two extended toda fields in three dimensions two extended toda fields associated with saveliev vershik s continuum lie algebras are studied such fields satisfy three dimensional integro differential equations structures such as the fundamental poisson relation classical yang baxter equation chiral exchange algebra and dressing transformations are recovered which are in complete analogy to the two dimensional case the formal solution is also considered using leznov saveliev analysis but this does not lead to explicit solutions because we have insufficient knowledge about the highest weight representations of the continuum lie algebras

tomographic representation of spin and quark states we present a short review of the general principles of constructing tomograms of quantum states we derive a general tomographic reconstruction formula for the quantum density operator of a system with a dynamical lie group in the reconstruction formula the multiplicity of irreducible representation in clebsch gordan decomposition is taken into account various approaches to spin tomography are discussed an integral representation for the tomographic probability is found and a contraction of the spin tomogram to the photon number tomography distribution is considered the case of su 3 tomography is discussed with the examples of quark states related to the simplest triplet representations and octet states

contractions nijenhuis and saletan tensors for general algebraic structures we study generalizations in many directions of the contraction procedure for lie algebras introduced by saletan we consider products of an arbitrary nature not necessarily lie brackets and we generalize to infinite dimension considering a modification of the approach by nijenhuis tensors to bilinear operations on sections of finite dimensional vector bundles we apply our general procedure to lie algebras lie algebroids and poisson brackets we also present results on contractions of n ary products and coproducts

kernel of star product for spin tomograms the spin state tomogram is presented as the modulus squared of the matrix element of the su 2 group irreducible representation for the spin system we established explicitly a realization of the set of operators defining for spin tomograms the star product formalism in terms of irreducible tensors on the set of spin tomograms the delta function and standard and moyal like kernels of the tomogram star product are calculated explicitly in terms of clebsch gordan and racah coefficients and matrix elements of the su 2 irreducible representation in the limit of infinite spin the spin tomogram is shown to become the tomogram of the harmonic oscillator state

finite size effects in a field theoretic model with long range exchange interaction we present a systematic approach to the calculation of finite size fs effects for ano n field theoretic model with both short range sr and long range lr exchange interactions the lr exchange interaction decays at large distances as 1 rd 2 2 0 0 renormalization group calculations ind du e are performed for a system with a fully finite block geometry under periodic boundary conditions we calculate the fs shift of the critical temperature and the fs renormalized coupling constant of the model to one loop order the universal scaling variable is obtained and the fs scaling hypothesis is verified

the segal bargmann coherent state transform for compact lie groups abstract let k be an arbitrary compact connected lie group we describe on k an analog of the segal bargmann coherent state transform and we prove theorem 1 that this generalized coherent state transform maps l 2 k isometrically onto the space of holomorphic functions in l 2 g where g is the complexification of k and where is an appropriate heat kernel measure on g the generalized coherent state transform is defined in terms of the heat kernel on the compact group k and its analytic continuation to the complex group g we also define a k averaged version of the coherent state transform and we prove a similar result for it theorem 2 in the appendix we describe the coherent states which motivate the definitions of these transforms in section 9 we obtain inversion formulas for both the coherent state transform and the k averaged coherent state transform theorems 3 4 as a consequence we obtain formulas for certain bergman kernels on the complex group g theorems 5 6 in section 10 we derive a general paley wiener theorem for k and we exhibit a family of convolution transforms each of which is an isometric isomorphism of l 2 k onto a certain l 2 space of holomorphic functions on g these transforms include the k averaged coherent state transform as a special case we also discuss the analogous results for r 1 the results of section 10 are theorems 7 10 finally in section 11 we discuss the case of quotient spaces we prove theorem 11 that both the coherent state transform and the k averaged coherent state transform pass in a natural way from k to k h where h is a closed connected subgroup of k

super toda theories and w algebras from superspace wess zumino witten models using a superspace approach it is proved that an 1 super toda theory can be seen as a constrained wzw model based on a supergroup the gauge transformations which survive the constraints are then useda la drinfeld sokolov to determine explicity the super w algebra underlying this theory the conformal spin content of any such super walgebra is provided in the general case

moyal like form of the star product for generalized su 2 stratonovich weyl symbols the star product is the basic tool used in the phase space formulation of quantum mechanics we find a differential form of the star product for a class of mbox s parametrized su 2 stratonovich weyl symbols which appear in the phase space representation of spin like systems the limit of large spin is considered and the asymptotic form of the differential operator defining the star product is obtained

the scale representation the authors considers scale a physical attribute of a signal and develop its properties he presents an operator which represents scale and study its characteristics and representation this allows one to define the scale transform and the energy scale density spectrum which is an indication of the intensity of scale values in a signal he obtains explicit expressions for the mean scale scale bandwidth instantaneous scale and scale group delay furthermore he derives expressions for mean time mean frequency duration frequency bandwidth in terms of the scale variable the short time transform is defined and used to obtain the conditional value of scale for a given time he shows that as the windows narrows one obtains instantaneous scale convolution and correlation theorems for scale are derived a formulation is devised for studying linear scale invariant systems he derives joint representations of time scale and frequency scale general classes for each are presented using the same methodology as for the time frequency case as special cases the joint distributions of marinovich altes 1978 1986 and bertrand bertrand 1984 are recovered also joint representations of the three quantities time frequency scale are devised a general expression for the local scale autocorrelation function is given uncertainty principles for scale and time and scale and frequency are derived

