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The objective of this research is to establish new results for set-valued dominated mappings that meet the criteria of advanced locally contractions in a complete extended b-metric space. Additionally, we intend to establish new fixed point outcomes for a couple of dominated multi-functions on a closed ball that satisfy generalized local contractions. In this study, we present novel findings for dominated maps in an ordered complete extended b-metric space. Additionally, we introduce a new concept of multi-graph dominated mappings on a closed ball within these spaces and demonstrate some original results for graphic contractions equipped with a graphic structure. To demonstrate the uniqueness of our new discoveries, we verify their applicability in obtaining a joint solution of integral and functional equations. Our findings have also led to modifications of numerous classical and contemporary results in existing research literature. [ABSTRACT FROM AUTHOR]

In this paper, we establish a common fixed point theorem for two multivalued mappings satisfying some dominated conditions on a complete metric space. This new rational type contractive inequality refines various results in the literature. The main theorem is illustrated with examples. As application, we found the existence of solutions of system nonlinear integral equations and functional equations. [ABSTRACT FROM AUTHOR]

In this paper, some generalized fixed point results of Banach and Ćirić type in the context of extended fuzzy b-metric spaces are established. For authenticity of the aforesaid results a nontrivial supporting example is also provided. Eventually, an application for the existence of a solution for an integral equation is established which shows corporeality of the obtained results. The presented work generalizes some well known fixed point results from the existing literature. [ABSTRACT FROM AUTHOR]

In this paper, we investigate a nonlocal boundary value problem for an equation of special type. For y > 0 it is a fractional diffusion equation, which contains the Riemann-Liouville fractional derivative. For y < 0 it is a generalized equation of moisture transfer. A unique solvability of the considered problem is proved. [ABSTRACT FROM AUTHOR]

In this note, the notion of a mixed weakly monotone pair of mappings is invoked to prove some coupled common fixed point theorems in partially ordered b-metric spaces. Results proved in this note are authenticated by some innovative examples. Demonstrative surfaces leading to better understanding of calculation done. Moreover as an application our results are utilized to establish existence of solutions of system of integral equations which is also substantiated by an example. [ABSTRACT FROM AUTHOR]

In this paper, we study the existence of the solutions of a class of functional integral equations by using some fixed point results in cone b-metric spaces over Banach algebras. In order to obtain these results we introduced and proved some properties of generalized weak φ-contractions, in which the φ are nonlinear weak comparison functions. The obtained results are generalizations of results of Van Dung N., Le Hang V. T., Huang H., Radenovic S. and Deng G. Also, some suitable examples are given to illustrate obtained results. [ABSTRACT FROM AUTHOR]

In this article, we use an effective coupled technique to solve singular integral equations with logarithmic kernel which it occurs in different branches of sciences such as mathematical physics, mechanics, isotropic elastic, etc. At first, we approximate the singular kernel by choosing suitable mesh points and multi-wavelet bases then, Galerkin method is used for solving integral equations. In addition, for simplification and to achieve to a more accuracy, we convert integral equation with logarithmic kernel to integro-differential equation with weakly singular kernel which is solvable with the proposed method. The numerical results show the high accuracy of the solution. [ABSTRACT FROM AUTHOR]

In this paper, a completely new integral equation for the price of an American put option as well as its optimal exercise price is successfully derived. Compared to existing integral equations for pricing American options, the new integral formulation has two distinguishable advantages: (i) it is in a form of one-dimensional integral, and (ii) it is in a form that is free from any discontinuity and singularities associated with the optimal exercise boundary at the expiry time. These rather unique features have led to a significant enhancement of the computational accuracy and efficiency as shown in the examples. [ABSTRACT FROM PUBLISHER]

