particle swarm optimization in electromagnetics the particle swarm optimization pso new to the electromagnetics community is a robust stochastic evolutionary computation technique based on the movement and intelligence of swarms this paper introduces a conceptual overview and detailed explanation of the pso algorithm as well as how it can be used for electromagnetic optimizations this paper also presents several results illustrating the swarm behavior in a pso algorithm developed by the authors at ucla specifically for engineering optimizations ucla pso also discussed is recent progress in the development of the pso and the special considerations needed for engineering implementation including suggestions for the selection of parameter values additionally a study of boundary conditions is presented indicating the invisible wall technique outperforms absorbing and reflecting wall techniques these concepts are then integrated into a representative example of optimization of a profiled corrugated horn antenna

periodic polya urns the density method and asymptotics of young tableaux polya urns are urns where at each unit of time a ball is drawn and replaced with some other balls according to its colour we introduce a more general model the replacement rule depends on the colour of the drawn ball and the value of the time operatorname mod p we extend the work of flajolet et al on polya urns the generating function encoding the evolution of the urn is studied by methods of analytic combinatorics we show that the initial partial differential equations lead to ordinary linear differential equations which are related to hypergeometric functions giving the exact state of the urns at time n when the time goes to infinity we prove that these periodic polya urns have asymptotic fluctuations which are described by a product of generalized gamma distributions with the additional help of what we call the density method a method which offers access to enumeration and random generation of poset structures we prove that the law of the southeast corner of a triangular young tableau follows asymptotically a product of generalized gamma distributions this allows us to tackle some questions related to the continuous limit of random young tableaux and links with random surfaces

fractal design of multiband and low side lobe arrays most array factor design techniques are highly dependent on the operating wavelength in this paper a novel technique based on fractal structures is described for multiband operation the analysis is focused in two different approaches the fractal spatial arrangement of array elements and the fractal design of array factors although the patterns of fractal arrays show some interesting similarity properties at several bands the directivity is not held constant through the bands nevertheless such structures have been shown to be useful for designing low side lobe arrays with equally weighted current elements on the other hand the fractal array factors presented do keep the same shape at several bands because they are designed as selfsimilar curves the arrays that would synthesize such patterns present a characteristic power law current distribution analogous to the spectral distribution of the bandlimited fractal weierstrass function

random sorting networks abstract a sorting network is a shortest path from 12 n to n 21 in the cayley graph of s n generated by nearest neighbour swaps we prove that for a uniform random sorting network as n the space time process of swaps converges to the product of semicircle law and lebesgue measure we conjecture that the trajectories of individual particles converge to random sine curves while the permutation matrix at half time converges to the projected surface measure of the 2 sphere we prove that in the limit the trajectories are holder 1 2 continuous while the support of the permutation matrix lies within a certain octagon a key tool is a connection with random young tableaux

jeu de taquin dynamics on infinite young tableaux and second class particles we study an infinite version of the jeu de taquin sliding game which can be thought of as a natural measure preserving transformation on the set of infinite young tableaux equipped with the plancherel probability measure we use methods from representation theory to show that the robinson schensted knuth rsk algorithm gives an isomorphism between this measure preserving dynamical system and the one sided shift dynamics on a sequence of independent and identically distributed random variables distributed uniformly on the unit interval we also show that the jeu de taquin paths induced by the transformation are asymptotically straight lines emanating from the origin in a random direction whose distribution is computed explicitly and show that this result can be interpreted as a statement on the limiting speed of a second class particle in the plancherel tasep particle system a variant of the totally asymmetric simple exclusion process associated with plancherel growth in analogy with earlier results for second class particles in the ordinary tasep

efficient analysis of large aperiodic antenna arrays using the domain green s function method an efficient method of moments mom based domain decomposition technique viz the domain green s function method dgfm is presented for analyzing large antenna arrays the dgfm is a perturbation technique where mutual coupling between array elements is accounted for during the formulation of an active impedance matrix for each domain array element the active current distribution on the entire array geometry is obtained by solving the smaller matrix equations related to the elements and not that of the problem as a whole this leads to a significant saving in both runtime and memory usage the method also takes into account the edge effects attributed to the finite size of the array complex excitations with nonlinear phase shift and is not limited to periodic array configurations the dgfm is an approximation and assumes a slowly varying current distribution between domains a novel way to mitigate the aforementioned by including secondary coupling effects is also discussed furthermore an efficient active impedance matrix fill strategy is presented where the active impedance matrix summation is truncated to include only a certain number of terms parallelization using both distributed and shared memory programming models have also been applied to the dgfm to further optimize runtime and memory usage

coexistence of bouncing and classical periodic solutions of generalized lazer solimini equation abstract the paper deals with the singular differential equation x g x p t where g has a weak singularity at x 0 sufficient conditions for a coexistence of two types of periodic solutions are presented the first type is a classical periodic solution which is strictly positive on r and does not reach the singularity the second type is a bouncing periodic solution which reaches the singularity at isolated points in particular we state a constant k 0 such that there exist at least two 2 periodic bouncing solutions having their maximum less than k and at least one 2 periodic classical solution having its minimum greater than k the proofs are based on the ideas of the poincare birkhoff twist map theorem and approximation principles

