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Copyright of Frontiers of Information Technology & Electronic Engineering is the property of Springer Nature and its content may not be copied or emailed to multiple sites or posted to a listserv without the copyright holder's express written permission. However, users may print, download, or email articles for individual use. This abstract may be abridged. No warranty is given about the accuracy of the copy. Users should refer to the original published version of the material for the full abstract. (Copyright applies to all Abstracts.)

Based on the image method and addition theorem of spherical vector wave functions, an analytical solution of the multiple scattering by a buried medium-coated conducting sphere is proposed in this paper. An iterative process to obtain the scattered electromagnetic field is discussed on the basis of the continuous boundary condition in the plane boundary, the medium inner and the outer surface of a coated conducting sphere, respectively. Applying an image method and the addition theorem of spherical vector wave functions, the scattering electromagnetic fields by the plane in a local coordinate system can be transformed into the globe coordinate, and they can be regarded as the next incident electromagnetic fields to the buried medium-coated conducting sphere. This process does not end until the scattering electrical field on the plane boundary is accurate enough. Numerical results are given and compared with commercial software FEKO, they coincide enough; the calculation times of the present method are very short compared to those of the software FEKO, and some discussion is given at the end of this paper. [ABSTRACT FROM AUTHOR]

This work establishes the existence of addition theorems and double-angle formulas for C k real scalar functions. Moreover, we determine necessary and sufficient conditions for a bivariate function to be an addition formula for a C k real function. The double-angle formulas allow us to generate a duplication algorithm, which can be used as an alternative to the classical numerical methods to obtain an approximation for the solution of an ordinary differential equation. We demonstrate that this algorithm converges uniformly in any compact domain contained in the maximal domain of that solution. Finally, we carry out some numerical simulations showing a good performance of the duplication algorithm when compared with standard numerical methods. [ABSTRACT FROM AUTHOR]

Electronic states of a single electron in doubly eccentric cylindrical quantum wire are theoretically investigated in this paper. The motion of electron in quantum wire is free along axial direction in a cylindrical quantum wire and restricted in annular regions by three different parallel finite cylindrical barriers as soft wall confinement. The effective mass Schrödinger equation with effective mass boundary conditions is used to find energy eigenvalues and corresponding wavefunctions. Addition theorem for cylindrical Bessel functions is used to shift the origin for applying boundary conditions at different circular boundaries. Fourier expansion is applied after addition theorem to get wavefunctions in analytical form. A determinant equation is obtained as a result of applications of effective mass boundary conditions which roots gives energy of various electronic states. The lowest root gives ground state energy. The variation in ground state energy with eccentricity is obtained numerically and presented graphically. Electronic states in massive wall confinement and hard wall confinement is further obtained as limiting behavior of the states obtained in soft wall confinement. The knowledge of electronic states in such cylindrical hetrostructures semiconductor material can lead to improve the efficiency of many quantum devices. [ABSTRACT FROM AUTHOR]

The paper provides a way to model axially symmetric random fields defined over the two-dimensional unit sphere embedded in the three-dimensional Euclidean space. Specifically, our strategy is to integrate an isotropic random field on the sphere over longitudinal arcs with a given central angle. The resulting random field is shown to be axially symmetric and to have the arc central angle as a tuning parameter that allows for isotropy as well as for longitudinal independence as limit cases. We then consider multivariate longitudinally integrated random fields, having the same properties of axial symmetry and a tuning parameter (arc central angle) proper to each random field component. This construction allows for a unified framework for vector-valued random fields that can be geodesically isotropic, axially symmetric, or longitudinally independent. Additionally, all the components of the vector random field are allowed to be cross-correlated. We finally show how to simulate the proposed axially symmetric scalar and vector random fields through a computationally efficient algorithm that exactly reproduces the desired covariance structure and provides approximately Gaussian finite-dimensional distributions. [ABSTRACT FROM AUTHOR]

