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In this article, we develop a hybrid method for studying wave scatterings and propagation in a vegetation field. The coherent multiple scatterings among the plants and the gaps in the vegetation field are considered through a two-step hybrid method. First, the T-matrix of a single plant is calculated using the Huygens principle and the vector cylindrical wave (VCW) expansion based on the full-wave solutions from the Ansys High Frequency Structure Simulator (HFSS). Second, the multiple scatterings between different plants are considered through the Foldy–Lax (FL) multiple-scattering equations using the calculated T-matrix and the translational addition theorem. The convergence and the accuracy of the hybrid method are verified with the HFSS by comparing the solutions of scatterings from four wheat plants. The full-wave Monte Carlo simulations of a field with 169 wheat plants at the $L$ -band are subsequently performed using the hybrid method. Numerical results show that the transmission in the gap region is significantly higher than that of the inner region with the difference given quantitatively. The transmissivity of microwave through the wheat field with a large vegetation water content (VWC) can be significantly underestimated by the classical radiative transfer equation (RTE) and distorted Born approximation (DBA) model.

This article describes two novel perturbation solutions for the electromagnetic analysis of eccentric coaxial waveguides. Different techniques have been used for solving this type of problem in the past. Most of them rely on solving a complicated transcendental equation obtained from the Graf’s addition theorem or on brute-force numerical methods such as finite differences and finite elements. The proposed approach, instead, employs transformation optics to map the original problem into a problem consisting of a concentric coaxial waveguide filled with an anisotropic and inhomogeneous medium. The corresponding (transformed) wave equation is then solved via a regular perturbation series. This method allows to compute field and wavenumber corrections of the transverse magnetic (TM) and transverse electric (TE) modes for coaxial waveguides with small eccentricities. In addition, another solution is obtained by using the cavity-material perturbation approach for providing the cutoff wavenumbers of TM and TE fields. The proposed perturbation solutions are validated against full-wave finite-element and finite-volume results in several examples.

An efficient modal solution for scattering by an arbitrary isosceles triangular groove (ITG) in an infinite ground plane is suggested. The procedure consists of expanding the fields in two distinct regions and three different cylindrical coordinate systems, employing Graf’s addition theorem for convenience in imposing boundary conditions on an arc-shaped boundary, and determining the field expansion coefficients by solving a system of linear equations. The method is in good agreement with the time-consuming methods such as the finite-element method (FEM) and the method of moment (MoM) while it has an appropriate computational efficiency especially when the width of a groove increases. This method is utilized to investigate the effects of the problem parameters such as the size of ITG, the wave polarization, and the incidence angle on the scattering signature.

A general mode-matching technique is proposed to analyze a 2-D truncated perfect electric conductor (PEC) wedge covered with a magnetodielectric semicircular boss, where a radial length of the wedge is semi-infinite. A system of simultaneous equations of the TM- and TE-modes is obtained using a mode-matching technique, partial overlapping regions, and Graf’s addition theorem. Our solutions are computed to yield the echowidth characteristics of concave, convex, and truncated PEC wedges, including thick PEC half-planes with sharp and rounded edges. Their scattering results are compared with a commercial electromagnetic software package and show favorable agreement. Appropriate change of the permittivity and permeability of a semicircular boss results in radar cross-section (RCS) reduction of the truncated wedge, where optimization is automatically conducted by a binary genetic algorithm (GA). Our approach is fundamentally useful and applicable to the structural design of an integrated mast or superstructure on modern warships.

A multiple scattering method is proposed for the analysis of substrate-integrated waveguide (SIW) structures in this letter. SIW structures are considered to be parallel plates embedded by the fence of metallic vias (labeled as SIW vias). The addition theorem of cylindrical waves is applied to the calculation of the multiple scattering among SIW vias and coaxial ports. The reflection matrix of SIW vias, which is derived by boundary conditions, can be connected to the radial scattering matrix obtained by the multiple scattering method. This leads to the network parameters in terms of coaxial ports of SIW structures on a plate pair. The accuracy and efficiency of the multiple scattering method are verified by numerical simulations in commercial full-wave solvers.

Based on the image theory and addition theorem of spherical vector wave functions, a multiple-reflection solution is described for the electromagnetic scattering by a buried sphere. An iterative process is introduced to obtain the scattered field by enforcing the boundary conditions at the plane interface between free space and an isotropic medium and the spherical surface of a dielectric sphere buried in the isotropic medium. Numerical results for the scattered fields are provided and compared with those obtained by the commercial software FEKO. A good agreement is observed, which verifies the presented formulation.

