on the representation theory of orthofermions and orthosupersymmetric realization of parasupersymmetry and fractional supersymmetry we construct a canonical irreducible representation for the orthofermion algebra of arbitrary order and show that every representation decomposes into irreducible representations that are isomorphic to either the canonical representation or the trivial representation we use these results to show that every orthosupersymmetric system of order p has a parasupersymmetry of order p and a fractional supersymmetry of order p 1

finite dimensional lie algebras of order f f lie algebras are natural generalizations of lie algebras f 1 and lie superalgebras f 2 when f 2 not many finite dimensional examples are known in this article we construct finite dimensional f lie algebras f 2 by an inductive process starting from lie algebras and lie superalgebras matrix realizations of f lie algebras constructed in this way from su n sp 2n so n and sl n m osp 2 m are given we obtain nontrivial extensions of the poincare algebra by inonu wigner contraction of certain f lie algebras with f 2

symmetric coherent choquet capacities choquet capacities are a generalization of probability measures that arise in robustness decision theory and game theory many capacities that arise in robustness are symmetric or can be transformed into sym metric capacities we characterize the extreme points of the set of upper distribution functions corresponding to coherent symmetric choquet ca pacities on 0 1 we also show that the set of 2 altemating capacities is a simplex and we give a choquet representation of this set

the mixed order bcgs fft method for the scattering of three dimensional inhomogeneous anisotropic magnetodielectric objects this paper presents the first fft based fast volume integral equation solver for inhomogeneous anisotropic magnetodielectric objects the volume integral equations are formulated by employing mixed order basis functions that expand the flux densities and vector potentials in the coupled field integral equations in terms of different sets of basis functions with different orders volumetric roof top basis functions are used for flux densities whereas second order curl conforming basis functions are used for vector potentials a fast volume integral equations solver namely the bcgs fft method is then applied to accelerate the solution of this mixed order weak form formulation examples show that the mixed order bcgs fft method has high accuracy compared to both analytical and numerical solutions examples also show the mixed order bcgs fft method has high computational efficiency compared to commercial software

electromagnetic scattering by radially inhomogeneous dielectric spheres a method to determine the electric field scattered by a dielectric sphere with a permittivity and conductivity varying only in the radial direction is presented in order to take advantage of the spherically symmetrical geometry the interior electric field is expanded in terms of vector spherical harmonics which are orthogonal over a spherical surface using the orthogonality of those functions with the vector wave functions in the expanded form of the free space dyadic green s function one can reduce the three dimensional 3 d electric field integral equation into a system of one dimensional 1 d integral equations the scalar coefficients of the series expansion for the interior electric field are then obtained by solving this system of equations for the medium outside the sphere the scattered field is evaluated through the same procedure comparisons with alternative methods for specific cases demonstrate that the method is reliable in determining the interior field and the scattered field for spherical objects with layered or continuously varying radial profile

closed form uniform asymptotic expansions of green s functions in layered media far field closed form expressions are derived for spatial domain multilayered green s functions gf for the derivation of these far field expressions the spectral domain multilayered gf are approximated by means of the total least square algorithm tlsa in terms of the spectral variable u0 k 2 k02 1 2 and uniform asymptotic expansions are determined for the sommerfeld integrals of the resulting tlsa approximations numerical results show that the far field asymptotic expressions are accurate within 0 1 for distances between source and field points larger than one free space wavelength also it is shown that the hybrid use of the discrete complex image method and the tlsa in terms of the spectral variable k leads to near field closed form expressions of multilayered gf that are typically accurate within 0 1 for distances between source and field points smaller than one free space wavelength therefore the combination of the novel far field asymptotic expressions and the well known near field expressions makes it possible to compute multilayered gf with a great accuracy in the whole range of distances between source and field points and in a wide range of frequencies

filiform lie algebras of order 3 the aim of this work is to generalize a very important type of lie algebras and superalgebras i e filiform lie super algebras into the theory of lie algebras of order f thus the concept of filiform lie algebras of order f is obtained in particular for f 3 it has been proved that by using infinitesimal deformations of the associated model elementary lie algebra it can be obtained families of filiform elementary lie algebras of order 3 analogously as that occurs into the theory of lie algebras m vergne cohomologie des algebres de lie nilpotentes application a l etude de la variete des algebres de lie nilpotentes bull soc math france 98 81 116 1970 also we give the dimension using an adaptation of the sl 2 c module method and a basis of such infinitesimal deformations in some generic cases

an improved discrete complex image method based on a special sampling path a special sampling path is proposed to improve the accuracy of the discrete complex image method dcim in evaluating the lateral wave different from all the previous dcim implementations the proposed sampling path goes through the branch point directly which helps to evaluate its contribution to the lateral wave more accurately in this communication different sampling paths of dcim have been implemented and compared it is found that in the situations where the lateral wave dominates the far field region dcim with the new path gives more accurate and stable results

