equivalence of q bosons using the exponential phase operator various forms of the q boson are explained and their hidden symmetry revealed by transformations using the exponential phase operator both the one component and the multicomponent q bosons are discussed as a byproduct we obtain a new boson algebra having a shifted vacuum structure and define a global operator u 1 gauge transformation

the q deformed boson realization of representations of quantum universal enveloping algebras for q a root of unity i the case of uqsl l the properties of q deformed boson operators with non generic q q is a root of unity are analysed by using the representation theory method and their finite dimensional representations are thereby obtained based on this discussion reducibilities and decompositions of q deformed boson realized representations of quantum universal enveloping algebra uqsl l are studied for non generic cases the explicit matrix elements of some indecomposable representations are obtained on the q deformed fock spaces necessary details are provided for uqsl 2 and uqsl 3 in particular the lusztig operator extension of uqsl 2 is discussed in an explicit form

unitary irreducible representations of covariant q oscillators unitary irreducible representations of a independent q oscillators are used for the construction of all unitary irreducible representations of the suq n covariant system of q oscillators

on the two q analogue logarithmic functions there is a simple multi sheet riemann surface associated with s inverse function for a principal sheet for can be defined however the topology of the riemann surface for changes each time q increases above the collision point of a pair of the turning points of there is also a power series representation for an infinite product representation for is used to obtain the ordinary natural logarithm and the values of the sum rules for the zeros of for where the values of the sum rules for the q trigonometric functions and are q deformations of the usual bernoulli numbers

finite dimensional representations of the quantum analog of the enveloping algebra of a complex simple lie algebra let g be a complex simple lie algebra we show that whent is not a root of 1 all finite dimensional representations of the quantum analogu t g are completely reducible and we classify the irreducible ones in terms of highest weights in particular they can be seen as deformations of the representations of the classical u g

quantum deformation of bose parastatistics a q deformation of the transformation of the chevalley basis to an odd basis of generators of the universal enveloping of the lie superalgebra g n osp 1 2n is presented it is shown that one thus obtains a reasonable quantum deformation of the algebra of n para bose oscillators

time reversal based imaging and inverse scattering of multiply scattering point targets the treatment of time reversal imaging of multiply scattering point targets developed by the present authors in gruber et al time reversal imaging with multiple signal classification considering multiple scattering between the targets j acoust soc am 115 3042 3047 2004 is reformulated and extended to the estimation of the target scattering strengths using the foldy lax multiple scattering model it is shown that the time reversal multiple signal classification music pseudospectrum computed using the background green function as the steering vector yields accurate estimates of the target locations even in the presence of strong multiple scattering between the targets and that the target scattering strengths are readily computed from the so determined target locations using a nonlinear iterative algorithm the paper includes computer simulations illustrating the theory and algorithms presented in the paper

complementarity of suq 3 and uq 2 and q boson realization of the suq 3 irreducible representations the complementarity relationship also termed duality that arises between the irreps of the su 3 and u 2 lie algebras when their direct sum su 3 u 2 is embedded into a larger u 6 algebra and single row irreps of the latter are considered is extended to the corresponding q algebras suq 3 and uq 2 it is demonstrated by explicitly constructing the unique q boson state that is simultaneously maximal in suq 3 and uq 2 for a given u q 2 weight in addition the relations between the suq 3 and uq 2 casimir operators resulting from their complementarity are explicitly found together with the q bargmann representation of q boson operators the complementarity relationship is then used to construct a gel fand tseitlin basis for arbitrary suq 3 irreps in terms of q boson operators

q analogues of the parabose and parafermi oscillators and representations of quantum algebras deformations of the one dimensional parabose oscillators are presented they are shown to provide fock representations of the quantum sp q 2 algebra and ospq 1 2 superalgebra the representations of suq 2 are used to define the q analogues of the parafermi oscillators

generalized commutators and deformation of strong coupling superconductivity we consider quantum deformation of a strong coupling superconductivity model based on creation annihilation operators which satisfy generalized commutator relations it is found that the nature of the superconducting phase transition can be changed from the usual second order to a first order transition if the deformation parameter exceeds a certain critical value metastable normal and superconducting states can exist when the transition is of the first order