The paper tackles the problem of simulating isotropic vector-valued Gaussian random fields defined over the unit two-dimensional sphere embedded in the three-dimensional Euclidean space. Such random fields are used in different disciplines of the natural sciences to model observations located on the Earth or in the sky, or direction-dependent subsoil properties measured along borehole core samples. The simulation is obtained through a weighted sum of finitely many spherical harmonics with random degrees and orders, which allows accurately reproducing the desired multivariate covariance structure, a construction that can actually be generalized to the simulation of isotropic vector random fields on the d-dimensional sphere. The proposed algorithm is illustrated with the simulation of bivariate random fields whose covariances belong to the F , spectral Matérn and negative binomial classes of covariance functions on the two-dimensional sphere. [ABSTRACT FROM AUTHOR]

In this paper we strengthen the result of Fomin and Zelevinsky (2002) on the Laurent phenomenon for Somos-4 and Somos-5 sequences. [ABSTRACT FROM AUTHOR]

Three-dimensional time-harmonic acoustic multiple scattering problems are considered for a finite number of prolate and oblate spheroidal objects adjacent to flat surfaces. Wave propagation by spheroids is modelled by the method of separation of variables equipped with the addition theorems in the spheroidal coordinates. The effect of flat surfaces is accounted for by using the method of images; hence, the flat surfaces are of (semi-)infinite extent and perfectly reflecting: either rigid or pressure release. Wedge-shaped acoustic domains are constructed including half-space and right-angled corners with the wedge angle of |$\pi /n$| rad with positive integer |$n$|⁠. First, Euler angles are implemented to rotate image spheroids to realize the mirror reflection. Then, the 'image conditions' are developed to reduce the number of unknowns by expressing the unknown expansion coefficients of image-scattered fields in terms of real counterparts. Use of image conditions to 2D wedges, therefore, leads to the |$4n^2$| -fold reduction in the size of a matrix for direct solvers and |$2n$| -times faster computation than the approach without using them; for 3D wedges, the savings are |$16n^2$| -fold and |$4n$| -times, respectively. Multiple scattering models (MSMs) are also formulated for fluid, rigid and pressure-release spheroids under either plane- or spherical-wave incidence; novel addition theorems are also derived for spheroidal wavefunctions by using two rotations of spherical wavefunctions and a |$z$| -axis translation in-between, which is shown numerically more efficient than other addition theorems based on an arbitrary-direction translation and a single rotation. Finally, MSMs using image conditions are numerically validated by the boundary element method for a configuration populated with both prolate and oblate spheroids. [ABSTRACT FROM AUTHOR]

A novel domain decomposition procedure is presented to analyze the electromagnetic wave multiple scattering among separate PEC objects. The method is based on the equivalence principle algorithm (EPA) that transfers the primary unknowns on the objects to the unknowns on the equivalence surfaces. Each equivalence surface is considered to be a spherical surface encompassing a PEC object. Inside the equivalence spheres, the analysis is performed based on the Rao–Wilton–Glisson (RWG) basis functions where the electromagnetic interactions outside them are considered by means of the addition theorem for spherical wave harmonics (SWHs). The translation procedures are presented to translate the RWG basis functions to SWHs and vice versa. The reduction of unknowns in the presented method versus the conventional EPA (which uses translation operators among equivalence surfaces) shows its efficiency. Some numerical examples are presented to evaluate the efficacy of the proposed approach. The acceptable consistency among the results of the proposed method and the conventional EPA as well as the direct method of moments validates the proposed method. [ABSTRACT FROM AUTHOR]

Let g be a linear combination with quasipolynomial coefficients of shifts of the Jacobi theta function and its derivatives in the argument. All entire functions f: ℂ → ℂ satisfying f(x+y)g(x−y) = α1(x)β1(y)+· · ·+αr(x)βr(y) for some r ∈ ℕ and αj, βj: ℂ → ℂ are described. [ABSTRACT FROM AUTHOR]