on the construction of generalized grassmann representatives of state vectors generalized zk graded grassmann variables are used to label coherent states related to the nilpotent representation of the q oscillator of biedenharn and macfarlane when the deformation parameter is a root of unity these states are then used to construct generalized grassmann representatives of state vectors

an efficient approach for extracting poles of green s functions in general multilayered media a fast approach of closed form green s functions for mixed potential integral equation analysis of both near field and far field in planar multilayered media is presented in this paper since all components of the green s functions in spectral domain are restructured concisely by four elementary functions the surface wave pole extraction is very effective in terms of a function related to the generalized reflection coefficients meanwhile the number of required two level discrete complex image method dcim with high order sommerfeld identities is also minimized under this scheme the numerical results show that this approach is more efficient and accurate for the electromagnetic scattering by and radiation in the presence of electrically large three dimensional 3 d objects in multilayered media although lossless examples are considered in the numerical examples the method presented here works also for the lossy materials where the poles move away from the real axis in the complex plane

discrete models of electromagnetic wave scatterers in a frequency range we investigate the spatial and frequency characteristics of electromagnetic fields scattered by some object frequency functions that allow the expression of all elements of the object scatter matrix are introduced the sampling theorems that are proved for the introduced functions make it possible to characterize the scatterer by a set of discrete parameters the application of the proved theorems provides for the creation of a versatile scatterer discrete model that determines the dependence of scattered fields both on spatial coordinates and frequency a random scatterer is considered and the conditions under which the discrete parameters are statistically independent normalized random variables are stated the article presents the results of a random scatterer modeling

efficient calculation of the electromagnetic dyadic green s function in spherical layered media a numerical methodology is proposed for the evaluation of the electromagnetic fields of an electric or magnetic dipole of arbitrary orientation in spherical stratified media the proposed methodology is based on the numerical solution of the differential equation in the radial coordinate that is satisfied by each coefficient in the spherical harmonics expansion of the governing helmholtz equation more specifically the finite difference solution of this equation may be cast in a pole residue form that allows the analytic evaluation of the spherical harmonics series by means of the watson transformation thus a closed form expression is obtained for the electromagnetic fields in terms of a short series of associated legendre functions p sup m sub spl nu cos spl theta of integer order m and complex degree spl nu the number of terms in the series is strongly dependent on the angle spl theta and decreases very fast when the point of observation moves away from the source the method allows for arbitrary variation in the permittivity and permeability profiles in the radial directions

acoustic field induced in spheres with inhomogeneous density by external sources acoustic or electromagnetic fields induced in the interior of inhomogeneous penetrable bodies by external sources can be evaluated via well known volume integral equations for bodies of arbitrary shape and or composition for which separation of variables fails a direct attack for the solution of these integral equations is the only available approach in a previous paper by the same authors the scalar acoustic field in inhomogeneous spheres of arbitrary compressibility but with constant density was considered in the present one the direct hybrid analytical numerical method applied to the much simpler integral equation for spheres with constant density is generalized to densities that vary with r or even this extension is by no means trivial owing to the appearance of the derivatives of both the density and the unknown function in the volume integral a fact necessitating a more subtle and accuracy sensitive approach again the spherical shape allows use of the orthogonal spherical harmonics and of dini s expansions of a general type for the radial functions the convergence of the latter shown to be superior to other possible sets of orthogonal expansions can be further optimized by the proper selection of a crucial parameter in their eigenvalue equation

asymptotic extraction approach for antennas in a multilayered spherical media an efficient algorithm is introduced to enhance the convergence of dyadic green s functions dgf in a layered spherical media where asymptotic expressions have been developed the formulated expressions involve an infinite series of spherical eigenmodes that can be reduced to the simple homogenous media green s function using the addition theorem of spherical hankel functions substantial improvements in the convergence speed have been attained by subtracting the asymptotic series representation from the original dgf the subtracted components are then added to the solution using the homogenous media green s function format

z3 graded differential geometry of the quantum plane in this work the z3 graded differential geometry of the quantum plane is constructed the corresponding quantum lie algebra and its hopf algebra structure are obtained the dual algebra i e the universal enveloping algebra of the quantum plane is explicitly constructed

noncommutative differential geometry of matrix algebras the noncommutative differential geometry of the algebra mn c of complex n n matrices is investigated the role of the algebra of differential forms is played by the graded differential algebra c sl n c mn c mn c sl n c sl n c acting by inner derivations on mn c a canonical symplectic structure is exhibited for mn c for which the poisson bracket is to within a factor i the commutator also a canonical riemannian structure is described for mn c finally the analog of the maxwell potential is constructed and it is pointed out that there is a potential with a vanishing curvature that is not a pure gauge

relativistic field theories in three dimensions we provide a complete classification of the unitary irreducible representations of the 2 1 dimensional poincare group we show in particular that only two types of spin are available for massless field theories we also construct generalized foldy wouthuysen transformations which connect the physical uir s with covariant field theories in three dimensions

