isophoric arrays massively thinned phased arrays with well controlled sidelobes traditional filled phased arrays have an element placed in every location of a uniform lattice with half wavelength spacing between the lattice points massively thinned arrays have fewer than half the elements of their filled counterparts such drastic thinning is normally accompanied by loss of sidelobe control this paper describes a class of massively thinned linear and planar arrays that show well behaved sidelobes in spite of the thinning the term isophoric is derived from greek roots to denote uniform weight in isophoric arrays element placement based on difference sets forces uniformly weighted spatial coverage this constraint forces the array power pattern to pass through v uniformly spaced equal and constant values that are less than 1 k times the main beam peak where v is the aperture size in half wavelengths and k is the number of elements in the array the net result is reduced peak sidelobes especially when compared to cut and try random placement approaches an isophoric array will exhibit this sidelobe control even when the array has been thinned to the extent that k is approximately the square root of v where more than one beam must be generated at a time isophoric array designs may be used to advantage even within a traditional filled array by interweaving two isophoric subarrays within a filled array and by appropriate cyclic shifting of the element assignments over time two independent antenna power patterns can be generated each with a sidelobe region that is approximately a constant value of 1 2k relative to the main beam where k is the number of elements in the subarray

reducing the number of elements in the synthesis of shaped beam patterns by the forward backward matrix pencil method the matrix pencil method mpm has been used to reduce the number of elements in the linear antenna array with a pencil beam pattern this work extends the mpm based synthesis method to the synthesis of shaped beam patterns by using the forward backward matrix pencil method fbmpm the fbmpm based synthesis method places a necessary restriction on the poles which correspond to element positions and consequently obtains more accurate synthesis results particularly for the synthesis of asymmetric patterns numerical examples show the effectiveness and advantages of the proposed method in the reduction of the number of elements for shaped beam patterns

new bounds on the lieb thirring constants improved estimates on the constants l d for 1 2 3 2 d n in the inequalities for the eigenvalue moments of schrodinger operators are established

carleman estimates and absence of embedded eigenvalues let l w be a schrodinger operator with a potential w in l frac n 1 2 mathbb r n n geq 2 we prove that there is no positive eigenvalue the main tool is an l p l p prime carleman type estimate which implies that eigenfunctions to positive eigenvalues must be compactly supported the carleman estimate builds on delicate dispersive estimates established in 7 we also consider extensions of the result to variable coefficient operators with long range and short range potentials and gradient potentials

optimization of sparse linear arrays using harmony search algorithms a sparse linear array composed of a uniformly spaced core subarray and an extended sparse subarray is synthesized using a harmony search hs and an exploratory harmony search ehs algorithms the optimal solution is searched by changing the amplitudes of all the elements and the positions of the extended elements under a set of practical constraints performance of the ehs the hs a genetic algorithm ga and a particle swarm optimization pso algorithm has also been compared in synthesizing these sparse linear arrays

nonresonance conditions for asymptotically positively homogeneous differential systems the fucik spectrum and its generalization in this article we propose how to define the fucik spectra for differential systems in rnwith jumping nonlinearities the propertyp a generalization of the non fucik spectra to positively homogeneous nonautonomous differential systems is also defined in the most general setting a quantitative estimate result concerning the parameterized completely continuous positively homogeneous perturbations of the identity in banach spaces is given in this article such a result is a generalization of one property in the spectrum theory for completely continuous linear operators using this estimate result we will give some significantly improved nonresonance results from the fucik spectra and propertypfor asymptotically positively homogeneous differential systems

a hybrid approach based on pso and hadamard difference sets for the synthesis of square thinned arrays a hybrid approach for the synthesis of planar thinned antenna arrays is presented the proposed solution exploits and combines the most attractive features of a particle swarm algorithm and those of a combinatorial method based on the noncyclic difference sets of hadamard type numerical experiments validate the proposed solution showing improvements with respect to previous results

lieb thirring inequality with semiclassical constant and gradient error term abstract in 1975 lieb and thirring derived a semiclassical lower bound on the kinetic energy for fermions which agrees with the thomas fermi approximation up to a constant factor whenever the optimal constant in their bound coincides with the semiclassical one is a long standing open question we prove an improved bound with the semiclassical constant and a gradient error term which is of lower order

