical significance of various system parameters on fluid velocity, concentration and temperature distributions are demonstrated through various graphs by using graphical software. Furthermore, for being validated the acquired solutions, accomplished a comparative analysis with some published work. It is also analyzed that for exponential heating and non-uniform velocity conditions, the CPC fractional operator is the finest fractional model to describe the memory effect of velocity, energy and concentration profile. Moreover, the graphical representations of the analytical solutions illustrated the main results of the present work. Also, in the literature, it is observed that to derived analytical results from fractional fluid models developed by the various fractional operators, is difficult and this article contributing to answer the open problem of obtaining analytical solutions the fractionalized fluid models. [ABSTRACT FROM AUTHOR]

The article concerns the modeling of the transverse impact of an impactor (test sample) on the surface of an infinite elastic layer. The Laplace transform with respect to time and the Hankel transform with respect to the radius for the axisymmetric case were applied. The propagation of elastic waves in the layer and local deformations in the contact zone are taken into account. Impact force, impact time and the coefficient of restitution were examined. The results are compared with the elastic half-space. The calculations carried out showed that for layer thicknesses of more than five impactor diameters, the layer can be considered as a half-space. [ABSTRACT FROM AUTHOR]

In this study, we introduce the first-of-its-kind class of tests for detecting change-points in the distribution of a sequence of independent matrix-valued random variables. The tests are constructed using the weighted square integral difference of the empirical orthogonally invariant Hankel transforms. The test statistics have a convenient closed-form expression, making them easy to implement in practice. We present their limiting properties and demonstrate their quality through an extensive simulation study. We utilize these tests for change-point detection in cryptocurrency markets to showcase their practical use. The detection of change-points in this context can have various applications in constructing and analyzing novel trading systems. [ABSTRACT FROM AUTHOR]

Warped time-frequency systems have recently been introduced as a class of structured continuous frames for functions on the real line. Herein, we generalize this framework to the setting of functions of arbitrary dimensionality. After showing that the basic properties of warped time-frequency representations carry over to higher dimensions, we determine conditions on the warping function which guarantee that the associated Gramian is well-localized, so that associated families of coorbit spaces can be constructed. We then show that discrete Banach frame decompositions for these coorbit spaces can be obtained by sampling the continuous warped time-frequency systems. In particular, this implies that sparsity of a given function f in the discrete warped time-frequency dictionary is equivalent to membership of f in the coorbit space. We put special emphasis on the case of radial warping functions, for which the relevant assumptions simplify considerably. [ABSTRACT FROM AUTHOR]

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In this paper, we introduced a numerical approach for estimating the solutions of nonlinear Fredholm integral equations in the complex plane. The main problem was transformed into a novel integral equation, which simplified the computation of integrals derived from the discretization technique. The combination of the standard collocation method with periodic quasi-wavelets, as well as their fundamental properties, was utilized to convert the solution of the newly formulated integral equation into a nonlinear complex system of algebraic equations. The convergence properties of the scheme were also presented. Finally, several numerical examples were provided to demonstrate the efficiency and precision of our proposed approach, which also confirmed its superiority over polynomial collocation methods. [ABSTRACT FROM AUTHOR]

The rapid development of high-speed railways has brought significant attention to the coupled vibration issues of the train–bridge system. Vertical track irregularities, as one of the primary excitation sources of train–bridge system vibrations, is essentially a stochastic process. In this study, a beam model considering spatial vibrations is established to analyze the dynamic response under the passage of a train. Statistical methods, Laplace transform and Duhamel’s integral technique, are employed to derive the mean square value (MSV) and autocorrelation function (ACF) of the train’s vertical response, as well as the average and standard deviation (SD) of the beam’s bending–torsional coupled vibration response. The accuracy of the proposed analytical approach was verified using the Newmark-β algorithm and Monte Carlo simulation. In numerical examples, the displacement response of the beam is mainly explored for the influence of train speed and beam span. The results indicate that the maximum SD of displacement at mid-span occurs when the train is about to leave, which diminishes with higher train speeds and shorter beam spans. For a speed ranging from 250km/h to 350km/h, an increase in speed leads to a noticeable rise in the peak value of vertical average displacement. Due to high-frequency excitation causing the attenuation of low-frequency structural response, the MSV of the train’s displacement decreases with increasing speed. [ABSTRACT FROM AUTHOR]