In this paper, the field analysis of a triangular corrugated coaxial cavity with misaligned insert is carried out for a megawatt-class sub-terahertz wave gyrotron. In misalignment analysis, both parallel displacement of the insert axis and tilting of the insert axis with the outer resonator axis are considered. Graff’s addition theorem is used for deriving the eigenvalue equation of the coaxial cavity with such a misaligned insert. Mathematical formulations are carried out to include the effect of insert misalignment on the beam coupling coefficient and ohmic wall loading of the outer cavity and insert of the coaxial cavity gyrotron. The effect of structural misalignment of the insert on the operation of 2-MW, 220-GHz coaxial cavity gyrotron is analyzed. It is shown that insert misalignment reduces RF output power as well as increases ohmic wall loading of the insert beyond the prescribed cooling limit. Compared to tilting of the insert, parallel displacement of the insert causes more deterioration in the gyrotron operation. Comparative studies are also performed for a coaxial cavity with rectangular slots on the insert.

Electromagnetic scattering from irregular array of arbitrarily oriented PEC scatterers is investigated using a novel domain decomposition method based on equivalence principle algorithm (EPA) in conjunction with addition theorems for spherical wave harmonics (SWHs). Each element is considered to be enclosed by a spherical equivalence surface as a single domain. The primary unknowns on each element are replaced by the equivalent electric and magnetic current distributions on the equivalence sphere in terms of RWG basis functions. From these current distributions, the scattered field outside its equivalence sphere is evaluated in terms of SWHs in the local coordinates system fixed to each element body. The SWHs in rotated local coordinates are translated as a new set of SWHs in other local coordinates with the same origin but axes parallel to the global coordinate’s axes using the rotation addition theorem. Furthermore, the mutual coupling effects among the separated domains are considered using the translation addition theorem for parallel local coordinate systems. It is shown that the proposed method effectively reduces the computational costs by reducing the number of unknowns versus the conventional EPA. The efficiency and validity of the proposed method are investigated through several numerical examples.

Antennas and metasurfaces have enabled a number of far-field manipulation functions. According to the addition theorem of multipoles, near fields have richer spatial spectra than far fields; hence, in the near-field region, it is easier to achieve complex manipulations on field distributions. In this paper, an algorithm is presented to synthesize the near fields of source arrays. Given target distributions of near-field intensities and also predefined source magnitudes, the algorithm will find the needed source phases, which can then be applied on active antenna arrays and passive metasurfaces to induce the target distribution of fields. The algorithm adopts the dyadic Green’s function as the propagator, and hence, it naturally takes account of the near-field and vector properties of electromagnetic fields. As a typical application of the algorithm, an example is given to obtain the excitation phases of a dipole array, which is then physically imitated by a coding metasurface. Experimental measurement is performed and the result proves the validity of the algorithm. From the perspective of information metasurface, the algorithm finds the phase-coding pattern of metasurface to achieve specific functions.

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.

A Gaussian point-adaptive grouping scheme for the multilevel fast multipole algorithm (MLFMA) has been proposed in this communication to significantly reduce the heavy memory cost resulted from using the basis functions defined on large patches without sacrificing the accuracy of the numerical solutions. The grouping process in the MLFMA has been considered as a single-objective optimization problem and is solved by using the clustering algorithm for Gaussian quadrature points on each patch. Meanwhile, the constraint of the addition theorem for MLFMA is still satisfied. As a result, the presented scheme is able to acquire an optimal number of multipoles for each basis function. Compared to the conventional octree grouping scheme or other grouping schemes used in the past, the method in this communication is advantageous in terms of the memory efficiency and the solution accuracy. Numerical examples have been given to demonstrate the validity and effectiveness of the proposed scheme.

A semianalytical method is presented for the evaluation of scattered fields from arbitrarily shaped 2-D Perfect Electric Conductor (PEC) scatterers under $\text {TM}^{z}$ wave incidence. Surface equivalence principle for scattered fields is used in conjunction with modal expansion of fields in terms of cylindrical eigenfunctions. It is assumed that no field variation exists in axial ( $z$ ) direction. Implementation of boundary conditions on scatterer surface leads to a system of linearly independent equations to solve for equivalent surface currents. Scattered fields are calculated by equivalent surface currents leading to evaluation of scattering widths (Radar Cross-Section of 2-D objects) for different observation angles. $\text {TM}^{z}$ polarized incident wave does not excite any $\text {TE}^{z}$ component. The novelty of proposed method is use of addition theorem of Bessel functions for representation of scattered fields in terms of equivalent surface currents, giving an integral equation with an analytic integrand and a well-behaved impedance matrix. Orthogonality of cylindrical modes results in excitation matrix to be a discrete function of mode numbers. Therefore, contrary to method of moments, there is no need for weighting functions. Four examples are considered, namely, line source and plane wave incidence on a 2-D PEC circular cylinder and also plane wave incidence on 2-D elliptical and equilateral triangular PEC cylinders.