fractional superlie algebras and groups the nth root of a lie algebra and its dual that is the fractional supergroup based on the permutation group sn invariant forms is formulated in the hopf algebra formalism detailed discussion of s3 graded sl 2 algebras is performed

numerical analysis of single microstrip antenna and antennas array in spherically layered media this communication presents a comprehensive numerical analysis of single microstrip antenna and antennas array in spherically layered media using the method of moments mom the curvilinear rao wilton glisson crwg triangular basis functions are employed to simulate the equivalent current on the antenna surface first the dyadic green s functions using debye potential are deduced then their efficient computation procedures are carried out to improve calculation efficiency finally the characteristic basis function method is employed to save memory and calculation time by reducing dimension of the impedance matrix the results of this study are in good agreement with those of the feko software and they show that the method proposed in this communication is more efficient than feko in the analysis process

a generalized asymptotic extraction solution for antennas in multilayered spherical media an efficient model is developed to accelerate the convergence of the dyadic green s function s dgf infinite summation when the source and observation points are placed in different layers of a dielectric sphere thereby expediting computational analysis the proposed procedure is based on asymptotic extraction principles in which the quasi static images are extracted from the spectral domain dgf the effectiveness of the approach is demonstrated in a method of moment model where a microstrip antenna as well as a conformal dipole array have been studied

modified spherical wave functions with anisotropy ratio application to the analysis of scattering by multilayered anisotropic shells we describe a novel and rigorous vector eigenfunction expansion of electric type green s dyadics for radially multi layered uniaxial anisotropic media in terms of the modified spherical vector wave functions which can take into account the effects of anisotropy ratio systematically in each layer the material constitutions e and epsiv macrmu macr are tensors and distribution of sources is arbitrary both the unbounded and scattering dyadic green s functions dgfs for rotationally uniaxial anisotropic media are derived in spherical coordinates r thetas phi the coefficients of scattering dgfs based on the coupling recursive algorithm satisfied by the coefficient matrix are derived and expressed in a compact form with these dgfs obtained the electromagnetic fields in each layer are straightforward once the current source is known a specific model is proposed for the scattering and absorption characteristics of multilayered uniaxial anisotropic spheres and some novel performance regarding anisotropy effects is revealed

an acoustic inverse scattering problem for spheres with radially inhomogeneous compressibility an inverse acoustic scattering problem the main aim of which is to reconstruct the one dimensional variation of the acoustical parameters of a spherical object is investigated the problem is first formulated conventionally through a coupled system of integral equations and then this system is reduced to one dimensional form by using the orthogonality properties of spherical harmonics the inverse problem is solved in an iterative fashion via classical newton algorithm some numerical simulations are carried out to test the feasibility of the method as well as to see the effects of some parameters on the solution it is shown that the method is very effective for the profiles having smooth variations provided that an appropriate initial guess is chosen however some of the classical disadvantages of the newton type algorithms are also observed in numerical experiments which may limit the applicability of the method to a certain extent

graded gauge theory the mathematical background for a graded extension of gauge theories is investigated after discussing the general properties of graded lie algebras and what may serve as a model for a graded lie group the graded fiber bundle is constructed its basis manifold is supposed to be the so called superspace i e the product of the minkowskian space time with the grassmann algebra spanned by the anticommuting lorentz spinors the vertical subspaces tangent to the fibers are isomorphic with the graded extension of the su n lie algebra the connection and curvature are defined then on this bundle the two different gradings are either independent of each other or may be unified in one common grading which is equivalent to the choice of the spin statistics dependence the yang mills lagrangian is investigated in the simplified case the conformal symmetry breaking is discussed as well as some other physical consequences of the model

bayes theorem for choquet capacities we give an upper bound for the posterior probability of a measurable set a when the prior lies in a class of probability measures p the bound is a rational function of two choquet integrals if p is weakly compact and is closed with respect to majorization then the bound is sharp if and only if the upper prior probability is 2 alternating the result is used to compute bounds for several sets of priors used in robust bayesian inference the result may be regarded as a characterization of 2 alternating choquet capacities

response of a source on top of a vertically stratified half space the solution of the response of a source on top of a horizontally stratified half space is well known however when the half space is vertically stratified the problem can only be solved with numerical methods like the finite element method here a semi analytic approach to solve such a problem is presented the three dimensional variation of the problem is reduced to two dimensional variation by fourier transform in one coordinate variable the remaining two dimensional problem is solved by finding the eigensolution in each of the half spaces the eigensolutions of each region are found from the partial differential equation directly using the same basis set of expansion functions this makes the calculation of the reflection and transmission operators very efficient the reflection and transmission operators account for the mode conversion reflection and transmission of the waves with the reflection and transmission operators the field everywhere can be calculated the solution reduces to that of the sommerfeld s half space problem when the two half spaces are homogeneous