star products a group theoretical point of view adopting a purely group theoretical point of view we consider the star product of functions which is associated in a natural way with a square integrable in general projective representation of a locally compact group next we show that for this implicitly defined star product explicit formulas can be provided two significant examples are studied in detail the group of translations on phase space and the one dimensional affine group the study of the first example leads to the groenewold moyal star product in the second example the link with wavelet analysis is clarified

field theory of directed percolation with long range spreading it is well established that the phase transition between survival and extinction in spreading models with short range interactions is generically associated with the directed percolation dp universality class in many realistic spreading processes however interactions are long ranged and well described by l evy flights char22 i e by a probability distribution that decays in d dimensions with distance r as r ensuremath d ensuremath ensuremath sigma we employ the powerful methods of renormalized field theory to study dp with such long range l evy flight spreading in some depth our results unambiguously corroborate earlier findings that there are four renormalization group fixed points corresponding to respectively short range gaussian l evy gaussian short range and l evy dp and that there are four lines in the ensuremath sigma d plane which separate the stability regions of these fixed points when the stability line between short range dp and l evy dp is crossed all critical exponents change continuously we calculate the exponents describing l evy dp to second order in an ensuremath epsilon expansion and we compare our analytical results to the results of existing numerical simulations furthermore we calculate the leading logarithmic corrections for several dynamical observables

driven diffusive system with non local perturbations we investigate the impact of non local perturbations on driven diffusive systems two different problems are considered here in one case we introduce a non local particle conservation along the direction of the drive and in another case we incorporate a long range temporal correlation in the noise present in the equation of motion the effect of these perturbations on the anisotropy exponent or on the scaling of the two point correlation function is studied using renormalization group analysis

bell s inequalities in the tomographic representation the tomographic approach to quantum mechanics is revisited as a direct tool to investigate the violation of bell like inequalities since quantum tomograms are well defined probability distributions the tomographic approach is emphasized to be the most natural one to compare the predictions of classical and quantum theory examples of inequalities for two qubits and two qutrits are considered in the tomographic probability representation of spin states

w gauge structures and their anomalies an algebraic approach starting from flat two dimensional gauge potentials we propose the notion of w gauge structure in terms of a nilpotent becchi rouet stora brs differential algebra the decomposition of the underlying lie algebra with respect to an sl 2 subalgebra is crucial for the discussion of conformal covariance in particular the appearance of a projective connection different sl 2 embeddings lead to different w gauge structures we present a general soldering procedure which allows one to express zero curvature conditions for the w currents in terms of conformally covariant differential operators acting on the w gauge fields and to obtain at the same time the complete nilpotent brs differential algebra generated by w currents gauge fields and the ghost fields corresponding to w diffeomorphisms as illustrations we treat the cases of sl 2 itself and the two different sl 2 embeddings in sl 3 viz the w 1 3 and w 2 3 gauge structures in some detail in these cases we determine algebraically w anomalie

frame transforms star products and quantum mechanics on phase space using the notions of frame transform and of square integrable projective representation of a locally compact group g we introduce a class of isometries tight frame transforms from the space of hilbert schmidt operators in the carrier hilbert space of the representation into the space of square integrable functions on the direct product group g g these transforms have remarkable properties in particular their ranges are reproducing kernel hilbert spaces endowed with a suitable star product which mimics at the level of functions the original product of operators a phase space formulation of quantum mechanics relying on the frame transforms introduced in the present paper and the link of these maps with both the wigner transform and the wavelet transform are discussed

regular conjugacy classes in the weyl group and integrable hierarchies generalized kdv hierarchies associated by drinfeld sokolov reduction with grade 1 regular semisimple elements from non equivalent heisenberg subalgebras of a loop algebra g x c lambda lambda 1 are studied the graded heisenberg subalgebras containing such elements are labelled by the regular conjugacy classes in the weyl group w g of the simple lie algebra g a representative w epsilon w g of a regular conjugacy class can be lifted to an inner automorphism of g given by w exp 2i pi ad i0 m where i0 is the defining vector of an sl2 subalgebra of g the grading is then defined by the operator d m i0 m lambda d d lambda ad i0 and any grade 1 regular element lambda from the heisenberg subalgebra associated with w takes the form lambda c lambda c where i0 c m 1 c and c is included in an sl2 subalgebra containing i0 the largest eigenvalue of adi0 is m 1 except for some cases in f4 e6 7 8 we explain how these lie algebraic results follow from known results and apply them to construct integrable systems if the largest ad i0 eigenvalue is m 1 then using any grade 1 regular element from the heisenberg subalgebra associated with w we can construct a kdv system possessing the standard w algebra defined by i0 as its second poisson bracket algebra for g a classical lie algebra we derive pseudo differential lax operators for those non principal kdv systems that can be obtained as discrete reductions of kdv systems related to gln non abelian toda systems are also considered

theory of group representations and integration of nonlinear systems xa zz exp kx a abstract a constructive proof of complete integrability of the system xa zf z exp kx a and its explicit solution are given for k coinciding with the cartan matrix of simple lie algebras the technique for dealing with this system of essentially nonlinear two dimensional partial differential equations involves lax type representation and representation theory of the corresponding group

