Search

There is an inaccurate formula in Huang et al. (1996). In fact, a substantial term is missing in their equation (14) for computing the value of an important option hedging parameter, i.e., the vega. We fix it in this note by providing its correct form and characterizing an associated (new) integral equation. Some related explanations and arguments are also corrected. [ABSTRACT FROM AUTHOR]

We build a numerical approximation method, for Fredholm integral equation solution of the second type. This method is based on the regularization by convolution and Fourier series expansion. It provides a better convergence order. [ABSTRACT FROM AUTHOR]

Consider the scattering of long ocean tidal waves by an island taking into account the influence of daily rotation of the Earth, which is modeled by an exterior boundary value problem for the two-dimensional Helmholtz equation with generalized oblique derivative boundary condition. In this paper, we are concerned with a corresponding inverse scattering problem which is to reconstruct the unknown obstacle (island) from the far-field data. After proving the unique solvability of the direct scattering problem in a suitable function space required for our inverse scattering problem, we establish the linear sampling method (LSM) for reconstructing the boundary of the obstacle from the far-field data. To clarify the validity of such a sampling-type method which essentially depends on the solvability of an interior boundary value problem, we show that, except a discrete set of wave numbers, such an interior problem has a unique solution. Finally, some numerical examples are presented to demonstrate the efficiency of the reconstruction scheme. [ABSTRACT FROM AUTHOR]

This work is to propose high asymptotic order methods for highly oscillatory Volterra integral equations. According to the error of the Filon quadrature method, the piecewise Hermite collocation method is considered. For the computation, the highly oscillatory integrals in the collocation equations are treated efficiently. Then, both the classical order and asymptotic order are analyzed in detail with the help of some estimates on highly oscillatory integrals. At last, some numerical examples are provided to verify the sharpness of the estimate in the final part. [ABSTRACT FROM AUTHOR]

• Wertheim's thermodynamic perturbation theory were applied to the rose model. • Liquid part of phase diagram were calculated. • Two critical points are observed. Monte Carlo simulations and Wertheim's thermodynamic perturbation theory (TPT) are used to predict the phase diagram and percolation curve for the simple two-dimensional rose model of water. In the rose model of water, the water molecules are modelled as two-dimensional Lennard-Jones disks, with additional rose potentials for orientation dependent pairwise interactions that mimic formation of hydrogen bonds. Modifying both the shape and range of a 3-petal rose function, it was constructed an efficient and dynamical mimic of the 2D Mercedes Benz (MB) water model and experimental water. The liquid part of the phase space is explored using grand canonical Monte Carlo simulations and two versions of Wertheim's TPT for associative fluids. We find that the theory reproduces well the physical properties of hot water but is less successful at capturing the more structured hydrogen bonding that occurs in cold water. In addition to reporting the phase diagram and percolation curve of the model, it is shown that the improved TPT predicts the phase diagram rather well, while the standard one predicts a phase transition at lower temperatures. For the percolation line, both versions have problems predicting the correct position of the line at high temperatures. [ABSTRACT FROM AUTHOR]

In this study, a novel integral effective medium approach (IEMA) to obtain the complex effective permittivity and permeability tensors of 3-D metal-dielectric composite is developed. An infinite isotropic homogenous dielectric medium with periodically imbedded spherical inclusions with spherical inhomogeneity is considered here as an artificial dielectric in subwavelength. Within full-scattering theory, it is shown that such composite belongs to a general class of metamaterials with spherical inclusions. The obtained expressions for the elements of the effective tensors are valid in the entire subwavelength range. In order to test the proposed IEMA, the problem for metallic spherical particles coated by a layer of dielectric is solved analytically in greater detail by using the approach proposed earlier by the first author of the study. We were able to show that a metal-dielectric composite/metamaterial with spherical inhomogeneous inclusions can be considered as a quasi-periodic artificial crystal with a tunable band gap in the subwavelength range. In certain sub-ranges in subwavelength, such crystals can exhibit the properties of homogeneous ferrite material. [ABSTRACT FROM AUTHOR]