directions of arrival estimation through bayesian compressive sensing strategies the estimation of the directions of arrival doas of narrow band signals impinging on a linear antenna array is addressed within the bayesian compressive sensing bcs framework unlike several state of the art approaches the voltages at the output of the receiving sensors are directly used to determine the doas of the signals thus avoiding the computation of the correlation matrix towards this end the estimation problem is properly formulated to enforce the sparsity of the solution in the linear relationships between output voltages i e the problem data and the unknown doas customized implementations exploiting the measurements collected at a unique time instant single snapshot and multiple time instants multiple snapshots are presented and discussed the effectiveness of the proposed approaches is assessed through an extensive numerical analysis addressing different scenarios signal configurations and noise conditions comparisons with state of the art methods are reported as well

sparse 2 d array placement for arbitrary pattern mask and with excitation constraints a simple deterministic approach we present a novel algorithm for the synthesis of planar 2 d arrays subject to arbitrary pattern masks and excitation constraints e g dynamic range the algorithm is simple and deterministic and considers the radiating element pattern the procedure starts with a conventional constrained fixed grid synthesis on a regular lattice yielding a goal radiated field next element locations are selected sequentially by maximizing projection on field difference to goal while excitation amplitudes are computed using fixed grid constrained synthesis for irregular lattices the final result is the sparse layout and constrained excitation coefficients the proposed method is validated against literature results application examples are given for circular flat top isoflux and triangular flat top shaped beam patterns with constraints on excitation coefficients dynamic range both for isotropic and patch type element patterns

the filter diagonalization method in antenna array optimization for pattern synthesis pattern synthesis of nonuniform antenna arrays has drawn significant attention because of its wide applications with the aim of reducing the number of elements in linear and planar arrays this paper introduces a novel non iterative method based on the filter diagonalization method fdm which was originally applied in the problem of identifying and quantifying chemical molecules with nuclear magnetic resonance nmr in quantum mechanical formalism the proposed method samples the data set from the desired discrete pattern and associates the sample data with a time autocorrelation function of a fictitious dynamical system which is described by an effective hamiltonian operator that contains the array element information the hamiltonian operator can be decomposed by a set of orthonormal eigenvectors therefore the original pattern synthesis is converted into solving the general eigenvalue decomposition with krylov bases the number of nonuniform array elements depends on the number of the krylov bases and the sample data the proposed method can obtain an optimized antenna array to reconstruct the desired radiation pattern with a high accuracy numerical examples show that proposed fdm pattern synthesis can use less prior knowledge to achieve the desired pattern with highly sparse antenna arrays

synthesis of modular contiguously clustered linear arrays through a sparseness regularized solver an innovative methodology for the design of modular and contiguously clustered linear arrays is proposed the approach formulates the subarraying problem as a pattern matching one in which elementary modules taken from a user defined dictionary are combined to synthesize the final antenna layout by recasting such a synthesis problem within the compressive sensing framework an efficient solver is used to determine the array architecture starting from the a priori specification of the features e g the length of the admissible subarrays a set of representative numerical experiments is discussed to assess the advantages and drawbacks of the proposed algorithm also in comparison with some state of the art methods

maximum likelihood direction of arrival estimation in unknown noise fields using sparse sensor arrays we address the problem of maximum likelihood ml direction of arrival doa estimation in unknown spatially correlated noise fields using sparse sensor arrays composed of multiple widely separated subarrays in such arrays intersubarray spacings are substantially larger than the signal wavelength and therefore sensor noises can be assumed to be uncorrelated between different subarrays this leads to a block diagonal structure of the noise covariance matrix which enables a substantial reduction of the number of nuisance noise parameters and ensures the identifiability of the underlying doa estimation problem a new deterministic ml doa estimator is derived for this class of sparse sensor arrays the proposed approach concentrates the ml estimation problem with respect to all nuisance parameters in contrast to the analytic concentration used in conventional ml techniques the implementation of the proposed estimator is based on an iterative procedure which includes a stepwise concentration of the log likelihood ll function the proposed algorithm is shown to have a straightforward extension to the case of uncalibrated arrays with unknown sensor gains and phases it is free of any further structural constraints or parametric model restrictions that are usually imposed on the noise covariance matrix and received signals in most existing ml based approaches to doa estimation in spatially correlated noise

dynamics and bifurcations of nonsmooth systems a survey abstract in this survey we discuss current directions of research in the dynamics of nonsmooth systems with emphasis on bifurcation theory an introduction to the state of the art also for non specialists is complemented by a presentation of the main open problems we illustrate the theory by means of elementary examples the main focus is on piecewise smooth systems which have recently attracted a lot of attention but we also briefly discuss other important classes of nonsmooth systems such as nowhere differentiable ones and differential variational inequalities this extended framework allows us to put the diverse range of papers and surveys in this special issue in a common context a dedicated section is devoted to concrete applications that stimulate the development of the field this survey is concluded by an extensive bibliography