new fuzzy control model and dynamic output feedback parallel distributed compensation a new fuzzy modeling based on fuzzy linear fractional transformations model is introduced this new representation is shown to be a flexible tool for handling complicated nonlinear models particularly the new fuzzy model provides an efficient and tractable way to handle the output feedback parallel distributed compensation problem we demonstrate that this problem can be given a linear matrix inequality characterization and hence is immediately solvable through available semidefinite programming codes the capabilities of the new fuzzy modeling is illustrated through numerical examples

barut girardello coherent states for and and their macroscopic superpositions the barut girardello bg coherent states cs representation is extended to the noncompact algebras and in reducible quadratic boson realizations the bg cs take the form of multimode ordinary schr dinger cat states macroscopic superpositions of cs canonical cs n 1 2 are pointed out which are overcomplete in the n mode hilbert space and the relation between the canonical cs and the bg type cs representations is established the sets of and bg cs and their discrete superpositions contain many states studied in quantum optics even and odd n mode cs pair cs and provide an approach to quadrature squeezing alternative to that of intelligent states new subsets of weakly and strongly nonclassical states are pointed out and their statistical properties first and second order squeezing photon number distributions are discussed for specific values of the angle parameters and small amplitude of the canonical cs components these states approach multimode fock states with one two or three bosons photons it is shown that eigenstates of a squared non hermitian operator generalized cat states can exhibit squeezing of the quadratures of a

on a special picture of dynamical evolution of nonlinear quantum systems in the phase space representation abstract a special picture of quantum evolution in the phase space representation is derived in this picture both the symbols of operators as well as the distribution density carry part of the time dependence the symbols of operators evolve classically whereas the distribution density carries the remaining time dependence which is needed to recover the full time dependence of quantum averages such representation is free of semiclassical expansions or a mixed classical quantum description the spin boson hamiltonian system is explicitly studied its phase space structure is established by obtaining analytical solutions for the three stable regions quantum averages are calculated

integrable graded manifolds and nonlinear equations a method is proposed for the classification of integrable embeddings of 2 2 dimensional supermanifoldsv2 2 into an enveloping superspace supplied with the structure of a lie superalgebra the approach is first applied to the even part of the scheme i e for the embeddings of 2 dimensional manifoldsv2 into riemannian or non riemannian enveloping space the general consideration is also illustrated by the example of superspaces supplied with the structure of the series sl n n 1 whose integrable supermanifolds are described by supersymmetrical 2 dimensional toda lattice type equations in particular forn 1 they are described by the supersymmetrical liouville and sine gordon equations

statistical mechanics of multipartite entanglement we characterize the multipartite entanglement of a system of n qubits in terms of the distribution function of the bipartite purity over all balanced bipartitions we search for those maximally multipartite entangled states whose purity is minimum for all bipartitions and recast this optimization problem into a problem of statistical mechanics

pohlmeyer reduction for superstrings in ads space the pohlmeyer reduced equations for strings moving only in the ads subspace of ads5 s5 have been used recently in the study of classical euclidean minimal surfaces for wilson loops and some semiclassical three point correlation functions we find an action that leads to these reduced superstring equations for example for a bosonic string in adsn such an action contains a liouville scalar part plus a k k gauged wzw model for the group k so n 2 coupled to another term depending on two additional fields transforming as vectors under k solving for the latter fields gives a non abelian toda model coupled to the liouville theory for n 5 we generalize this bosonic action to include the s5 contribution and fermionic terms the corresponding reduced model for the ads2 s2 truncation of the full ads5 s5 superstring turns out to be equivalent to super liouville theory our construction is based on taking a limit of the previously found reduced theory actions for bosonic strings in adsn s1 and superstrings in ads5 s5 this new action may be useful as a starting point for possible quantum generalizations or deformations of the classical pohlmeyer reduced theory we give examples of simple extrema of this reduced superstring action which represent strings moving in the ads5 part of the space expanding near these backgrounds we compute the corresponding fluctuation spectra and show that they match the spectra found in the original superstring theory

holomorphic discrete series and harmonic series unitary irreducible representations of non compact lie groups sp 2n r u p q and so 2n generalised characters of the infinite dimensional holomorphic discrete series unitary irreducible representations of the non compact groups u p q sp 2n r and so 2n are explicitly expressed in terms of characters of finite dimensional unitary group representations these formulae are remarkably succinct despite involving certain infinite series of schur functions similar formulae are derived for harmonic series unitary representation of both u p q and sp 2n r consideration of the branching rules from u p q to u q p and from sp 2n r to u n enables holomorphic representations to be identified as a subset of the harmonic representations the branching rules are established in full generality and are then used in the evaluation of tensor products of both holomorphic and harmonic representations in the case of the former a known result is recast in terms of closed formulae involving schur functions and for the latter various generalisations of these formulae are given a conjecture is also made regarding what might be the simplest possible formulae covering all holomorphic and harmonic representations of sp 2n r and u p q illustrative examples are presented

alternative commutation relations star products and tomography invertible maps from operators of quantum observables onto functions of c number arguments and their associative products are first assessed different types of maps such as the weyl wigner stratonovich map and s ordered quasi distribution are discussed the recently introduced symplectic tomography map of observables tomograms related to the heisenberg weyl group is shown to belong to the standard framework of the maps from quantum observables onto the c number functions the star product for symbols of the quantum observable for each one of the maps including the tomographic map and explicit relations among different star products are obtained deformations of the moyal star product and alternative commutation relations are also considered