integral equation based analysis of scattering from 3 d inhomogeneous anisotropic bodies this paper presents an integral equation based scheme to analyze scattering from inhomogeneous bodies with anisotropic electromagnetic properties both the permittivity and permeability are assumed to be generalized tensors requisite integral equations are derived using volume equivalence theorem with the electric and magnetic flux densities being the unknown quantities matrix equations are derived by discretizing these unknowns using three dimensional rao wilton glisson basis functions reduction of the integral equation to a corresponding matrix equation is considerably more involved due to the presence of anisotropy and the use of vector basis function methods for evaluation of the integrals involved in the construction of this matrix is elucidated in detail the method of moments technique is augmented with the fast multipole method and a compression scheme the latter two enable large scale analysis finally several numerical results are presented and compared against analytical solutions to validate the proposed scheme an appendix provides analytical derivations for the formulae that are used to validate numerical method and the necessary formulae that extends the approach presented herein to the analysis of scattering bianisotropic bodies

a numerical methodology for efficient evaluation of 2d sommerfeld integrals in the dielectric half space problem the analysis of 2d scattering in the presence of a dielectric half space by integral equation formulations involves repeated evaluation of sommerfeld integrals deformation of the contour to the steepest descent path results in a well behaved integrand that can be readily integrated a well known drawback of this method is that an analytical expression for the path is available only for evaluation of the reflected fields but not for the evaluation of the transmitted fields a simple scheme for numerical determination of the steepest descent path valid for both cases is presented the computational cost of the numerical determination is comparable to that of evaluating the analytical expression for the steepest descent path for reflected fields when necessary contributions from branch cut integrals and a second saddle point are taken into account certain ranges of the input parameters which result in integrands that vary rapidly in the neighborhood of the saddle point require special treatment alternative paths and specialized gaussian quadrature rules for these cases are also proposed an implementation of the proposed numerically determined steepest descent path nd sdp method is freely available for download

hypersymmetry a z3 graded generalization of supersymmetry we propose a generalization of non commutative geometry and gauge theories based on ternary z3 graded structures in the new algebraic structures we define all products of two entities are left free the only constraining relations being imposed on ternary products these relations reflect the action of the z3 group which may be either trivial i e abc bca cab generalizing the usual commutativity or non trivial i e abc jbca with j e 2 i 3 the usual z2 graded structures such as grassmann lie and clifford algebras are generalized to the z3 graded case certain suggestions concerning the eventual use of these new structures in physics of elementary particles and fields are exposed

generalized grassmannian coherent states for pseudo hermitian n level systems the purpose of this paper is to generalize fermionic coherent states for two level systems described by pseudo hermitian hamiltonian cherbal et al 2007 j phys a math theor 40 1835 to n level systems central to this task is the expression of the coherent states in terms of generalized grassmann variables these kinds of grassmann coherent states satisfy the bi overcompleteness condition instead of the overcompleteness one as it is reasonably expected because of the biorthonormality of the system choosing an appropriate grassmann weight function the resolution of identity is examined moreover grassmannian coherent and squeezed states of the deformed group suq 2 for the three level pseudo hermitian system are presented

the model based parameter estimation of antenna radiation patterns using windowed interpolation and spherical harmonics techniques previously reported for interpolating antenna radiation patterns simultaneously in both the spatial and frequency domains are reexamined here in order to develop new algorithms with improved efficiency and speed while maintaining comparable accuracy to this end interpolation in the frequency domain is constrained to a windowed scheme whereby a series of reduced order pade spl acute rational function fitting models of only three or four sampling frequencies are used to interpolate over a relatively large bandwidth the use of this piece wise technique is shown to reduce the complexity of determining the unknown coefficients without any significant loss in the resulting interpolation accuracy or increase in the required number of sampling frequencies in this paper exact analytical expressions are found for the unknown coefficients that allow the spatial domain interpolation to be performed entirely separate from the frequency domain interpolation the technique is applied to the case of a 0 5 meter dipole modeled from 150 to 950 mhz and for spl theta from 0 spl deg to 90 spl deg using fitting windows with three and four sampling frequencies the results are compared to those obtained using a previously developed generalized simultaneous interpolation procedure in the spatial domain spherical harmonics are introduced as model based fitting functions for antenna radiation patterns specifically interpolation procedures are developed using zonal harmonics and tesseral harmonics to model one and two dimensional far field radiation patterns respectively the case of a z oriented 0 5 meter dipole is considered to demonstrate the efficiency and accuracy obtained by applying these physically based fitting models in the spatial domain zonal harmonics are used to interpolate far field radiation patterns of this antenna for spl theta from 0 spl deg to 180 spl deg for several different frequencies over the range from 150 to 950 mhz this example demonstrates the attractiveness of using spherical harmonics functions to accurately and efficiently interpolate radiation patterns in the spatial domain

quantum z3 graded space in this paper the quantum z3 graded space is discussed and its differential calculus is investigated and the quantum matrices in quantum z3 graded space are obtained

