truncation diffraction phenomena of floquet waves radiated from semi infinite phased array antenna in a general focus problem this paper presents uniform formulations of radiation mechanisms analogous to the ray decompositions of diffraction theory from a semi infinite and periodic array of antennas the antenna array is excited to radiate the electromagnetic em fields focused at a relatively arbitrarily selected location the ray decomposition results from a closed form formulation by asymptotically evaluating the radiation integral of floquet modes that are obtained by applying the poisson sum formula to the summation of elemental radiations the analysis is relatively general and will reduce to the case of a conventional phased array antenna that is excited to radiate directive beams focused in the far zone and exhibits consistent phenomena theoretical investigations as well as numerical examinations are presented to demonstrate the radiation mechanisms

riemann integrability and lebesgue measurability of the composite function abstract if f is continuous on the interval a b g is riemann integrable resp lebesgue measurable on the interval and g a b then f g is riemann integrable resp measurable on a well known fact on the other hand states that f g might not be riemann integrable resp measurable when f is riemann integrable resp measurable and g is continuous if c stands for the continuum in this paper we construct a 2 c dimensional space v and a c dimensional space w of respectively riemann integrable functions and continuous functions such that for every f v 0 and g w 0 f g is not riemann integrable showing that nice properties such as continuity or riemann integrability can be lost in a linear fashion via the composite function similarly we construct a c dimensional space w of continuous functions such that for every g w 0 there exists a c dimensional space v of measurable functions such that f g is not measurable for all f v 0

bounded and unbounded polynomials and multilinear forms characterizing continuity in this paper we prove a characterization of continuity for polynomials on a normed space namely we prove that a polynomial is continuous if and only if it maps compact sets into compact sets we also provide a partial answer to the question as to whether a polynomial is continuous if and only jilt transforms connected sets into connected sets these results motivate the natural question as to how many non continuous polynomials there are on an infinite dimensional normed space a problem on the lineability of the sets of non continuous polynomials and multilinear mappings on infinite dimensional normed spaces is answered

structure constants for lie algebras an orthogonal basis in root space related to the weights of the smallest representation is used to provide a list of the algebraic conditions which the structure constants n must satisfy for all simple lie algebras a particular explicit set of solutions for all the n is given

moduleability algebraic structures and nonlinear properties we show that some pathological phenomena occur more often than one could expect existing large algebraic structures infinite dimensional vector spaces algebras positive cones or infinitely generated modules enjoying certain special properties in particular we construct infinite dimensional vector spaces of non integrable measurable functions completing some recent results shown in garcia pacheco et al 2009 13 garcia pacheco and seoane sepulveda 2006 15 munoz fernandez et al 2008 20 we prove as well the existence of dense and not barrelled spaces of sequences every non zero element of which has a finite number of zero coordinates giving partial answers to a problem originally posed by r m aron and v i gurariy in 2003

the semisimple subalgebras of lie algebras techniques for obtaining generators of nonregular maximal subalgebras of lie algebras alternative to those of dynkin are developed they exploit the use of orthogonal bases in weight space which are related to quark weights the projection from an algebra g to its nonregular subalgebras g is related to an orthogonal matrix the roots of g which project onto roots of g can be simply specified in the orthogonal bases the phases of the expansion coefficients of generators of g in terms of generators of g are specified in such a manner that for a given g the entire set g of maximal subalgebras have consistent phases the condition e e is satisfied for all generators of g the generators of all maximal nonregular subalgebras of all exceptional algebras are exhibited

an efficient computation scheme for the free space green s function of a two dimensional semiinfinite phased array a simple scheme is developed to compute the green s function of a periodic semiinfinite array in free space it is based on the spectral representation of the fields radiated by an infinite linear array of dipoles results related to successive linear arrays are added in the space domain this summation can be accelerated tremendously by using an elementary extrapolation technique the resulting formulation converges everywhere in the plane containing the array and the number of terms required to achieve a given precision increases slowly away from this plane

field patterns of resonant noncircular closed loop arrays further analysis previous papers have introduced the continuous current model for resonant closed loop arrays of cylindrical dipoles and for a certain class of array shapes have determined the resulting field patterns analytically those analytical calculations involve several approximations in the present paper we first study the aforementioned model numerically for the case of elliptical closed loop arrays the results which involve fewer approximations than those of the previous papers but which refer to different array shapes imply that elliptical arrays have a bidirectional highly directive field and unlike conventional arrays have no sidelobes combining analytical and numerical methods we then investigate the relationship between the aforementioned continuous current model and what we call the discrete current model which in a certain sense is more realistic the results indicate that subject to suitable conditions the two models yield virtually identical results in our analytical investigations an important tool is the poisson summation formula for finite sums we have devoted a stand alone section to this formula which supplements recent unrelated publications in antenna theory