eigenfunction analysis of stochastic backscatter for characterization of acoustic aberration in medical ultrasound imaging presented here is a characterization of aberration in medical ultrasound imaging the characterization is optimal in the sense of maximizing the expected energy in a modified beamformer output of the received acoustic backscatter aberration correction based on this characterization takes the form of an aberration correction filter the situation considered is frequently found in applications when imaging organs through a body wall aberration is introduced in a layer close to the transducer and acoustic backscatter from a scattering region behind the body wall is measured at the transducer surface the scattering region consists of scatterers randomly distributed with very short correlation length compared to the acoustic wavelength of the transmit pulse the scatterer distribution is therefore assumed to be delta correlated this paper shows how maximizing the expected energy in a modified beamformer output signal naturally leads to eigenfunctions of a fredholm integral operator where the associated kernel function is a spatial correlation function of the received stochastic signal aberration characterization and aberration correction are presented for simulated data constructed to mimic aberration introduced by the abdominal wall the results compare well with what is obtainable using data from a simulated point source

multiple emitter location and signal parameter estimation processing the signals received on an array of sensors for the location of the emitter is of great enough interest to have been treated under many special case assumptions the general problem considers sensors with arbitrary locations and arbitrary directional characteristics gain phase polarization in a noise interference environment of arbitrary covariance matrix this report is concerned first with the multiple emitter aspect of this problem and second with the generality of solution a description is given of the multiple signal classification music algorithm which provides asymptotically unbiased estimates of 1 number of incident wavefronts present 2 directions of arrival doa or emitter locations 3 strengths and cross correlations among the incident waveforms 4 noise interference strength examples and comparisons with methods based on maximum likelihood ml and maximum entropy me as well as conventional beamforming are included an example of its use as a multiple frequency estimator operating on time series is included

music imaging and electromagnetic inverse scattering of multiple scattering small anisotropic spheres the foldy lax equation is used to derive a multiple scattering model for the multiple scattering small anisotropic spheres by this model if the number of the non zero singular values of the multistatic response msr matrix is smaller than the number of the antennas the range space of the msr matrix is found to be spanned by the background green s function vectors corresponding to the and components of the electric and magnetic dipoles induced in each scatterer which indicates that the multiple signal classification music method could be implemented to obtain the locations of the scatterers after estimating the positions of the scatterers a non iterative analytical method is proposed for retrieving the polarization strength tensors as well as the orientations of the principle axes of each scatterer two numerical simulations show that the music method and the non iterative method are efficacious for the nonlinear inverse scattering problem of determining the locations and polarization strength tensors of multiple scattering small anisotropic spheres such methods could also be applied to the inversion of small isotropic spheres or extended to the inversion of small bianisotropic spheres

extension of q deformed analysis and q deformed models of classical mechanics the author presents the generalization of the q derivative and investigates its properties the formula of conjugation for scalar products with respect to the lebesgue and discrete measures is obtained this formalism is applied to classical mechanical systems depending on functional derivatives he derives the deformed euler lagrange equations and deformed poisson bracket by an assumption that it determines the functional evolution of the systems it appears that in such models a hamiltonian analogue is no longer conserved in time for a few examples the explicit forms of constants of evolution are given

on cohomology isomorphisms of groups abstract we show how mislin s theorem on group homomorphisms that induce an isomorphism in cohomology can be proved based on ideas of alperin and the use of lannes s t functor this enables us to extend the class of groups to include groups of finite virtual cohomological dimension and profinite groups

parabosons virasoro type algebras and their deformations two parameter p q deformation of a parabosonic algebra underlying the two particle calogero model is considered the fock space representation bargmann fock representation coherent states spectrum generating algebra and a hidden supersymmetry are discussed the paraboson algebra induces a centreless virasoro type algebra with a doubling of the space of generators a two parameter deformation of this virasoro type algebra is studied

the q deformed boson realization of representation of quantum universal enveloping algebras for q a root of unity ii the subalgebra chain of uq cl for pt i see ibid vol 24 p 3265 1991 applying the method of the q deformed boson realization for the quantum group to the case where q is a root of unity the authors establish a set of standard basis for the representation space of the quantum universal enveloping algebra uq cl associated with a typical subalgebra chain of uq cl on this basis they systematically obtain irreducible and indecomposable representations of uq cl and its subalgebras they discuss uq c2 in detail

