a modified real ga for the sparse linear array synthesis with multiple constraints this paper describes a modified real genetic algorithm mga for the synthesis of sparse linear arrays the mga has been utilized to optimize the element positions to reduce the peak sidelobe level psll of the array and here the multiple optimization constraints include the number of elements the aperture and the minimum element spacing unlike standard ga using fixed corresponding relationship between the gene variables and their coding the mga utilized the coding resetting of gene variables to avoid infeasible solution during the optimization process also the proposed approach has reduced the size of the searching area of the ga by means of indirect description of individual the simulated results confirming the great efficiency and the robustness of this algorithm are provided in this paper

classical scattering theory in one dimension we discuss various scattering properties of the classical system ofn repelling particles on the real line in the integrable case i e if the asymptotic velocities are preserved under the scattering map the asymptotic phases behave as if the particles collided pairwise

asymptotics of trajectories for cone potentials abstract we study the asymptotics of trajectories of the classical hamiltonian dynamics for hamiltonians with cone potentials we have shown earlier that all trajectories are asymptotically free 5 i e the asymptotic velocities exist here we show that the generic trajectories are asymptotically uniform i e the asymptotic phases exist

rectangular thinned arrays based on mcfarland difference sets a new class of analytical rectangular thinned arrays with low peak sidelobe level psl is introduced the proposed synthesis technique exploits binary sequences derived from mcfarland difference sets to design thinned layouts on a lattice of p p p 2 positions for any prime p the pattern features of the arising massively thinned arrangements characterized by only p p 1 active elements are discussed and the results of an extensive numerical analysis are presented to assess advantages and limitations of the mcfarland based arrays

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

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

an effective deterministic procedure for the synthesis of shaped beams by means of uniform amplitude linear sparse arrays a rigorous deterministic approach is proposed for the mask constrained power pattern synthesis of shaped beams through one dimensional sparse arrays having uniform amplitude excitations and variable phases the approach includes the well known density taper procedure as a special case the corresponding technique which exploits an analytical formulation of the problem and convex programming routines results in fast computation and is able to achieve optimal solutions without recurring to any global optimization numerical results assessing the capabilities of the proposed design method are provided opening the way to the development of an effective approach for the synthesis of circularly symmetric shaped beams via uniformly excited circular ring arrays

a global local synthesis approach for large non regular arrays a method is proposed for the synthesis of large planar non regular arrays assuming constant magnitude for the excitation of the elements the approach which combines global and local optimization is based on distinguishing aperture type and non coherent parts of the array factor the following constraints are considered minimal separation of the antennas maximum size of the array and fixed mainbeam width the level of the sidelobes is reduced via the minimization of a new type of flexible averaging cost function based on an lp norm possible applications of this model lie in the field of radio astronomy satellite communications and radar systems the proposed optimization strategy consists of three successive steps designed to be independent of each other starting with an equivalent continuous aperture the first two steps act as global transformations of the radial and azimuthal positions of the elements in the initial array while the third step performs a local optimization of individual elements of the array this last step heavily relies on computations of the gradient of the cost function which can be done quickly using an fft based procedure the method is illustrated for several large scale examples by considering as inputs four different types of non regular arrays

eigenvalue branches of the schrodinger operatorh λw in a gap of σ h the authors study the eigenvalue branches of the schrodinger operatorh w in a gap of h in particular they consider questions of asymptotic distribution of eigenvalues and bounds on the number of branches they also address the completeness problem

kam tori and whiskered invariant tori for non autonomous systems abstract we consider non autonomous dynamical systems which converge to autonomous or periodic systems exponentially fast in time such systems appear naturally as models of many physical processes affected by external pulses we introduce definitions of non autonomous invariant tori and non autonomous whiskered tori and their invariant manifolds and we prove their persistence under small perturbations smooth dependence on parameters and several geometric properties if the systems are hamiltonian the tori are lagrangian manifolds we note that such definitions are problematic for general time dependent systems but we show that they are unambiguous for systems converging exponentially fast to autonomous the proof of persistence relies only on a standard implicit function theorem in banach spaces and it does not require that the rotations in the tori are diophantine nor that the systems we consider preserve any geometric structure we only require that the autonomous system preserves these objects in particular when the autonomous system is integrable we obtain the persistence of tori with rational rotational we also discuss fast and efficient algorithms for their computation the method also applies to infinite dimensional systems which define a good evolution e g pde s when the systems considered are hamiltonian we show that the time dependent invariant tori are isotropic hence the invariant tori of maximal dimension are lagrangian manifolds we also obtain that the un stable manifolds of whiskered tori are lagrangian manifolds we also include a comparison with the more global theory developed in blazevski and de la llave 2011

eigenvalues in spectral gaps of the two dimensional pauli operator we consider purely magnetic two dimensional pauli operators h with a spectral gap perturbed by a magnetic field bs das 0 assuming that bs and as vanish at infinity we ask whether eigenvalues will cross the gap as furthermore we give an example of a two dimensional pauli operator h with periodic magnetic field of zero flux which has at least one spectral gap

quasi classical asymptotics for the pauli operator we study the behaviour of the sums of the eigenvalues of the pauli operator in in a magnetic field and electric field v x as the planck constant tends to zero and the magnetic field strength tends to infinity we show that for the sum obeys the natural weyl type formula where d 2 2 with an explicit constant c d if the field b has a constant direction then this formula is uniform in 0 the method is based on colin de verdiere s approach proposed in his work on magnetic bottles commun math phys 105 327 335 1986