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

a stochastic mathematical framework for the analysis of spherically bound random arrays random arrays bound by a spherical volume are rigorously analyzed through a stochastic approach for uniform and gaussian element distributions the full mathematical derivation and process to determine the array characteristics are discussed and a key result is the form solution which describes both the sidelobe behavior and main beam characteristics it is also shown that the proposed approach shares many conceptual similarities to the probabilistic approach applied to circular random arrays and comparisons are made the 3 db beamwidth directivity grating lobes and sidelobe level are examined analytically and in numerical simulation for a conceptual system of isotropic wide band radiators with a 100 1 bandwidth

synthesis of two dimensional antenna array using independent compression regions the synthesis of two dimensional antenna arrays that allows to optimize the number of its elements is of great interest for long term evolution lte advanced wireless systems in this communication we present a novel synthesis approach which focuses on reducing the number of antenna elements using independent compression regions icr we base our approach on the non iterative matrix pencil method mpm and the iterative bayesian compressive sampling bcs method both of these techniques have been previously used for the compression of linear arrays and now we apply them in the context of two dimensional arrays our compression method is based on the idea of segmenting the array in independent regions a set of numerical experiments small and large 2d arrays shaped beam antenna patterns are presented to assess the performance and potentialities of icr design approach

generalized analytical technique for the synthesis of unequally spaced arrays with linear planar cylindrical or spherical geometry an effective method for optimizing the performance of a fixed current distribution uniformly spaced antenna array has been to adjust its element positions to provide performance improvement in comparison with the default uniform structure this approach yields performance improvements such as smaller sidelobe levels or beamwidth values additionally it provides practical advantages such as reductions in size weight and number of antenna elements the objective of this paper is to describe a unified mathematical approach to nonlinear optimization of multidimensional array geometries the approach utilizes a class of limiting properties of sinusoidal bessel or legendre functions that are dictated by the array geometry addressed the efficacy of the method is demonstrated by its generalized application to synthesis of rectangular cylindrical and spherical arrays the unified mathematical approach presented below is a synthesis technique founded on the mathematical transformation of the desired field pattern followed by the application of limiting forms of the transformation and resulting in the development of a closed form expression for the element positions the method offers the following advantages over previous techniques such as direct nonlinear optimization or genetic algorithms first it is not an iterative searching algorithm and provides element spacing values directly in a single run of the algorithm thereby saving valuable cpu time and memory storage second it permits the array designer to place practical constraints on the array geometry e g the minimum maximum spacing between adjacent elements

sparse array beampattern synthesis via alternating direction method of multipliers in this paper we devise beampattern synthesis algorithms for sparse arrays using the alternating direction method of multipliers admm unlike the usual weighted l 1 norm we utilize the l p norm of the array weight vector where 0 as the objective function to enhance its sparsity for arbitrary array configurations to solve the resultant nonconvex and nonlinear optimization problem we introduce auxiliary variables to decouple the array weight vector in the objective function from the complicated constraints on main lobes and sidelobes and then the array weight vector and auxiliary variables are updated alternately via admm to determine the array weight vector with the l p norm we analyze the convexity or concavity of the subfunction related to each weight element using its derivatives on the other hand we divide the objective function of auxiliary variables into multiple nonlinear subfunctions each of which is only dependent of the magnitude of the corresponding auxiliary variable and is calculated in parallel via analyzing simplified two sided constraints furthermore we extend our methodology to the symmetric excitation case with symmetric array configurations numerical examples show that the proposed methods can obtain satisfactory radiation pattern with fewer antennas than the existing techniques and are applicable for arbitrary or symmetric array configurations

reducing the number of elements in a linear antenna array by the matrix pencil method the synthesis of a nonuniform antenna array with as few elements as possible has considerable practical applications this paper introduces a new non iterative method for linear array synthesis based on the matrix pencil method mpm the method can synthesize a nonuniform linear array with a reduced number of elements and can be also used to reduce the number of elements for linear arrays designed by other synthesis techniques in the proposed method the desired radiation pattern is first sampled to form a discrete pattern data set then we organize the discrete data set in a form of hankel matrix and perform the singular value decomposition svd of the matrix by discarding the non principal singular values we obtain an optimal lower rank approximation of the hankel matrix the lower rank matrix actually corresponds to fewer antenna elements the matrix pencil method is then utilized to reconstruct the excitation and location distributions from the approximated matrix numerical examples show the effectiveness and advantages of the proposed synthesis method