Frequency domain Mie solutions to scattering from spheres have been used for a long time. However, deriving their transient analog is a challenge, as it involves an inverse Fourier transform of the spherical Hankel functions (and their derivatives) that are convolved with inverse Fourier transforms of spherical Bessel functions (and their derivatives). Series expansion of these convolutions is highly oscillatory (therefore, poorly convergent) and unstable. Indeed, the literature on numerical computation of this convolution is very sparse. In this paper, we present a novel quasi-analytical approach to compute transient Mie scattering that is both stable and rapidly convergent. The approach espoused here is to use vector tesseral harmonics as basis function for the currents in time-domain integral equations (TDIEs) together with a novel addition theorem for the Green’s functions that render these expansions stable. This procedure results in an orthogonal, spatially meshfree, and singularity-free system, giving us a set of one-dimensional (1-D) Volterra Integral equations. Time-dependent multipole coefficients for each mode are obtained via a time-marching procedure. Finally, several numerical examples are presented to show the accuracy and stability of the proposed method.

The cold parameters including the dispersion properties and the average interaction impedance of a sheath eccentric helix slow-wave structure in a circular waveguide are investigated. With the applications of orthogonal properties of the helix modes and Graf’s addition theorem for modified Bessel functions, the closed-form characteristic equations concerning the helix modes are derived rigorously. The obtained characteristic equations show that the misaligned structure admits only the field solutions existing in the form of the superposition of hybrid modes. Numerical calculations show that the normalized phase velocity and the average interaction impedance of the helix dominant mode decrease as the misalignment of the inner helix increases and that more hybrid modes must be considered for satisfactory convergence with the increase in the misalignment. The effects of different misalignments on the cold parameters of the eccentric structure are investigated and the results are discussed.

In this paper, the translational addition theorem for spherical functions is employed to calculate the acoustic radiation force produced by an arbitrary shaped beam on a sphere arbitrarily suspended in an inviscid fluid. The procedure is also based on the partial-wave expansion method, which depends on the beam-shape and scattering coefficients. Given a set of beam-shape coefficients (BSCs) for an acoustic beam relative to a reference frame, the translational addition theorem can be used to obtain the BSCs relative to the sphere positioned anywhere in the medium. The scattering coefficients are obtained from the acoustic boundary conditions across the sphere's surface. The method based on the addition theorem is particularly useful to avoid quadrature schemes to obtain the BSCs. We use it to compute the acoustic radiation force exerted by a spherically focused beam (in the paraxial approximation) on a silicone-oil droplet (compressible fluid sphere). The analysis is carried out in the Rayleigh (i.e., the particle diameter is much smaller than the wavelength) and Mie (i.e., the particle diameter is of the order of the wavelength or larger) scattering regimes. The obtained results show that the paraxial focused beam can only trap particles in the Rayleigh scattering regime.

In this letter, a novel hybrid method is proposed to efficiently analyze the electromagnetic (EM) scattering from arbitrarily shaped, perfect electrically conducting (PEC) bodies that penetrate the interface of a half-space. Due to different integrands involved in the reflection- and transmission-type Green’s functions, a partition scheme is introduced where the adaptive cross approximation (ACA) and the multilevel fast multipole algorithm (MLFMA) are integrated seamlessly. In this scheme, different fast solvers are invoked automatically to achieve an optimal efficiency. The reconstruction of the Green’s function via an image-based translational addition theorem is first investigated, and the empirical partitioning parameters are suggested. The performance of this hybrid method is then examined via two examples, including a benchmark target and a more realistic scenario in the near-surface scattering.

Inspired by the previous work of Tu and Deng, we propose two infinite classes of Boolean functions of 2k variables where k ≥ 2. The first class contains unbalanced functions having high algebraic degree and nonlinearity. The functions in the second one are balanced and have maximal algebraic degree and high nonlinearity (as shown by a lower bound that we prove; as a byproduct we also prove a better lower bound on the nonlinearity of the Carlet-Feng function). Thanks to a combinatorial fact, first conjectured by the authors and later proved by Cohen and Flori, we are able to show that they both possess optimal algebraic immunity. It is also checked that, at least for numbers of variables n ≤ 16, functions in both classes have a good behavior against fast algebraic attacks. Compared with the known Boolean functions resisting algebraic attacks and fast algebraic attacks, both of them possess the highest lower bounds on nonlinearity. These bounds are however not enough for ensuring a sufficient nonlinearity for allowing resistance to fast correlation attack. Nevertheless, as for previously found functions with the same features, there is a gap between the bound that we can prove and the actual values computed for bounded numbers of variables (n ≤ 38). Moreover, these values are very good. The infinite class of functions we propose in Construction 2 presents, among all currently known constructions, the best provable tradeoff between all the important cryptographic criteria.