statistically thinned arrays with quantized element weights the use of statistical thinning and quantized element weights to produce low sidelobe patterns using large circular array apertures is investigated the major results of the analysis show that by using either of several thinning algorithms it is possible to obtain substantial sidelobe reduction by a combination of statistical thinning and the use of discrete amplitude quantization the paper includes generalized formulas for sidelobe level eirp effective isotropic radiated power and curves to show how these parameters vary as a function of the design sidelobe level for the selected taylor pattern

spectral asymptotics of pauli operators and orthogonal polynomials in complex domains we consider the spectrum of a two dimensional pauli operator with a compactly supported electric potential and a variable magnetic field with a positive mean value the rate of accumulation of eigenvalues to zero is described in terms of the logarithmic capacity of the support of the electric potential a connection between these eigenvalues and orthogonal polynomials in complex domains is established

on eigenvalues in gaps for perturbed magnetic schrodinger operators we study schrodinger operators h0 with a gap in the essential spectrum perturbed by either a decreasing electric potential or a decreasing magnetic field in both cases the strength of the perturbation is measured by a coupling constant 0 here we are mainly interested in the asymptotic behavior as of certain counting functions for the eigenvalues that are produced by the perturbation inside the spectral gap the case where we perturb by a potential can be handled using current technology even if h0 contains a fixed magnetic background for perturbations by magnetic fields however we require rather strong assumptions like exponential decay of the perturbations to obtain a lower bound on the counting function to gain some additional intuition we use separation of variables in the closely related model of a schrodinger operator with constant magnetic field in r2 perturbed by a rotationally symmetric magnetic field that decays at infinity

integrable hamiltonians with exponential potential abstract we construct a large class of integrable hamiltonian systems with n degrees of freedom this class naturally extends the nonperiodic hamiltonians of toda lattice type

efficient prediction of array element patterns using physics based expansions and a single far field measurement a method is proposed to predict the antenna array beam through employing a relatively small set of physics based basis functions called characteristic basis function patterns cbfps for modeling the embedded element patterns the primary cbfp can be measured or extracted from numerical simulations while additional secondary cbfps are derived from the primary one furthermore each numerically generated cbfp which is typically simulated measured for discrete directions only can in turn be approximated by analytical basis functions with fixed expansion coefficients to evaluate the resulting array pattern at any angle through interpolation this hierarchical basis reduces the number of unknown expansion coefficients significantly accordingly the cbfp expansion coefficients can be determined through a single far field measurement of only a few reference sources in the field of view this is particularly important for multibeam array applications where only a limited number of reference sources are available for predicting the beam shape furthermore this instantaneous beam calibration is fast i e potentially capable to speed up the array calibration by one or two orders of magnitude which is particularly important if the antenna radiation characteristics are subject to drifts

time dependent scattering theory for odes and applications to reaction dynamics we develop a time dependent scattering theory for general vector fields in euclidean space we give conditions that ensure that the wave maps exist are smooth invertible and depend smoothly on parameters we then discuss the intertwining relations and how they can be used to compute stable unstable manifolds for time dependent normally hyperbolic invariant manifolds the theory is particularly effective for hamiltonian mechanics we also give perturbative calculations of the scattering map that are analogous to fermi s golden rule in quantum mechanics we apply this theory to a problem in transition state theory concerning the exposure of molecules to a laser pulse for a short time we present a method to compute invariant manifolds for the laser driven henon heilies system and give perturbative calculations of the change in the branching ratio

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

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

on the existence of eigenvalues of the schrodinger operatorh λw in a gap of σ h the authors prove a number of results asserting the existence of eigenvalues of the schrodinger operatorh w in a gap of h whereh v andv andw are bounded the existence of these eigenvalues is an important element in the theory of the colour of crystals the basic theorems are proved in v stronger results forv 1 are also presented

geometric properties of the scattering map of a normally hyperbolic invariant manifold given a normally hyperbolic invariant manifold for a map f whose sta ble and unstable invariant manifolds intersect transversally we consider its associated scattering map that is the map that given an asymptotic orbit in the past gives the asymptotic orbit in the future we show that when f and are symplectic resp exact symplectic then the scattering map is symplectic resp exact symplectic furthermore we show that in the exact symplectic case there are extremely easy formulas for the primitive function which have a variational interpretation as dierence of actions we use this geometric information to obtain ecien t perturbative calculations of the scattering map using deformation theory this perturbation theory generalizes and extends several results already obtained using the melnikov method analogous results are true for hamiltonian o ws the proofs are obtained by geometrically natural methods and do not involve the use of particular coordinate systems hence the results can be used to obtain intersection properties of objects of any type we also reexamine the calculation of the scattering map in a geodesic o w perturbed by a quasi periodic potential we show that the geometric theory reproduces the results obtained in dls06b using methods of fast slow systems moreover the geometric theory allows to compute perturbatively the dependence on the slow variables which does not seem to be accessible to the previous methods

melnikov s method and arnold diffusion for perturbations of integrable hamiltonian systems we start with an unperturbed system containing a homoclinic orbit and at least two families of periodic orbits associated with action angle coordinates we use kolmogorov arnold moser kam theory to show that some of the resulting tori persist under small perturbations and use a vector of melnikov integrals to show that under suitable hypotheses their stable and unstable manifolds intersect transversely this transverse intersection is ultimately responsible for arnold diffusion on each energy surface the method is applied to a pendulum oscillator system