linear array thinning exploiting almost difference sets this paper describes a class of linear thinned arrays with predictable and well behaved sidelobes the element placement is based on almost difference sets and the array power pattern is forced to pass through n uniformly spaced values that although neither equal nor constant as for difference sets are a priori known from the knowledge of the aperture size the number of active array elements k and the features of the correlation function such a property allows one to predict the bounds of the confidence range of the peak sidelobe of the admissible arrays obtainable through simple shift operations on a binary sequence the expected peak sidelobe performances turn out to be comparable with those from difference sets even though obtainable in a wider set of array configurations and improved in comparison with cut and try random placements

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

on the sampling of the electromagnetic field radiated by sparse sources the aim of this paper is to discuss the effectiveness of random sampling of the electromagnetic field in problems involving sparse radiating sources the method adopted in this paper uses an intuitive geometrical approach based on the johnson linderstrauss lemma applied to the epsilon net of the set of the fields radiated by the sparse source the paper shows that a proper non uniform random sampling nurs using some a priori information on the problem allows a significant reduction in the cardinality of the set of the measured data compared to uniform random sampling and to random sampling from a lambda 2 equispaced set of data it is also shown that there is a limiting number of data after which random sampling is not convenient in this case a deterministic sampling strategy called modified non uniform sampling mnus is proposed numerical results on linear sparse arrays confirm the effectiveness of nurs and mnus

wavelet based compressive imaging of sparse targets the application of the compressive sensing cs paradigm to retrieve non single pixels contrast profiles is discussed by exploiting a wavelet representation to model complex scatterer distributions with sparse vectors of coefficients an efficient bayesian cs bcs strategy is adopted to solve the arising inverse scattering problem a set of representative numerical examples is presented to illustrate the advantages and the limitations of the proposed approach also with respect to comparable state of the art inversion methods

rate of decay of stable periodic solutions of duffing equations abstract in this paper we consider the second order equations of duffing type bounds for the derivative of the restoring force are given that ensure the existence and uniqueness of a periodic solution furthermore the stability of the unique periodic solution is analyzed the sharp rate of exponential decay is determined for a solution that is near to the unique periodic solution

the spectral density of a difference of spectral projections let h0 and h be a pair of self adjoint operators satisfying some standard assumptions of scattering theory it is known from previous work that if lambda belongs to the absolutely continuous spectrum of h0 and h then the difference of spectral projections d lambda mathbb 1 infty 0 h lambda mathbb 1 infty 0 h 0 lambda in general is not compact and has non trivial absolutely continuous spectrum in this paper we consider the compact approximations d varepsilon lambda of d lambda given by d varepsilon lambda psi varepsilon h lambda psi varepsilon h 0 lambda where psi varepsilon x psi x varepsilon and psi x is a smooth real valued function which tends to mp1 2 as x to pm infty we prove that the eigenvalues of d varepsilon lambda concentrate to the absolutely continuous spectrum of d lambda as varepsilon to 0 we show that the rate of concentration is proportional to log varepsilon and give an explicit formula for the asymptotic density of these eigenvalues it turns out that this density is independent of psi the proof relies on the analysis of hankel operators

periodic oscillations for a nonlinear suspension bridge model abstract we look for time periodic solutions of the suspension bridge equation lazer and mckenna showed that for a certain configuration of the parameters one may expect the existence of large amplitude periodic solutions having the same period as the forcing term we prove the existence of large scale subharmonic solutions

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

critical lieb thirring bounds in gaps and the generalized nevai conjecture for finite gap jacobi matrices we prove bounds of the form e i d h dist e e h 1 2 l 1 norm of a perturbation where i is a gap included are gaps in continuum one dimensional periodic schrodinger operators and finite gap jacobi matrices where we get a generalized nevai conjecture about an l 1 condition implying a szeg condition one key is a general new form of the birman schwinger bound in gaps

ads based guidelines for thinned planar arrays we propose an analytical technique based on almost difference sets adss for thinning planar arrays with well controlled sidelobes the method allows one to synthesize bidimensional arrangements with peak sidelobe levels psls predictable and deducible from the knowledge of the array aperture the filling factor and the autocorrelation function of the ads at hand the numerical validation concerned with both small and very large apertures points out that the expected psl values are significantly below those of random arrays and comparable with those from different sets dss although obtainable in a wider range of configurations