the poisson bracket for q deformed systems it is shown that the quantum system of q deformed oscillators with the uq n group symmetry can be obtained by the canonical quantization of a classical system with a modified poisson bracket the modification of the poisson bracket is connected with a non canonical transformation of phase space variables in this approach the deformation parameter turns out to be a function of the planck constant and some dimensional parameters characterizing the classical system

real de sitter and conformal algebras in terms of q oscillators we express the cartan weyl basis of all quantum real d 4 de sitter and d 4 conformal algebras in terms of q deformed oscillators

deformation of the embedding the cartan chevalley generators of g being a maximal singular sub algebra of are written in terms of the generators of using a q boson realization then a deformation scheme for is presented starting from i e in a basis which manifestly exhibits for q 1 the content of the singular subalgebra g

a new generalisation of macdonald polynomials we introduce a new family of symmetric multivariate polynomials whose coefficients are meromorphic functions of two parameters q t and polynomial in a further two parameters u v we evaluate these polynomials explicitly as a matrix product at u v 0 they reduce to macdonald polynomials while at q 0 u v s they recover a family of inhomogeneous symmetric functions originally introduced by borodin

generalized q oscillators and their hopf structures we study the relationships among the various forms of the q oscillator algebra and consider the conditions under which it supports a hopf structure we also present a generalization of this algebra together with its corresponding hopf structure its multimode extensions are also considered

the metaplectic representation of suq 1 1 and the q gegenbauer polynomials the metaplectic representation of the quantum algebra suq 1 1 is shown to provide a group theoretic setting for certain basic orthogonal polynomials generalizing the usual gegenbauer polynomials

imaging small three dimensional elastic inclusions by an enhanced multiple signal classification method in this paper an enhanced multiple signal classification music algorithm is introduced to retrieve small three dimensional elastic inclusions first the multistatic response msr matrix is built by two different ways depending on considering the multiple scattering effect or not the eigenvalue structure of the msr matrix is analyzed to identify the degenerate case of inclusions second the pseudo spectrum function is built with an optimal test direction on each node where a balancing technique is employed to ensure the numerical stability benefitting from this music indicator the degenerate inclusions can be located with a good performance against noise numerical simulations show the proposed method has wider applicability better resolution and more robust in the presence of noise than the standard music methods

three dimensional quadratic algebras some realizations and representations four classes of three dimensional quadratic algebra of the type q0 q q q q aq02 bq0 c where a b c are constants or central elements of the algebra are constructed using a generalization of the well known two mode bosonic realizations of su 2 and su 1 1 the resulting matrix representations and single variable differential operator realizations are obtained some remarks on the mathematical and physical relevance of such algebras are given

q analogues of clifford and weyl algebras spinor and oscillator representations of quantum enveloping algebras we introduceq analogues of clifford and weyl algebras using these we construct spinor and oscillator representations of quantum enveloping algebras of typean 1 bn cn dn andan 1 1 also we discuss the irreducibility and the unitarity of these representations

quantum deformations of certain simple modules over enveloping algebras soit f un corps soit f 0 un sous corps de f soit u l algebre enveloppante universelle sur f 0 de l algebre de lie de kac moody correspondant a la matrice a d entiers on montre qu un module integrable de poids le plus eleve v de u admet une deformation quantique

the q analog of the boson algebra its representation on the fock space and applications to the quantum group in this paper a realization of the q deformed boson operators on the fock space from a generally algebraic point of view is given the representations of the quantum group cn q are thereby constructed in terms of this realization some infinite and finite dimensional representations of the q analog of the heisenberg weyl algebra are obtained on certain quotient spaces finally the q deformed differential realization of quantum group given by alvarez gaume gomez and sierra preprint cern th 5369 89 is derived from the boson realization