generalized exclusion and hopf algebras we propose a generalized oscillator algebra at the roots of unity with generalized exclusion and we investigate the braided hopf structure we find that there are two solutions these are the generalized exclusions of the bosonic and fermionic types we also discuss the covariance properties of these oscillators

linearization of polynomials it is well known that the linearization of quadratic forms is accomplished using dirac matrices the general problem of linearization of any polynomial of degree n having p variables is considered first the homogeneous polynomials are considered and it is shown that we only need to study two basic homogeneous forms namely the sum and the product one the sum is linearized using matrices which turn out to be a matrix representation of a generalized clifford algebra the homogeneous form is linearized using matrices the size of which is large for practical use some clues are given to reduce their size since any polynomial of degree n can be made homogeneous by introducing a supplementary variable the method proposed is quite general it constitutes an algorithm for the linearization of any polynomial

poincare and sl 2 algebras of order 3 in this paper we initiate a general classification for lie algebras of order 3 and we give all lie algebras of order 3 based on sl 2 c and iso 1 3 the poincare algebra in four dimensions we then set the basis of the theory of the deformations in the gerstenhaber sense and contractions for lie algebras of order 3

the reflection of electromagnetic waves from stratified anisotropic media a direct approach to the investigation of the reflection of electromagnetic waves from a plane interface separating a vacuum half space and a stratified anisotropic layer is presented the formulation involves the generation of a riccati differential equation for a certain 2 2 reflection matrix the approach is already well established for scalar problems but its implementation in cases which allow mode conversion is believed to be new the reflection matrix concerned is unitary when the anisotropic layer is nondissipative and an efficient numerical method to solve the equation is outlined sample results are presented to illustrate the theory

fractional supersymmetry and fth roots of representations a generalization of super lie algebras is presented it is then shown that all known examples of fractional supersymmetry can be understood in this formulation however the incorporation of three dimensional fractional supersymmetry in this framework needs some care the proposed solutions lead naturally to a formulation of a fractional supersymmetry starting from any representation d of any lie algebra g this involves taking the fth roots of d in an appropriate sense a fractional supersymmetry in any space time dimension is then possible this formalism finally leads to an infinite dimensional extension of g reducing to the centerless virasoro algebra when g sl 2 r

em field induced in inhomogeneous dielectric spheres by external sources the electromagnetic field induced in the interior of inhomogeneous dielectric bodies by external sources can be evaluated by solving the well known electric field integrodifferential equation efide for spheres with constant magnetic permeability but variable dielectric constant a direct mainly analytical solution can be used even in case when the inhomogeneity in renders separation of variables inapplicable this approach constitutes a generalization of the hybrid analytical numerical scalar method developed by the authors in two recent papers for the corresponding acoustic scalar field induced in spheres with variable density and or compressibility this extension by no means trivial owing to the vector and integrodifferential nature of the equation is based on field vector expansions using the set of three harmonic surface vectors orthogonal and complete over the surface of the sphere for their angular dependence and dini s expansions of a general type for their radial functions the use of the latter has been shown to be superior to other possible sets of orthogonal expansions and as far as its convergence is concerned it may further be improved by properly choosing a crucial parameter in their eigenvalue equation the restriction to the spherical shape is imposed here to allow use of the well known expansion of green s dyadic in spherical eigenvectors of the vector wave equation

a z3 graded generalization of supermatrices we introduce z3 graded objects which are the generalization of the more familiar z2 graded objects that are used in supersymmetric theories and in many models of non commutative geometry first we introduce the z3 graded grassmann algebra and we use this object to construct the z3 matrices which are the generalizations of the supermatrices then we generalize the concepts of supertrace and superdeterminant

fast calculations of dyadic green s functions for electromagnetic scattering in a multilayered medium abstract in this paper we introduce a novel acceleration method for the calculation of dyadic green s functions for the mixed potential integral equation formulation of electromagnetic scattering of scatterers embedded in a multilayered medium numerical results are provided to demonstrate the efficiency and accuracy of the proposed method

stripline fed arbitrarily shaped printed aperture antennas a full wave analysis method is presented for modeling the radiation properties of a stripline fed planar printed aperture antenna element in this formulation both the finite length of stripline and the finite aperture may be of any arbitrary shape since their equivalent electric and magnetic currents are modeled with triangular patch basis functions galerkin s method is applied to numerically solve the coupled mixed potential integral equation mpie exact spatial domain green s functions are used to account for all radiation surface wave and mutual coupling effects interactions between the stripline feed and the radiating aperture are rigorously included numerical analysis is presented for the following nonrectangular shapes an exponentially tapered slot an annular slot an annular slot with opposing stubs and a monofilar archimedean spiral slot element results are shown for input return loss radiation patterns and axial ratio for the circularly polarized elements

