multilayered media green s functions in integral equation formulations a compact representation is given of the electric and magnetic type dyadic green s functions for plane stratified multilayered uniaxial media based on the transmission line network analog along the aids normal to the stratification furthermore mixed potential integral equations are derived within the framework of this transmission line formalism for arbitrarily shaped conducting or penetrable objects embedded in the multilayered medium the development emphasizes laterally unbounded environments but an extension to the case of a medium enclosed by a rectangular shield is also included

on modules with cyclic vertices in the auslander reiten quiver in studying indecomposable modules of a finite dimensional k algebra where k is a field the auslander reiten quiver r has proved to be a powerful tool if the algebra is a group algebra kg or a block b then properties of the group are related to the graph structure of the auslander reiten quiver for example the graph f kg or t b is finite if and only if a sylow p subgroup of g or a defect group of b is cyclic where p is the characteristic of k it is now well known that an indecomposable kg module has a vertex which is a minimal subgroup q of g such that a4 is q projective and q is unique up to g conjugation 7 we ask whether there are constraints on the position of modules with a given vertex in the auslander reiten quiver here we are concerned with this problem for modules with cyclic vertices which are not projective there is not much to say in the case when the defect group of the block is cyclic in this case all its modules have cyclic vertices we assume therefore that the block containing these modules has a non cyclic defect group assume that m is indecomposable with a cyclic vertex and that a4 is not projective it is well known that m is n periodic hence r periodic for group algebras the auslander reiten translate r is the same as 02 where 52 is the usual heller operator by a more general theorem 2 p 1631 the component o say of the stable auslander reiten quiver containing m is a tube 151 given such a tube 0 then the vertices in each row form a single r orbit the end of the tube is the unique row where each vertex has only one predecessor that is if m is a module corresponding to a vertex it41 in 0 and o rm e m o i 289 002 l 8693 86 3 00

analysis of a circular microstrip disk antenna with a thick dielectric substrate the problem of a circular microstrip disk excited by a probe is solved using rigorous analysis the disk is assumed to have zero thickness and the current on the probe is taken to be uniform using vector hankel transforms the problem is formulated in terms of vector dual integral equations from which the unknown current can be solved for due to the singular nature of the current distribution arising from probe excitation the direct application of galerkin s basis function expansion method gives a slowly convergent result therefore the singular part of the current is removed since the singularity is known a priori the unknown current to be solved for is then regular and tenable to galerkin s method of analysis it is shown that this analysis agrees with the single mode approximation when the dielectric substrate layer is thin and that it deviates from the single mode approximation when the substrate layer is thick excellent agreement of both the computed real and imaginary parts of the input impedance with experimental data is noted the radiation patterns and the current distributions on the disk are also presented

unbounded and scattered field representations of the dyadic green s functions for planar stratified bianisotropic media this paper presents a rigorous formulation of the spectral domain dyadic green s functions for planar stratified bianisotropic media the media may consist of any number of layers bounded by optional impedance admittance walls both electric and magnetic dyadic green s functions for arbitrary field and source locations are derived simultaneously based on the principle of scattering superposition these dyadics are decomposed into unbounded and scattered parts the scattered dyadic green s functions are determined without cumbersome operations using the concepts of effective reflection and transmission of outward bounded and inward bounded waves the scattering coefficient matrices are expressed in compact and convenient forms involving global reflection and transmission matrices corresponding to the impedance admittance boundary walls the global reflection matrices are related directly to the wall impedance admittance dyadics for illustration the general expressions of dyadic green s functions are applied to the configuration of a grounded bianisotropic slab embedded in isotropic halfspace

two dimensional periodicity in rectangular arrays string matching is rich with a variety of algorithmic tools in contrast multidimensional matching has had a rather sparse set of techniques this paper presents a new algorithmic technique for two dimensional matching periodicity analysis its strength appears to lie in the fact that it is inherently two dimensional periodicity in strings has been used to solve string matching problems multidimensional periodicity however is not as simple as it is in strings and was not formally studied or used in pattern matching in this paper we define and analyze two dimensional periodicity in rectangular arrays one definition of string periodicity is that a periodic string can self overlap in a particular way an analogous concept is true in two dimensions the self overlap vectors of a rectangle generate a regular pattern of locations where the rectangle may originate based on this regularity we define four categories of periodic arrays nonperiodic lattice periodic line periodic and radiant periodic and prove theorems about the properties of the classes we give serial and parallel algorithms that find all locations where an overlap originates in addition our algorithms find a witness proving that the array does not self overlap in any other location the serial algorithm runs in time o m2 linear time when the alphabet size is finite and in o m2log m otherwise the parallel algorithm runs in time o log m using o m2 crcw processors