Within the framework of the three‐dimensional linearized theory of stability of deformable bodies, the plane problem on compression of a piecewise‐homogeneous half‐plane along a defect, which is a frictionless sliding zone located at the rectilinear interface between two rigidly connected media, a semi‐bounded homogeneous body (base) and a homogeneous thin coating layer, have been studied. The initial stage of body fracture is associated with the loss of material stability in a local area near the specified defect. The base and coating materials are considered as highly elastic materials described by an elastic potential with different mechanical characteristics. The boundary value problem, formulated in terms of potential harmonic functions, using Fourier integral transforms, is reduced to an eigenvalue problem for the Fredholm integral equation of the first kind, which is studied numerically by employing Bubnov—Galerkin method. For a compressible material with a harmonic potential, critical values of the load parameters that correspond to local instability have been found. The critical load parameters obtained have also been compared with similar values of the critical parameters corresponding to the near‐surface instability of a piecewise‐homogeneous half‐plane (without a defect) compressed along the interface between the media that are rigidly connected or slide without friction against each other. [ABSTRACT FROM AUTHOR]

In this paper, we propose a new numerical method to simulate acoustic scattering problems in two‐dimensional periodic structures with non‐periodic incident fields. Applying the Floquet‐Bloch transform to the scattering problem yields a family of quasi‐periodic boundary value problems dependent on the Floquet‐Bloch parameter. Consequently, the solution of the original scattering problem is written as the inverse Floquet‐Bloch transform of the solutions to these boundary value problems. The key step in our method is the numerical approximation of this integral transform by a quadrature rule with a nonuniform choice of quadrature points adapted to the regularity of the family of quasi‐periodic solutions. This achieved by a graded subdivision of the full interval for the Floquet‐Bloch parameter and applying a Gauss‐Legrendre quadrature rule on each subinterval. We prove that the numerical method converges exponentially with respect to both the number of subintervals and the number of Gaussian quadrature points. Some numerical experiments are provided to illustrate the results. [ABSTRACT FROM AUTHOR]

This paper presents a systematic approach to investigating the existence of solutions for fractional integro-differential equation systems incorporating delay and relaxation impulsive terms. By employing suitable definitions of fractional derivatives, we establish physically interpretable boundary conditions. To account for abrupt state changes, impulsive conditions are integrated into the model. The system is transformed into an equivalent integral equation, facilitating the application of Banach and Schaefer fixed-point theorems to prove the existence and uniqueness of solutions. The practical applicability of our findings is demonstrated through an illustrative example. [ABSTRACT FROM AUTHOR]

ABSTRACT Energy piles are commonly deployed in vertically layered geological conditions due to the geological structure and pile foundation backfill. The imperfect contact between adjacent soil layers results in resistance to heat transfer at the interface, known as the interfacial thermal resistance effect. In this paper, the energy pile was simplified as a finite‐length solid cylindrical heat source, and an analytical model was established for layered heat transfer of energy piles considering the interfacial thermal resistance effect. The Laplace‐domain solutions to the temperatures in the layered ground were derived by using the finite Hankel and Laplace transforms. The Crump method was subsequently employed to numerically invert Laplace‐domain solutions to the time‐domain solutions. The proposed model was validated by comparing with an analytical solution of a homogeneous model and COMSOL numerical solution. These solutions were used to analyze the temperature response around energy piles considering interfacial thermal resistance. Finally, a parametric study was performed to explore the effects of interfacial thermal resistance and other thermal properties of the soil layer on the layered heat transfer of energy piles. [ABSTRACT FROM AUTHOR]

We prove the Parseval theorem and the Plancherel Theorem among the analytic Feynman integral and the Fourier Feynman transform and the convolution for the function F : B ν → C in the Class F (B ν) : F ( x → ) = ∫ H exp { i ∑ j = 1 ν (h , x j) ∼ } d μ (h) , μ ∈ M (H) on the Product Abstract Wiener Space (H , B ν , m ν) , where B ν = B × B × ⋯ × B (ν times) and M (H) is the space of a complex valued countably additive measure μ defined on B (H) , the Borel class of a real separable infinite dimensional Hilbert space H. [ABSTRACT FROM AUTHOR]