Recently, several construction methods of highly nonlinear Boolean functions with relatively good algebraic properties were proposed. These approaches manage in optimizing most of the relevant cryptographic criteria, but not all of them at the same time. Usually, either the nonlinearity bounds are rather loose (though the actual nonlinearity is relatively high) or the functions do not provide a good resistance to fast algebraic cryptanalysis. In this paper, we develop a theoretical framework for using objects in suitable projective geometry spaces for construction of highly nonlinear Boolean functions. This allows us to establish tight bounds on the nonlinearity using simple counting arguments, thus avoiding rather complicated estimates of certain trace sums. Our method generates a class of almost fully optimized functions, that is the functions apart from very high nonlinearity also have the maximum algebraic degree and optimal algebraic immunity. Compared to the classes of functions proposed by Carlet and Feng, Wang , and Zeng , our functions achieve a slightly better nonlinearity which is traded-off against a little worse resistance against fast algebraic attacks. On the other hand, compared to the functions by Tang and Tu and Deng, our nonlinearity is somewhat lower, but the algebraic properties are slightly better.

The cylindrical wave decomposition of fields from a normal-to-cylinder point source is derived using a modified addition theorem. The fields scattered from a lossy cylinder, as an approximation of the human body, are also calculated and tabulated for use in an integral equation study of dipoles. The transmittance between two optimized radially polarized dipoles is evaluated on the body trunk surface, using the method of moments (MoM) in the 2.45 GHz ISM band. An anechoic chamber measurement is performed and the measured transmittance between two dipoles on the human body has been compared to the simulated one on the lossy cylinder. Although the abdominal cross section of the body does not have exactly a circular shape, strong similarities have been observed in their path-loss trends around the body. A very good agreement has been obtained between the dipoles transmittances provided by the analytical/MoM model, CST Microwave Studio simulations, and experiments, including interference effects attributed to the body-attached radiating waves.

Parker considered a new type of discrete Fourier transform, called nega-Hadamard transform. We prove several results regarding its behavior on combinations of Boolean functions and use this theory to derive several results on negabentness (that is, flat nega-spectrum) of concatenations, and partially symmetric functions. We derive the upper bound ⌈n/2⌉ for the algebraic degree of a negabent function on n variables. Further, a characterization of bent-negabent functions is obtained within a subclass of the Maiorana-McFarland set. We develop a technique to construct bent-negabent Boolean functions by using complete mapping polynomials. Using this technique, we demonstrate that for each l ≥ 2, there exist bent-negabent functions on n = 12l variables with algebraic degree n/4 + 1 = 3l + 1. It is also demonstrated that there exist bent-negabent functions on eight variables with algebraic degrees 2, 3, and 4. Simple proofs of several previously known facts are obtained as immediate consequences of our work.

A new fast dipole method (FDM) is proposed for the electromagnetic scattering from arbitrarily shaped three-dimensional (3D), electrically large, perfect electric conducting (PEC) targets in free space based on the concept of equivalent dipole-moment method (EDM) and the fast multipole method (FMM). The electric-field, magnetic-field and combined-field integral equations (CFIE) for this algorithm have been developed and implemented. Although the basic acceleration idea in the FDM has been borrowed from the FMM, the specific implementation of these two algorithms is completely different. In the FDM, a simple Taylor's series expansion of the distance between two interacting equivalent dipoles is used, which transforms the impedance element into another aggregation-translation-disaggregation form naturally. Furthermore, this algorithm is very simple for numerical implementation for it does not involve the calculation of a number of Bessel functions, Legendre functions for the addition theorem and complex integral operators. The FDM can achieve O(N1.5) computational complexity and memory requirement, where N is the number of unknowns. Numerical results are presented to validate the efficiency and accuracy of this method through comparison with other rigorous solutions.

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.

In this paper, three constructions of balanced Boolean functions with optimal algebraic immunity are proposed. It is checked that, at least for small numbers of input variables, these functions have good behavior against fast algebraic attacks as well. Other cryptographic properties such as algebraic degree and nonlinearity of the constructed functions are also analyzed. Lower bounds on the nonlinearity are proved, which are similar to the best bounds obtained for known Boolean functions resisting algebraic attacks and fast algebraic attacks. Moreover, it is checked that for the number n of variables with 5 ≤ n ≤ 19, the proposed n-variable Boolean functions have in fact very good nonlinearity.

Bent functions are maximally nonlinear Boolean functions with an even number of variables. They were introduced by Rothaus in 1976. For their own sake as interesting combinatorial objects, but also because of their relations to coding theory (Reed-Muller codes) and applications in cryptography (design of stream ciphers), they have attracted a lot of research, specially in the last 15 years. The class of bent functions contains a subclass of functions, introduced by Youssef and Gong in 2001, the so-called hyper-bent functions, whose properties are still stronger and whose elements are still rarer than bent functions. Bent and hyper-bent functions are not classified. A complete classification of these functions is elusive and looks hopeless. So, it is important to design constructions in order to know as many of (hyper)-bent functions as possible. This paper is devoted to the constructions of bent and hyper-bent Boolean functions in polynomial forms. We survey and present an overview of the constructions discovered recently. We extensively investigate the link between the bentness property of such functions and some exponential sums (involving Dickson polynomials) and give some conjectures that lead to constructions of new hyper-bent functions.