a new approach to dyadic green s function in spectral domain a new method is proposed to derive the dyadic green s function for stratified dielectric layers from the wave equation in spectral domain the result is a clear equivalent circuit of the whole structure which combines the te and tm modes by hybrid block matrices it is simple to apply and evaluate the relation to the conventional immittance approach is shown by means of a similarity transform which diagonalizes the submatrices the simplicity of the method is demonstrated in the application to the well known example of a single microstrip patch on a grounded dielectric layer as well as structures with multiple layers and metallizations in arbitrary interfaces

accurate approximation of green s functions in planar stratified media in terms of a finite sum of spherical and cylindrical waves a robust and computationally expedient methodology is presented for accurate closed form approximation of the green s functions used in the mixed potential integral equation statement of the electromagnetic boundary value problem in planar stratified media the proposed methodology is based on the fitting of the spectrum of the green s function after the extraction of the quasistatic part making use of rational functions the effectiveness and robustness of the proposed methodology rely upon the proper sampling of the spectrum in order to improve the accuracy of the rational function fit the resulting closed form approximation is in terms of both spherical and cylindrical waves thus high accuracy is obtained in the approximation of the green s function irrespective of the distance of the observation point from the source the methodology is validated through its application to the approximation of the green s function for a multi layered planar dielectric stack

spectral dyadic green s function formulation for planar integrated structures the problem of the complete determination of the dyadic spectral green s function for an integrated planar structure with a grounded dielectric slab has been considered and solved in a rigorous way by using the spectral theory of the electromagnetic field the reciprocity theorem and the geometrical symmetry of the structure have demonstrated the different roles played by the independent terms of the spectral green s function in the evaluation of the electromagnetic characteristics of the grounded slab excited with a general source furthermore an equivalent circuit representation of the structure allowing a noteworthy simplification in the determination of the total power has been obtained these equivalent circuits and the derived spectral green s function presented here can be used to analyze and design microstrip antennas of arbitrary shape with a general type of loading such as matched or unmatched loads parasitic and shorting pins

rigorous and efficient full wave analysis of trapezoidal patch antennas a rigorous full wave analysis in the spectral domain for trapezoidal patch antennas is presented particularly a new set of entire domain basis functions for an efficient implementation of the method of moments mom is carried out by properly imposing the boundary conditions the simulated results obtained through the presented method are compared to the measurements showing a good agreement finally a parametric analysis of the main antenna features matching radiation pattern cross polarization levels is also carried out

on the vertices of indecomposable modules over dihedral 2 groups abstract let k be an algebraically closed field of characteristic 2 we calculate the vertices of all indecomposable k d 8 modules for the dihedral group d 8 of order 8 we also give a conjectural formula of the induced module of a string module from k t 0 to kg where g is a dihedral group of order 8 and where t 0 is a dihedral subgroup of index 2 of g some cases where we verified this formula are given

parametric analysis of slot loaded trapezoidal patch antennas slot loaded trapezoidal patch antennas are analyzed in order to achieve a multifrequency operation a moment method formulation based on new analytical entire domain basis functions is developed and compared to the one involving the rao wilton glisson 1982 rwg triangular discretization the numerical results obtained through the new efficient implemented code are compared to the measurements showing a good agreement a parametric analysis of such antennas is also presented leading to useful design graphs showing the main antenna properties resonance frequencies cross polarization levels matching etc as a function of the patch geometrical dimensions symmetric collocation of the slots on the patch and slot dimensions

usefulness of the karp miller rosenberg algorithm in parallel computations on strings and arrays abstract the karp miller rosenberg 1972 algorithm was one of the first efficient almost linear sequential algorithms for finding repeated patterns and for string matching in the area of efficient sequential computations on strings it was soon superseded by more efficient and more sophisticated algorithms we show that the karp miller rosenberg algorithm kmr must be considered as a basic technique in parallel computations for many problems variations of kmr give the known most efficient parallel algorithms the representation of the set of basic factors subarrays of a string array produced by the algorithm is an extremely useful data structure in parallel algorithms on strings and arrays this gives also a general unifying framework for a large variety of problems we show that the following problems for strings and arrays can be solved by almost optimal parallel algorithms pattern matching longest repeated factor subarray longest common factor subarray maximal symmetric factor subarray also the following problems for strings can be solved within the same complexity bounds finding squares testing even palstars and compositions of k palindromes for k 2 3 4 computing lyndon factorization and building minimal pattern matching automata in the model without concurrent writes the parallel time is o log n 2 with n processors and in the model with concurrent writes the time for most of the problems is o log n with n processors for two problems related to the one dimensional case longest repeated factor and longest common factor there were designed parallel algorithms using suffix trees apostolico et al 1988 however our data structure is simpler and furthermore for the two dimensional case suffix trees do not work the complexity of our algorithms does not depend on the size of the alphabet except for the computation of pattern matching automata