Many physical problems represented as initial and boundary value problems are usually solved by transforming them into integral equations on the real line. Therefore, this paper proposes polynomially based projection and modified projection methods to solve Hammerstein integral equations on the real line with sufficiently smooth kernels. The approximating operator employed is either the orthogonal projection or an interpolatory projection using Hermite polynomials as basis functions. We analyse the convergence of the proposed approaches and its iterated version and we establish superconvergence results. Through different numerical tests, the effectiveness of the proposed methods is presented to demonstrate the given theoretical framework. [ABSTRACT FROM AUTHOR]

The Convertible Bonds (CBs) market has witnessed an unprecedented level of activity over the last few years not only in developed countries such as the United States but also in BRICK countries such as China. Exploring new properties of CBs or CBs with clauses becomes important for academia communities in financial mathematics. In this paper, we build two coupled partial differential equations (PDEs) for pricing a callable CB, and find a newly identified inherent property of this bond. The new property is that the conversion ratio will not affect the critical recall time indicating the time beyond the callability. Besides this property, we also find that solving the critical recall time separately and superimposing later using a non-callable CB is the same as the method of a hybrid free boundary (the critical recall time) and a moving boundary (the optimal conversion price) though the callability and the American-style conversion are nonlinearly coupled. [ABSTRACT FROM AUTHOR]

The feasibility of extrapolation of completely monotone functions can be quantified by examining the worst-case scenario, whereby a pair of completely monotone functions agree on a given interval to a given relative precision, but differ as much as it is theoretically possible at a given point. We show that extrapolation is impossible to the left of the interval, while the maximal discrepancy to the right exhibits a power law typical for extrapolation of similar classes of complex analytic functions. The power law exponent is derived explicitly and shows a precipitous drop immediately beyond the right end-point, with a subsequent decay to zero inversely proportional to the distance from the interval. The local extrapolation problem, where the worst discrepancy from a given completely monotone function is sought, is also analyzed. In this case explicit and easily verifiable optimality conditions are derived, enabling us to solve the problem exactly for a single decaying exponential. In the general case, our approach leads to a natural algorithm for computing solutions to the local extrapolation problem numerically. The methods developed in this paper can easily be adapted to other classes of analytic functions represented as integral transforms of positive measures with analytic kernels. [ABSTRACT FROM AUTHOR]

Sandwich structures with ceramic honeycomb cores are extensively employed in thermal protection systems owing to their exceptional ability to resist high temperatures. This work aims at exploring the effect of cracking on the transient thermal process of the sandwich panel subject to impulsive and cyclic thermal loadings. Both the conventional and re-entrant hexagonal alumina honeycombs are considered for the core material. By the integral transform method, combined with singular integral equations, the transient temperatures of the whole sandwich panel are determined from the semi-analytical solution. The straightforward temperature difference of the crack face's midpoints is exploited to characterize the heat intensification near the crack. Parametric investigations are carried out for the internal cell angle, the relative density, crack length, crack position, and thickness of face sheets, which provides a better understanding of the honeycomb materials working in thermal protection systems. [ABSTRACT FROM AUTHOR]

Modified Green–Lindsay generalized thermoelasticity theory was established by Yu et al. (Meccanica 53(10):2543–2554, 2018). On the basis of this theory, transient motions remove discontinuities in displacement fields. The goal of this article is to address a dynamical problem involving finite linear mode-I cracks in an isotropic and homogeneous elastic medium in a two-dimensional infinite space using the innovative framework of modified Green–Lindsay generalized thermoelasticity theory. There is a specified temperature and stress distribution on the crack's boundary. The integral transform techniques are used to obtain the numerical values of temperature, stress, displacement and stress intensity factor for copper material. These non-dimensional physical fields are explained graphically. Specifically, the present undertaking demonstrates its utility in addressing challenges related to fracture mechanics, geophysics and mining particularly in the context of coupling thermal and mechanical fields. This concerted effort proves valuable in exploring and resolving issues within these fields. [ABSTRACT FROM AUTHOR]