In this paper, we describe a Nyström integration method for the integral operator T which is the normal derivative of the double-layer potential arising in problems of two-dimensional acoustic scattering by infinite rough interfaces. The hypersingular kernel and unbounded integral interval of T are the key difficulties. By using a mollifier, we separately deal with these two difficulties and propose its Nyström integration method. Furthermore, we establish convergence of the method. Finally, we apply the method to the scattering problem by infinite rough interfaces and carry out some numerical experiments to show the validity. [ABSTRACT FROM AUTHOR]

We show that, by correctly selecting the probability distribution function p ( s ) for a particle’s distance-to-collision, the nonclassical diffusion equation can be represented exactly by the nonclassical linear Boltzmann equation for an infinite homogeneous medium. This choice of p ( s ) preserves the true mean-squared free path of the system, which sheds new light on the results obtained in previous work. [ABSTRACT FROM AUTHOR]

An inverse coefficient problem of thermal conductivity for a functionally graded hollow cylinder is considered. After applying the Laplace transform, the direct thermal conductivity problem is solved by using two methods: (1) based on a reduction to the Fredholm integral equation of the 2nd kind; (2) by means of the Galerkin method. A comparison of the direct problem solving techniques is provided. The nonlinear inverse problem is solved on the basis of an iterative process; at every step of the latter the linear Fredholm integral equation of the 1st kind is solved. Results of the computational experiments on a reconstruction of variation laws of thermal conductivity and specific volumetric heat capacity are presented. [ABSTRACT FROM AUTHOR]

Absorption spectroscopy is an advanced tool for flow diagnostics in measuring multiple parameters of species. Such kinds of problems can be modeled by some integral equations with known kernel, aiming to the determination of the integrands from their integration values along all possible paths of injected lasers. This paper considers the parameters detection problems in combustion process, with the purpose of recovering the gas temperature and the concentration of burned gas simultaneously using injected lasers along two directions with multiple frequencies. After establishing the nonlinear integral equations describing the energy absorption process, this ill-posed model is transformed into a nonlinear optimization problem with some penalty terms. Then we present an alternative iteration scheme (AIS) to solve this problem. The convergence of the iterative sequence for AIS algorithm together with the estimate on the value of cost functional is established, ensuring that AIS can indeed generate a satisfactory approximate solution to the original optimization problem. Numerical implementations using simulant data are presented to show the validity of the proposed scheme. [ABSTRACT FROM AUTHOR]

In this paper we obtain some equivalences between cyclic contractions and non-cyclic contractions in the framework of b -metric spaces. Our results improve and complement several recent fixed point results for cyclic contractions in b -metric spaces established by George et al. (2015) and Nashine et al. (2014). Moreover, all the results are with much shorter proofs. In addition, an application to integral equations is given to illustrate the usability of the obtained results. [ABSTRACT FROM AUTHOR]

This paper deals with a new approach to study the nonlinear inviscid flow over arbitrary bottom topography. The problem is formulated as a nonlinear boundary value problem which is reduced to a Dirichlet problem using certain transformations. The Dirichlet problem is solved by applying Plemelj–Sokhotski formulae and it is noticed that the solution of the Dirichlet problem depends on the solution of a coupled Fredholm integral equation of the second kind. These integral equations are solved numerically by using a modified method. The free-surface profile which is unknown at the outset is determined. Different kinds of bottom topographies are considered here to study the influence of bottom topography on the free-surface profile. The effects of the Froude number and the arbitrary bottom topography on the free-surface profile are demonstrated in graphical forms for the subcritical flow. Further, the nonlinear results are validated with the results available in the literature and compared with the results obtained by using linear theory. [ABSTRACT FROM AUTHOR]