This paper presents a parallel algorithm for frequency-domain acoustic modeling by the method of integral equations (IE). The algorithm is applied to seismic simulation. The IE method reduces the size of the problem but leads to a dense system matrix. A tolerable memory consumption and numerical complexity were achieved by applying an iterative solver, accompanied by an effective matrix-vector multiplication operation, based on the fast Fourier transform (FFT). We demonstrate that, the IE system matrix is better conditioned than that of the finite-difference (FD) method, and discuss its relation to a specially preconditioned FD matrix. We considered several methods of matrix-vector multiplication for the free-space and layered host models. The developed algorithm and computer code were benchmarked against the FD time-domain solution. It was demonstrated that, the method could accurately calculate the seismic field for the models with sharp material boundaries and a point source and receiver located close to the free surface. We used OpenMP to speed up the matrix-vector multiplication, while MPI was used to speed up the solution of the system equations, and also for parallelizing across multiple sources. The practical examples and efficiency tests are presented as well. [ABSTRACT FROM AUTHOR]

A full-wave integral equation scheme for modeling resonant coils applied in wireless power transfer systems is presented. An A-\Phi formulation is applied with current and charge densities on the wire surface as unknowns. The method overcomes the limitation of the “thin-wire approximation” as it enables the unknowns to vary on the wire surface. Thus, proximity effects (that typically emerge when modeling dense windings) are taken into account. The numerical implementation of the formulation has smaller computation cost than, for example, finite element methods. The proposed scheme is tested against closed-form solutions and alternative simulations. [ABSTRACT FROM AUTHOR]

This study is concerned with the dwell‐time stability for impulsive systems under periodic or aperiodic impulses. A Lyapunov‐like functional approach is established to study the stability for impulsive systems. The Lyapunov‐like functional is time‐varying and decreasing but is not imposed definite positive nor continuous. A specific Lyapunov‐like functional is constructed by introducing the integral of state together with the cross‐terms of the integral and impulsive states. A tight bounding is obtained for the derivative of this functional with the help of the improved Jensen inequality reported recently and the integral equation of the impulsive system. On the basis of the Lyapunov‐like functional approach, new dwell‐time‐dependent stability results with ranged dwell‐time, maximal dwell‐time and minimal dwell‐time are derived for periodic or aperiodic impulsive systems. The stability results have less conservatism than some existing ones, which are illustrated by numerical examples. [ABSTRACT FROM AUTHOR]

We consider some classes of functional equations posed in PB-spaces, for which we establish existence and uniqueness of solutions that belong to a cone. An application to integral equations is presented. [ABSTRACT FROM AUTHOR]

In this paper the set of trajectories of the control system is investigated. It is assumed that the behavior of the control system is described by a Volterra integral equation which is nonlinear with respect to the state vector and is affine with respect to the control vector, and the control functions have an integral constraint. An approximation of the set of trajectories by the set which consists of a finite number of trajectories is given. The Hausdorff distance between the set of trajectories of the system and the set, consisting of a finite number of trajectories is evaluated. [ABSTRACT FROM AUTHOR]

The third article of this series continues to deal with the calculation of the aerodynamic unsteady forces on lifting surfaces. Here we present how the theory of oscillating wing in subsonic flow can be applied to the aerodynamic response to certain kinds of wing motions or gusts. [ABSTRACT FROM AUTHOR]

Solving electromagnetic (EM) problems with thin conducting objects by integral equation approach could encounter some unfavorable factors. The individual electric field integral equation (EFIE) and magnetic field integral equation (MFIE) may deteriorate the conditioning of matrix equations due to their degeneration when the thickness reduces. Also, there are more evaluations of near-singular integrals in filling the impedance matrix because the near interactions between observation points and source patches are common. In addition, many triangular meshes could have a high aspect ratio owing to the small thickness and this will present a difficulty for the accurate evaluation of self- and near-interaction elements. Aiming to these factors, we use the combined field integral equation (CFIE) as a governing equation and develop an efficient Nyström solver for the problems based on a singularity treatment technique without subdividing triangular patches. Typical numerical examples are presented to demonstrate its robustness. [ABSTRACT FROM PUBLISHER]