linear signal synthesis using the radon wigner transform thresholding the radon wigner transform rwt followed by filtered backprojection to the time frequency plane reduces noise and cross term power for multicomponent linear fm signals although the rwt is bilinear it may be calculated as the magnitude squared of two linear functions in this paper we derive a linear synthesis algorithm from the rwt and demonstrate its efficacy

signals on graphs transforms and tomograms abstract development of efficient tools for the representation of large datasets is a precondition for the study of dynamics on networks generalizations of the fourier transform on graphs have been constructed through projections on the eigenvectors of graph matrices by exploring mappings of the spectrum of these matrices we show how to construct more general transforms in particular wavelet like transforms on graphs for time series tomograms a generalization of the radon transforms to arbitrary pairs of non commuting operators are positive bilinear transforms with a rigorous probabilistic interpretation which provide a full characterization of the signals and are robust in the presence of noise here the notion of tomogram is also extended to signals on arbitrary graphs

renormalisation of random walks with memory the renormalisation of field theoretic models of the true self avoiding random walk is analysed for short range interactions the field theory is shown to be renormalisable only in a special case which corresponds to the problem of a random walk in a random environment and non renormalisable otherwise the long range version of the field theory is shown to be renormalisable in a larger region of the parameter space in the case which corresponds to the original long range true self avoiding random walk the renormalisation group analysis is carried out to two loop order anomalous dimensions of various composite operators are calculated and the crossover between scaling regimes described by short range and long range models is discussed

the quantum group suq 2 and a q analogue of the boson operators a new realisation of the quantum group suq 2 is constructed by means of a q analogue to the jordan schwinger mapping determining thereby both the complete representation structure and q analogues to the wigner and racah operators to achieve this realisation a new elementary object is defined a q analogue to the harmonic oscillator the uncertainty relation for position and momentum in a q harmonic oscillator is quite unusual

two dimensional sir epidemics with long range infection we extend a recent study of susceptible infected removed epidemic processes with long range infection referred to as i in the following from 1 dimensional lattices to lattices in two dimensions as in i we use hashing to simulate very large lattices for which finite size effects can be neglected in spite of the assumed power law p x x 2 for the probability that a site can infect another site a distance vector x apart as in i we present detailed results for the critical case for the supercritical case with 2 and for the supercritical case with 0 2 for the latter we verify the stretched exponential growth of the infected cluster with time predicted by m biskup for 2 we find generic power laws with dependent exponents in the supercritical phase but no kosterlitz thouless kt like critical point as in 1 d instead of diverging exponentially with the distance from the critical point the correlation length increases with an inverse power as in an ordinary critical point finally we study the dependence of the critical exponents on in the regime 0 2 and compare with field theoretic predictions in particular we discuss in detail whether the critical behavior for slightly less than 2 is in the short range universality class as conjectured recently by f linder et al as in i we also consider a modified version of the model where only some of the contacts are long range the others being between nearest neighbors if the number of the latter reaches the percolation threshold the critical behavior is changed but the supercritical behavior stays qualitatively the same

linear integral transformations and hierarchies of integrable nonlinear evolution equations abstract integrable hierarchies of nonlinear evolution equations are investigated on the basis of linear integral equations these are riemann hilbert type of integral transformations which leave invariant an infinite sequence of ordinary differential matrix equations of increasing order in an indefinite parameter k the potential matrices in these equations obey a set of nonlinear recursion relations leading to a heirarchy of nonlinear partial differential equations in decreasing order the same equations give rise to a reciprocal hierarchy associated with heisenberg ferromagnet type of equations central in the treatment is an embedding of the hierarchy into an infinite matrix structure which is constructed on the basis of the integral equations in terms of this infinite matrix structure the equations governing the hierarchies become quite simple furthermore it leads in a straightforward way to various generalizations such as to other types of linear spectral problems multicomponent system and lattice equations generalizations to equations associated with noncommuting flows follow as a direct consequence of the treatment finally some results on conserved densities and the hamiltonian structure are briefly discussed

about the self dual chern simons system and toda field theories on the noncommutative plane the relation of the noncommutative self dual chern simons ncsdcs system to the noncommutative generalizations of toda and of affine toda field theories is investigated more deeply this paper continues the programme initiated in cabrera carnero i 2005 j high energy phys jhep10 2005 071 where it was presented how it is possible to define toda field theories through second order differential equation systems starting from the ncsdcs system here we show that using the connection of the ncsdcs to the noncommutative chiral model exact solutions of the toda field theories can also be constructed by means of the noncommutative extension of the uniton method proposed in lee k m 2004 j high energy phys jhep08 2004 054 by lee particularly some specific solutions of the nc liouville model are explicitly constructed