In this paper, an integral equation approach is adopted to price American-style down-and-out calls. Instead of using the probability theory as used in the literature, we use the continuous Fourier sine transform to solve the partial differential equation system governing the option prices. As a way of validating our approach, we show that the “early exercise premium representation” for American-style down-and-out calls without rebate can be re-derived by using our approach. We then examine the case that time-dependent rebates are included in the contract of American-style down-and-out calls. As a result, a more general integral representation for the price of an American-style down-and-out call, with the presence of an extra term associated with the rebate, is obtained. Our numerical method based on the newly-derived integral representation appears to be efficient in computing the price and the hedging parameters for American-style down-and-out calls with rebates. In addition, significant effects of rebates on the option prices and the optimal exercise boundaries are illustrated through selected numerical results. [ABSTRACT FROM AUTHOR]

Many geophysical computational problems can be referred to as “embarrassingly parallel”. Parallel computing utilises linked CPU cores to solve computational problems. We create a “macro” parallelisation method that rapidly recovers solutions to large scale electromagnetic forward and inverse modelling problems. The method involves software operating above a generic electromagnetic data structure. Two examples are provided. The first example quantifies the reduction in computational time where macro-parallelisation is applied to forward modelling of data generated during synthetic marine controlled source electromagnetic surveys. In the second numerical experiment we apply macro-parallelisation to recover the subsurface conductivity distribution from a large airborne transient electromagnetic survey spanning more than 2000 km 2 . The computation time for inverting 98 thousand soundings with a serial batch approach on an i7 with a single thread was 65 h. Computational time from inverting 98 thousand soundings on a single thread of a standard i7 processor was 65 h. A 1700 times improvement in computation time was achieved through macro-parallelisation across just 350 cores of a Cray XC30 Supercomputer. Inversion of data for the full AEM survey took just 135 s. Parallel computing is rapidly becoming an essential for geophysicists. We provide description, sequence diagrams, pseudo-code and examples to illustrate its implementation. In summary we present applied parallelisation for the masses. [ABSTRACT FROM AUTHOR]

Transient dynamic stresses around three stacked parallel cracks in an infinite elastic plate are estimated for an incident impact stress wave impinging normal to the cracks. Using Fourier and Laplace transform techniques, the boundary conditions are reduced to six simultaneous integral equations in the Laplace domain. The differences in the displacements inside the cracks are expanded in a series of functions that have zero value outside the cracks. The Schmidt method is used to solve the unknown coefficients in the series such that the conditions inside the cracks are satisfied. The stress intensity factors are defined in the Laplace domain, and these are inverted using the numerical method. The stress intensity factors are calculated numerically for some crack configurations. [ABSTRACT FROM AUTHOR]

We discuss the accurate and efficient implementation of hp -BEM for the Laplace operator in two dimensions. Using Legendre polynomials and their antiderivatives as local bases for the discrete ansatz spaces, we are able to reduce both the evaluation of potentials and the computation of Galerkin entries to the evaluation of basic integrals. For the computation of these integrals we derive recurrence relations and discuss their accurate evaluation. Our implementation of p - and hp -BEM produces accurate results even for large polynomial degrees ( p > 1000 ) while still being efficient. While this work only treats Symm's integral equation for the Laplace operator in 2D, our approach can be used to solve Symm's, hypersingular and mixed integral equations for Laplace, Lamé and Stokes problems in two dimensions. [ABSTRACT FROM AUTHOR]

In the present paper there is proposed an analytical approach to study vibration of a rectangular elastic wing in the stationary stream of non-viscous fluid. We first develop a basic two-dimensional integral equation. Then a series expansion along the short coordinate is applied. This reduces the problem to an infinite set of one-dimensional integral equations which is studied asymptotically with respect to the large aspect ratio parameter. An example of optimization of thickness of the wing is demonstrated, to test the efficiency of the proposed method in applications. [ABSTRACT FROM AUTHOR]

The differential transform method is extended to solve the Cauchy type singular integral equations (CSIEs) over a finite interval. New theorems for transformation of Cauchy singular integrals are given with proofs. Approximate solutions of CSIEs with two types of kernels, Degenerate and convolution, are obtained. The system of linear equations for characteristic equation is solved analytically. Numerical results are shown to illustrate the efficiency and accuracy of the present method. [ABSTRACT FROM AUTHOR]