lineability criteria with applications lineability is a property enjoyed by some subsets within a vector space x a subset a of x is called lineable whenever a contains except for zero an infinite dimensional vector subspace if additionally x is endowed with richer structures then the more stringent notions of dense lineability maximal dense lineability and spaceability arise naturally in this paper several lineability criteria are provided and applied to specific topological vector spaces mainly function spaces sometimes such criteria furnish unified proofs of a number of scattered results in the related literature families of strict order integrable functions hypercyclic vectors non extendable holomorphic mappings riemann non lebesgue integrable functions sequences not satisfying the lebesgue dominated convergence theorem nowhere analytic functions bounded variation functions entire functions with fast growth and peano curves among others are analyzed from the point of view of lineability

a one sided version of the poisson sum formula for semi infinite array green s functions the poisson sum formula provides an efficient method for transforming many slowly converging infinite summations into equivalent but more rapidly converging infinite summations electromagnetic applications for this result come in the analysis of infinite arrays of periodic scatterers such as frequency selective surfaces however in some applications such as when one desires the radiation of a semi infinite array of periodically spaced currents the original form of the poisson sum formula is inappropriate for such applications we derive a one sided version of the formula and apply it to the radiation from a semi infinite array of line sources with currents dictated by floquet s theorem the one sided poisson sum transformation yields enhanced convergence characteristics for certain regions of application as a result of the inverse bandwidth relationship between fourier transform pairs the application of it to a semi infinite line source array also provides a plane wave representation for the fields which makes for an extension of the solution to geometries with stratified dielectric media

asymptotic floquet mode investigation over two dimensional infinite array antennas phased to radiate near zone focused fields this paper extends the previous work in to consider the radiation from an infinite 2 d antenna array for the near field focus applications it employs the poisson sum formula to expand the radiation into floquet modes which may exhibit a class of wave phenomena in terms of geometrical ray fields this analysis automatically reduces to the conventional case of a linearly phased antenna array and results in consistent radiation phenomena it can be considered as a generalization of phased array analysis theoretical investigations as well as numerical illustrations are presented

accelerating the convergence of series representing the free space periodic green s function a method for improving the convergence of the series representing the doubly periodic free space green s function is presented the method consists of successively applying three different transformations to the green s function spectral representation kummer s transformation is first applied to convert the slowly converging spectral representation into the sum of a rapidly converging series and a slowly converging series the latter series is recognized as the spectral representation of the original periodic source distribution radiating in a medium with an imaginary wavenumber application of the poisson transformation to this series renders it exponentially convergent since it effectively represents propagation of point source contributions through a medium with imaginary wavenumber finally shanks transform is plotted versus the number of terms taken in the series numerical results confirm that an improvement in the convergence rate of the series is achieved for a particular convergence criterion

some characteristics of radiation from linearly phased sequentially excited periodic rectangular arrays of dipoles floquet wave and element by element summation representations are implemented to investigate the radiation from a periodic rectangular array of linearly phased sequentially pulsed dipoles in the frequency and time domains a synthetic aperture type formulation for floquet wave representation and an asymptotic formulation for the element by element summation representation are developed numerical results are presented to demonstrate the efficiency of the floquet wave representation in terms of radiating non radiating and diffracted wave constituents and then validated via comparison with direct summation over the contributions of individual dipole radiations

linear structure of sets of divergent sequences and series abstract we show that there exist infinite dimensional spaces of series every non zero element of which enjoys certain pathological property some of these properties consist on being i conditional convergent ii divergent or iii being a subspace of l of divergent series we also show that the space l 1 x of all weakly unconditionally cauchy series in x has an infinite dimensional vector space of non weakly convergent series and that the set of unconditionally convergent series on x contains a vector space e of infinite dimension so that if x e 0 then i xi

spaceability in banach and quasi banach sequence spaces abstract let x be a banach space we prove that for a large class of banach or quasi banach spaces e of x valued sequences the sets e q l q x where is any subset of 0 and e c 0 x contain closed infinite dimensional subspaces of e if non empty of course this result is applied in several particular cases and it is also shown that the same technique can be used to improve a result on the existence of spaces formed by norm attaining linear operators