irregular phased array tiling by means of analytic schemata driven optimization the design of subarrayed planar phased arrays characterized by an irregular organization of domino shaped tiles is addressed starting from optimal tiling theorems drawn from mathematical theory an enumerative approach able to retrieve the optimal clustering providing the maximum aperture coverage and the best radiation performance is proposed to deal with the synthesis of low medium size rectangular arrays based on the same optimal theorems and still exploiting the algorithmic procedures at the basis of the enumerative approach an innovative schemata based optimization method is introduced for designing large arrays as well a set of representative results concerned with ideal as well as real radiating elements is reported and discussed to highlight the features and the potentialities of the proposed analytically based design framework

periodic solutions of singular second order differential equations upper and lower functions abstract in this paper we continue the study of the periodic problem for the second order equation u f u u g u h t u where h is a caratheodory function and f g are continuous functions on 0 which may have singularities at zero both attractive and repulsive singularities are considered the method relies on a novel technique of construction of lower and upper functions as an application we obtain new sufficient conditions for the existence of periodic solutions to the rayleigh plesset equation

bouncing solutions of an equation with attractive singularity for any n m 2 in it is proved the existence of 2m periodic solutions with n bouncings in each period for a second order forced equa tion with attractive singularity by using the approach of successor map and poincare birkho twist theorem

mixing times of the biased card shuffling and the asymmetric exclusion process consider the following method of card shuffling start with a deck of n cards numbered 1 through n fix a parameter p between 0 and 1 in this model a shuffle consists of uniformly selecting a pair of adjacent cards and then flipping a coin that is heads with probability p if the coin comes up heads then we arrange the two cards so that the lower numbered card comes before the higher numbered card if the coin comes up tails then we arrange the cards with the higher numbered card first in this paper we prove that for all p 1 2 the mixing time of this card shuffling is o n 2 as conjectured by diaconis and ram 2000 our result is a rare case of an exact estimate for the convergence rate of the metropolis algorithm a novel feature of our proof is that the analysis of an infinite asymmetric exclusion process plays an essential role in bounding the mixing time of a finite process

optimal far field focusing of uniformly spaced arrays subject to arbitrary upper bounds in nontarget directions a new approach providing new theoretical results to the optimal far field focusing of uniformly spaced arrays subject to a completely arbitrary mask for sidelobe bounds is presented and discussed in both cases of linear or planar arrays with rectangular boundaries it is first shown that the problem can be formulated without any loss to performances on the maximum as a linear programming one guaranteeing a globally optimal solution second a sufficient uniqueness criterion for the solution of the overall problem is also developed which shows how the solution may not be unique as is actually the case when planar arrays are considered in addition further globally effective optimization procedures are proposed for the latter case in order to optimize directivity smoothness of excitations or other performance parameters in the set of equivalent solutions last an extension to planar arrays with a nonrectangular boundary is also given a thorough numerical analysis confirms the effectiveness of the approach proposed and of the solution codes developed

investigation of scattering properties of large scale aperiodic tilings using a combination of the characteristic basis function and adaptive integral methods this paper presents a hybrid approach for efficient analysis of electromagnetic em scattering from large scale aperiodic structures e g aperiodic penrose and danzer tilings which integrates the characteristic basis function method cbfm and the adaptive integral method aim by performing a domain decomposition a series of characteristic basis functions cbfs that are defined on a macro block and comprised of a relatively large number of sub domain basis functions facilitate a substantial reduction in the method of moments mom matrix size enabling the use of a direct solver for large problems the aim is applied to accelerate the calculation of cbfm reduced mom matrices significantly decreasing the cpu time and memory required for solving large scale problems as the size of one block becomes electrically large the original cbfm combined with the aim is employed to generate the initial cbfs by solving a large problem with multiple excitations which results in efficiently constructing the final cbfs afforded by the singular value decomposition svd procedure this methodology produces a two level cbfm aim hybrid algorithm for efficiently characterizing large scale objects the numerical results presented demonstrate the accuracy and efficiency of the proposed hybrid algorithm then the developed solver is applied to investigate em scattering properties of large scale aperiodic tilings the numerical results show that penrose danzer tilings exhibit significantly improved grating lobe suppression as compared to their periodic counterparts

hydrodynamics and large deviation for simple exclusion processes we prove the hydrodynamical limit for weakly asymmetric simple exclusion processes a large deviation property with respect to this limit is established for the symmetric case we treat also the situation where a slow reaction creation and annihilation of particles is present

aperiodic array layout optimization by the constraint relaxation approach an optimization procedure for the layout assessment of electrically large but finite planar arrays is presented the synthesis takes into account the desired directivity pattern that is prescribed employing bound constraints moreover the size of the radiators is taken into account which results in a hard nonoverlapping between the elements constraint the latter should not be violated if we want the attained solution not only to obey the far field mask but also to be physically realizable as stated the optimization problem is twofold an antenna design is associated with a packing problem in order to take the constraints on the layout into account and solve the whole problem we propose the constraint relaxation approach which is equipped with a packing algorithm our study is applied to various initial geometries and the resulting arrays appear to comply with the desired pattern and the nonoverlapping constraint several examples for different cases including symmetric arrays and a study on maximally sparse arrays are presented which show the applicability and merit of the method

design of planar arrays with reduced nonuniform excitation subject to constraints on the resulting pattern and the directivity a design procedure for the synthesis of planar arrays is presented synthesis takes into account the desired pattern and the constraint on the directivity index it makes use of the perturbation method in conjunction with the lagrange multiplier theory starting from an initial array we perturb the element positions by employing an iterative technique in the iteration by setting the first variation of the lagrangian cost function equal to zero we derive the perturbed positions perturbation is applied simultaneously along two independent variables element coordinates x and y the final position of the elements results from the last iteration where the stopping criteria are met the choice of the initial array takes into account the number of elements and the reduction need of nonuniformity in the excitation our study is used for various initial geometries and the resulting arrays are shown to comply with the desired pattern and the directivity index