a new coherent paired state with possible applications to fluctuation dissipation phenomena the authors extend their previous work on coherent paired states associated with the lie group su 1 1 whereas the earlier states were defined with respect to a single type of canonical boson or linear quantum harmonic oscillator the new states are defined in terms of two distinct types of bosons or oscillators the new coherent states may again on the one hand be viewed as ordinary glauber coherent states in the two boson hilbert space spanned by arbitrary numbers of two distinct bogoliubov quasiparticles associated with the original bosons via a generalised bogoliubov transformation alternatively expressed wholly in terms of the original bosons these new coherent states are reached from the ordinary coherent states via a unitary pairing transformation which is shown to be associated with the entire so called discrete series of representations of the group su 1 1 as an important illustration of the use of these states and transformations they study in detail a rather general class of quantum lagrangians which includes the damped linear harmonic oscillator they thereby illustrate their possible usefulness in applications to quantum many body or field theoretic processes involving fluctuation dissipation phenomena in general

geometrical evaluation of star products the geometric picture of the star product based on its fourier representation kernel is utilized in the evaluation of chains of star products and the intuitive appreciation of their associativity and symmetries such constructions appear even simpler for a variant asymmetric product and carry through for the standard star product supersymmetrization

critical behaviour of the long range ϕ2 2 model in the short range limit the relation between scaling regimes described by 2 2 field theories with long range and short range exchange is analysed it is shown that the crossover from the long range regime to the short range regime takes place due to the singular behaviour of three loop and higher order contributions to the beta function of the renormalization group which controls the scaling behaviour of the long range model the critical exponents eta and nu are shown to be continuous functions of the parameter alpha which characterises the power like fall off of the exchange interaction

wigner distribution function for euclidean systems euclidean systems include poly and monochromatic wide angle optics acoustics and also infinite discrete data sets we use a recently defined wigner operator and quasiprobability distribution function to set up and study the phase space evolution of these models subject to differential and difference equations respectively infinite data sets and two dimensional monochromatic helmholtz fields are thus shown by their wigner function on a cylinder of direction and location the wigner function for polychromatic wavefields has c number coordinates of two dimensional wavenumber and position

classical statistical mechanics approach to multipartite entanglement we characterize the multipartite entanglement of a system of n qubits in terms of the distribution function of the bipartite purity over balanced bipartitions we search for maximally multipartite entangled states whose average purity is minimal and recast this optimization problem into a problem of statistical mechanics by introducing a cost function a fictitious temperature and a partition function by investigating the high temperature expansion we obtain the first three moments of the distribution we find that the problem exhibits frustration

a generalized wigner function for quantum systems with the su 2 dynamical symmetry group we introduce a wigner like quasidistribution function to describe quantum systems with the su 2 dynamic symmetry group this function is defined in a three dimensional group manifold and can be used to represent the states defined in several su 2 invariant subspaces the explicit differential moyal like form of the star product is found and analyzed in the semiclassical limit

star product and ordered moments of photon creation and annihilation operators we develop a star product scheme of symbols defined by the normally ordered powers of the creation and annihilation photon operators the corresponding phase space is a two dimensional lattice with nodes m n given by pairs of non negative integers the star product kernel of symbols on the lattice and intertwining kernels to other schemes are found in an explicit form analysis of peculiar properties of the star product kernel results in new sum relations for factorials advantages of the developed star product scheme for describing dynamics of quantum systems are discussed and time evolution equations in terms of the ordered moments are derived

globally optimized power allocation in multiple sensor fusion for linear and nonlinear networks the present paper is concerned with a sensor network where each sensor is modeled by either a linear or nonlinear sensing system these sensors team up in observing either static or dynamic random targets and transmit their observations through noisy communication channels to a fusion center fc for locating tracking the targets physically the network is limited by energy resource according to the available sum power budget we develop a novel technique for power allocation to the sensor nodes that enables the fc produce the best linear estimate in terms of the mean square error mse regardless of whether the sensor measurements are linear or nonlinear the targets are scalar or vectors static or dynamic the corresponding optimization problems are shown to be semidefinite programs sdps of tractable optimization and thus are globally and efficiently solved by any existing sdp solver in other words new tractably computational algorithms of distributed bayes filtering are derived with full multisensor diversity achieved intensive simulation shows that these algorithms clearly outperform previously known algorithms

zero curvature conditions and conformal covariance two dimensional zero curvature conditions with special emphasis on conformal properties are investigated in detail and the appearance of covariant higher order differential operators constructed in terms of a projective connection is elucidated the analysis is based on the kostant decomposition of simple lie algebras in terms of representations with respect to their principal sl 2 subalgebra

general solutions of nonlinear equations in the geometric theory of the relativistic string general solutions for the system of nonlinear equations in the second order partial derivatives with two independent variables are obtained they determine the basic differential forms of the two dimensional minimal surface embedded inton dimensional pseudo euclidean space

crossover between field theories with short range and long range exchange or correlations the relation between scalar field theories with short range and long range exchange or correlations is studied it is shown to all orders in perturbation theory that the critical exponents of fields and composite operators are continuous functions of the parameters alpha xi characterising the decay rate of the long range exchange correlations with power like falloff 1 rd 2 2 alpha 1 rd 2 xi the scaling law d 2 xi v 2 where v is the correlation length exponent as well as the harris criteria 1970 are shown to be exact to all orders in perturbation theory a discrepancy between two widely used approaches to the crossover problem is pointed out