basic sequences and spaceability in lp spaces let x be a sequence space and denote by z x the subset of x formed by sequences having only a finite number of zero coordinates we study algebraic properties of z x and show among other results that for p is an element of 1 infinity z l p does not contain infinite dimensional closed subspaces this solves an open question originally posed by r m aron and v i gurariy in 2003 on the linear structure of z l infinity in addition to this we also give a thorough analysis of the existing algebraic structures within the sets z x and x z x and their algebraic genericities

realisation of lie algebras and of representations of lie groups in terms of harmonic oscillators the algebras and irreducible representations irreps of compact lie groups including the exceptional groups are realised in terms of sets of bose oscillator sho creation and annihilation operators in particular not only the tensor irreps but also the spinor irreps of orthogonal groups of all ranks can be constructed using bose rather than the more customary fermi oscillators

frequency domain green s function for a planar periodic semi infinite phased array i truncated floquet wave formulation this two part sequence deals with the derivation and physical interpretation of a uniform high frequency solution for the field radiated at finite distance by a planar semi infinite phased array of parallel elementary electric dipoles the field obtained by direct summation over the contributions from the individual radiators is restructured into a double series of wavenumber spectral integrals whose asymptotic reduction yields a series encompassing propagating and evanescent floquet waves fws together with corresponding diffracted rays which arise from scattering of the fw at the edge of the array the formal aspects of the solution are treated in the present paper they involve a sequence of manipulations in the complex spectral wavenumber planes that prepare the integrands for subsequent efficient and physically incisive asymptotics based on the method of steepest descent different species of spectral poles define the various species of propagating and evanescent fw their interception by the steepest descent path sdp determines the variety of shadow boundaries for the edge truncated fw the uniform asymptotic reduction of the sdp integrals performed by the van der waerden 1951 procedure and yielding a variety of edge diffracted fields completes the formal treatment

on the use of rho algorithm in series acceleration the rho algorithm a nonlinear transformation is shown to be applicable to monotonic series the results of applying the algorithm to a series involving the zeroth order hankel function of the second kind and its associated fourier transform are given it is shown that the algorithm performs better than the epsilon algorithm derived from shanks transform 1955 numerical results include a relative error measure versus number of terms taken in the series

linear subsets of nonlinear sets in topological vector spaces for the last decade there has been a generalized trend in mathematics on the search for large algebraic structures linear spaces closed subspaces or infinitely generated algebras composed of mathematical objects enjoying certain special properties this trend has caught the eye of many researchers and has also had a remarkable influence in real and complex analysis operator theory summability theory polynomials in banach spaces hypercyclicity and chaos and general functional analysis this expository paper is devoted to providing an account on the advances and on the state of the art of this trend nowadays known as lineability and spaceability

non lipschitz functions with bounded gradient and related problems let e be a topological vector space and let us consider a property p we say that the subset m of e formed by the vectors in e which satisfy p is lineable for certain cardinal finite or infinite if m 0 contains an infinite dimensional linear space of dimension in this note we prove that there exist uncountably infinite dimensional linear spaces of functions enjoying the following properties 1 being continuous on 0 1 a e differentiable with a e bounded derivative and not lipschitz 2 differentiable in r2 r and not enjoying the mean value theorem 3 real valued differentiable on an open connected and non convex set having bounded gradient non lipschitz and therefore not verifying the mean value theorem

floquet mode phenomena of infinite phased array antennas in near field focus applications this paper presents a theoretical investigation on the radiation of an infinite one dimensional antenna array which is phased to radiate electromagnetic fields focused in the near zone of the array aperture in particular the wave phenomena in each of the floquet modes obtained by applying the poisson sum formula to the array excitations are investigated the analysis reduces to the case of a conventional phased antenna array when the radiation is focused in the far zone and exhibits consistent phenomena theoretical investigations as well as numerical illustrations are presented

on the poisson sum formula for the analysis of wave radiation and scattering from large finite arrays poisson sum formulas have been previously presented and utilized in the literature for converting a finite element by element array field summation into an alternative representation that exhibits improved convergence properties with a view toward more efficiently analyzing wave radiation scattering from electrically large finite periodic arrays however different authors appear to use two different versions of the poisson sum formula one of these explicitly shows the end point discontinuity effects due to array truncation whereas the other contains such effects only implicitly it is shown via the sifting property of the dirac delta function that first of all these two versions of the poisson sum formula are equivalent second the version containing implicit end point contributions has often been applied in an incomplete fashion in the literature to solve finite array problems it is also demonstrated that the latter can lead to some errors in finite array field computations