The goal of this work is to reduce the cost of computing the coefficients in the Karhunen–Loève (KL) expansion. The KL expansion serves as a useful and efficient tool for discretizing second-order stochastic processes with known covariance function. Its applications in engineering mechanics include discretizing random field models for elastic moduli, fluid properties, and structural response. The main computational cost of finding the coefficients of this expansion arises from numerically solving an integral eigenvalue problem with the covariance function as the integration kernel. Mathematically this is a homogeneous Fredholm equation of second type. One widely used method for solving this integral eigenvalue problem is to use finite element (FE) bases for discretizing the eigenfunctions, followed by a Galerkin projection. This method is computationally expensive. In the current work it is first shown that the shape of the physical domain in a random field does not affect the realizations of the field estimated using KL expansion, although the individual KL terms are affected. Based on this domain independence property, a numerical integration based scheme accompanied by a modification of the domain, is proposed. In addition to presenting mathematical arguments to establish the domain independence, numerical studies are also conducted to demonstrate and test the proposed method. Numerically it is demonstrated that compared to the Galerkin method the computational speed gain in the proposed method is of three to four orders of magnitude for a two dimensional example, and of one to two orders of magnitude for a three dimensional example, while retaining the same level of accuracy. It is also shown that for separable covariance kernels a further cost reduction of three to four orders of magnitude can be achieved. Both normal and lognormal fields are considered in the numerical studies. [ABSTRACT FROM AUTHOR]

A small-angle X-ray scattering has been used to probe protein–protein interaction in solution. Conventional methods need to input modeled potentials with variable/invariable parameters to reproduce the experimental structure factor. In the present study, a model-free method for extracting the excess part of effective interaction potential between protein molecules in solutions over an introduced hard-sphere potential by using experimental data of small-angle X-ray scattering is presented on the basis of liquid-state integral equation theory. The reliability of the model-free method is tested by the application to experimentally derived structure factors for dense lysozyme solutions with different solution conditions [Javid et al., Phys. Rev. Lett. 99 , 028101 (2007), Schroer et al., Phys. Rev. Lett. 106 , 178102 (2011)]. The structure factors calculated from the model-free method agree well with the experimental ones. The model-free method provides the following picture of the lysozyme solution: these are the stabilization of contact-pair configurations, large activation barrier against their formations, and screened Coulomb repulsion between the charged proteins. In addition, the model-free method will be useful to verify whether or not a model for colloidal system is acceptable to describing protein–protein interaction. [ABSTRACT FROM AUTHOR]

In this paper, based on the principle of virtual work, we formulate the equivalent eigenstrain approach for inhomogeneous inclusions. It allows calculating the elastic deformation of an arbitrarily connected and shaped inhomogeneous inclusion, by replacing it with an equivalent homogeneous inclusion problem, whose eigenstrain distribution is determined by an integral equation. The equivalent homogeneous inclusion problem has an explicit solution in terms of a definite integral. The approach allows solving the problems about inclusions of arbitrary shape, multiple inclusion problems, and lends itself to residual stress analysis in non-uniform, heterogeneous media. The fundamental formulation introduced here will find application in the mechanics of composites, inclusions, phase transformation analysis, plasticity, fracture mechanics, etc. [ABSTRACT FROM AUTHOR]

In this study, the frictional contact with partial slide between two dissimilar elastic cylinders is considered. According to the Spence׳s self-similarity condition, a system of singular integral equations is constructed with respect to the normal pressure and the shear traction in the contacting area. Based on the Goodman׳s hypothesis, the preceding system is uncoupled. From this, the tangential load in the central sticking zone is possible to be obtained analytically by means of the theory on the singular integral equation. Besides, a nonlinear equation in regard to the ratio of the adhesive and slip zone sizes is derived on the basis of the continuity of the tangential load. The sticking zone size can thus be determined by solving the nonlinear equation mentioned above iteratively. The problem in question is additionally solved by utilizing numerical method to make verification and validation of the theory and the related prevision found in the present paper. Numerical examples are provided to instantiate the theroy and method proposed. [ABSTRACT FROM AUTHOR]