We investigate an integral equation with Bessel potential in ℝ n+ and prove that every positive solution of the integral equation is rotationally symmetric about some line parallel to the -axis. Furthermore, we consider an overdetermined problem of the same integral equation in a cylinder type domain and obtain the symmetry of both domains and solutions, where is a bounded domain with . [ABSTRACT FROM AUTHOR]

We investigate an integral equation with Bessel potential in ℝ n+ and prove that every positive solution of the integral equation is rotationally symmetric about some line parallel to the -axis. Furthermore, we consider an overdetermined problem of the same integral equation in a cylinder type domain and obtain the symmetry of both domains and solutions, where is a bounded domain with . [ABSTRACT FROM AUTHOR]

The purpose of this article is to give the intelligible procedure for undergraduate students to grasp proof of the fact that the magnetic field outside the hollow superconducting sphere (superconducting shell) coincides with the field of a point magnetic dipole both when an uniform external magnetic field is applied as when a ferromagnetic sphere is located at the shell's geometric center. The proof is based on the London's equation transformation to an integral equation for the vector potential of system. The integral equation may be solved completely in case of the solid sphere. [ABSTRACT FROM AUTHOR]

In this paper we deal with an M/G/1 vacation system with the sojourn time (wait plus service) limit and two typical vacation rules, i.e. multiple and single vacation rules. Using the level crossing approach, we derive recursive equations for the steady-state distributions of the virtual waiting times in M/G/1 vacation systems with a general vacation time and two vacation rules. [ABSTRACT FROM AUTHOR]

In this paper, we study the properties of the positive solutions of a nonlinear integral system involving Wolff potentials: {u1 = Wβ,γ(f1(u)) um = Wβ,γ(fm(u)), where u = (u1, … , um) and Wβ,γ(f)(x) = ∫ ∞ 0 [ ∫Bt(x) f(y)dy/tn-βγ ] 1/γ-1 dt/t with 1 < γ < 2 and n > βγ. First, we estimate the decay rate of the positive solutions at infinity. Based on this, we prove radial symmetry and monotonicity for those solutions by the refined method of moving planes in integral forms, which was established by Chen, Li and Ou. Since the Kelvin transform cannot be used in such a Wolff type system, we have to find a new technique to study the asymptotic estimate, which is essential when we move the planes. [ABSTRACT FROM AUTHOR]

In this paper we deal with an M/G/1 vacation system with the sojourn time (wait plus service) limit and two typical vacation rules, i.e. multiple and single vacation rules. Using the level crossing approach, explicit expressions for the steady-state distributions of the virtual waiting times are obtained in vacation systems with exponential and constant service times, a general vacation time, and two vacation rules. [ABSTRACT FROM AUTHOR]

In this article, we prove the existence of positive nondecreasing solutions for a multi-term fractional-order functional differential equations. We consider Cauchy boundary problems with: nonlocal conditions, two-point boundary conditions, integral conditions, and deviated arguments. [ABSTRACT FROM AUTHOR]

The quasi-Green's function method is used to solve the free vibration problem of clamped thin plates on the Winkler foundation. Quasi-Green's function is established by the fundamental solution and the boundary equation of the problem. The function satisfies the homogeneous boundary condition of the problem. The mode-shape differential equation of the free vibration problem of clamped thin plates on the Winkler foundation is reduced to the Fredholm integral equation of the second kind by Green's formula. The irregularity of the kernel of the integral equation is overcome by choosing a suitable form of the normalized boundary equation. The numerical results show the high accuracy of the proposed method. [ABSTRACT FROM AUTHOR]

We consider the problem to invert an integral equation obtained from integral geometry. We apply a consistencymethodsuggestedbytheauthortosolvetheproblemandfindarepresentationforthegeneratingdensityofcentrally symmetrical convex bodies. Finally, we check the representation. [ABSTRACT FROM AUTHOR]