Abstract: Coding representation of metamaterials builds up a bridge between the physical world and the digital world, making it possible to manipulate electromagnetic (EM) waves by digital coding sequences and reach field‐programmable metamaterials. Here, the coding space is extended to complex domain and proposed complex digital codes to provide closer essence of EM‐wave propagation. Based on the analytic geometry and complex variable functions, an addition theorem on complex coding is established, which reveals inherent connections among digital codes with different bits and enables all higher‐bit digital codes to be represented by the 1‐bit complex codes. According to the complex coding and addition theorem, multifunctional metamaterials can be directly designed and realized without considering mutual coupling. When two different coding patterns with different functions are added together via the addition theorem in complex form, the combined coding pattern will directly generate the two functions simultaneously without any perturbations. A series of realistic coding metasurfaces is presented to demonstrate the powerful and flexible performance of the complex coding and addition theorem for independent controls of EM waves to reach multiple functions. Good agreements between numerical simulations and experimental results prove the feasibility of the proposed concept and theorem in practical applications. [ABSTRACT FROM AUTHOR]

It is proved that if an entire function f: ℂ → ℂ satisfies an equation of the form α ( x) β ( y) + α ( x) β ( y) + α ( x) β ( y), x, y ∈ C, for some α , β : ℂ → ℂ and there exist no $${\widetilde \alpha _j}$$ and ˜ $${\widetilde \beta _j}$$ for which $$f\left( {x + y} \right)f\left( {x - y} \right) = {\overline \alpha _1}\left( x \right){\widetilde \beta _1}\left( y \right) + {\overline \alpha _2}\left( x \right){\widetilde \beta _2}\left( y \right)$$ , then f( z) = exp( Az + Bz + C) ∙ σ ( z - z ) ∙ σ ( z - z ), where Γ is a lattice in ℂ; σ is the Weierstrass sigma-function associated with Γ; A, B, C, z , z ∈ ℂ; and $${z_1} - {z_2} \notin \left( {\frac{1}{2}\Gamma } \right)\backslash \Gamma $$ . [ABSTRACT FROM AUTHOR]

Copyright of Applied Mathematics & Mechanics (1000-0887) is the property of Applied Mathematics & Mechanics and its content may not be copied or emailed to multiple sites or posted to a listserv without the copyright holder's express written permission. However, users may print, download, or email articles for individual use. This abstract may be abridged. No warranty is given about the accuracy of the copy. Users should refer to the original published version of the material for the full abstract. (Copyright applies to all Abstracts.)

A method is presented to analyze the maximum power transfer efficiency of a wireless power transfer system and its electromagnetic fields via spherical modes. The Z-parameter and Y-parameter for two coupled antennas are derived using the antenna scattering matrix and an addition theorem. In addition, formulas for calculating the maximum power transfer efficiency and optimum load impedance are presented. A formula is derived to calculate the electromagnetic field generated by a wireless power transfer system from the antenna scattering matrix. [ABSTRACT FROM PUBLISHER]

The radial Slater-type orbitals (STO) ${r^\mu }{e^{ - \alpha r}}$ can be simply obtained by repeated parametric differentiation of the Yukawa Potential $({e^{ - \alpha r}}/r)$ with respect to α. A new compact two-range addition theorem (AdT) for the STO is herein derived by explicit parametric differentiation of the well-known Yukawa AdT. The resulting addition formula is combined with the single-range AdT for solid spherical harmonics $({r^l}Y_l^m(\hat r))$ to present a new AdT for three-dimensional spherical coordinate STOs. We advance the proposition that this formula is 'canonical' in the same sense that the Laplace expansion of the Coulomb potential is considered canonical. We demonstrate how this procedure can be employed for all exponential-type orbitals. © 2012 Wiley Periodicals, Inc. [ABSTRACT FROM AUTHOR]

Considering the generalized Bessel functions satisfying a special ordinary differential equation of mth order, we derive some addition theorems and generating functions with the help of some algebra constructed for a group of first order partial differential operators grounding on the recurrence relations for these functions. [ABSTRACT FROM AUTHOR]