A unified full-wave characterization of massive number of vias with or without circular pads is formulated analytically by means of equivalent magnetic frill array model and Galerkin's procedure. The proposed method takes advantage of the parallel-plate structure and employs image theory and Fourier transform to simplify the problem from 3-D configuration into 2-D frame. Based on the cylindrical symmetry with Bessel's functions and addition theorem, the final matrix equation is formulated analytically which can be used immediately for sensitivity analysis in both via dimensions and pad size. As a result, the new method is simple, efficient, and accurate. Numerical examples demonstrate good agreement between our analytical solution and the results obtained by commercial software (high frequency structure simulator) over a frequency range up to 20 GHz.

A mixed-form thin-stratified medium fast-multipole algorithm is proposed for fast simulation of general microstrip structures at both low and mid-frequencies. The newly developed matrix-friendly formula of layered medium Green's function is applied in this algorithm. For well-separated interactions, the path deformation technique is implemented to achieve a smoother and exponentially convergent integral. The two-dimensional addition theorem is then incorporated into the integrand to expedite the matrix-vector product. In our approach, multipole expansion (low-frequency fast-multiple algorithm) as well as the plane wave expansion (mid-frequency fast-multipole algorithm) of the translational addition theorem are combined into a single multilevel tree to capture quasi-static physics and wave physics simultaneously. The outgoing wave is represented first in terms of multipole expansion at leafy levels, and then switched to plane wave expansion automatically at higher levels. This seamless connection makes the algorithm applicable in simulations, where subwavelength interaction and wave physics both exist.

The complex impedance of an air-cored coil in a conductive tube with eccentric inner and outer cylindrical surfaces is calculated. The analytic expressions for the induced fields and the impedance variation due to the eddy-current flow inside the tube wall are derived using a second-order potential approach. The addition theorem of Bessel functions is employed to perform the transition between the local coordinate systems that conform to the boundaries of the structure. Although the model can be used for any coil shape and orientation, we focus our study on the configuration of a bobbin coil with axis parallel to the axes of the tube surfaces, but not necessarily coinciding with either of them. The results of the presented analysis are verified by a finite-element-method (FEM) solution.

In this paper, the 3-D interaction of a time-harmonic plane-progressive incident sound wave with a bilaminate hollow sphere, composed of an outer layer of steel perfectly bonded to an inner layer of radially polarized piezoceramic material (PZT4), and submerged near a free/rigid flat boundary, is considered. The translational addition theorem for spherical wave functions along with the classical transfer matrix approach within the context of state-space formulation is employed to obtain an analytical solution for the acoustic scattering problem. When the transducer is operating in the receive mode, the frequency spectrum of voltage induced within the piezoelectric sensor layer along with the associated backscattering form functions are calculated and discussed for selected distance parameters, angles of incidence, and interface impedance conditions. Also, when the transducer is operating in the active transmission mode, the effects of latter parameters on the control voltages required for partial or complete cancellation of the reflected pressure field are investigated.

An efficient algorithm is introduced to enhance the convergence of dyadic Green's functions (DGF) in a layered spherical media where asymptotic expressions have been developed. The formulated expressions involve an infinite series of spherical eigenmodes that can be reduced to the simple homogenous media Green's function using the addition theorem of spherical Hankel functions. Substantial improvements in the convergence speed have been attained by subtracting the asymptotic series representation from the original DGF. The subtracted components are then added to the solution using the homogenous media Green's function format.

A dual-series approach is used to formulate scattering of a TE-polarized plane wave by a circular, PEC cylinder, having a longitudinal slot and enclosing two, eccentric, cylindrical dielectric layers. The dual-series equations are analytically regularized to a matrix Fredholm equation of the second kind by use of the Abel integral-transform method. The resulting infinite set of linear algebraic equations (i.s.l.a.e.) is truncated and solved numerically. The aforementioned analytical-numerical solution intrinsically takes into consideration the correct edge behavior of the field. Furthermore, the addition theorem of cylindrical wave functions is used to match the field components on any cylindrical interface. The numerical application manifests how the structure of the inner loading of this cylindrical cavity is imprinted on backscattering. Moreover, it is shown how the location of the innermost dielectric cylinder may contribute to the suppression or enhancement of resonances.