representation and properties of para bose oscillator operators ii coherent states and the minimum uncertainty states the energy position and momentum eigenstates of a para bose oscillator system were considered in paper i here we consider the bargmann or the analytic function description of the para bose system this brings in in a natural way the coherent states z defined as the eigenstates of the annihilation operator the transformation functions relating this description to the energy position and momentum eigenstates are explicitly obtained possible resolution of the identity operator using coherent states is examined a particular resolution contains two integrals one containing the diagonal basis z z and the other containing the pseudodiagonal basis z z we briefly consider the normal and antinormal ordering of the operators and their diagonal and discrete diagonal coherent state approximations the problem of constructing states with a minimum value of the product of the position and momentum uncertainties and the possible dependence of this minimum value is considered

bicomplexes and conservation laws in non abelian toda models a bicomplex structure is associated with the leznov saveliev equation of integrable models the linear problem associated with the zero curvature condition is derived in terms of the bicomplex linear equation the explicit example of a non abelian conformal affine toda model is discussed in detail and its conservation laws are derived from the zero curvature representation of its equation of motion

gain scheduled filtering for time varying discrete systems this paper deals with the design of gain scheduled filters whose state space realization depends on real time parameters of plants similar to well recognized advantages of gain scheduled controllers in control theory gain scheduled filters are expected to provide enhanced performance in comparison with customary nonadjustable filters our construction technique is based on nonlinear fractional transformation nft representations of systems that are a generalization of widely used linear fractional transformation lft representations both generalized h sub 2 and h sub spl infin discrete time filter design problems are investigated together with their extension to mixed designs this study leads to new linear matrix inequality lmi formulations which in turn provide an effective and reliable design tool the proposed design technique is finally evaluated in the light of simulation examples

entropy energy inequalities for qudit states we establish a procedure to find the extremal density matrices for any finite hamiltonian of a qudit system these extremal density matrices provide an approximate description of the energy spectrum of the hamiltonian in the case of restricting the extremal density matrices by pure states we show that the energy spectrum of the hamiltonian is recovered for d 2 and 3 we conjecture that by means of this approach the energy spectrum can be recovered for the hamiltonian of an arbitrary finite qudit system for a given qudit system hamiltonian we find new inequalities connecting the mean value of the hamiltonian and the entropy of an arbitrary state we demonstrate that these inequalities take place for both the considered extremal density matrices and generic ones

coprimeness preserving non integrable extension to the two dimensional discrete toda lattice equation we introduce a so called coprimeness preserving non integrable extension to the two dimensional toda lattice equation we believe that this equation is the first example of such discrete equations defined over a three dimensional lattice we prove that all the iterates of the equation are irreducible laurent polynomials of the initial data and that every pair of two iterates is co prime which indicate confined singularities of the equation by reducing the equation to two or one dimensional lattices we obtain coprimeness preserving non integrable extensions to the one dimensional toda lattice equation and the somos 4 recurrence

vertex operators and soliton solutions of affine toda model with u 2 symmetry the symmetry structure of the non abelian affine toda model based on the coset sl 3 sl 2 u 1 is studied it is shown that the model possess non abelian noether symmetry closing into a q deformed sl 2 u 1 algebra specific two vertex soliton solutions are constructed

generating all wigner functions in the context of phase space quantization matrix elements and observables result from integration of c number functions over phase space with wigner functions serving as the quasiprobability measure the complete sets of wigner functions necessary to expand all phase space functions include off diagonal wigner functions which may appear technically involved nevertheless it is shown here that suitable generating functions of these complete sets can often be constructed which are relatively simple and lead to compact evaluations of matrix elements new features of such generating functions are detailed and explored for integer indexed sets such as for the harmonic oscillator as well as continuously indexed ones such as for the linear potential and the liouville potential the utility of such generating functions is illustrated in the computation of star functions spectra and perturbation theory in phase space

identical particle states in the probability representation of quantum mechanics we study the symmetry properties under permutation of tomograms describing the states of a system of identical particles in the probability representation starting from the action of the permutation group on the density matrix we define its action on the tomographic probability distribution explicit calculations are performed for the two dimensional harmonic oscillator

critical dynamics in systems controlled by fractional kinetic equations abstract the field theory renormalization group is used for analyzing the fractional langevin equation with the order of the temporal derivative 0 1 fractional laplacian of the order and gaussian noise correlator the case of non linearity m with odd m 3 is considered it is proved that the model is multiplicatively renormalizable propagators were found in the momentum and coordinate representation expressed in terms of fox s h functions existence of the dissipative scaling regime in the framework of the e expansion for 2 1 l l 1 2 is proved requirement of the continuous dependence of the critical exponents on imposes the condition m 3 the main quantitative result is the calculation of the dynamical critical exponent z for 1 2 up to e 2 we have obtained for it the expression z 1 2 4 0 1555 e 2 o e 3

robust filtering for uncertain nonlinearly parameterized plants we address the robust filtering problem for a wide class of systems whose state space data assume a very general nonlinear dependence in the uncertain parameters our resolution methods rely on new linear matrix inequality characterizations of spl hscr sub 2 and spl hscr sub spl infin performances which in conjunction with suitable linearization transformations of the variables give rise to practical and computationally tractable formulations for the robust filtering problem

superposition formulas for exterior differential systems abstract in this article we solve an inverse problem in the theory of quotients for differential equations we characterize a family of exterior differential systems that can be written as a quotient of a direct sum of two associated systems that are constructed from the original the fact that a system can be written as a quotient can be used to find the general solution to these equations some examples are given to demonstrate the theory