Starting from one-range addition theorems for Slater-type functions, which are expansion in terms of complete and orthonormal functions based on the generalized Laguerre polynomials, Guseinov constructed addition theorems that are expansions in terms of Slater-type functions with a common scaling parameter and integral principal quantum numbers. This was accomplished by expressing the complete and orthonormal Laguerre-type functions as finite linear combinations of Slater-type functions and by rearranging the order of the nested summations. Essentially, this corresponds to the transformation of a Laguerre expansion, which in general only converges in the mean, to a power series, which converges pointwise. Such a transformation is not necessarily legitimate, and this contribution discusses in detail the difference between truncated expansions and the infinite series that result in the absence of truncation. [ABSTRACT FROM AUTHOR]

An extended mode-based analysis for near-field coupled antennas is proposed. Based on this analysis, a method for estimating 3 dB bandwidth of near-field communication (NFC) systems with non-identical electrically small antennas is also proposed. The estimated results are in good agreement with the results from a full EM simulation. [ABSTRACT FROM PUBLISHER]

This letter proposes a new mode-based method for estimating the channel characteristics of a near-field multiple-input–multiple-output (MIMO). When an antenna array composed of a short electric dipole and a small solenoidal loop is used, a 2\,\times\,2 near-field MIMO can be effectively constructed according to the orthogonality of the TM10 and TE10 modes. By using the proposed method, the transmission characteristics of the MIMO and the mutual coupling effect at the antenna array can be easily calculated. In addition, the capacity of the MIMO can also be calculated by using the analysis results. [ABSTRACT FROM PUBLISHER]

A new method for estimating the 3 dB bandwidth of near-field communication (NFC) systems using identical electrically small antennas is proposed. The method is based on equivalent circuit representation using the addition theorem, an approach used in the analysis of coupled antennas, and the correction factor derived from antenna impedance characteristics. In addition, variation in the 3 dB bandwidth with respect to the relative position and orientation of the NFC system is investigated using the proposed method. [ABSTRACT FROM AUTHOR]

The optimum operating frequency of wireless power transfer is investigated for near-field coupled resonant small antennas. The existence of the frequency can be inferred from the equivalent circuit representation for coupled small antennas, based on mode-based analysis using the addition theorem, and the frequency dependence of the radiation efficiency. From the EM simulation results, it is demonstrated that there is an optimum operating frequency for maximum matched gain. In addition, it is shown that the optimum frequency can be accurately estimated using the addition theorem and the EM simulation results of a single antenna. [ABSTRACT FROM AUTHOR]

Based on equivalent magnetic frill array model and Galerkin's procedure, we present a simplified full-wave algorithm to characterize the propagation behavior and signal integrity of massive number of through silicon vias (TSV) for the 3-D system-in-package (SIP) and system-on-chip (SOC) applications. The proposed method employs the Fourier transform and takes advantage of circular cylindrical shapes with Bessel's functions and the addition theorem to solve the Helmholtz equations without resorting numerical discretization. As a result, it provides closed form solutions with high precision. Since the algorithm does not rely on numerically generated meshes, it gains one to two orders of magnitude in speed, compared to popular commercial software packages. Numerical examples demonstrate that the new method provides good agreement with the HFSS results. As the number of vias increases the new method gains more in both speed and accuracy. [ABSTRACT FROM AUTHOR]

Starting from the Rodrigues representation of polynomial solutions of the general hypergeometric-type differential equation complementary polynomials are constructed using a natural method. Among the key results is a generating function in closed form leading to short and transparent derivations of recursion relations and addition theorem. The complementary polynomials satisfy a hypergeometric-type differential equation themselves, have a three-term recursion among others and obey Rodrigues formulas. Applications to the classical polynomials are given. [ABSTRACT FROM AUTHOR]