shape fluctuations and random matrices we study a certain random growth model in two dimensions closely related to the one dimensional totally asymmetric exclusion process the results show that the shape fluctuations appropriately scaled converges in distribution to the tracy widom largest eigenvalue distribution for the gaussian unitary ensemble gue

on the distribution of the length of the longest increasing subsequence of random permutations let sn be the group of permutations of 1 2 n if 7r e sn we say that 7 i1 7f ik is an increasing subsequence in 7r if il i2 ik and 7r ii 7r i2 7r ik let 1n r be the length of the longest increasing subsequence for example if n 5 and 7r is the permutation 5 1 3 2 4 in one line notation thus 7r 1 5 7r 2 1 then the longest increasing subsequences are 1 2 4 and 1 3 4 and n 3 equip sn with uniform distribution

an autopolyploidy based genetic algorithm for enhanced evolution of linear polyfractal arrays there has been considerable recent interest in techniques for the optimization of large n antenna arrays unfortunately the successful development of such techniques has been hindered by the large number of independent parameters that must be optimized and the complexity of the calculations needed for the electromagnetic evaluation of large n arrays one promising new design methodology for large n arrays which has recently been introduced is based on properties of a subset of fractal random arrays called polyfractal arrays polyfractal arrays have many embedded self similar structures thereby allowing very large and seemingly complex array layouts to be described with only a small set of independent parameters in addition by effectively utilizing the self similarity of polyfractal arrays a considerable reduction can be achieved in the amount of time required to evaluate the radiation patterns of large n arrays this paper introduces a type of nature based design process that applies a specially formulated genetic algorithm ga technique to evolve optimal polyfractal array layouts the most unique aspect of this optimization technique is a new autopolyploidy based chromosome expansion that maximizes the efficiency of the gas simple polyfractal geometries are used in the initial stage or first epoch of the optimization because the number of independent parameters is small and the computation times are relatively fast after the optimization converges for the first epoch more complicated descriptions of these polyfractal arrays are introduced to provide additional independent parameters for the optimizer as it progresses through later epochs of evolution this process has been shown to be very effective in creating optimized large n arrays the largest example considered here being a 1616 element linear array with a 24 30 db sidelobe level and a 0 056deg half power beamwidth

canonical substitutions tilings of ammann beenker type we present a large class of parallelogram tilings that have two important features in common with the ammann beenker tiling they can be constructed by canonical projection from z4 r4 to a plane and they admit substitution rules

bayesian compressive sampling for pattern synthesis with maximally sparse non uniform linear arrays a numerically efficient technique based on the bayesian compressive sampling bcs for the design of maximally sparse linear arrays is introduced the method is based on a probabilistic formulation of the array synthesis and it exploits a fast relevance vector machine rvm for the problem solution the proposed approach allows the design of linear arrangements fitting desired power patterns with a reduced number of non uniformly spaced active elements the numerical validation assesses the effectiveness and computational efficiency of the proposed approach as a suitable complement to existing state of the art techniques for the design of sparse arrays

minimum sidelobe levels for linear arrays a method of finding the optimum sidelobe minimizing weights for an arbitrary linear array is derived that holds for any scan direction beamwidth and type of antenna element used optimum linear array positions are then determined via the particle swarm optimization method hence the two together can give a global bound on antenna array performance with regards to sidelobe minimization results are presented for linear arrays of 2 6 elements for different scan angles beamwidths and antenna elements

nonuniform fast fourier transforms using min max interpolation the fast fourier transform fft is used widely in signal processing for efficient computation of the ft of finite length signals over a set of uniformly spaced frequency locations however in many applications one requires nonuniform sampling in the frequency domain i e a nonuniform ft several papers have described fast approximations for the nonuniform ft based on interpolating an oversampled fft this paper presents an interpolation method for the nonuniform ft that is optimal in the min max sense of minimizing the worst case approximation error over all signals of unit norm the proposed method easily generalizes to multidimensional signals numerical results show that the min max approach provides substantially lower approximation errors than conventional interpolation methods the min max criterion is also useful for optimizing the parameters of interpolation kernels such as the kaiser bessel function

modular broadband phased arrays based on a nonuniform distribution of elements along the peano gosper space filling curve the peano gosper space filling curve provides an excellent framework for designing broadband planar antenna arrays with highly modular architectures uniformly distributing elements along the curve leads to an element distribution with a triangular lattice that has an irregular fractal boundary contour this boundary contour allows for a modular subarray configuration and better sidelobe suppression than conventional triangular lattice arrays with a regular boundary contour while they have a greater bandwidth than square lattice distributions arrays based on a triangular lattice still possess a rather limited bandwidth for beam steering applications due to the formation of grating lobes in this communication it will be shown that the beam steering capabilities of the peano gosper array can be enhanced by introducing perturbations into the basic recursive array generation scheme with the proper implementation the perturbed arrays retain the attractive features of modularity and recursive beamforming that are associated with the standard peano gosper array examples will be presented for several stages of peano gosper arrays that were designed for 2 1 broadband performance while scanning within a 30 conical volume full wave simulations will be used to examine the effects of mutual coupling on these aperiodic array layouts