z3 graded algebras and the cubic root of the supersymmetry translations a generalization of supersymmetry is proposed based on z3 graded algebras introducing the objects whose ternary commutation relations contain the cubic roots of unity e2 i 3 e4 i 3 and 1 the operators whose trilinear combinations yield the supersymmetric translation generators can be constructed cubic matrices forming a ternary algebra are the generalization of pauli s matrices the general properties of z3 grading some other representations of such algebras and their possible pertinence with regard to the quark model are briefly discussed

symmetric upper probabilities as a first step toward developing statistical models based on upper and lower probabilities we study upper probabilities and upper expectations on the unit interval that are symmetric by which we mean invariant with respect to equimeasurability these upper probabilities are generalizations of uniform probability measures we give some characterizations of these upper probabilities specifically we show that symmetry of the upper expectation functional is equivalent to the underlying set of densities being closed under majorization we also show that a function is the upper distribution for a symmetric upper probability if and only if its lower graph is star shaped with respect to the origin and to the point 1 1 we derive inner and outer approximations to symmetric classes of probabilities based on the upper probability the class of symmetric upper expectations that are completely determined by their values on the indicator functions is characterized we provide a geometric characterization of a hierarchy of upper probabilities including fine s generalized upper probabilities and 2 alternating choquet capacities in particular we establish a 1 1 correspondence between symmetric 2 alternating capacities and nonincreasing density functions we prove that undominated generalized upper probabilities do not exist in the symmetric case examples from robust statistics are considered an example is given that shows that symmetry of upper probabilities does not imply symmetry of upper expectations a corollary is that symmetry of the choquet integral does not imply symmetry of the upper expectation functional

quantum group covariance and the braided structure of deformed oscillators the connection between braided hopf algebra structure and quantum group covariance of the deformed oscillators is constructed explicitly in this context we provide deformations of the hopf algebra of functions on su 1 1 quantum subgroups and their representations are also discussed

simultaneously least favorable experiments a concept of worst case sufficiency is defined generalizing le cam s approximate sufficiency instead of using total variation norm as did le cam 1964 neighborhoods are described by upper expectations a corresponding version of the theorem of le cam blackwell sherman stein is proved in the case of finite parameter space as a main tool serve standard experiments and their upper limits here to be called upper standard functionals a characterization of simultaneously least favorable experiments dominated by a family of upper expectations is proved it says that least favorable experiments exist if and only if the upper standard functional acts additively on a cone of concave functions

group theoretical foundations of fractional supersymmetry fractional supersymmetry denotes a generalization of supersymmetry which may be constructed using a single real generalized grassmann variable n 0 for arbitrary integer n 2 3 an explicit formula is given in the case of general n for the transformations that leave the theory invariant and it is shown that these transformations possess interesting group properties it is shown also that the two generalized derivatives that enter the theory have a geometric interpretation as generators of left and right transformations of the fractional supersymmetry group careful attention is paid to some technically important issues including differentiation that arise as a result of the peculiar nature of quantities such as

the resonance mode theory for exterior problems of electrodynamics and its application to discrete antenna modeling in a frequency range the problem under consideration here is that of building a versatile discrete antenna model in a frequency range the eigenfunction mode expansion or singularity expansion method sem is used in working out the problem a detailed substantiation of sem is provided and an expression determining the dependence of mode amplitudes on exterior source fields is derived a simple example is provided in support of the theory the sem is used in inquiring into the frequency dependence of antenna generalized matrix entries it is intimated that all of the matrix entries contain resonance factors and factors that are hankel transforms of radial coordinate functions a sampling theorem which is a generalized extension of the classic sampling theorem is used for the hankel transform the application of the generalized sampling theorem completes the process of building a versatile discrete antenna model in a frequency range

field induced in inhomogeneous spheres by external sources i the scalar case the evaluation of acoustic or electromagnetic fields induced in the interior of inhomogeneous penetrable bodies by external sources is based on well known volume integral equations this is particularly true for bodies of arbitrary shape and or composition for which separation of variables fails in this paper the investigation focuses on acoustic scalar fields in inhomogeneous spheres of arbitrary composition i e with r or even dependent medium parameters the volume integral equation is solved by a hybrid analytical numerical method which takes advantage of the orthogonal properties of spherical harmonics and in particular of the so called dini s expansions of the radial functions whose convergence is optimized the numerical part comes at the end it involves the evaluation of certain definite integrals and the matrix inversion for the expansion coefficients of the solution the scalar case treated here serves as a steppingstone for the solution of the more difficult electromagnetic problem

on the huber strassen theorem we show that the huber strassen theorem can be applied to many common robust neighborhood models without restrictive compactness assumptions our method is to replace the original polish topology with a compact topology which is possible according to the kuratowski isomorphism theorem

parafermions for higher order extensions of the poincare algebra and their associated superspace parafermions of orders 2 and 3 are shown to be the fundamental tool to construct superspaces related to cubic and quartic extensions of the poincare algebra the corresponding superfields are constructed and some of their main properties are analyzed in detail in this context the existence problem of operators acting like covariant derivatives is analyzed and the associated operators are explicitly constructed