time harmonic and transient scattering by finite periodic flat strip arrays hybrid ray floquet mode mom algorithm a frequency and short pulse sp time domain td study of two dimensional plane wave scattering from a finite periodic array of thin flat coplanar perfectly conducting strips is presented rigorous analytical numerical reference solutions are established by spatial spectral wave number decomposition and the method of moments mom followed by frequency inversion the analytical portion is approximated so as to yield via high frequency asymptotics for a sufficiently large number of strips a hybrid ray floquet mode mom algorithm that not only explains the phenomena in physical terms but is also numerically efficient and reasonably accurate when compared with the reference solution of special interest are the td floquet modes with their space time dependent frequencies and wave numbers by superposition they can synthesize the highly resolved pulse train return under sp conditions attention is given also to direct sp td synthesis and to processing options for sp td data

comparative analysis of acceleration techniques for 2 d and 3 d green s functions in periodic structures along one and two directions the problem of accelerating the calculation of the periodic green s function is addressed here for both 3 d and 2 d free space configurations in the 3 d case periodicity is considered both along one axis and along two generally skew axes a comprehensive review of the existing methods is first presented and some extensions are developed the possibility of treating the case of complex phase shifts between unit cells necessary for the study of complex modes in periodic structures is also investigated comparisons among the various acceleration methods are performed thus providing fundamental information on their actual efficiency in typical problems

a truncated floquet wave diffraction method for the full wave analysis of large phased arrays i basic principles and 2 d cases this two part sequence deals with the formulation of an efficient method for the full wave analysis of large phased array antennas this is based on the method of moments mom solution of a fringe integral equation ie in which the unknown function is the difference between the exact solution of the finite array and that of the associated infinite array the unknown currents can be interpreted as produced by the field diffracted at the array edge which is excited by the floquet waves fws pertinent to the infinite configuration following this physical interpretation the unknown in the ie is efficiently represented by a very small number of basis functions with domain on the entire array aperture in order to illustrate the basic concepts the first part of this sequence deals with the two dimensional example of a linearly phased slit array it is shown that the dominant phenomenon fur describing the current perturbation with respect to the infinite array is accurately represented in most cases by only three diffracted ray shaped unknown functions this also permits a simple interpretation of the element by element current oscillation which was described by other authors

on lineability of sets of continuous functions we study the existence of vector spaces of dimension at least two of continuous functions on subsets of r every non zero element of which admits one and only one absolute maximum

quasi periodic green s functions of the helmholtz and laplace equations a classical problem of free space green s function g0 representations of the helmholtz equation is studied in various quasi periodic cases i e when an underlying periodicity is imposed in less dimensions than is the dimension of an embedding space exponentially convergent series for the free space quasi periodic g0 and for the expansion coefficients dl of g0 in the basis of regular cylindrical in two dimensions and spherical in three dimension 3d waves or lattice sums are reviewed and new results for the case of a one dimensional 1d periodicity in 3d are derived from a mathematical point of view a derivation of exponentially convergent representations for schlomilch series of cylindrical and spherical hankel functions of any integer order is accomplished exponentially convergent series for g0 and lattice sums dl hold for any value of the bloch momentum and allow g0 to be efficiently evaluated also in the periodicity plane the quasi periodic green s functions of the laplace equation are obtained from the corresponding representations of g0 of the helmholtz equation by taking the limit of the wave vector magnitude going to zero the derivation of relevant results in the case of a 1d periodicity in 3d highlights the common part which is universally applicable to any of remaining quasi periodic cases the results obtained can be useful for the numerical solution of boundary integral equations for potential flows in fluid mechanics remote sensing of periodic surfaces periodic gratings and infinite arrays of resonators coupled to a waveguide in many contexts of simulating systems of charged particles in molecular dynamics for the description of quasi periodic arrays of point interactions in quantum mechanics and in various ab initio first principle multiple scattering theories for the analysis of diffraction of classical and quantum waves

efficient calculation of lattice sums for free space periodic green s function an efficient method to calculate the lattice sums is presented for a one dimensional 1 d periodic array of line sources the method is based on the recurrence relations for hankel functions and the fourier integral representation of the zeroth order hankel function the lattice sums of arbitrary high order are then expressed by an integral of elementary functions which is easily computed using a simple scheme of numerical integration the calculated lattice sums are used to evaluate the free space periodic green s function the numerical results show that the proposed method provides a highly accurate evaluation of the green s function with far less computation time even when the observation point is located near the plane of the array

spaceability of strict order integrability abstract in this paper sharp conditions on a measure space are provided in order that the subset of functions in the corresponding lebesgue space l p which are in no other l q contains except for zero an infinite dimensional closed subspace this completes earlier work of several authors the main result is derived from a new general criterion for spaceability on function spaces a further application to spaceability of the class of non absolutely continuous functions is supplied