Pocklington's model consists in a one-dimensional integral equation relating the current at the surface of a straight finite wire to the tangential trace of an incident electromagnetic field. It is a simplification of the more usual single layer potential equation posed on a two-dimensional surface. We are interested in estimating the error between the solution of the exact integral equation and the solution of Pocklington's model. We address this problem for the model case of acoustics in a smooth geometry using results of asymptotic analysis. [ABSTRACT FROM AUTHOR]

It is well known that the value of an American option can be expressed as the sum of the corresponding European option and a premium, which reflects the additional right of early exercise. Based on this expression, it is possible to derive an integral equation for the early-exercise curve. Because the early-exercise curve is not sufficiently smooth at expiry, an ad hoc Nystrom discretization of high order for solving the integral equation is not guaranteed. In this paper, we present a Nystrom-type discretization, which uses an adequate integral transformation to circumvent the non-sufficient smoothness at expiry and results in a method of second order. [ABSTRACT FROM AUTHOR]

Exact solutions have been obtained for relativistic one-dimensional integral equations that describe the scattering of two particles with potentials of the “delta function n-th derivative” type for n = 1, 2, 3. Based on the solutions, the transmission and reflection coefficients have been found and some their properties have been investigated. [ABSTRACT FROM AUTHOR]

In this paper, we discuss the numerical simulation for a class of constrained optimal control problems governed by integral equations. The Galerkin method is used for the approximation of the problem. A priori error estimates and a superconvergence analysis for the approximation scheme are presented. Based on the results of the superconvergence analysis, a recovery type a posteriori error estimator is provided, which can be used for adaptive mesh refinement. [ABSTRACT FROM AUTHOR]

Abstract: In a piled raft, the length and arrangement of piles has a significant effect on the stresses and deflections of the raft. The use of piles with different dimensions and properties below a raft is an innovative concept and can optimize the design of a piled raft. In this study, an integral equation method with a fictitious pile model was adopted to analyze the piled raft foundation with dissimilar piles. The Fredholm integral equations of the second kind were obtained for this problem. The loads shared by piles and subsoil, the load transfer, and the settlement of the piled raft were obtained using numerical calculation. The results from the present method were compared with those in the literature. An optimization technique was introduced to design piled rafts with dissimilar piles. The stiffening effect of piles on the surrounding soil is also discussed as compared the conventional interaction factor approach. [Copyright &y& Elsevier]

Abstract: In this work, a functional approximation method for calculating the linear functional of the solution of second-kind Fredholm integral equations is developed. When the method is applied to the collocation method or to the multi-projection method, it generates approximations which exhibit superconvergence. [Copyright &y& Elsevier]

Using the mixed monotone method we establish existence and uniqueness results for a singular integral equation. The theorem obtained is very general and complements previous known results. [ABSTRACT FROM AUTHOR]

Abstract: We take a fairly comprehensive approach to the problem of solving elliptic partial differential equations numerically using integral equation methods on domains where the boundary has a large number of corners and branching points. Use of non-standard integral equations, graded meshes, interpolatory quadrature, and compressed inverse preconditioning are techniques that are explored, developed, mixed, and tested on some familiar problems in materials science. The recursive compressed inverse preconditioning, the major novelty of the paper, turns out to be particularly powerful and, when it applies, eliminates the need for mesh grading completely. In an electrostatic example for a multiphase granular material with about two thousand corners and triple junctions and a conductivity ratio between phases up to a million we compute a common functional of the solution with an estimated relative error of . In another example, five times as large but with a conductivity ratio of only a hundred, we achieve an estimated relative error of . [Copyright &y& Elsevier]