This paper analyzes complexities of decision diagrams for elementary functions such as polynomial, trigonometric, logarithmic, square root, and reciprocal functions. These real functions are converted into integer-valued functions by using fixed-point representation. This paper presents the numbers of nodes in decision diagrams representing the integer-valued functions. First, complexities of decision diagrams for polynomial functions are analyzed, since elementary functions can be approximated by polynomial functions. A theoretical analysis shows that binary moment diagrams (BMDs) have low complexity for polynomial functions. Second, this paper analyzes complexity of edge-valued binary decision diagrams (EVBDDs) for monotone functions, since many common elementary functions are monotone. It introduces a new class of integer functions, Mp-monotone increasing function, and derives an upper bound on the number of nodes in an EVBDD for the Mp-monotone increasing function. A theoretical analysis shows that EVBDDs have low complexity for Mp-monotone increasing functions. This paper also presents the exact number of nodes in the smallest EVBDD for the n-bit multiplier function, and a variable order for the smallest EVBDD.

This letter proposes a new approach for estimating resonant characteristics of near-field coupled small antennas. It is based on the equivalent circuit representation of the interaction of two antennas using the addition theorem of spherical modes. Using the proposed method, the splitting of the resonant frequency and the resonant impedance of the near-field coupled small antennas can be obtained by the impedance characteristics of the isolated antenna. The results are shown to be in good agreement with the full electromagnetic (EM) simulation.

A novel method, called the nondirective stable plane wave multilevel fast multipole algorithm (NSPWMLFMA), is presented to evaluate the low-frequency (LF) interactions that cannot be handled by the multilevel fast multipole algorithm (MLFMA). It is well known that the MLFMA cannot be used for LF interactions, since it suffers from numerical instability. Contrary to current techniques, the proposed technique is not based on the spectral representation of the Green function. Instead the addition theorem of the MLFMA is manipulated into a form that allows numerically stable translations along the z axis. The translation operator for these translations is derived in closed form. A QR-based method is devised to allow stable translations in all the other directions. Interpolations and anterpolations are also provided, allowing a full multilevel algorithm. Since the NSPWMLFMA is based on the same mathematical foundations as the MLFMA, it requires limited adaptations to existing MLFMA codes. The fact that a QR is needed limits this algorithm to LF interactions. However, a coupling with the MLFMA is straightforward, allowing the easy construction of a broadband algorithm. The DC limit of the algorithm is also presented and it is shown that the algorithm remains valid for static problems. Finally, it is shown that the error introduced in the different steps of the algorithm is controllable, and a single-level vectorial version of the algorithm is applied to a generic scattering application to demonstrate its validity.

This article presents a rigorous mathematical analysis of spherical stacked-patch arrays with emphasis on the physical interpretation of mutual coupling mechanisms present in doubly- curved convex structures. The analysis method is based on electromagnetic field representation in terms of spherical harmonics where each harmonic has the same angular variation as the spectral source component. To obtain the spectral representation the vector-Legendre transformation is applied to currents and fields. A novel approach to the mutual coupling calculation within the Moment Method (MoM) analysis of spherical arrays is applied. By expressing the patch current in terms of two suitable potential-like auxiliary functions, it is possible to avoid the use of Euler’ s formulas for coordinate system rotation and the related lengthy integrations. Instead, the rotation of antenna elements and corresponding current distributions can be done in closed form with the help of Vilenkin’ s addition theorem for associated Legendre functions. It is shown that the new approach results in significant acceleration and improved accuracy of the analysis of spherical patch antenna arrays. The algorithm is successfully tested against a commercially available EM software and measurements performed on the developed laboratory model, confirming its accuracy for both input impedance and mutual coupling calculation and with only a small difference between the predicted and measured resonant frequencies, due to limitations in the experimental model. The influence of the structure parameters on mutual coupling level is extensively investigated, including all coupling mechanisms and leakage of energy due to curvature of the structure. It is shown that stacked-patch antennas can have reduced coupling level comparing to single patch antennas with possible deep nulls above the antenna resonant frequency.

A series solution for TM scattering from a dielectric biconvex cylinder, which is formed by a semicircle and a portion of circular arc, buried in a shallow circular gap of a perfectly conducting plane is derived in this paper. The electric fields of biconvex cylinder region and its outer semi-unbounded region are represented in terms of an infinite series of cylindrical waves with unknown coefficients respectively. By employing Graf's addition theorem and matching the boundary conditions, the unknown coefficients are determined. The comparisons with available data in the literature point out a good agreement for the circular cylinder case. Some plotted results for the backscattering width and far-field radiation pattern reveal how the scattering properties have influenced by varying the depth-to-half-width ratio of the dielectric biconvex cylinder.