multiple signal classification method for detecting point like scatterers embedded in an inhomogeneous background medium the multiple signal classification music type method has been widely used to detect point like scatterers embedded in a homogeneous background medium this paper extends the music type method to the detection of point like scatterers that are embedded in an inhomogeneous background although the background green s function at each test point is not directly available in inhomogeneous background scenario this paper proposes an approach based on the finite element method to simultaneously obtain the green s function at all test points numerical simulations illustrate the efficacy of the proposed theory and algorithm presented in this paper and some interesting observations which are absent in homogeneous background scenario are highlighted and discussed

deforming maps for lie group covariant creation and annihilation operators any deformation of a weyl or clifford algebra a can be realized through a deforming map i e a formal change of generators in a this is true in particular if a is covariant under a lie algebra g and its deformation is induced by some triangular deformation uhg of the hopf algebra ug we propose a systematic method to construct all the corresponding deforming maps together with the corresponding realizations of the action of uhg the method is then generalized and explicitly applied to the case that uhg is the quantum group uhsl 2 a preliminary study of the status of deforming maps at the representation level shows in particular that deformed fock representations induced by a compact uhg can be interpreted as standard undeformed fock representations describing particles with ordinary bose or fermi statistics

noniterative analytical formula for inverse scattering of multiply scattering point targets this paper derives in the exact framework of multiple scattering theory for point targets a noniterative analytical formula for the nonlinear inversion of the target scattering strengths from the scattering or response matrix that can be applied after the target positions have been estimated in a previous step via e g time reversal multiple signal classification or another approach the new formula provides a noniterative analytical alternative to the iterative numerical solution approach for the same problem presented in a recent paper a j devaney e a marengo and f k gruber time reversal based imaging and inverse scattering of multiply scattering point targets j acoust soc am 118 3129 3138 2005 the two methods noniterative versus iterative are comparatively investigated with two numerical examples

centralizers of elementary abelian p subgroups and mod p cohomology of profinite groups 1 1 let g be a profinite group and p be a fixed prime in this paper we will be concerned with h c g fp the continuous cohomology of g with coefficients in the trivial module fp we will abbreviate h c g fp by h g fp or simply by h g if p is understood from the context we recall that if g is the inverse limit of finite groups gi then h g colim h gi throughout this paper we will assume that h g is finitely generated as fp algebra by work of lazard la it is known that this holds for many interesting groups for example for profinite p analytic groups like gl n zp the general linear groups over the p adic integers in case h g is finitely generated as fp algebra quillen has shown q1 that there are only finitely many conjugacy classes of elementary abelian p subgroups of g i e groups isomorphic to z p for some natural number n in other words the following category a g is equivalent to a finite category objects of a g are all elementary abelian p subgroups of g and if e1 and e2 are elementary abelian p subgroups of g then the set of morphisms from e1 to e2 in a g consists precisely of those homomorphisms e1 e2 of abelian groups for which there exists an element g g with e geg 1 e e1 the category a g plays an important role both in quillen s results and in the work presented here this category entered into quillen s work as follows the assignment e 7 h e extends to a functor from the opposite category a g op to graded fp algebras and the restriction homomorphisms h g h e for e running through the elementary abelian p subgroups of g induce a canonical map of algebras q h g lima g op h e

q deformed oscillator algebra as a quantum group it is proved that the q deformed oscillator algebra is a quantum group the hopf algebraic structure is set up and verified to be consistent and compatible the universal r matrix and yang baxter equation are constructed the q differential operator algebra is briefly discussed

group cohomology and control of p fusion we show that if an inclusion of finite groups h g of index prime to p induces a homeomorphism of mod p cohomology varieties or equivalently an f isomorphism in mod p cohomology then h controls p fusion in g if p is odd this generalizes classical results of quillen who proved this when h is a sylow p subgroup and furthermore implies a hitherto difficult result of mislin about cohomology isomorphisms for p 2 we give analogous results at the cost of replacing mod p cohomology with higher chromatic cohomology theories