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

a symmetry theorem and applications to nonlinear partial differential equations on donne des applications d un nouveau theoreme sur les proprietes de symetrie des solutions des equations differentielles non lineaires de la forme lu f x u dans u 0 ou u n 0 ou est une region bornee ou non bornee de r n

synthesis of sparse planar arrays using modified real genetic algorithm in array design the positions of sparse array elements is an important concern for optimal performance in terms of its ability to achieve minimum peak sidelobe level sll this paper proposes a modified real genetic algorithm mga based on resetting of chromosome for the element position optimization of sparse planar arrays with rectangular boundary and here the multiple optimization constraints include the number of elements the aperture and the minimum element spacing by simplifying the space between the elements from the actual distance to chebychev distance the mga searches a smaller solution space by means of indirect description of individual and it can avoid infeasible solution during the optimization process by two novel genetic operators finally the simulation results confirming the great efficiency and the robustness of the proposed method are shown in this paper

hybrid design of non regular linear arrays with accurate control of the pattern sidelobes the hybridization of an analytical thinning technique based on almost difference sets adss and a convex programming cp strategy is proposed for designing non regular linear arrays over a half wavelength lattice that fit arbitrary upper bounds on the far field pattern the proposed approach combines the efficiency of the ads procedure in defining a low sidelobe thinned arrangement with the effectiveness of the cp approach in deducing the optimal tapering to control the beam shape a set of numerical results is presented to assess features and potentialities of the ads cp method

hybrid bcs deterministic approach for sparse concentric ring isophoric arrays an innovative methodology for the synthesis of sparse concentric ring isophoric arrays matching a user defined reference pattern is proposed the synthesis problem is recast as a two step approach firstly aimed at a determining the sparsest auxiliary layout of concentric current rings matching the reference pattern through a bayesian compressive sensing method and successively b yielding the concentric ring isophoric array by means of a density tapering technique a selected set of numerical experiments is presented to provide some insights about the effectiveness the numerical efficiency and the flexibility of the proposed hybrid method

chaotic dynamics in periodically forced asymmetric ordinary differential equations abstract using a topological approach we prove the existence of infinitely many periodic solutions and the presence of chaotic dynamics for the periodically forced second order ode u b u a u p t the choice of the equation is motivated by the studies about the dancer fucik spectrum and the lazer mckenna suspension bridge model

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

nonlinear resonance in asymmetric oscillations in this paper we study the periodic problem f p x email protected f p x email protected f p x f x t where f p u u p 2u p 1 a 1 email protected 1 p 2n 1 email protected n by computing the associated topological degree we prove existence of periodic solutions and stability of large amplitude oscillations for equations with a small damping term

restriction theorems for orthonormal functions strichartz inequalities and uniform sobolev estimates we generalize the theorems of stein tomas and strichartz about surface restrictions of fourier transforms to systems of orthonormal functions with an optimal dependence on the number of functions we deduce the corresponding strichartz bounds for solutions to schr odinger equations up to the endpoint thereby solving an open problem of frank lewin lieb and seiringer we also prove uniform sobolev estimates in schatten spaces extending the results of kenig ruiz and sogge we finally provide applications of these results to a limiting absorption principle in schatten spaces to the well posedness of the hartree equation in schatten spaces to lieb thirring bounds for eigenvalues of schr odinger operators with complex potentials and to schatten properties of the scattering matrix

periodic and unbounded motions in asymmetric oscillators at resonance abstract we consider the existence of periodic and unbounded solutions for the asymmetric oscillator x a x b x g x p t where x max x 0 x max x 0 a and b are two positive constants p t is a 2 periodic smooth function and g x satisfies lim x x 1 g x 0 we have proved previously that the boundedness of all the solutions and the existence of unbounded solutions have a close relation to the interaction of some well defined functions p and h in this paper we consider some critical cases and obtain some new sufficient conditions for the existence of 2 periodic and unbounded solutions in particular the obtained periodic solutions are new and cannot be deduced from landesman lazer s and fabry fonda s existence conditions in contrast with many existing results the function g x may be unbounded or oscillatory without asymptotic limits