The rigorous electromagnetic analysis of the coupling between two nonparallel optical-fiber waveguides is developed for the first time. Green's theorem, involving the dyadic Green's function of the fiber guiding the incident mode, is used to formulate the electric-field integral equation inside the second fiber. By applying the entire-domain Galerkin technique and by utilizing the generalized addition theorem for cylindrical waves for nonparallel axis translation, which is derived by the authors, this equation is analytically transformed into a system of coupled integral equations for the spectral weights of the field on the basis of TE and TM cylindrical vector wave functions. The Neumann-series iterative procedure is adopted to solve this system and obtain analytical expressions for the field scattering coefficients, which are sufficiently accurate for weakly coupled fibers

In this paper, we consider a subclass of the Maiorana-McFarland class used in the design of resilient nonlinear Boolean functions. We show that these functions allow a simple modification so that resilient Boolean functions of maximum algebraic degree may be generated instead of suboptimized degree in the original class. Preserving a high-nonlinearity value immanent to the original construction method, together with the degree optimization gives in many cases functions with cryptographic properties superior to all previously known construction methods. This approach is then used to increase the algebraic degree of functions in the extended Maiorana-McFarland (MM) class (nonlinear resilient functions F : GF (2)(n) -> GF (2)(m) derived from linear codes). We also show that in the Boolean case, the same subclass seems not to have an optimized algebraic immunity, hence not providing a maximum resistance against algebraic attacks. A theoretical analysis of the algebraic properties of extended Maiorana-McFarland class indicates that this class of functions should be avoided as a filtering function in nonlinear combining generators.

Recently, algebraic attacks have received a lot of attention in the cryptographic literature. It has been observed that a Boolean function f used as a cryptographic primitive, and interpreted as a multivariate polynomial over F/sub 2/, should not have low degree multiples obtained by multiplication with low degree nonzero functions. In this paper, we show that a Boolean function having low nonlinearity is (also) weak against algebraic attacks, and we extend this result to higher order nonlinearities. Next, we present enumeration results on linearly independent annihilators. We also study certain classes of highly nonlinear resilient Boolean functions for their algebraic immunity. We identify that functions having low-degree subfunctions are weak in terms of algebraic immunity, and we analyze some existing constructions from this viewpoint. Further, we present a construction method to generate Boolean functions on n variables with highest possible algebraic immunity /spl lceil/n/2/spl rceil/ (this construction, first presented at the 2005 Workshop on Fast Software Encryption (FSE 2005), has been the first one producing such functions). These functions are obtained through a doubly indexed recursive relation. We calculate their Hamming weights and deduce their nonlinearities; we show that they have very high algebraic degrees. We express them as the sums of two functions which can be obtained from simple symmetric functions by a transformation which can be implemented with an algorithm whose complexity is linear in the number of variables. We deduce a very fast way of computing the output to these functions, given their input.

The two main criteria evaluating, from cryptographic viewpoint, the complexity of Boolean functions are the nonlinearity and the algebraic degree. Two other criteria can also be considered: the algebraic thickness and the nonnormality. Simple proofs are given that, asymptotically, almost all Boolean functions have high algebraic thicknesses and are deeply nonnormal, as well as they have high algebraic degrees and high nonlinearities. We also study in detail the relationship between nonnormality and nonlinearity. We derive simple proofs of known results on symmetric Boolean functions and we prove several new and more general results on a class containing all symmetric functions.

Based on the addition theorem, the principle of a multilevel ray-propagation fast multipole algorithm (RPFMA) and fast far-field approximation (FAFFA) has been demonstrated for three-dimensional (3-D) electromagnetic scattering problems. From a rigorous mathematical derivation, the relation among RPFMA, FAFFA, and a conventional multilevel fast multipole algorithm (MLFMA) has been clearly stated. For very large-scale problems, the translation between groups in the conventional MLFMA is expensive because the translator is defined on an Ewald sphere with many sampling k/spl circ/ directions. When two groups are well separated, the translation can be simplified using RPFMA, where only a few sampling k/spl circ/ directions are required within a cone zone on the Ewald sphere. When two groups are in the far-field region, the translation can be further simplified by using FAFFA where only a single k/spl circ/ is involved in the translator along the ray-propagation direction. Combining RPFMA and FAFFA with MLFMA, three algorithms RPFMA-MLFMA, FAFFA-MLFMA, and RPFMA-FAFFA-MLFMA have been developed, which are more efficient than the conventional MLFMA in 3-D electromagnetic scattering and radiation for very large structures. Numerical results are given to verify the efficiency of the algorithms.

A full-wave analysis of an inhomogeneous waveguide region with both planar and circular cylindrical boundaries is presented in this paper. Circular cylindrical modal functions are used to represent the fields. Field matching on the planar walls and apertures is rigorously achieved by the finite plane-wave series expansion of each modal field, whereas the addition theorem for cylindrical waves is used for rigorous field matching on the circular cylindrical boundaries. Numerical results are given for rectangular waveguides with 90/spl deg/ bends and rounded outer corners.

An iterative algorithm is given for producing the parity-check functions for one-point algebraic-geometry (AG) codes, in particular (but not limited to) those related to the two towers of function fields introduced by Garcia and Stichtenoth (1995). This simple method, based on the linearity of the Qth-power map over F/sub Q/, is an alternative to the method of using Laurent series expansions. Examples are given for small values of m with characteristic p=2 for both towers.