Multilayered power-ground (PG) planes are commonly used to supply power to circuits in high-speed electronic packages and printed circuit boards (PCBs). In this paper, we propose an efficient integral equation equivalent network method to simulate the interference produced by the rerouted return currents of signal traces inside such PG planes. The integral equation is created based on the geometrical features of the PG planes. Therefore, it could reduce the computing time and will be maintaining good accuracy. By discretizing the integral equation, a multiport equivalent network model is derived for each layer of the PG planes. Their [Z] matrices are then obtained. These [Z] matrices can be smoothly integrated with signal traces and other circuit models of lumped components mounted in the package and on the PCB, so that the system-level signal integrity and power integrity can be simulated efficiently. [ABSTRACT FROM AUTHOR]

Abstract: A direct function theoretic method is applied to solve a weakly singular integral equation whose kernel involves logarithmic singularity. This method avoids the occurrence of strong singularity. The solution of this integral equation is then applied to re-investigate the well known problem of water wave scattering by a partially immersed vertical barrier. [Copyright &y& Elsevier]

Abstract: Within the framework of two-dimensional linear elasticity, the unilateral frictionless contact between two conformal cylindrical surfaces is governed by an integral equation in which the first and second Dundurs’ constants are involved. In the case of elastic similarity characterized by the zero second Dundurs’ constant, the integral equation is considerably simplified so as to lend itself to a closed-form solution. However, in the case of elastic dissimilarity defined by the non-zero second Dundurs’ constant, the question of obtaining a closed-form solution to the integral equation is a much tougher one. Starting from the integral equation established by To et al. [To, Q.D., He Q.-C., Cossavella, M., Morcant, K., Panait, A., 2007. Closed-form solution for the contact problem of reinforced pin-loaded joints used in glass structures. Int. J. Solids Struct. 44, 3887–3903] for the conformal contact problem originating from a reinforced pin-loaded joint used in tempered glass structures, the present work proposes a new approximate analytical method to solve it in the case of elastic dissimilarity by minimizing an error function. The derived closed-form solution, valid not only for the conformal contact between a pin and an infinite holed plate but also for the one between a pin and a finite holed plate, is shown to be in very good agreement with available numerical results. [Copyright &y& Elsevier]

Abstract: We study the travelling wave problem with an asymmetric kernel J and a monostable nonlinearity. We prove the existence of a minimal speed, and under certain hypothesis the uniqueness of the profile for . For we show examples of nonuniqueness. [Copyright &y& Elsevier]

In this article we derive existence and comparison results for discontinuous non-absolute functional integral equations of Volterra type in an ordered Banach space which has a regular order cone. The obtained results are then applied to first-order impulsive differential equations. [ABSTRACT FROM AUTHOR]

Traditional control charts for process monitoring are based on taking samples of fixed size from the process using a fixed sampling interval. A recent development in control charts is the use of adaptive control charts, i.e. the variable sampling interval (VSI) and variable sampling size charts. This paper extends this idea to the autocorrelated process. We consider a time series model which is a first-order autoregressive process plus a random error. With variable intervals, the sampling time may be inconvenient, so using only two intervals, referred to as ‘variable sampling interval at fix times’ makes the method easier to use in practice. The sampling rate can also be adjusted by the number of samples collected, VSRFT, for ‘variable sampling rate at fixed times’. We study what we call ‘variable sampling at fixed times’, VSFT, which includes both VSIFT and VSRFT schemes, using a Markov chain model and integral equations. We show that our methods detect process shifts faster, on average, than fixed sampling X-bar charts, and at least comparable detection ability with the less practical VSI charts. Copyright © 2007 John Wiley & Sons, Ltd. [ABSTRACT FROM AUTHOR]

A skeletal muscle is composed of motor units, each consisting of a motoneuron and the muscle fibers it innervates. The input to the motor units is formed of electrical signals coming from higher motor centers and propagated to the motoneurons along a network of nerve fibers. Because of its complexity, this network still escapes actual direct observations. The present model describes the steady state activation of a muscle, i.e., of its motor units. It incorporates the network as an unknown quantity and, given the latter, predicts the input-force relation (activation curve) of the muscle. Conversely, given a suitable activation curve, our model enables the recovery of the network. This step is performed by using experimental data about the activation curve, and the whole activation process of a muscle can then be theoretically investigated. In this way, this approach provides a link between the macroscopic (activation curve) and microscopic (network) levels. From a mathematical viewpoint, solving the preceding inverse problem is equivalent to solving an integral equation of a new type. [ABSTRACT FROM AUTHOR]