sparse array quiescent beamformer design combining adaptive and deterministic constraints in this paper we examine sparse array quiescent beamforming for multiple sources in interference free environment to maximize the output signal to noise ratio snr the beamformer design comprises two intertwined stages the determination of beamforming weights and the reconfiguration of array structure the snr maximization may produce high sidelobe levels making the receiver vulnerable to interferences we consider the problem of achieving maximum snr beamforming subject to specified quiescent pattern constraints and as such combine both adaptive and deterministic approaches for sparse array configurations we employ two convex relaxation methods and an iterative linear fractional programming algorithm to solve the nonconvex antenna selection problem for sparse array beamformers simulation examples demonstrate that the array configuration plays a vital role in determining the beamforming performance in interference free scenarios

nonlinear resonance in asymmetric oscillators we study the periodic solutions of equations with asymmetric nonlinearities at resonance with the fucik spectrum we compute the associated topological degree and prove existence multiplicity and stability of large amplitude oscillations for equations with a small friction term such equations can be viewed e g as simple models for investigating vertical oscillations of long span suspension bridges the results are typically of a nonlinear nature as some of the situations observed cannot occur with a linear equation c 1998 academic press

peak sidelobe level reduction with a hybrid approach based on gas and difference sets this paper presents an approach for the optimization of the beam pattern produced by massively thinned arrays the method which combines the most attractive features of a genetic algorithm and those of a combinatorial technique namely the difference sets method is aimed at synthesizing massively thinned antenna arrays in order to suitably reduce the peak sidelobe level selected numerical results are presented in order to assess the effectiveness and reliability of the proposed approach

reducing the number of elements in multiple pattern linear arrays by the extended matrix pencil methods previously the matrix pencil method mpm and the forward backward mpm fbmpm were used to effectively reduce the number of antenna elements in the single pattern linear arrays this work extends the mpm and fbmpm based synthesis methods to the synthesis of multiple pattern linear arrays with a smaller number of elements the extended mpm resp the extended fbmpm method organizes all the multiple pattern data into a composite hankel resp composite hankel toeplitz matrix from which the minimum number of elements and the common poles corresponding to element positions can be obtained with similar processing used in the original mpm or fbmpm synthesis method in particular the extended fbmpm inherits the advantage of the original fbmpm that a useful restriction is put on the distribution of poles which makes the element positions obtained much more accurate and robust numerical experiments are conducted to validate the effectiveness and robustness of the proposed methods for the tested cases the element saving is about 20 25 for reconfigurable shaped patterns and can be even more for electrically large linear arrays with scanned pencil beams

spectral theory of discontinuous functions of self adjoint operators and scattering theory in the smooth scattering theory framework we consider a pair of self adjoint operators h0 h and discuss the spectral projections of these operators corresponding to the interval 1 the purpose of the paper is to study the spectral properties of the dierence d of these spectral projections we completely describe the absolutely continuous spectrum of the operator d in terms of the eigenvalues of the scattering matrix s for the operators h0 and h we also prove that the singular continuous spectrum of the operator d is empty and that its eigenvalues may accumulate only at thresholds in the absolutely continuous spectrum

synthesis of sparse arrays with frequency invariant focused beam patterns under accurate sidelobe control by iterative second order cone programming it is shown in this communication that the problem of synthesizing a frequency invariant fi beam pattern with as few elements as possible can be transformed into a sequence of weighted ell 1 optimizations under multiple convex constraints the objective of the weighted ell 1 optimization is to minimize the number of radiating elements for the filter and sum beamforming structure this is equivalent to minimizing the number of filters each with a set of optimized coefficients the multiple constraints are adopted to individually control the mainlobe and sidelobe pattern characteristics so as to preserve the fi property in the mainlobe region while satisfying a given upper bound in the sidelobe region the wng constraint can also be incorporated into the proposed method to enhance the synthesis robustness this method can be easily implemented by iterative second order cone programming socp and only few iterations are required to reach the convergence a set of examples for the synthesis of fi patterns with uniform sidelobe level sll or multiple nulls scannable fi patterns and the synthesis of fi pattern for an arc array with directive elements is presented to validate the effectiveness and advantages of the proposed method the element saving is about 23 3 50 for the test cases

sparsening conformal arrays through a versatile bcs based method sparsening conformal arrangements is carried out through a versatile multi task bayesian compressive sensing mt bcs strategy the problem formulated in a probabilistic fashion as a pattern matching synthesis is that of determining the sparsest excitation set locations and weights fitting a reference pattern subject to user defined geometrical constraints results from a set of representative numerical experiments are presented to illustrate the key features of the proposed approach as well as to assess also through comparisons its potentials in terms of matching accuracy element saving and computational costs