Nowadays, several applications in engineering and science are considering fractional partial differential equations. However, this type of equation presents new challenges to obtaining analytical solutions, since most existing techniques have been developed for integer order differential equations. In this sense, this work aims to investigate the potential of fractional derivatives in the mathematical modeling of the dispersion of atmospheric pollutants by obtaining a semi-analytical solution of the time-dependent fractional, two-dimensional advection–diffusion equation. To reach this goal, the GILTT (Generalized Integral Laplace Transform Technique) and conformal derivative methods were combined, taking fractional parameters in the transient and longitudinal advective terms. This procedure allows the anomalous behavior in the dispersion process to be considered, resulting in a new methodology called α-GILTT. A statistical comparison between the traditional Copenhagen experiment dataset (moderately unstable) with the simulations from the model showed little influence on the fractional parameters under lower fractionality conditions. However, the sensitivity tests with the fractional parameters allow us to conclude that they effectively influence the dispersion of pollutants in the atmosphere, suggesting dependence on atmospheric stability. [ABSTRACT FROM AUTHOR]

In this article, a novel spectral method based on the integral transform and Finite Element (FE) method is introduced for nonlinear thermal analysis of a hollow cylinder under asymmetric boundary excitations. The material properties are temperature-dependent and vary in terms of spatial coordinates. This dependency makes the problem to be nonlinear. The intended nonlinear heat conduction equation is discretized using FEs in the radial direction. Fast Fourier transform (FFT) technique with the uniform distribution of the harmonics in the circumferential direction, is used to discretize the periodic domain and boundary conditions. The use of the FFT algorithm is accompanied by a significant save in computational times and efforts. In such problems, the pseudo-spectral technique, as an evolved model of the spectral method, is utilized whenever the material properties vary in terms of the periodic variables or there exists a nonlinear term. The convolution sum technique is appropriately used to transform the nonlinear terms in the Fourier space. Thermal boundary conditions at the inner surface of the cylinder are considered in asymmetrical form. In compliance with the other analytical and numerical solutions, the present mixed-method benefits from the fast rate of convergence and high accuracy. [ABSTRACT FROM AUTHOR]

Horizontal wells have gained popularity as a technology for exploring water resources and remediating aquifers over the last decades, due to costs and numerous technical benefits compared to traditional vertical wells. This study presents a set of analytical solutions for drawdown distribution and various components of water budget contributing to flow toward a horizontal well in an aquifer-aquitard system interacting with a fully penetrating stream. It is assumed that the water level in the upper unconfined aquifer remains fixed at a specific elevation during the course of the pumping in the lower leaky aquifer. The water budget components account for inflows from aquifer storage, stream depletion, and leakage across the aquifer-aquitard interface. Analytical solutions to this three-dimensional, transient, non-axisymmetric Darcian flow model are given for both transient and steady-state flow conditions, relying on a four-fold integral transform technique that includes a Robin-type boundary condition at the aquifer-aquitard interface. It is shown how various components of water budget collectively counterbalance the effect of pumping discharge, confirming that the mass is conserved under both continuous and non-continuous pumping scenarios. Response maps are prepared to assess how different components of water budget react to changes in the well position. Furthermore, it is found that the components of water budget are most sensitive to the well-to-stream distance and anisotropy ratio of the leaky aquifer. [ABSTRACT FROM AUTHOR]

The paper considers the issue of constructing differential relations for the Lauricella hypergeometric function $ F_D^{(N)} $ F D (N) . The formulas found give explicit expressions for the derivative of the product of the function $ F_D^{(N)} $ F D (N) and some binomials through the product of other binomials and a combination of adjacent Lauricella functions whose parameters differ by 1 or $ -1 $ − 1. The derived differential relations generalize the Jacobi identity and other differential formulas known in the theory of the Gauss hypergeometric function on the multidimensional case. With special parameter values $ F_D^{(N)} $ F D (N) , the right-hand side of such Jacobi-type formulas are simplified and have the form of a product of binomials and a polynomial. Such formulas can be used to transform a Cauchy-type integral to the form of the Schwartz–Christoffel integral and have an application to the Riemann–Hilbert problem with piecewise constant coefficients. [ABSTRACT FROM AUTHOR]