tomograms and other transforms a unified view a general framework is presented which unifies the treatment of wavelet like quasidistribution and tomographic transforms explicit formulae relating the three types of transforms are obtained the case of transforms associated with the symplectic and affine groups is treated in some detail special emphasis is given to the properties of the scale time and scale frequency tomograms tomograms are interpreted as a tool to sample the signal space by a family of curves or as the matrix element of a projector

moyal quantization with compact symmetry groups and noncommutative harmonic analysis the phase space approach to quantization of systems whose symmetry group is compact and semisimple is developed from two basic principles covariance and traciality this generalizes results and methods already implemented for spin systems j c varilly and j m gracia bondia ann phys 190 107 1989 the twisted product of phase space functions is shown to be the image of group convolution in the context of a novel fourier theory on the coadjoint orbits

wigner distribution function for finite systems we construct a wigner distribution function for finite data sets it is based on a finite optical system a linear wave guide where the finite number of discrete sensors is equal to the number of modes which the guide can carry the dynamical group for this model is su 2 and the wave functions are sets of n 2l 1 data points the wigner distribution function assigns classical c numbers to the operators of position momentum and wave guide mode

a new method for the nonlinear transformation of means and covariances in filters and estimators this paper describes a new approach for generalizing the kalman filter to nonlinear systems a set of samples are used to parametrize the mean and covariance of a not necessarily gaussian probability distribution the method yields a filter that is more accurate than an extended kalman filter ekf and easier to implement than an ekf or a gauss second order filter its effectiveness is demonstrated using an example

the effect of correlated observations on the performance of distributed estimation estimating unknown signal in wireless sensor networks wsns requires sensor nodes to transmit their observations of the signal over a multiple access channel to a fusion center fc the fc uses the received observations which is corrupted by observation noise and both channel fading and noise to find the minimum mean square error mse estimate of the signal in this paper we investigate the effect of the source node correlation the correlation between sensor node observations and the source signal and the inter node correlation the correlation between sensor node observations on the performance of the linear minimum mean square error lmmse estimator for three correlation models in the presence of channel fading first we investigate the asymptotic behavior of the achieved distortion i e mse resulting from both the observation and channel noise in a non fading channel then the effect of channel fading is considered and the corresponding distortion outage probability the probability that the distortion exceeds a certain value is found by representing the distortion as a ratio of indefinite quadratic forms a closed form expression is derived for the outage probability that shows its dependency on the correlation finally the new representation of the outage probability allows us to propose an iterative solution for the power allocation problem to minimize the outage probability under total and individual power constraints numerical simulations are provided to verify our analytic results

point symmetries of generalized toda field theories ii symmetry reduction the lie symmetries of a large class of generalized toda field theories are studied and used to perform symmetry reduction reductions lead to generalized toda lattices on one hand and to periodic systems on the other boundary conditions are introduced to reduce theories on an infinite lattice to those on semi infinite or finite ones

fundamentals of statistical signal processing estimation theory minimum variance unbiased estimation cramer rao lower bound linear models general minimum variance unbiased estimation best linear unbiased estimators maximum likelihood estimation least squares method of moments the bayesian philosophy general bayesian estimators linear bayesian estimators kalman filters summary of estimators extension for complex data and parameters

linear estimation of correlated data in wireless sensor networks with optimum power allocation and analog modulation in this paper we study the energy efficient distributed estimation problem for a wireless sensor network where a physical phenomena that produces correlated data is sensed by a set of spatially distributed sensor nodes and the resulting noisy observations are transmitted to a fusion center via noise corrupted channels we assume a gaussian network model where i the data samples being sensed at different sensors have a correlated gaussian distribution and the correlation matrix is known at the fusion center ii the links between the local sensors and the fusion center are subject to fading and additive white gaussian noise awgn and the fading gains are known at the fusion center and iii the central node uses the squared error distortion metric we consider two different distortion criteria i individual distortion constraints at each node and ii average mean square error distortion constraint across the network we determine the achievable power distortion regions under each distortion constraint taking the delay constraint into account we investigate the performance of an uncoded transmission strategy where the noisy observations are only scaled and transmitted to the fusion center at the fusion center two different estimators are considered i the best linear unbiased estimator blue that does not require knowledge of the correlation matrix and ii the minimum mean square error mmse estimator that exploits the correlations for each estimation method we determine the optimal power allocation that results in a minimum total transmission power while satisfying some distortion level for the estimate under both distortion criteria the numerical comparisons between the two schemes indicate that the mmse estimator requires less power to attain the same distortion provided by the blue and this performance gap becomes more dramatic as correlations between the observations increase furthermore comparisons between power distortion region achieved by the theoretically optimum system and that achieved by the uncoded system indicate that the performance gap between the two systems becomes small for low levels of correlation between the sensor observations if observations at all sensor nodes are uncorrelated the uncoded system with mmse estimator attains the theoretically optimum system performance

optimal nonlinear filtering of quantum state the aim of this paper is to give an interpretation of the linear or nonlinear filtration problem as a quantization problem based on this we extend the optimal filtering equation known from the stratonovich filtering theory on the quantum process case in contrast to the kalman filter often used in such problems the stratonovich equation provides the optimal solution for nonlinear observation models the observation model is based on an indirect measurement method where the measurement is performed on an ancilla system that is interacted with an unknown one the latter model is interpreted in case of a single qudit system since the measured random variables and experiment are fundamentally different from each other the obtained single qudit observation model has a substantially different physical nature from the two qubit one however in both problems the stratonovich optimal filter equation is equally applicable

