Analytic expressions for a function occurring in diffraction theory

Simple expressions are derived for the Maliuzhinets (integral) function which arises in connection with diffraction by an impedance wedge. The given expressions allow the computation of the function with remarkable accuracy throughout the entire complex plane for any exterior wedge angle.     

Mutual impedance between probes in a waveguide

The general formulas for mutual impedance between two probes arbitrarily located in a rectangular waveguide are given by means of dyadic Green's function (DGF), field transformation, and reaction concept. In the formulation presented, the waveguide is semi-infinite. Lengths, feeding points, and orientations of the two probes in the waveguide are all arbitrary. As examples, expressions of mutual impedance for eight specific cases are given and discussed     

A Multifilament Method-of-Moments Solution for the Input Impedance of a Probe-Excited Semi-Infinite Waveguide

The input impedance and surface currents of a probe-excited, short-circuited semi-infinite waveguide are determined by the method of moments. Expressions are given for the impressed electric field used to excite the probe from the coaxial source input using a semi-infinite-waveguide Green's function, and expressions are given for a free-space approximate impressed electric field which arises from the coaxial source input. The method-of-moments formulation used is based on a multifilament current approximation and solves for the surface currents of the probe as a function of probe angle around the probe. Comparison of theory and experiment is made.     

Modulo-2 expressions of switching functions

An algorithm is given for obtaining the modulo-2 sum of cascade realisable function expressions, for a given switching function. The expressions can then be used for the economical realisation of cutpoint cellular arrays with EXCLUSIVE-OR collector row.     

Characteristic mode analysis of a slot in a conducting planeseparating different media

The authors analyze a slot in a conducting plane separating different media when the slot is illuminated by a transverse electric and a transverse magnetic plane wave. The general characteristic mode theory for different media is used for the solution of this problem. The characteristic modes, which are computed using the method of moments, provide numerical results for the characteristic currents, the equivalent magnetic currents, and the field pattern for a slot whose width is a function of the wavelength. Analytical expressions for the narrow slot are also given     

Radiation from a slot in an impedance surface

The effects of a lossy-ground plane on the radiation from a slot are analyzed by using a Green's function of an impedance surface. Numerical results of the radiation field, radiated power, and loss power are presented for various lossy ground planes. In particular, the radiation field and the radiated power from a short slot are given by simple closed expressions. The analytical model of a slot in an impedance surface is validated by radiation field measurements     

斜程大气传输激光束的平均光强与短期光束扩展

基于广义惠更斯-菲涅耳原理、修正von Karman 湍谱、贝塞耳权重函数的高斯函数近似和误差小于4%的波结构函数平方近似,研究得出了包含湍流尺度影响的湍流大气中传输高斯光束的平均光强新关系和包含湍流外尺度影响的光束短期扩展因子。研究了高斯光束等效半径与传输距离、初始光束束径和光波波长间的关系,结果表明,在给定折射率结构参量和传输距离情况下,存在极小短期光束扩展对应的特征初始束径和特征光波波长。     

Analysis of a static power converter under unbalance: a novelapproach

A general analysis procedure for a static power converter using the transfer function approach is presented. This method provides for closed-form expressions for all harmonics under balanced and unbalanced operating conditions. Unbalance in voltage magnitude and phase angle and errors in switching angles can be easily incorporated into the analysis. An example illustrating the effectiveness of this approach is given     

Estimation in a Pareto Distribution: Theory & Computation

This paper treats the theoretical and computational problems of maximum likelihood parameter estimation in a Pareto distribution. Logarithmic likelihood estimating equations and the associated conditional log-likelihood function are derived, and expressions for the asymptotic variances and covariances of the parameters are given. Discussions pertinent to tests of hypotheses and the construction of simultaneous s-confidence contours are provided. The computations required for estimation are illustrated by an example in which the parameters are estimated by numerically maximizing the conditional log-likelihood function and by using an algorithm for global optimization which exploits the mathematical structure of this function. The parameter estimates obtained in this way are guaranteed to be those at which the likelihood function is globally maximum over the space of permissible parameter values. A Fortran program exists for performing these calculations.     

Electromagnetic Response of a Medium Loaded with Coated Conductive Particles

We consider a model of a mineralized ore zone in the form of a dissemination of metal particles of spheroidal shape. To account for electrochemical effects, the surface of the particles exhibits an interface impedance that can be any specified function of frequency. A quasi-static analysis is used, which is justified because the particles are electrically small. Explicit expressions for the induced dipole are given for the prolate spheroidal geometry and the oblate case follows a simple transformation. The result is exact only for the case where the angular dependence of the interface impedance has a special form. A general expression is given for the transient response of the particles when the primary field is abruptly terminated. The resulting decay of the secondary field is shown to be a strong function of the particle shape.     

Availability of a Renewable, Checked System

Recurrent expressions are given for point and interval unavailability of a renewable system subjected to periodic checking/repair. The expressions are generalizations of the basic relations in the theory of discrete renewal processes. The asymptotic limits for long times follow simply from a general theorem of this theory. The connection to previous expressions is established.     

Four-terminal analysis of the Hall generator

The four-terminal parameters of the Hall generator are derived and then used to develop expressions for input impedance, output impedance, current gain, and voltage gain. The theoretically determined expressions are then verified for a Hall generator using indium antimonide. The four-terminal equations are given as a function of conductivity, Hall constant, temperature, magnetic field, and dimensions of the material. Thus, the designer may use these expressions in the application of Hall-effect devices.     