• An analytical solution for a piezoelectric rectangular plane made of piezoelectric materials weakened by multiple cracks and cavities is presented. • The plane is under combined in-plane electric displacement and anti-plane shear stress. • Multiple arbitrarily oriented curved cracks and cavities in the piezoelectric plane are considered. • Stress intensity factors at the crack tips and hoop stress around the cavities are obtained. • The plastic zone in the vicinity of crack tips is determined using Von Mises yield criterion. This study presents an analytical model for a piezoelectric rectangular plane weakened by multiple cracks and cavities, under in-plane electric displacement and anti-plane shear stress. The defects are considered either electrically permeable or impermeable. First, the piezoelectric rectangular plane is weakened by a Volterra-type screw dislocation. The electric and stress displacement fields of the domain under consideration are determined using finite Fourier transform. Then, the problem is reduced into a set of Cauchy integral equations in the piezoelectric rectangular plane using the distributed dislocation approach. The solution to these integral equations determines electric displacement and stress intensity factors and hoop stress around cavities in the piezoelectric rectangular plane. Also, the boundary of the plastic zone is found using the stress field in the vicinity of crack tips and the Von Mises yield criterion. Finally, multiple numerical results are provided to illustrate the capability of the dislocation method in handling different cases of crack and cavity configurations and arrangements. [ABSTRACT FROM AUTHOR]

The aim of this paper is to establish the existence and uniqueness of the common solution for the system of nonlinear Fredholm integral equations, nonlinear Volterra integral equations and nonlinear fractional differential equations using the common fixed point results equipped with illustrative examples. Some common fixed point results satisfying the generalized contraction condition involving w -distance and weak altering distance functions are proved. Then, an example is provided to support the usability of our result along with numerical experiments. [ABSTRACT FROM AUTHOR]

In this paper, we use a modification of Krasnoselskii's fixed point theorem introduced by Burton (2002) (see [6] Theorem 3) to obtain stability results of the zero solution of the totally nonlinear neutral differential equations with functional delay x′(t)=-a(t)h(x(t-τ(t)))+d/dtQ(t,x(t-τ(t)))+G(t,x(t-τ(t))). The stability of the zero solution of this equation provided that h(0)=Q(t,0)=G(t,0,0)=0. The Caratheodory condition is used for the functions Q and G. [ABSTRACT FROM AUTHOR]

The presented paper deals with an approach to analytical periodic solution and to stability assessment of one-degree-of-freedom linear vibrating systems. It is supposed that these systems are excited by the time periodic force and contain time periodic stiffness. The periodic Green's function determined as a response to a Dirac chain of unit impulses repeating with period of excitation is used to transform the equation of motion into the Fredholm integral equation with degenerated kernel. If the Dirac chain is expressed as a Fourier series and a limited number of terms is taken into account, the solution of the integral equation can also be obtained in a series form. It has been found that the real eigenvalues of the system matrix determine the critical values of the fluctuation stiffness parameter. The values of this real parameter correspond to the borders of (in)stability in the plane given by the variation of the angle frequency and of the fluctuation stiffness parameter. Moreover, very interesting property of the system matrix was observed. The positive sign of the real valued determinant of the system matrix means the existence of periodic solution (system is stable). In the opposite case, the periodic solution does not exist (system is unstable). The verification of obtained results was performed on two case studies. The Floquet method was used to validate the stability assessment. Presented analytical periodic solution was compared with steady state obtained by the Runge-Kutta continuation. A very good agreement was achieved in both cases. [ABSTRACT FROM AUTHOR]