porous sets and lineability of continuous functions on locally compact groups abstract let g be a non compact locally compact group in this paper we study the size of the set f g a b f g is well defined on g where a and b are normed spaces of continuous functions on g we also consider the problem of the spaceability of the set c 0 g c 0 g c 0 g c 00 g and among other results we show that for g r n the above set is strongly c algebrable and therefore algebrable and lineable with respect to the convolution product

lineability in subsets of measure and function spaces we show among other results that if lambda denotes the lebesgue measure on the borel sets in 0 1 and x is an infinite dimensional banach space then the set of measures whose range is neither closed nor convex is lineable in ca lambda x we also show that in certain situations we have lineability of the set of x valued and non sigma finite measures with relatively compact range the lineability of sets of the type l p i l q i is studied and some open questions are proposed some classical techniques together with the converse of the lyapunov convexity theorem are used

large structures in certain subsets of orlicz spaces abstract assume that and n n 1 are young functions in this paper we prove that under sharp conditions on a measure space and the young functions and n s the subset of functions in the corresponding orlicz space l which are not in l n for all n n admits various large linear structures

the weyl orbits of g2 f4 e6 and e7 simple methods are described for constructing the weyl orbits of exceptional lie algebras and for identifying the orbit of an arbitrary weight the methods make use of convenient bases in weight space they are applied to g2 f4 e6 and e7 a complete table of all weights of all orbits of f4 is given the weights of the 37 orbits of smallest weight length of e6 and e7 are given in tabular form the depth structures of the orbits are discussed

extension and replacement bases for semisimple lie algebras two simple prescriptions are given for obtaining sets of orthogonal bases for semisimple lie algebras the first method allows one to obtain the irreducible representations of all the simple lie algebras starting from su 2 and dynkin s method for constructing representations from simple roots and highest weights the second method relates algebras of the same rank several examples are discussed a method is given for listing the bases that may be obtained from the prescriptions

edge born waves in connected arrays a finite times infinite analytical representation connected arrays constitute one of the most promising options for wideband phased arrays like most phased arrays they are designed using infinite array theory however when finiteness is included edge effects perturb their behavior these effects are more severe when the arrays are designed to operate over very broad frequency ranges since the mutual coupling between the elements facilitates the propagation of edge born waves that can become dominant over large portions of the arrays finite array simulations which would predict these behaviors are computationally unwieldy in this paper we present a green s function based procedure to assess edge effects in finite connected arrays first the electric current distribution on the array is rigorously derived later on the introduction of a few simplifying assumptions allows the derivation of an analytical approximation for the current distribution this latter provides meaningful insights in the induced dominant edge wave mechanism the efficiency of connected arrays as a function of their dimension in terms of the wavelength and of the loading feed impedances is investigated

bounded linear non absolutely summing operators abstract we show that in certain situations we have lineability in the set of bounded linear and non absolutely summing operators examples on lineability of the set p e f i p e f are also presented and some open questions are proposed

lp 0 1 q plq 0 1 is spaceable for every p 0 abstract in this short note we prove the result stated in the title that is for every p 0 there exists an infinite dimensional closed linear subspace of l p 0 1 every nonzero element of which does not belong to q p l q 0 1 this answers in the positive a question raised in 2010 by r m aron on the spaceability of the above sets for both the banach and quasi banach cases we also complete some recent results from botelho et al 2011 3 for subsets of sequence spaces

electromagnetic wave diffraction by semi infinite strip grating a nonlinear operator equation in terms of the operator of reflection by a plane periodic semi infinite grating of thin metal strips is obtained for the h polarized electromagnetic wave incidence this equation is solved numerically for an incident plane wave the algorithm created allows the solution of a nonlinear operator equation in the fourier amplitude of the reflected field with the method of successive iterations the initial approach chosen is substantiated and the solution convergence is numerically verified the field reflected by a semi infinite grating is calculated and analyzed for different numerical values of the exciting wave angle of incidence the strip width and the incident field wavelength

lineability and algebrability of pathological phenomena in analysis we show that in analysis many pathological phenomena occur more often than one could expect that is in a linear or algebraic way we show this by means of the construction of large algebraic structures infinite dimensional vector spaces or infinitely generated algebras enjoying some special or pathological properties

algebraic structure of continuous unbounded and integrable functions abstract in this paper we study the large linear and algebraic size of the family of unbounded continuous and integrable functions in 0 and of the family of sequences of these functions converging to zero uniformly on compacta and in l 1 norm in addition we concentrate on the speed at which these functions grow their smoothness and the strength of their convergence to zero