diffuse scattering on graphs abstract we formulate and analyze difference equations on graphs analogous to time independent diffusion equations arising in the study of diffuse scattering in continuous media moreover we show how to construct solutions in the presence of weak scatterers from the solution to the homogeneous background problem using born series providing necessary conditions for convergence and demonstrating the process through numerous examples in addition we outline a method for finding green s functions for cayley graphs for both abelian and non abelian groups finally we conclude with a discussion of the effects of sparsity on our method and results outlining the simplifications that can be made provided that the scatterers are weak and well separated

non periodic tessellations with unit and non unit pisot inflation factors non periodic planar patterns generated by deterministic inflation rules are described several types of patterns with both unit and non unit pisot numbers as inflation factors are formed by triangular prototiles when the inflation factor is the silver mean the patterns can be obtained by superimposing two subpatterns and some of them can be converted into face to face patterns the geometric constructions corresponding to 12 fold symmetry are also studied the fourier transform of point masses placed in vertex positions of the transformed subpatterns exhibit two fold four fold and six fold symmetries although the peaks with highest intensities are situated in rings with apparent octagonal and dodecagonal symmetries

element positioning for linear arrays using generalized gaussian quadrature we present a novel approach for designing small narrowband linear arrays with unequally spaced elements our approach involves discretising a line source with a desirable beam pattern and relies on the fact that beam patterns are bandlimited we show that given a nonnegative weighting function for a line source one can design a linear array of elements whose beam pattern approximates that of the line source to any desired degree of accuracy we make use of the prolate spheroidal wave functions to analyze line source beam patterns since they are eigenfunctions of the finite fourier transform these functions form a tchebycheff system which allows us to calculate exactly integrals involving these functions via a generalized gaussian quadrature rule this quadrature rule then gives the appropriate set of element positions and weights we give results for several weighting functions and we consider both broadside and electronically scanned linear arrays as an example we show how a broadside array with half wavelength spacing and dolph tchebycheff weights may be improved upon using the method described

combinatorial aspects of the lascoux schutzenberger tree abstract in 1982 richard stanley introduced the formal series f x in order to enumerate reduced decompositions of a given permutation stanley european j combin 5 4 1984 359 not only showed f x to be symmetric but in certain cases f x was a schur function stanley conjectured that for arbitrary f x was always schur positive edelman and greene subsequently proved this fact combinatories and algebra boulder co 1983 amer math soc providence ri 1984 pp 155 162 adv in math 63 1 1987 42 using the techniques of lascoux and schutzenberger lett math phys 10 2 3 1985 111 for computing littlewood richardson coefficients we will exhibit a new bijective proof of the schur positivity of f x

the tasep speed process in the multi type totally asymmetric simple exclusion process tasep each site ofz is occupied by a labeled particle and two neighboring particles are int erchanged at rate one if their labels are in increasing order consider the process with the initial con figuration where each particle is labeled by its position it is known that in this case a s each particle has an asymptotic speed which is distributed uniformly on 1 1 we study the joint distribution of these speeds the tasep speed process we prove that the tasep speed process is a stationary measure for the multi type tasep dynamics consequently we can describe every ergodic stationary measure as a projection of the speed process measure this generalizes previous descriptions restricted to finitely many classes by combining this result with known stationary measures for taseps with finitely many types we compute several marginals of the speed process including the joint density of two and three consecutive speeds one striking property of the distribut ion is that two speeds are equal with positive probability and for any given particle there are infinitely m any others with the same speed we also study the partially asymmetric simple exclusion process asep we prove that the states of the asep with the above initial configuration seen as permutations ofz are symmetric in distribution this allows us to extend some of our results i ncluding the stationarity and description of all ergodic stationary measures also to the asep

quaquaversal tilings and rotations we construct a hierarchical tiling of 3 dimensional euclidean space based on a triangular prism using repeated rotations about orthogonal axes by angles 2 m and 2 n to analyze the structure of the tiling we are led to determine the group g m n generated by such a pair of rotations for m n 3 and for m 3 n 4

an efficient recursive procedure for evaluating the impedance matrix of linear and planar fractal arrays the self similar geometrical properties of fractal arrays are exploited in this paper to develop fast recursive algorithms for efficient evaluation of the associated impedance matrices as well as driving point impedances the methodology is demonstrated by considering two types of uniformly excited fractal arrays consisting of side by side half wave dipole antenna elements these examples include a triadic cantor linear fractal array and a sierpinski carpet planar fractal array this class of self similar antenna arrays become significantly large at higher order stages of growth and utilization of fractal analysis allows the impedance matrix and hence the driving point impedances to be obtained much more efficiently than would be possible using conventional analysis techniques

a hierarchical strongly aperiodic set of tiles in the hyperbolic plane we give a new construction of strongly aperiodic set of tiles in h 2 exhibiting a kind of hierarchical structure simplifying the central framework of margenstern s proof that the domino problem is undecidable in the hyperbolic plane margenstern 2008 16

representations of symmetric groups and free probability abstract we consider representations of symmetric groupssqfor largeq we give the asymptotic behaviour of the characters when the corresponding young diagrams rescaled by a factorq 1 2 converge to some prescribed shape this behaviour can be expressed in terms of the free cumulants for a probability measure associated with the limit shape of the diagram we also show that the basic operations of representation theory like taking tensor products restriction or induction have a limiting behavior which can be described using the free probability theory of d voiculescu