experimental subwavelength localization of scatterers by decomposition of the time reversal operator interpreted as a covariance matrix the d o r t method french acronym for decomposition of the time reversal operator is an active remote sensing technique using arrays of antennas for the detection and localization of scatterers prada et al j acoust soc am 99 2067 2076 1996 the analogy between the time reversal operator and the covariance matrix used for classical sources separation in passive remote sensing bienvenu et al ieee trans assp 31 1235 1247 1983 is established then an experiment of subwavelength detection and localization of point like scatterers with a linear array of transducers is presented using classical estimators in reception like maximum likelihood and multiple signal characterization music two point like scatterers separated by 3 and placed at 100 from the array of transducers are resolved in these experiments the role of multiple scattering and the existence of additional eigenvectors associated with dipolar and monopolar radiation of each scatterer is discussed

unitary representations of the q oscillator algebra we classify the unitary irreducible representations of the q oscillator algebra bb q2b b 1 by the sign of the definite operator k bb b b k 0 corresponds to fock representations and k 0 to non fock ones k 0 being a degenerate case we present their link to representations of extended q oscillator algebra aa qa a q n obtained earlier we give examples of all representations besides standard ones we describe a new non fock representation of the macfarlane type

multistatic response matrix of a 3 d inclusion in half space and music imaging recent work on the retrieval of 3 d bounded dielectric and or magnetic inclusions in free space is extended to burial in a half space though emphasis is on the case of a single inclusion enabling the derivation of closed form mathematical results in illuminating fashion the approach extends to the case of an unknown number of well separated inclusions within an asymptotic field formulation derived from exact contrast source vector integral formulations satisfied by the time harmonic fields and using proper reciprocity relationships of the dyadic green s functions the multistatic response matrix of the inclusion is constructed from the leading order term of the fields its singular value structure is analyzed in detail for a dielectric or a magnetic contrast or both contrasts this is performed in the case of a unique electric dipole array operated in the transmit receive mode at a single frequency a multiple signal classification type algorithm follows from the decomposition yielding a cost functional the magnitude of which peaks at the inclusion center numerical results illustrate the above as a function of the geometric and electromagnetic parameters of the configuration imaging of a spherical inclusion is in particular investigated from severely noisy synthetic data as well as of two inclusions embedded within a non conductive or conductive half space

q oscillators realization of fq 4 and gq 3 a realization of the quantum superalgebras corresponding to f 4 and g 3 is given in terms of q deformed bosonic and fermionic oscillators

unitarizable representations of the deformed para bose superalgebra uq osp 1 2 at roots of 1 the unitarizable irreps of the deformed para bose superalgebra pbq which is isomorphic to uq osp 1 2 are classified at q being root of 1 new finite dimensional irreps of uq osp 1 2 are found explicit expressions for the matrix elements are written down

the q boson realization of parametrized cyclic representations of quantum algebras at qp 1 a parametrized cyclic representation of the q deformed heisenberg weyl algebras is constructed the cyclic representations of any quantum algebras are studied in terms of their q boson realizations a general method to construct the q boson realizations of quantum algebras from their verma representations is proposed two explicit examples sl 2 q and sl 3 q are studied in detail some cyclic representations of quantum algebras sl n q and uqcn are presented by using their q boson realizations

the q boson realizations of the quantum group uq sl n 1 c the authors give an explicit expression of the recurrency formulae of canonical realization for quantum enveloping algebras uq sl n 1 c in these formulae the generators of the algebra uq sl n 1 c are expressed by means of n canonical q boson pairs one auxiliary representation of the algebra uq gl n c

vertex representations of quantum affine algebras we construct vertex representations of quantum affine algebras of ade type which were first introduced in greater generality by drinfeld and jimbo the limiting special case of our construction is the untwisted vertex representation of affine lie algebras of frenkel kac and segal our representation is given by means of a new type of vertex operator corresponding to the simple roots and satisfying the defining relations in the case of the quantum affine algebra of type a we introduce vertex operators corresponding to all the roots and determine their commutation relations this provides an analogue of a chevalley basis of the affine lie algebra unk n in the basic representation

on the decoupling of the homogeneous and inhomogeneous parts in inhomogeneous quantum groups we show that if there exists a realization of a hopf algebra h in a h module algebra then one can split their cross product into the tensor product algebra of itself with a subalgebra isomorphic to h and commuting with this result applies in particular to the algebra underlying inhomogeneous quantum groups like the euclidean groups which are obtained as cross products of the quantum euclidean spaces qn with the quantum groups of rotation uq so n of qn for which it has no classical analogue