Acoustic radiation from a spherical source, vibrating with an arbitrary, axisymmetric, time-harmonic surface velocity distribution, while immersed near a thermoviscous fluid sphere suspended in an unbounded viscous thermally conducting fluid medium is computed. The formulation utilizes the appropriate wave field expansions and boundary conditions along with the translational addition theorem for spherical wave functions to develop a closed-form solution in form of infinite series. The prime objective is to investigate the thermoviscous loss effects on acoustic radiation and its associated field quantities. The analytical results are illustrated with a numerical example in which the spherical source, that may vibrate either in a monopole-like or a dipole-like mode, is suspended in a thermoviscous fluid medium near an equal-sized viscous thermally conducting fluid sphere. To avoid numerical difficulties normally arising in process of solving thermoviscous radiation/scattering problems in the frequency range of interest, a basic multiple precision FORTRAN computation package was utilized in developing specialized codes for computing special mathematical functions including spherical Bessel functions of complex argument and performing large complex matrix manipulations on floating point numbers of arbitrarily high precision. The essential acoustic field quantities such as the modal acoustic radiation impedance load on the source, the radiated far-field pressure directivity pattern and the radiated on-axis pressure are evaluated and discussed for representative values of the parameters characterizing the system. Limiting cases are examined and excellent agreements with well known solutions are attained. [ABSTRACT FROM AUTHOR]

Scattering of elastic waves in unidirectional fiber-reinforced porous-matrix composites is studied using novel features of Biot classic model for dynamic poroelasticity. The method of separation of variables along with the appropriate wave field expansions, the pertinent boundary conditions, and the translational addition theorems for cylindrical wave functions are employed to develop a closed-form solution in form of infinite series. The analytical results are illustrated with numerical examples in which a pair of rigid or elastic fibers are insonified by a plane fast compressional or shear wave at end-on/broadside incidence. The effects of incident wave frequency, proximity of the two fibers, fiber material properties and angle of incidence on the far-field backscattered radial and shearing stress amplitudes are examined. Particular attention has been focused on multiple scattering interactions in addition to the slow wave coupling effects which is known to be the primary distinction of the scattering phenomenon in poroelasticity from the classical elastic case. Limiting cases are considered and fair agreements with well-known solutions are established. [ABSTRACT FROM AUTHOR]

In this paper, based on the theory of elastodynamics, the multiple scattering of elastic waves and dynamic stress in multiparticle reinforced composites is investigated, and the analytical solution of this problem is obtained. By using the wave function expansion method, the expressions of total wave fields in each medium are presented. The addition theorem of spherical Bessel functions is employed to accomplish the translation for different local coordinate systems. According to the continuous boundary conditions around the particles, the expanded mode coefficients are determined. As an example, the variation of dynamic stress concentration factors at the interface between the particles and the matrix under different parameters is analyzed. It can be seen from the results that when the incident frequency is different, the effect of the distance between the centers of the particles on the dynamic stress varies greatly. Only when the distance is greater than a certain number can its effect be ignored. When the distance is fixed, the effect of material properties on dynamic stress is also examined. [ABSTRACT FROM AUTHOR]

This study considers the most fundamental problem of 2-D acoustic scattering in fiber suspensions. It treats the interaction of a plane compressional sound wave with a cluster of two flexible fibers submerged in a boundless viscous fluid medium. The dynamic viscoelastic properties of the fibers and the viscosity of the surrounding fluid are rigorously taken into account in the solution of the problem. The translational addition theorem for cylindrical wave functions, the Havriliak-Negami model for viscoelastic material behaviors and the appropriate wave field expansions and the pertinent boundary conditions are employed to develop a closed-form solution in the form of an infinite series. The prime objectives are to investigate the influence of dynamic viscoelastic properties of fiber material as well as multiple scattering interaction effects on acoustic scattering and its associated quantities. The analytical results are illustrated with a numerical example in which two identical viscoelastic fibers are insonified by a plane sound wave at broadside/end-on incidence. The backscattering form function amplitude and the spatial distribution of the total acoustic pressure are numerically evaluated and discussed for representative values of the parameters characterizing the system. The effects of incident wave frequency, angle of incidence, material properties, and proximity of the two fibers are examined. A limiting case involving a pair of rigid cylinders in an ideal fluid is considered, and fair agreement with a well-known solution is established. [ABSTRACT FROM AUTHOR]