on the schrodinger equation and the eigenvalue problem if k is thekth eigenvalue for the dirichlet boundary problem on a bounded domain in n h weyl s asymptotic formula asserts that lambda k sim c n left frac k v d right 2 n hence sum limits i 1 k lambda i sim frac nc n n 2 k frac n 2 n v d 2 n we prove that for any domain and for all sum limits i 1 k lambda i geqq frac nc n n 2 k frac n 2 n v d 2 n a simple proof for the upper bound of the number of eigenvalues less than or equal to for the operator v x defined on n n 3 in terms of int limits mathbb r n v alpha n 2 is also provided

near field radar imaging via compressive sensing a novel two dimensional 2 d compressive sensing cs based method is presented for near field radar imaging first an accurate near field approximation is proposed based on which the circular wavefront curvature of spherical waves can be compensated by mapping the images to a rectified new grid more importantly the near field approximation makes the two dimensions of the scattered data separable for the range and cross range directions which makes it possible to solve the 2 d reflectivity matrix for the image reconstruction directly then a 2 d proximal subgradient algorithm for near field radar imaging based on a fast iterative shrinkage thresholding algorithm fista is introduced to resolve the memory usage and computation time issues simulation and experimental results are provided to demonstrate the performance of the proposed method with comparisons to the traditional fourier based method and to the conjugate gradient cg based method which proves that the proposed method is an effective way to solve the near field radar imaging problem

matrix pencil method for estimating parameters of exponentially damped undamped sinusoids in noise a study of a matrix pencil method for estimating frequencies and damping factors of exponentially damped and or undamped sinusoids in noise is presented comparison of this method to a polynomial method svd prony method shows that the matrix pencil method and the polynomial method are two special cases of a matrix prediction approach and that the pencil method is more efficient in computation and less restrictive about signal probes it is found through perturbation analysis and simulation that for signals with unknown damping factors the pencil method is less sensitive to noise than the polynomial method an expression of the cramer rao bound for the exponential signals is presented

positively homogeneous hamiltonian systems in the plane i try to give a general description of the dynamics of the solutions for a planar hamiltonian system with positively homogeneous hamiltonian function and periodic forcing term most of the results obtained are already known in the special case of a scalar second order differential equation with asymmetric nonlinearity

array thinning of coupled antennas based on the orthogonal matching pursuit method and a spherical wave expansion for far field synthesis this work is focused on the array thinning problem in shaped beam far field synthesis the orthogonal matching pursuit algorithm which allows finding sparse solutions in linear systems is combined with a fast full wave analysis method for antenna arrays based on a spherical wave expansion thereby taking mutual coupling between real antennas into account in the thinning process to this aim the original iterative algorithm is modified so that the current residual is obtained for the selected real coupled antennas in each step of the algorithm in this way the remaining nonselected elements are effectively removed instead of turned off results for arrays made up of microstrip patch antennas and dielectric resonator antennas arranged in triangular and rectangular lattices are presented

boundedness for sublinear reversible systems with a nonlinear damping and periodic forcing term abstract in this paper we are concerned with the sublinear reversible systems with a nonlinear damping and periodic forcing term x f x g x x 1 x p t where f x p t are odd functions p t is smooth 1 periodic function and 0 is a constant a sufficient and necessary condition for the boundedness of all solutions of the above equation is established moreover we show the existence of aubry mather sets as well

a positive density analogue of the lieb thirring inequality the lieb thirring inequalities give a bound on the negative eigenvalues of a schrodinger operator in terms of an l p norm of the potential these are dual to bounds on the h 1 norms of a system of orthonormal functions here we extend these bounds to analogous inequalities for perturbations of the fermi sea of noninteracting particles i e for perturbations of the continuous spectrum of the laplacian by local potentials

a non variational version of a max min principle f u w 4 2 milwl12 1 then there exists a unique uo e h such that vf ug 0 furthermoref uo min f u in 1975 ueh lazer landesman meyer l l m 3 extended these results to the following situation let x and y be two closed subspaces of h such that h x y x is finite dimensional and x and y are not necessarily orthogonal let t vf then t h h and is a c mapping its frechet derivative at u e his given by t rc d f u let ml and ml be two positive constants such that vu e h vx e x and vy e y we have

existence of positive radial solutions for a semipositone elliptic equation abstract in this paper we study the existence of positive radial solutions for a semipositone elliptic equation u f u in u 0 on where is a ball or an annulus in r n with n 2 0 is a parameter and f is a continuous function satisfying the semipositone condition f 0 0 we give a weak and general sufficient condition on f for the existence of positive radial solutions for 0 large we show that the linearized operator at each solution has the nonnegative first eigenvalue these solutions are obtained as minimizers of a lagrangian functional