fast iterative method of power synthesis for antenna arrays a fast and simple method of power synthesis for antenna arrays of arbitrary geometry is presented the method adopts an auxiliary function having the desired amplitude pattern and a generic phase pattern and determines in closed form the array pattern approximating the auxiliary function in both amplitude and phase a cost function involving the auxiliary function and the approximating pattern is minimized by modifying the phase pattern of the auxiliary function using a simple and fast iterative technique once the optimal phase pattern has been found the array pattern approximating the corresponding auxiliary function is the synthesized pattern the proposed method allows to satisfy stringent requirements on the amplitude pattern including multibeam synthesis and radiation suppression within large angular regions numerical results show the effectiveness of the algorithm and are compared to those obtained using other existing methods in order to achieve a more significant comparison such methods have been properly modified to improve their performances such comparison shows that the presented algorithm allows a significant reduction of cpu time with respect to the other considered methods as well as a weaker dependence on the starting point finally the presented method is extended in such a way as to reduce the dynamic range ratio drr of the array excitations

design of broadband planar arrays based on the optimization of aperiodic tilings antenna arrays based on aperiodic tilings have been shown to exhibit low sidelobe levels and modest bandwidths over which grating lobes are suppressed in addition compared to conventional periodic arrays these arrays are naturally thinned i e mean inter element spacing is greater than the generation of these arrays involves placing array elements at the locations of the vertices of an aperiodic tiling to obtain a realizable design the entire array is then scaled and truncated to achieve a desired minimum element spacing and aperture size this paper demonstrates that it is possible to greatly extend the bandwidth of these arrays by incorporating a simple perturbation scheme into the basic array generation process the implementation of this perturbation scheme is straightforward and it lends itself well to being combined with an optimization technique such as the genetic algorithm it is successfully used to generate arrays that have large bandwidths peak sidelobe level db with no grating lobes of up to a minimum element spacing of moreover the flexibility of this technique will be further demonstrated by introducing a slight variation of the basic scheme that is capable of generating arrays with extremely wide bandwidths an example will be presented for an array design that has a bandwidth corresponding to a minimum element spacing of up to

generalizations of the poincare birkhoff theorem in this article we prove some generalizations of the classical poincar birkhoff theorem on area preserving homeomorphisms of the annulus which satisfy a boundary twist condition the work of g d birkhoff on this theorem and its applications can be found in b1 b2 and chapter v of b3 a more modern treatment can be found in b n we prove a theorem for the open annulus a s1 x 0 1 since as we will see the theorem for the closed annulus can easily be obtained from this result for the open annulus however it is not immediately obvious what should be the analogue of the twist condition it turns out that the most general hypothesis and the most natural from the point of view of our proof involves the notion of positively and negatively returning disks for some lift of f to the covering space a r x 0 1 more precisely if f a a is a lift of f a a we will say that the e is a positively returning disk for f if there is an open disk u c a such that f u n u 0 and fp u n u k 0 forsome n k 0 here u k denotes the set x k t i x t e u thus u is disjoint from its image but under iteration by f returns to a positive translate of itself a negatively returning disk is defined similarly but with k 0 such that fl u n u 0 in section 2 we prove the following

on the design of maximally sparse beamforming arrays the problem of designing nonuniformly spaced arrays is formulated as one of constrained optimization in which the cost function is chosen to select the array with the minimum number of elements the response of the array is controlled by a set of inequality point response constraints it is shown that a suitable cost function for this problem is the l sub p quasi norm for 0

fast analysis of large antenna arrays using the characteristic basis function method and the adaptive cross approximation algorithm the characteristic basis function method cbfm has been hybridized with the adaptive cross approximation aca algorithm to construct a reduced matrix equation in a time efficient manner and to solve electrically large antenna array problems in core with a solve time orders of magnitude less than those in the conventional methods various numerical examples are presented that demonstrate that the proposed method has a very good accuracy computational efficiency and reduced memory storage requirement specifically we analyze large 1 d and 2 d arrays of electrically interconnected tapered slot antennas tsas the entire computational domain is subdivided into many smaller subdomains each of which supports a set of characteristic basis functions cbfs we also present a novel scheme for generating the cbfs that do not conform to the edge condition at the truncated edge of each subdomain and provide a minor overlap between the cbfs in adjacent subdomains as a result the cbfs preserve the continuity of the surface current across the subdomain interfaces thereby circumventing the need to use separate ldquoconnectionrdquo basis functions

constrained pareto optimization of wide band and steerable concentric ring arrays a multi objective evolutionary algorithm that explicitly introduces the management of a single or multiple constraints on the solutions of an electromagnetic problem is presented in this paper the proposed strategy is based upon a modified genetic algorithm which evaluates the strength of a solution by considering both the match to the desired performance objectives as well as the satisfaction of specific requirements imposed to the design constraints the key issue is represented by the adaptive constraints management and its influence on the selective pressure of the genetic algorithm the procedure is applied to the optimization of concentric ring arrays several design examples of steerable and wideband arrays are provided to prove the flexibility and reliability of the approach a particular emphasis is given to the changes in array performance when the same objectives are requested but different kinds of constraints are forced

periodic bouncing solutions for attractive singular second order equations abstract in this paper by using an approximation approach and phase plane analysis for the successor map of the impact oscillator we obtain an existence result for periodic bouncing solutions for a second order forced equation x g x p t where g has an attractive singularity which improves on the previous result in the conditions for both g and p