on special classes of n algebras we define n algebras as linear spaces on which the internal composition law involves n elements m v n v it is known that such algebraic structures are interesting for their applications to problems of modern mathematical physics using the notion of a commutant of two subalgebras of an n algebra we distinguish certain classes of n algebras with reasonable properties semisimple abelian nilpotent solvable we also consider a few examples of n algebras of different types and show their properties

two dimensional fractional supersymmetry from the quantum poincare group at roots of unity a group theoretical understanding of the two dimensional fractional supersymmetry is given in terms of the quantum poincaregroup at roots of unity the fractional supersymmetry algebra and the quantum group dual to it are presented and the pseudo unitary and irreducible representations of them are obtained the matrix elements of these representations are explicitly constructed

a robust method for the computation of green s functions in stratified media closed form green s functions for unbounded planar stratified media are derived in terms of cylindrical and spherical waves the methodology is based on a two level approximation of the spectral domain representation of green s functions this robust efficient and fully numerical approach does not call for an analytical extraction of ldquoproblematicrdquo behaviors such as the quasi static terms and the surface wave poles prior to the spectrum fitting instead the spatial domain green s functions derived in this paper provide an accurate description of both the near field singularity in the vicinity of the source and the far field dominant behavior of the surface waves

extrapolation methods for sommerfeld integral tails a review is presented of the extrapolation methods for accelerating the convergence of sommerfeld type integrals i e semi infinite range integrals with bessel function kernels which arise in problems involving antennas or scatterers embedded in planar multilayered media attention is limited to partition extrapolation procedures in which the sommerfeld integral is evaluated as a sum of a series of partial integrals over finite subintervals and is accelerated by an extrapolation method applied over the real axis tail segment spl alpha spl infin of the integration path where spl alpha 0 is selected to ensure that the integrand is well behaved an analytical form of the asymptotic truncation error or the remainder which characterizes the convergence properties of the sequence of partial sums and serves as a basis for some of the most efficient extrapolation methods is derived several extrapolation algorithms deemed to be the most suitable for the sommerfeld integrals are described and their performance is compared it is demonstrated that the performance of these methods is strongly affected by the horizontal displacement of the source and field points spl rho and by the choice of the subinterval break points furthermore it is found that some well known extrapolation techniques may fail for a number of values of spl rho and ways to remedy this are suggested finally the most effective extrapolation methods for accelerating sommerfeld integral tails are recommended

fast volumetric integral equation solver for acoustic wave propagation through inhomogeneous media elements are described of a volumetric integral equation based algorithm applicable to accurate large scale simulations of scattering and propagation of sound waves through inhomogeneous media the considered algorithm makes possible simulations involving realistic geometries characterized by highly subwavelength details large density contrasts and described in terms of several million unknowns the algorithm achieves its competitive performance characterized by o nlogn solution complexity and o n memory requirements where n is the number of unknowns through a fast and nonlossy fast fourier transform based matrix compression technique the adaptive integral method previously developed for solving large scale electromagnetic problems because of its ability of handling large problems with complex geometries the developed solver may constitute an efficient and high fidelity numerical simulation tool for calculating acoustic field distributions in anatomically realistic models e g in investigatin

at roots of unity the quantum group at roots of unity is introduced by means of duality pairings with the quantum algebra its irreducible representations corresponding to the type of the quantum algebra are constructed through the universal t matrix the irreducible representations corresponding to the type are also found an invariant integral on this quantum group is given endowed with that some properties like unitarity and orthogonality of the irreducible representations are discussed

dyadic green s function for a multilayered planar medium a dyadic eigenfunction approach a new formulation of the dyadic green s function for a planarly layered medium is presented based on dyadic eigenfunctions of the green s function operator the general development of the dyadic green s function is shown resulting in a three dimensional purely spectral representation the spectral form is converted to a hankel function form using standard techniques analogous to the sum of residues plus branch cut representation often obtained from the sommerfeld green s function advantages and disadvantages of both the eigenfunction and hankel function forms are outlined and compared to other green s function representations examples of the green s dyadic for free space and for a grounded dielectric slab environment are provided and the role of the continuous and discrete spectrum is discussed

analysis of the zonal and rectangular slots on a conducting spherical cavity the zonal slot cut on a conducting spherical cavity is analyzed rigorously the slot is excited asymmetrically which excites higher order azimuthal modes the green s function approach is used to formulate an integral equation for the magnetic current in the slot which is solved using the moment method mom new recurrence formulas are derived so that within their stable region the admittance integrals can be evaluated without the need for any numerical integration in this case the solution is very easy to implement with extremely short computation time the effects of the latitude angle on the peak resistance and percentage bandwidth are investigated furthermore the cavity resonance modes and their degeneracy are examined by plotting the expansion coefficients of the magnetic current in addition the problem of a rectangular slot in the nonequatorial plane is also studied measurements are carried out and good agreement between theory and experiment is obtained