A system of difference equations of the first order with meromorphic coefficients (not necessary periodic ones) subject to certain conditions of symmetry is analysed. These conditions arise in model problems of diffraction theory. A method for the constructive solution of the system of difference equations is proposed. It consists of three steps. First, it requires factorization of a certain function. Then, scalar integral equations with the same kernel and different right-hand sides should be solved. The kernel of the equations has a fixed singularity, and the solution belongs to a class of functions with a power singularity. Finally, arbitrary constants are fixed from some conditions which guarantee the equivalence of the original system of difference equations and the integral equations. The method is illustrated by solving a model electromagnetic problem of a plane wave diffracted from an anisotropic impedance half-plane at oblique incidence. [ABSTRACT FROM PUBLISHER]

The internal resonance problem of integral equations is a problem that has plagued solutions of scalar and vector integral equations. A lucid way to explain the occurrence of the internal resonance problem for integral equations of scattering is given in this paper. The physical insight is gotten by performing Gedanken experiments for MFIE for PEC, and for penetrable scatterers when EFIE and MFIE alone are applied. These proofs provide with physical clarity the reasons of the internal resonance problem, as well as the physical character of the internal resonance problem. The connection of the uniqueness of CFIE and the cavity resonance problem is reported. [ABSTRACT FROM AUTHOR]

Abstract: This article in devoted to the study of the nonlocal dispersal equation and its stationary counterpart. We prove global existence for the initial value problem, and under suitable hypothesis on g and J, we prove that positive bounded stationary solutions exist. We also analyze the asymptotic behavior of the finite mass solutions as , showing that they converge locally to zero. [Copyright &y& Elsevier]

The effects of introducing rational quadrature into a recently developed algorithm for the computation of the stress field in edge-cracked specimens are studied. The algorithm is based on an integral equation of the second kind which is solved using a Nyström method. Rational quadrature can handle the presence of corners and triple-junctions in a more accurate manner than can polynomial quadrature. A preconditioner is also included in the scheme. The rational quadrature together with the preconditioner results in a scheme that reduces the number of discretization points needed for a certain accuracy by up to 70% and the number of iterations needed by an iterative solver by up to 50%, compared to a scheme using only polynomial quadrature. For validation, several setups with a single edge crack are studied. Larger setups containing up to 1500 edge cracks are also investigated. Copyright © 2006 John Wiley & Sons, Ltd. [ABSTRACT FROM AUTHOR]

In this paper, several integral equations are solved by He’s variational iteration method. Comparison with exact solution shows that the method is very effective and convenient for solving integral equations. [Copyright &y& Elsevier]

Abstract: In this paper we investigate the exponential dichotomy of linear skew-product semiflows over semiflows by considering the operators generated by the integral equation related to strongly continuous cocycles over metric spaces acting on Banach bundles. We characterize the existence of exponential dichotomy by properties of these operators and use this characterization to prove the robustness of exponential dichotomy. [Copyright &y& Elsevier]

Abstract: In this paper first, Fredholm integral equation of the first kind is introduced. Then we decide to solve this kind of equations by projection methods such as Galerkin and collocation methods. Then we use Haar Wavelet as a base function to estimate the solution of the integral equation of the first kind. Finally by some numerical examples the efficiency of these methods are discussed. [Copyright &y& Elsevier]

Abstract: Finding a formulation for electromagnetic scattering of surfaces which is both well-posed and produces a well-conditioned linear system is still a challenging problem. We here propose one such formulation valid in the high-frequency regime. The mathematical analysis is provided and numerical results on rather complex geometries show the performance of the method. [Copyright &y& Elsevier]