the pinwheel tilings of the plane prototiles in euclidean n space en for n 2 the prototiles are usually required to be rather nice topologically at least homeomorphs of the closed unit ball one then makes arbitrarily many congruent copies called tiles of these prototiles and considers all ways called tilings that such tiles may provide a simultaneous covering and packing of en a tiling is thus an unordered collection of tiles for which the union is all of en but such that the interiors of each pair of tiles do not intersect wang s original problem was to determine if it was possible to have a finite set of prototiles with associated tilings of space for which all the tilings were nonperiodic a tiling is nonperiodic if it is not invariant under any single simultaneous translation of its tiles this was settled in the affirmative in the thesis of wang s student robert berger 1

generalized space filling gosper curves and their application to the design of wideband modular planar antenna arrays the peano gosper space filling curve provides an excellent framework for designing planar antenna array distributions with modular architectures and suppressed sidelobes over a relatively wide bandwidth the curve consists of a self avoiding path that intersects a triangular lattice and its construction is based on the iterative application of a generating curve there exist a number of other recently discovered curves coined generalized gosper curves that possess properties similar to those of the peano gosper curve but are based on larger and more complex generating curves in this paper these generalized curves will be examined as the framework for antenna array layouts it will be shown that arrays based on these curves have a number of excellent characteristics while offering modular array configurations and sizes that are not inherent to peano gosper arrays moreover when combined with a simple recursive perturbation technique the element distributions of these arrays can be efficiently adjusted to generate designs with bandwidths that far exceed that of standard periodic and triangular lattice arrays the efficacy of this technique will be demonstrated through design examples including one that has more than a 10 1 bandwidth full wave simulations of a wideband patch array will also be used to investigate the effects of mutual coupling on these array distributions

synthetic functions analysis of large aperture coupled antennas the application is described the synthetic function expansion sfx approach to large arrays of aperture coupled antennas the problem is formulated in terms of coupled magnetic field continuity integral equations mfcie and electric field integral equations efie and discretized via the method of moments mom the sfx is a domain decomposition technique on each block of the broken down structure functions are generated with domain over the entire block these ldquosynthetic functionsrdquo sf are obtained from the solution of the electromagnetic problem for the isolated block upon specification of appropriate sources on the block bounding box and from a further singular value decomposition svd based procedure to select the relevant terms the complete problem is solved using the sfs as basis functions for the mom this results in a strong reduction of the mom matrix size applications are presented to configurations of open and cavity backed radiators

an iteration free mom approach based on excitation independent characteristic basis functions for solving large multiscale electromagnetic scattering problems we describe a numerically efficient strategy for solving a linear system of equations arising in the method of moments for solving electromagnetic scattering problems this novel approach termed as the characteristic basis function method cbfm is based on utilizing characteristic basis functions cbfs special functions defined on macro domains blocks that include a relatively large number of conventional sub domains discretized by using triangular or rectangular patches use of these basis functions leads to a significant reduction in the number of unknowns and results in a substantial size reduction of the mom matrix this in turn enables us to handle the reduced matrix by using a direct solver without the need to iterate in addition the paper shows that the cbfs can be generated by using a sparse representation of the impedance matrix resulting in lower computational cost and that in contrast to the iterative techniques multiple excitations can be handled with only a small overhead another important attribute of the cbfm is that it is readily parallelized numerical results that demonstrate the accuracy and time efficiency of the cbfm for several representative scattering problems are included in the paper

symmetries of quasicrystals we consider tiling models of round quasicrystals which would have diffraction patterns which are fully rotation invariant rings instead of bragg peaks they can be distinguished from glasses by self similarity of the pattern of radii of the rings

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 the application of parametric models to the transient analysis of resonant and multiband antennas the transient responses of a resonant antenna and a fractal multiband antenna both formed by conducting surfaces are calculated the surfaces are modeled by planar triangular patches and the study is carried out by solving the time domain electric field integral equation td efie linear parametric modeling techniques are applied to considerably reduce the computation time numerical results are compared with experimental measurements

on periodic solutions of second order differential equations with attractive repulsive singularities abstract sufficient conditions for the existence of a solution to the problem u t g t u t h t u t f t for a e t 0 u 0 u u 0 u are established

random sorting networks local statistics via random matrix laws this paper finds the bulk local limit of the swap process of uniformly random sorting networks the limit object is defined through a deterministic procedure a local version of the edelman greene algorithm applied to a two dimensional determinantal point process with explicit kernel the latter describes the asymptotic joint law near 0 of the eigenvalues of the corners in the antisymmetric gaussian unitary ensemble in particular the limiting law of the first time a given swap appears in a random sorting network is identified with the limiting distribution of the closest to 0 eigenvalue in the antisymmetric gue moreover the asymptotic gap in the bulk between appearances of a given swap is the gaudin mehta law the limiting universal distribution for gaps between eigenvalues of real symmetric random matrices the proofs rely on the determinantal structure and a double contour integral representation for the kernel of random poissonized young tableaux of arbitrary shape

the peano gosper fractal array this paper investigates the radiation characteristics of a new type of array that is based on the family of space filling and self avoiding fractals known as peano gosper curves the elements of the fractal array are uniformly distributed along a peano gosper curve which leads to a planar array configuration with parallelogram cells that is bounded by a closed koch curve these unique properties are exploited in order to develop a design methodology for deterministic arrays that have no grating lobes even when the minimum spacing between elements is increased to at least one wavelength this leads to a class of arrays that are relatively broad band when compared to more conventional periodic planar arrays with square or rectangular cells and regular boundary contours an efficient iterative procedure for calculating the radiation patterns of these peano gosper fractal arrays to arbitrary stage of growth p is also introduced in this paper