a braided interpretation of fractional supersymmetry in higher dimensions a many variable q calculus is introduced using the formalism of braided covector algebras its properties are discussed in detail and related to fractional supersymmetry when certain of its deformation parameters are roots of unity the special cases of two dimensional supersymmetry and fractional supersymmetry are developed in detail

a full vectorial contrast source inversion scheme for three dimensional acoustic imaging of both compressibility and density profiles imaging the two acoustic medium parameters density and compressibility requires the use of both the acoustic pressure and velocity wave fields described via integral equations imaging is based on solving for the unknown medium parameters using known measured scattered wave fields and it is difficult to solve this ill posed inverse problem directly using a conjugate gradient inversion scheme here a contrast source inversion method is used in which the contrast sources defined via the product of changes in compressibility and density with the pressure and velocity wave fields respectively are computed iteratively after each update of the contrast sources an update of the medium parameters is obtained total variation as multiplicative regularization is used to minimize blurring in the reconstructed contrasts the method successfully reconstructed three dimensional contrast profiles based on changes in both density and compressibility using synthetic data both with and without 50 white noise the results were compared with imaging based only on the pressure wave field where speed of sound profiles were solely based on changes in compressibility it was found that the results improved significantly by using the full vectorial method when changes in speed of sound depended on changes in both compressibility and density

further improvement for fast computation of mixed potential green s functions for cylindrically stratified media a method of fast computation of the mixed potential green s functions mpgfs in spatial domain for cylindrically stratified media has been developed based on the convergence behavior of the mpgfs in spectral domain the discrete complex image method dcim and the extrapolation technique are employed to perform the inverse fourier transform which is different from that of planarly stratified media in order to evaluate the summation of cylindrical eigenmode from order of negative infinity to order of positive infinity the green s functions in spectral domain are rearranged so that acceleration technique can be well applied to speed up the convergence of summation process for the integral along the deformed sommerfeld integral path with respect to k sub z dcim is used to speed up the computation after the quasistatic components are completely subtracted from the spectral domain green s functions the inverse transform of the remaining parts has an approximated analytical form the proposed method can be used to accurately and efficiently calculate the spatial domain mpgfs which are useful for characterizing conformal patch structures mounted on cylindrically stratified media

a new technique for the derivation of closed form electromagnetic green s functions for unbounded planar layered media a closed form electromagnetic green s function for unbounded planar layered media is derived in terms of a finite sum of hankel functions the derivation is based on the direct inverse hankel transform of a pole residue representation of the spectral domain form of the green s function such a pole residue form is obtained through the solution of the spectral domain form of the governing green s function equation numerically through a finite difference approximation rather than analytically the proposed methodology can handle any number of layers including the general case where the planar media exhibit arbitrary variation in their electrical properties in the vertical direction the numerical implementation of the proposed methodology is straightforward and robust and does not require any preprocessing of the spectrum of the green s function for the extraction of surface wave poles or its quasi static part the number of terms in the derived closed form expression is chosen adaptively with the distance between source and observation point as parameter the development of the closed form green s function is presented for both vertical and horizontal dipoles its accuracy is verified through a series of numerical examples and comparisons with results from other established methods

an asymptotic extraction technique for evaluating sommerfeld type integrals an asymptotic extraction process is developed which leads to an efficient method for the evaluation of the electric field from a hertzian dipole in a layered geometry this technique allows for a rapidly converging expression for the electric field which remains well behaved as the source and observation heights z z coincide a useful application of this method is in the calculation of mutual impedance between printed dipoles

special capacities the hunt stein theorem and transformation groups the problem of maximin testing between families of probability measures generated by special capacities and transformation groups is solved by showing that the hunt stein theorem is applicable to such generally nondominated families of probability measures and that the problem reduces to maximin testing between neighbourhoods of distributions of maximal invariant defined by special capacities closely related to the initial ones an application to testing approximate binormality is also sketched

hopf algebras for ternary algebras we construct a universal enveloping algebra associated with the ternary extension of lie super algebras called lie algebra of order three a poincare birkhoff witt theorem is proven is this context it this then shown that this universal enveloping algebra can be endowed with a structure of hopf algebra the study of the dual of the universal enveloping algebra enables to define the parameters of the transformation of a lie algebra of order of 3 it turns out that these variables are the variables which generate the three exterior algebra

generalized grassmann variables for quantum kit k level systems and barut girardello coherent states for su r 1 algebras this paper concerns the construction of su r 1 barut girardello coherent states in terms of generalized grassmann variables we first introduce a generalized weyl heisenberg algebra a r r 1 generated by r pairs of creation and annihilation operators this algebra provides a useful framework to describe qubit and qukit k level systems it includes the usual weyl heisenberg and su 2 algebras we investigate the corresponding fock representation space the generalized grassmann variables are introduced as variables spanning the fock bargmann space associated with the algebra a r the barut girardello coherent states for su r 1 algebras are explicitly derived and their over completion properties are discussed