optimal parallel algorithms for string matching let wram pram be a parallel computer with p processors rams which share a common memory and are allowed simultaneous reads and writes only simultaneous reads the only type of simultaneous writes allowed is a simultaneous and a subset of the processors may write 0 simultaneously into the same memory cell let t be the time bound of the computer we design below families of parallel algorithms that solve the string matching problem with inputs of size n n is the sum of lengths of the pattern and the text and have the following performance in terms of p t and n 1 for wram pt o n for p n log n i e t log n 2 for pram pt o n for p n log 2 n i e t log 2 n 3 for wram t constant for p n 1 e and any e 0 4 for wram t o log n log log n for p n similar families are also obtained for the problem of finding all initial palindromes of a given string

contour fft based spectral domain mbf analysis of large printed antenna arrays a fast spectral domain method is proposed to evaluate the reaction terms between the macro basis functions in regular and non regular arrays made of identical printed antennas the presented technique first exploits the filtering capabilities of the macro basis functions in the spectral domain the method is then strongly accelerated with the help of a newly formulated fast fourier transform fft based technique which is applicable to a contour integration in the complex plane we name the method as contour fft c fft besides an effective homogeneous medium term treated with multipoles a computational complexity of order n log2 n is achieved for the tabulation of substrate related reaction terms for any possible relative positions the complexity of the proposed method is independent from the complexity of the elements numerical results obtained with the proposed method are compared with those from a pre validated reference solution based on the traditional macro basis functions technique an excellent agreement is observed

on two dimensional pattern matching by optimal parallel algorithms simplified versions of kedem landau palem algorithms for parallel one dimensional and two dimensional pattern matching on a crcw pram are presented we show that the only nontrivial part of klp algorithm is the preprocessing part computation of consistent names of very small factors the crucial part in klp algorithm is a suffix prefix matching subprocedure in our algorithm such a subprocedure is avoided a novel algorithm for 2 dimensional matching is presented which is more directly designed for two dimensional objects it does not use the multi text multi pattern approach as in klp algorithm techniques for constructing parallel image identification algorithms are introduced cutting images into small factors and compressing images by a parallel reduction of a large number of such independent factors into smaller objects the importance of five types of factors is emphasized a new useful type of two dimensional factors is introduced thin factors

spectral electromagnetic modeling of a planar integrated structure with a general grounded anisotropic slab a formulation for the solution of the electromagnetic field in vertically stratified structures with a general anisotropic grounded slab under planar electric excitation conditions is presented the development of the solution is obtained by using the two dimensional fourier transform applied to the partial differential equations describing the electromagnetic field which can be expressed in terms of dyadic electric green s functions moreover a spectral equivalent circuit representation of the solution separated into its spectral transverse electric te and transverse magnetic tm components with respect to the vertical direction is given it is demonstrated that such a spectral circuit representation is always possible when the constitutive epsilon and mu tensors are reduced to their diagonal form the transmission line representation for an unbounded gyrotropic medium with vertical preferred axis is presented this theory is applied to a planar structure with an anisotropic biaxial grounded slab and an electric horizontal point source embedded in it numerical examples of evaluation of the radiated pattern and noteworthy information about the radiation on the horizon plane are given

semantics of dyadic and mixed potential field representation for 3 d current distributions in planar stratified media the full spectral electric dyadic green s function for three dimensional current distributions in planar stratified media can be obtained straight from maxwell s equations by following a physical reasoning analogous with the free space case but using general derivative relations for multilayered green s functions we derive a basic mixed potential form with a simple vector potential kernel but multiple scalar potential kernels and also obtain the well established single scalar potential formulations with a dyadic vector potential kernel mixed potential forms are thus arrived at without the a priori introduction of scalar and vector potential or choice of gauge condition the nonuniqueness of the scalar potential kernel and the dyadic nature of the scalar and or vector potentials are believed to be clarified by the proposed approach a discussion of the different formulations focuses on physical meaning and numerical consequences for the solution of integral equations

fast parallel and serial multidimensional approximate array matching abstract consider the multidimensional array matching problem where differences between characters of the pattern and characters of the text are permitted a difference may be due to a mismatch between a text and pattern character superfluous text character or superfluous pattern character given a d dimensional array of size nd text and a d dimensional array of size md pattern we present the following algorithms for a given k find all occurrences of the pattern in the text with at most k differences our serial algorithm runs in time o nd dk k2 and the parallel algorithm runs in time o d dlog n k k2 using nd processors if superfluous characters are not allowed and the only permitted errors are mismatches we solve the problem serially in time o nddk and in parallel in time o d dlogn k using nd processors we present an alternate algorithm for the mismatches problem which runs serially in time o 2dndlog2 m and in parallel in time o d log n using nd processors this algorithm is more efficient for large k we also give an efficient solution to the close match problem here a mismatch weight function f 0 1 is assigned the weight function gives weight to the mismatches some mismatches being worse than others we present a serial algorithm for finding all appearances of the pattern in the text with a bounded total error in time o 2dnd log2 m our parallel algorithm is again of time complexity o d log n using nd processors