pareto optimization of thinned planar arrays with elliptical mainbeams and low sidelobe levels a multi objective pareto genetic algorithm design methodology is applied to thinned planar arrays to simultaneously minimize peak side lobe levels and target an elliptical mainbeam with specific minimum and maximum half power beamwidths this new radiation pattern synthesis technique for thinned planar arrays provides antenna engineers with a set of tradeoffs between low side lobe levels and close adherence to mainbeam design objectives i e the specified half power beamwidths corresponding to the major and minor axes of an elliptical mainbeam one pareto optimization example is presented for a thinned low side lobe planar array with a desired minimum and maximum beamwidth of 8 4 and 12 respectively two designs from the pareto front are discussed one with a 20 92 db side lobe level and beamwidths between 11 5 and 7 5 and a second with a 18 97 db side lobe level with beamwidths between 12 and 7 93

the lattice structure of the set of domino tilings of a polygon abstract fix a polygon p with vertical and horizontal sides we first recall how each tiling of p with dominoes i e rectangles 2 1 can be encoded by a height function such an encoding induces a lattice structure on the set tp of the tilings of p we give some applications of this structure and we especially describe the order of meet irreducible elements of tp

existence of nonnegative and nonpositive solutions for second order periodic boundary value problems we are interested in nonnegative and nonpositive solutions of the boundary value problem u f t u u 0 u 1 u 0 u 1 where f fulfils the caratheodory conditions on 0 1 r we generalize the results reached by m n nkashama j santanilla and l sanchez and present estimates for solutions in addition we apply our existence theorems to periodic boundary value problems for nonlinear duffing equations whose right hand sides have a repulsive or attractive singularity at the origin we extend or generalize existence results by a c lazer and s solimini and other authors moreover we get some multiplicity results and in the case of a repulsive singularity we also admit a weak singularity in constrast to the previous papers on this subject our proofs are based on the method of lower and upper functions and topological degree arguments and the results are tested on examples

the oriented swap process particles labelled 1 n are initially arranged in increasing order subsequently each pair of neighboring particles that is currently in increasing order swaps according to a poisson process of rate 1 we analyze the asymptotic behavior of this process as n oo we prove that the space time trajectories of individual particles converge when suitably scaled to a certain family of random curves with two points of non differentiability and that the permutation matrix at a given time converges to a certain deterministic measure with absolutely continuous and singular parts the absorbing state where all particles are in decreasing order is reached at time 2 o 1 n the finishing times of individual particles converge to deterministic limits with fluctuations asymptotically governed by the tracy widom distribution

fast fourier transforms for nonequispaced data a group of algorithms is presented generalizing the fast fourier transform to the case of noninteger frequencies and nonequispaced nodes on the interval pi pi the schemes of this paper are based on a combination of certain analytical considerations with the classical fast fourier transform and generalize both the forward and backward ffts each of the algorithms requires o n cdot log n n cdot log 1 varepsilon arithmetic operations where varepsilon is the precision of computations and n is the number of nodes the efficiency of the approach is illustrated by several numerical examples

dynamics of a periodic differential equation with a singular nonlinearity of attractive type where c g 0 a 0 and p is a continuous t periodic function for some t 0 we are interested in the existence and stability of positive t periodic solutions of 1 the existence of t periodic solutions of this class of equations where the restoring force is a singular nonlinearity that becomes infinite in zero w x has been proved by lazer and solimini 2 for the case without friction w x c s 0 and by habets and sanchez 1 for the damped case however the stability properties of these solutions have been less studied it is well known that for the autonomous case p t p 0 this equation has a 0 unique saddle point in this paper we prove that the dynamics of the periodic equation 1 is similar to the autonomous case for our study is n w x fundamental a massera s convergence theorem in r given by smith in 6 the paper is divided in three sections in section 1 the main results are stated it is seen that 1 has a unique unstable periodic solution w

design of subarrayed linear and planar array antennas with sll control based on an excitation matching approach in this paper the synthesis of subarrayed antennas with subarrays having different weights and dimensions is considered the problem is formulated as the definition of the element clustering into spatially contiguous subarrays and the corresponding weights to obtain a pattern with the lowest i e minimum achievable sidelobe level sll the problem is addressed with an unconstrained approach based on an excitation matching method where the synthesis of subarray weights and sizes is simultaneously carried out successively a hybrid version of such an approach is proposed to directly enforce into the optimization procedure the sll constraints a set of representative results concerned with both sum and difference patterns are shown furthermore some comparisons with state of the art hybrid evolutionary based techniques are reported as well

fractile arrays a new class of tiled arrays with fractal boundaries in this paper a new class of antenna arrays are introduced which we call fractile arrays a fractile array is defined as any array with a fractal boundary contour that tiles the plane without gaps or overlaps it will be shown that the unique geometrical features of fractiles may be exploited in order to make available a family of deterministic arrays that offer several highly desirable performance advantages over their conventional periodic planar array counterparts most notably fractile arrays have no grating lobes even when the minimum spacing between elements is increased to at least one wavelength this has led to the development of a new design methodology for modular broadband low sidelobe arrays that is based on fractal tilings several examples of fractile arrays will be considered including peano gosper terdragon 6 terdragon and fudgeflake arrays efficient iterative procedures for calculating the radiation patterns of these fractile arrays to arbitrary stage of growth p are also introduced in this paper