synthesis of linear and planar arrays with minimum element selection a new method for the synthesis of linear and planar arrays having prescribed beamwidth and sidelobe levels and a minimum number of elements is proposed in the method the number of elements in an array is minimized while constraining the amplitude response error in the mainlobe region the attenuation in the sidelobe region and the array dimensions an iterative constrained optimization method is used where the amplituderesponse error is linearly approximated at each iteration while concurrently minimizing a re weighted l1 norm of the array coefficients to ensure robustness of the array we constrain a sensitivity parameter namely the white noise gain to be above a prescribed level furthermore the method also provides the additional flexibility of controlling the array dimensions symmetry properties and element positions of the array two variants have been developed in the first variant both the array coefficients and the positions of the elements are optimized in the second variant only the array coefficients are optimized while the elements are fixed at predefined positions experimental comparisons with several state of the art competing methods show that the proposed method provides greater flexibility of controlling the robustness beampattern response error array dimensions and element positions while at the same time the number of elements is less than or equal to that of the competing methods

trace class conditions for functions of schrodinger operators we consider the difference f delta v f delta of functions of schrodinger operators in l 2 mathbb r d and provide conditions under which this difference is trace class we are particularly interested in non smooth functions f and in v belonging only to some l p space this is motivated by applications in mathematical physics related to lieb thirring inequalities we show that in the particular case of schrodinger operators the well known sufficient conditions on f based on a general operator theoretic result due to v peller can be considerably relaxed we prove similar theorems for f delta v f delta frac d d alpha f delta alpha v alpha 0 our key idea is the use of the limiting absorption principle

existence uniqueness and stability of oscillations in differential equations with asymmetric nonlinearities we give conditions for the existence uniqueness and asymptotic stability of periodic solutions of a second order differential equation with piecewise linear restoring and 27r periodic forcing where the range of the derivative of the restoring term possibly contains the square of an integer with suitable restrictions on the restoring and forcing in the undamped case we give a necessary and sufficient condition

an effective method for synthesizing multiple pattern linear arrays with a reduced number of antenna elements an innovative technique based on the enhanced unitary matrix pencil mp method is presented for the design of sparse multiple pattern linear arrays by virtue of the equivalent mp obtained with a unitary transformation the relation between the element positions and the generalized eigenvalues is achieved in this method which contributes to the real solutions of the common element positions for all multiple patterns owing to the utilization of a unitary transformation that can convert a complex matrix to a real one the computational complexity can be significantly reduced since only the real computations are involved in the singular value decomposition and eigenvalue decomposition procedures consequently by only varying the obtained excitation distributions different patterns are generated with a higher matching accuracy representative experiments are provided to validate the effectiveness and advantages of the proposed method

complex weight sparse linear array synthesis by bayesian compressive sampling an innovative method for the synthesis of maximally sparse linear arrays matching arbitrary reference patterns is proposed in the framework of sparseness constrained optimization the approach exploits the multi task mt bayesian compressive sensing bcs theory to enable the design of complex non hermitian layouts with arbitrary radiation and geometrical constraints by casting the pattern matching problem into a probabilistic formulation a relevance vector machine rvm technique is used as solution tool the numerical assessment points out the advances of the proposed implementation over the extension to complex patterns of and it gives some indications about the reliability flexibility and numerical efficiency of the mt bcs approach also in comparison with state of the art sparse arrays synthesis methods

synthesis of nonuniformly spaced linear arrays with frequency invariant patterns by the generalized matrix pencil methods this work extends the matrix pencil method mpm based synthesis technique to the case of nonuniformly spaced linear arrays with wideband frequency invariant fi patterns a new sampling strategy is proposed to obtain multiple pattern data of different frequencies having the same poles that correspond to the fi element positions the obtained multiple pattern sequences have the same shape for the fi pattern requirement but with different lengths the generalized mpm gmpm and its forward backward version gfbmpm are developed to estimate the best common element positions for different frequencies which can significantly reduce the number of elements required for the specified wideband pattern shape the element excitations are solved by the regularized least square ls method at each frequency then an efficient method by utilizing the fft is presented to obtain real coefficient finite impulse response fir filters for implementing the frequency varying excitations a set of numerical examples for the fi synthesis of pencil beams shaped patterns scannable patterns and taylor patterns with low slls are presented to validate the effectiveness and advantages of the proposed methods the element saving is about 11 2 49 4 for usual cases