Error rates of M-ary signals with. Multichannel reception in Nakagami-m fading channels

In this letter, we present closed. form expressions for the exact average symbol-error rate (SER) of M-ary modulations with multichannel reception over Nakagami-m fading channels. The derived expressions extend already available results for the nondiversity case, to maximal-ratio combining-(MRC) and postdetection equal-gain combining (EGC) diversity systems. The average SERs are given in terms of Lauricella's multivariate hypergeometric function F/sub D//sup (n)/. This function exhibits a finite integral representation that can be used for fast and accurate numerical computation of the derived expressions.     

Excitation of surface waves on a unidirectionally conducting screen by a phased line source

The excitation of surface waves on a unidirectionally conducting screen produced by a phased line source located above the screen and perpendicular to the wire elements is considered. The screen consists of an infinite number of straight, perfectly conducting, parallel wires and conducts only in the direction of the wire elements. The phased line source consists of a periodic line current with an electric charge distributed along its length. The complete electromagnetic field is determined exactly and simple expressions are given for the scattered far field. It is shown that surface waves exist and simple expressions for the amplitudes are given. Another principal result is the determination of the magnitude of the complex Poynting vector for the radiated power. It is found that the pattern function lies on a cone independent of the presence of the screen and that the cone angle depends only on the phasing of the source. The pattern function at points below the screen is independent of the location of the source above the screen. Furthermore, the pattern function vanishes in the direction of the screen and this seems concomittant to the existence of surface waves. Two pattern functions are drawn for typical cases of interest. The power propagated by the surface waves is also determined. The method employed to solve the problem is based on the deduction that the scattered magnetic field component in the direction of the wire elements is zero. A consequence of this deduction is that the electromagnetic field can be derived from a single scalar wave function that satisfies a partial differential equation in the plane of the screen and a jump condition across the screen. This method is quite general and can be applied to a large class of interesting propagation problems arising from different types of excitation. The scattered far field is obtained using another method that is algebraic in character and does not require a complete solution of the problem.     

Variance of least squares estimators for a damped sinusoidalprocess

The variance of least squares estimators for the parameter estimation of a damped sinusoidal process is analyzed, based on first-order perturbation. Analytical expressions for the variances of the frequency, damping factor, amplitude, and phase estimators are derived. Explicit expressions are given for both damped and undamped single-mode cases. The effect of mode separation on the accuracy is investigated through the two-mode case. The dependence of the variances on number of data points, model order, signal-to-noise ratio, and mode separation is investigated, both analytically and numerically, for practical applications. Extensive Monte Carlo simulation results are given to verify, enhance, and illustrate the analytical expressions     

Variational Principles and Mode Coupling in Periodic Structures

Variational techniques are used in analyzing periodic "cold" microwave structures for the angular frequency, omega, as a function of assumed phase shift per periodic cell. Two variational expressions are given: one for omega in terms of the E- and H-fields, and one for k² = omega²µ epsilon in terms of the E-field. For structures with relatively light coupling between cells, the trial fields to be used with the variational expressions are composed of closed cavity modes, phase shifted by phi radians from cell to cell. Both variational expressions yield determinantal equations for k²(phi) which agree with equations previously derived from a mode coupling point of view. One form of an equivalent lumped circuit is given to represent the structure within one of its pass bands. Curves compare the variational-mode coupling expression for k²(phi) of a periodically lumped loaded transmission line with exact expressions.     

Electromagnetic Backscattering from a Layer of Vegetation: A Discrete Approach

Electromagnetic backscattering from a layer of vegetation over a flat lossy ground is studied. The vegetated region is composed of leaves which are modeled by lossy circular dielectric discs with prescribed orientation statistics. The mean field in the layer is computed by using the Foldy approximation and a two-variable technique which is valid for small fractional volume. Simple expressions are given for the skin depth of the mean wave. Following this, the distorted Born approximation is used to calculate the co-polarized and cross polarized backscattering coefficients. These are then computed as a function of angle of incidence for different layer depths and leaf configurations.     

On the upper bound of the probability of error of a linear pattern classifier for probabilistic pattern classes

Given a set of sample patterns for two pattern classes, some simple expressions for the upper bound of the probability of error for a linear pattern classifier and the optimal linear discriminant function minimizing the upper bound are obtained. Using these results, if the tolerable probability of error of classifying patterns in the two pattern classes is not smaller than this upper bound, not only a linear pattern classifier is known to be feasible, but also a satisfactory linear discriminant function is given. The results presented here are independent of the probability distribution of the patterns in the pattern classes. For some special cases, a smaller upper bound is found.     

四种桥函数的数学表达式

本文给出了四种桥函数的数学表达式及其证明，指出沃尔什函数系、方块脉冲函数系、哈尔函数系、赫尔函数系、特尔函数系都是桥函数系的一部分。     

Average Error Performance of M-ary Modulation Schemes in Nakagami-q (Hoyt) Fading Channels

Presented are exact-form expressions for the average error performance of various coherent, differentially coherent, and noncoherent modulation schemes in Nakagami-q (Hoyt) fading channels. The expressions are given in terms of the Lauricella hypergeometric function, F_D ⁽ⁿ⁾; for nges1, which can be evaluated numerically using its integral or converging series representation. It is shown that the derived expressions reduce to some existing results for Rayleigh fading as special cases