a fast impedance and pattern computation scheme for finite antenna arrays a fast numerical method well suited to the analysis of moderate size arrays made of complex elements is presented it combines macro basis functions and multipole approaches without an iterative procedure this method is exploited to estimate the impedance matrix and active element patterns for the latter an efficient formulation is provided as a series of pattern multiplication problems examples are shown for arrays of broadband dipoles the computational gain obtained for the reduction of the original method of moments system of equations is briefly described

a self similar fractal radiation pattern synthesis technique for reconfigurable multiband arrays a novel method for designing reconfigurable multiband linear and planar antenna arrays is presented the technique is based on a generalized fourier series synthesis approach that exploits the self similarity of a specified fractal radiation pattern in order to achieve the desired multiband performance the fractal radiation patterns are composed of scaled and shifted copies of an appropriately chosen generating window function that exhibits low sidelobe levels and rapid spectral rolloffs in the transform domain a newly developed thinning algorithm is presented which may be employed to reduce considerably both the overall physical size and the total number of elements in a synthesized multiband array finally a band switching scheme is introduced that is well suited for implementation in the form of a reconfigurable common aperture array

analysis of large complex structures with the synthetic functions approach an innovative procedure is presented that allows the method of moments mom analysis of large and complex antenna and scattering problems at a reduced memory and cpu cost bounded within the resources provided by a standard 32 bit personal computer the method is based on the separation of the overall geometry into smaller portions called blocks and on the degrees of freedom of the field the blocks need not be electrically unconnected on each block basis functions are generated with support on the entire block that are subsequently used as basis functions for the analysis of the complete structure only a small number of these functions is required to obtain an accurate solution therefore the overall number of unknowns is drastically reduced with consequent impact on storage and solution time these entire domain basis functions are called synthetic functions they are generated from the solution of the electromagnetic problem for the block in isolation under excitation by suitably defined sources the synthetic functions are obtained from the responses to all sources via a procedure based on the singular value decomposition because of the strong reduction of the global number of unknowns one can store the mom matrix and afford a direct solution the method is kernel free and can be implemented on existing mom codes

conjugacies for tiling dynamical systems we consider tiling dynamical systems and topological conjugacies between them we prove that the criterion of being of finite type is invariant under topological conjugacy for substitution tiling systems under rather general conditions including the penrose and pinwheel systems we show that substitutions are invertible and that conjugacies are generalized sliding block codes

asymptotics of plancherel measures for symmetric groups 1 1 plancherel measures given a finite group g by the corresponding plancherel measure we mean the probability measure on the set g of irreducible representations of g which assigns to a representation g the weight dim g for the symmetric group s n the set s n is the set of partitions of the number n which we shall identify with young diagrams with n squares throughout this paper the plancherel measure on partitions arises naturally in representation theoretic combinatorial and probabilistic problems for example the plancherel distribution of the first part of a partition coincides with the distribution of the longest increasing subsequence of a uniformly distributed random permutation 31 we denote the plancherel measure on partitions of n by mn

effective beam forming networks for large arbitrary array of antennas a deterministic and effective strategy to reduce as much as possible the number of amplitude controls points in large arrays is herein proposed and applied to cases of practical interest the proposed strategy exploits two important concepts the first one coming from a special class of aperiodic tiling and the second one based on nufft non uniform fast fourier transform techniques the first one allows designing innovative front end architectures made of a reduced number of control points while nufft algorithms lead to computationally effective synthesis procedures the overall results and design guidelines allow to achieve simplified beamforming networks derived from aperiodic tilings and to know the performances that can be achieved using this approach particularly in case of low sidelobe requirements to confirm the usefulness of the proposed tools numerical examples are discussed conclusion follows

interpolatory macro basis functions analysis of non periodic arrays an efficient method of moments mom technique for analyzing non periodic antenna arrays of identical elements with fixed orientation is presented the proposed method which uses macro basis functions mbfs is based on a compact representation of the interactions between mbfs these interactions are expressed via a low order harmonic polynomial function after an explicit pre computation of the reaction integrals in a very limited set of relative positions this is possible for arrays of arbitrary size thanks to three transformations subtraction of the far field expression for the interactions phase correction and modified radial distance applied successively to the pre computed interactions after obtaining the harmonic polynomial expressions the computation time for the reaction integral between two mbfs is independent from the complexity of the antenna array element

the evolution of optimal linear polyfractal arrays using genetic algorithms recently in order to successfully combine the positive attributes of both periodic and random arrays into one design a novel class of arrays known as fractal random arrays has been introduced in addition several researchers have successfully used genetic algorithms robust global optimization techniques based on natural selection to find solutions to complex array layout problems this paper introduces a type of nature based design process that applies a specially formulated genetic algorithm to evolve optimal layouts of an important subset of fractal random arrays which we call polyfractal arrays also this paper discusses how the underlying self similar properties of polyfractal arrays can be exploited to increase the speed of the associated array factor calculations this speed increase dramatically reduces the time required for the genetic algorithm to converge thereby making it possible to effectively evolve optimal array configurations which are much larger than has been previously possible moreover the fractal random properties of these polyfractal arrays are shown to provide substantially wider bandwidth performance than their conventional counterparts finally several design examples of genetically optimized linear polyfractal arrays with narrow beamwidths improved sidelobe suppression and wide bandwidths are presented