The far field characteristics are investigated for a circular cylinder with two infinite axial slots coated by an eccentric dielectric material. Radiations are determined by applying the boundary-value method to the cylindrical wave functions of the fields in the Fourier–Bessel series form. The addition theorem and the orthogonality of Bessel and trigonometric functions are employed to find an infinite series solution. Numerical and graphical results are obtained by shortening the infinite series produced in the solution to a finite number of terms and compared to other published data. [ABSTRACT FROM AUTHOR]

This paper presents an extension of a new approach to select the truncation number for translation operators in a 3D multilevel fast multipole algorithm (MLFMA). Although error is harder to control in 3D than in 2D problems, this recently developed new approach provides better error control in 3D problems over the excess bandwidth formula. © 2003 Wiley Periodicals, Inc. Microwave Opt Technol Lett 37: 184–188, 2003; Published online in Wiley InterScience (www.interscience.wiley.com). DOI 10.1002/mop.10862 [ABSTRACT FROM AUTHOR]

The addition theorem for a free-space scalar Green's function plays an important role in the fast multipole method (FMM). Therefore, both the accuracy and convergence are issues of concern in the code implementation of the FMM. In this paper, the addition theorem, when used in an unbounded Green's function, is numerically analyzed, and its accuracy is thus addressed and discussed. Specifically, the number of terms kept in the multipole expansion L is discussed in detail, and comparisons are made among the cases where difference parameters are used. A simple example applying the FMM to compute RCSs by a rectangular plate is given. © 2001 John Wiley & Sons, Inc. Microwave Opt Technol Lett 31: 439–442, 2001. [ABSTRACT FROM AUTHOR]

We have constructed Green's function to Stokes's boundary-value problem with the gravity data distributed over an ellipsoid of revolution. We show that the problem has a unique solution provided that the first eccentricity e0 of the ellipsoid of revolution is less than 0·65041. The ellipsoidal Stokes function describing the effect of ellipticity of the boundary is expressed in the $$O(e_0^2 )$$ E-approximation as a finite sum of elementary functions which describe analytically the behaviour of the ellipsoidal Stokes function at the singular point ψ = 0. We prove that the degree of singularity of the ellipsoidal Stokes function in the vicinity of its singular point is the same as that of the spherical Stokes function. [ABSTRACT FROM AUTHOR]

Green's function for the boundary-value problem of Stokes's type with ellipsoidal corrections in the boundary condition for anomalous gravity is constructed in a closed form. The `spherical-ellipsoidal' Stokes function describing the effect of two ellipsoidal correcting terms occurring in the boundary condition for anomalous gravity is expressed in O( e2 0)-approximation as a finite sum of elementary functions analytically representing the behaviour of the integration kernel at the singular point ψ=0. We show that the `spherical-ellipsoidal' Stokes function has only a logarithmic singularity in the vicinity of its singular point. The constructed Green function enables us to avoid applying an iterative approach to solve Stokes's boundary-value problem with ellipsoidal correction terms involved in the boundary condition for anomalous gravity. A new Green-function approach is more convenient from the numerical point of view since the solution of the boundary-value problem is determined in one step by computing a Stokes-type integral. The question of the convergence of an iterative scheme recommended so far to solve this boundary-value problem is thus irrelevant. [ABSTRACT FROM AUTHOR]

One of the most important mathematical formulas in fast multipole algorithms (FMA) is the addition theorem. In the numerical implementation of the addition theorem, the infinite series should be truncated. In this paper, the number of terms needed for the scalar Green's function is derived, and the error analysis for the truncation error in the multipole expansion of the vector Green's functions is given. We have found that the error term in vector Green's functions is proportional to 1/R. If the scalar Green's function is truncated at the L-th term and the relative error is ε, then the relative error in the dyadic Green's function is ε/4, if it is truncated at the (L+2)-th term. For the vector Green's function related to MFIE, the relative error is ε/2 if it is truncated at the (L+1)-th term [ABSTRACT FROM PUBLISHER]