In this paper, authors demonstrate the efficiency of optimal homotopy asymptotic method (OHAM). This is done by solving nonlinear Volterra integral equation of first kind. OHAM is applied to Volterra integral equations which involves exponential, trigonometric function as their kernels. It is observed that solution obtained by OHAM is more accurate than existing techniques, which proves its validity and stability for solving Volterra integral equation of first kind. [ABSTRACT FROM AUTHOR]

Abstract: In the anti-plane problem about a high-frequency diffraction by an interface crack located between two different elastic materials we propose a new asymptotic approach, which reduces the problem to the Wiener–Hopf integral equations. The key point of the method is a factorization of the symbolic function which is performed in an efficient way. As a result, the leading asymptotic term is written out in an explicit analytical form. [Copyright &y& Elsevier]

Highlights: [•] Novel, nondestructive method to measure layered dielectric absorbers is presented. [•] Measurement results compare well with traditional, destructive approaches. [•] Valuable tool for design and evaluation of Salisbury-screen-like RF absorbers. [ABSTRACT FROM AUTHOR]

Abstract: Using Helmholtz’s wake model, we reduce the study of the free boundary flow past an obstacle consisting of an arc of circle to the investigation of a Hammerstein nonlinear integral equation depending on a real parameter . The papers dedicated to this problem investigated the case which corresponds to a convex obstacle with respect to the incoming fluid. Herein, we apply for the first time in the literature the arclength continuation method for the case corresponding to a concave arc of a circle. For the existence and the uniqueness of the solution was demonstrated, but for , depending on its value compared to the one of a turning point, the integral equation has either no solution or two distinct solutions corresponding to two different obstacles. We numerically calculate the free lines, the velocity field and the stream lines. A diagram of the drag coefficient versus the arc measure for both convex and concave obstacles suggests us to draw some conclusions concerning the optimization of the blades of a vertical axis (Savonius) wind turbine. [Copyright &y& Elsevier]

Abstract: In order to compute an approximate solution of a weakly singular integral equation, we first regularize the kernel and then truncate the associated Fourier series. Applications to Green and Abel operators are given. [Copyright &y& Elsevier]

Highlights: [•] Classical density functional theory for liquid water is formulated. [•] Triplet correlations and bridge functions are taken into account. [•] Factorization approximation for ternary direct correlation functions is employed. [•] Radial distribution functions for liquid water are calculated and compared with simulation results. [ABSTRACT FROM AUTHOR]

Abstract: By making use of asymptotic properties of nonoscillatory solutions, the oscillation behavior of solutions for the integro-dynamic equation and the integral equation on time scales is investigated. Easily verifiable sufficient conditions are established for the oscillation of all solutions. The results are new for both continuous and discrete cases. The paper is concluded by an open problem. [Copyright &y& Elsevier]

Abstract: In recent years, different fields of engineering have been increasingly incorporating functionally graded materials with variable physical properties that significantly improve a quality of elements of designs. The efficiency of practical application of thermoelastic inhomogeneous materials depends on knowledge of exact laws of heterogeneity, and to define them it is necessary to solve coefficient inverse problems of thermoelasticity. In the present research a scheme of solving the inverse problem for an inhomogeneous thermoelastic rod is presented. Two statements of the inverse problem are considered: in the Laplace transform space and in the actual space. The direct problem solving is reduced to a system of the Fredholm integral equations of the 2nd kind in the Laplace transform space and an inversion of the solutions obtained on the basis of the theory of residues. The inverse problem solving is reduced to an iterative procedure, at its each step it is necessary to solve the Fredholm integral equation of the 1st kind; to solve it the Tikhonov method is used. Specific examples of a reconstruction of variable characteristics required are given. [Copyright &y& Elsevier]

Abstract: In this paper, we consider a Sparre Andersen risk model perturbed by a Brownian motion, where the individual claim sizes are dependent on the interclaim times. We assume that dividends are paid off under a threshold strategy. Integral and integro-differential equations satisfied by the Gerber–Shiu functions are obtained, and a solution procedure is also proposed. [Copyright &y& Elsevier]