The separation of variables method along with an addition theorem of Mathieu functions are employed in this paper to analyze the problem of a nonconfocal suspended strip in an elliptical waveguide. An infinite-dimensional determinant is obtained, which represents the characteristic equation of the proposed structure. To obtain the cutoff wavenumbers for both TE and TM cases of such a structure, the infinite determinant is truncated. Convergence when truncating was observed. Numerical results for the special case of a confocal structure is discussed first for comparison with published data. Results of other interesting cases are also presented.

The cutoff characteristics of an asymmetrically loaded cylindrical waveguide are analyzed using the null-field method. The fields in the metallic waveguide and dielectric loading are expressed in their corresponding guided-wave modes. The addition theorem of the Bessel function is used to relate the fields across the air-dielectric boundary.

In 2013, Tang, Carlet, and Tang [IEEE TIT 59(1): 653–664, 2013] presented two classes of Boolean functions. The functions in the first class are unbalanced and the functions in the second one are balanced. Both of those two classes of functions have high nonlinearity, high algebraic degree, optimal algebraic immunity, and high fast algebraic immunity. However, they are not 1-resilient which represents a drawback for their use as filter functions in stream ciphers. In this paper, we first propose a large family of 1-resilient Boolean functions having high lower bound on nonlinearity, optimal algebraic immunity, and optimal algebraic degree, that is, meeting the Siegenthaler bound. Most notably, we can mathematically prove that every function in $n$ variables belonging to this family has fast algebraic immunity no less than $n-6$ , which is the first time that an infinite family of 1-resilient functions with provably high fast algebraic immunity has been invented. Furthermore, we exhibit a subclass of the family which has higher lower bound on nonlinearity than all the known 1-resilient functions with (potentially) optimal algebraic immunity and potentially high fast algebraic immunity.

This paper presents an analytic method allowing us to take into account the multiple scattering effect in heterogeneous media made with spherical inclusions dispersed in a dielectric matrix. The Mie formalism used in the case of a single sphere, is extended to calculate the multiple scattered fields between two particles. The translation addition theorem for vector spherical waves functions is used to express the field scattered by one sphere in terms of the spherical coordinates of the other spheres and impose the boundary conditions. Numerical results of RCS and scattering diagrams of systems of two spheres are compared with free-space measurements made by using vectorial network analyzer. >

In many areas of signal, system, and control theory, orthogonal functions play an important role in issues of analysis and design. In this paper, it is shown that there exist orthogonal functions that, in a natural way, are generated by stable linear dynamical systems and that compose an orthonormal basis for the signal space l/sub 2sup n/. To this end, use is made of balanced realizations of inner transfer functions. The orthogonal functions can be considered as generalizations of, for example, the pulse functions, Laguerre functions, and Kautz functions, and give rise to an alternative series expansion of rational transfer functions. It is shown how we can exploit these generalized basis functions to increase the speed of convergence in a series expansion, i.e., to obtain a good approximation by retaining only a finite number of expansion coefficients. Consequences for identification of expansion coefficients are analyzed, and a bound is formulated on the error that is made when approximating a system by a finite number of expansion coefficients. >

The recursive aggregate interaction matrix algorithm (RAIMA) for calculating a wave scattering solution is developed. This algorithm combines the strength of both the recursive aggregate T matrix algorithm (RATMA) and the recursive interaction matrix algorithm (RIMA) that have been previously developed. The resultant algorithm is robust for scattering problems involving highly singular Green's functions by avoiding the violation of the addition theorem. It also has reduced computational complexity for inverting the volume integral equation of scattering. The computational complexity of RAIMA is O(N/sup 7/3/) in three dimensions and O(N/sup 2/) in two dimensions.

An exact analytic solution of a plane electromagnetic (EM) wave scattered by an eccentric multilayered sphere (EMS) is obtained. It is assumed that the layers are perfect dielectrics and that the innermost core is a perfectly conducting sphere. Each center of a layer is translated along the incident axis. All fields are expanded in terms of the spherical vector wave functions with unknown expansion coefficients. The addition theorem for spherical wave functions is used prior to applying the boundary conditions. The unknown coefficients are determined by solving a system of linear equations derived from the boundary conditions. Numerical results of the scattering cross sections are presented on the plane of /spl phi/=0 degrees and /spl phi/=90 degrees. The convergence of modal solutions and the characteristics of patterns are examined with various geometries and permittivity distributions. >

A formally exact solution is described for the problems of scattering at a junction between two circular waveguides with their axes offset and at a thick off-centered iris in a circular waveguide. The analysis method uses Graf's addition theorem for cylindrical functions and the conservation of complex power technique (CCPT). Sample numerical results are presented and compared with available data in the literature. >