squeeze tomography of quantum states a new type of tomogram squeeze tomograms of quantum states of light is introduced which is based on measuring photon statistics after the action of a squeeze operator on the states density matrix the introduced tomograms are photon number probability functions depending on two real parameters which are a scaling factor and a rotation angle the rotation angle and scaling factor label the reference frame in the phase space of field quadratures in which the photon statistics is measured the expressions of the squeeze tomogram in terms of the wigner function and density matrix in quadrature representation are obtained the examples of squeezed states even and odd coherent states and thermal states are considered in detail the multimode generalization is discussed

coherent states on the m sheeted covering group of su 1 1 coherent states associated with the m sheeted covering group of su 1 1 are considered and such properties as overcompleteness and resolution of the identity are studied they are used to define analytic representations in which the transformations of the m sheeted covering group of su 1 1 are implemented as extended mobius conformal mappings applications of this formalism in the study of hamiltonians that describe m particle clustering are also considered

analytic representations in quantum mechanics various euclidean hyperbolic and elliptic analytic representations are introduced and relations among them are discussed the bargmann analytic representation in the complex plane is considered and its relation to other phase space methods for the harmonic oscillator is reviewed the general theory that relates the growth of analytic functions with the density of their zeros is applied to bargmann functions and it leads to theorems on the completeness of sequences of glauber coherent states two hyperbolic analytic representations in the unit disc based on su 1 1 coherent states and also on phase states are introduced a third analytic representation in the complex plane based on barut girardello states is also considered and transformations which relate it to the other ones are studied in the case of systems with finite dimensional hilbert space an elliptic analytic representation in the extended complex plane and also another analytic representation based on theta functions are introduced the berezin formalism in the euclidean hyperbolic and elliptic cases is discussed contour analytic representations in these three cases are also presented

the wavelet transform time frequency localization and signal analysis two different procedures for effecting a frequency analysis of a time dependent signal locally in time are studied the first procedure is the short time or windowed fourier transform the second is the wavelet transform in which high frequency components are studied with sharper time resolution than low frequency components the similarities and the differences between these two methods are discussed for both schemes a detailed study is made of the reconstruction method and its stability as a function of the chosen time frequency density finally the notion of time frequency localization is made precise within this framework by two localization theorems

a class of affine wigner functions with extended covariance properties affine wigner functions are phase space representations based on the affine group in place of the usual weyl heisenberg group of quantum mechanics such representations are relevant to the time frequency analysis of real signals an interesting family is singled out by the requirement of covariance with respect to each solvable three parameter group containing the affine group explicit forms are given in each case and properties such as unitarity and localization are discussed some particular distributions are recovered

point symmetries of generalized toda field theories a class of two dimensional field theories with exponential interactions is introduced the interaction depends on two coupling matrices and is sufficiently general to include all toda field theories existing in the literature lie point symmetries of these theories are found for an infinite semi infinite and finite number of fields special attention is accorded to conformal invariance and its breaking

classical mathcal w algebras in types a b c d and g we produce explicit generators of the classical mathcal w algebras associated with the principal nilpotents in the simple lie algebras of all classical types and in the exceptional lie algebra of type g 2 the generators are given by determinant formulas in the context of the poisson vertex algebras we also show that the images of the mathcal w algebra generators under the chevalley type isomorphism coincide with the elements defined via the corresponding miura transformations

two dimensional exactly and completely integrable dynamical systems monopoles instantons dual models relativistic strings lund regge model generalized toda lattice etc an investigation of two dimensional exactly and completely integrable dynamical systems associated with the local part of an arbitrary lie algebra mathfrak g whose grading is consistent with an arbitrary integral embedding of 3d subalgebra in mathfrak g has been carried out we have constructed in an explicit form the corresponding systems of nonlinear partial differential equations of the second order and obtained their general solutions in the sense of a goursat problem a method for the construction of a wide class of infinite dimensional lie algebras of finite growth has been proposed

w algebras and superalgebras from constrained wzw models a group theoretical classification we present a classification ofw algebras and superalgebras arising in abelian as well as non abelian toda theories each model obtained from a constrained wzw action is related with ansl 2 subalgebra resp osp 1 2 superalgebra of a simple lie algebra resp superalgebra g however the determination of anu 1 y factor commuting withsl 2 resp osp 1 2 appears when it exists particularly useful to characterize the correspondingw algebra the super conformal spin contents of eachw super algebra is performed the class of all the superconformal algebras i e with conformal spinss 2 is easily obtained as a byproduct of our general results

rational von neumann lattices a rational von neumann lattice is defined as a lattice in phase space with the constants a and b in the x and p directions given by a ratio of integers zeros of harmonic oscillator functions in the kq representation on such lattices are found it is shown that the number of zeros of the kq function determines the number of states by which a set on a von neumann lattice is overcomplete interesting relations between theta functions are derived on the basis of their connection with the harmonic oscillator states in the kq representation

classical diffusion in random fields with long range correlations the effect of long range random static fields on classical diffusion is investigated it is shown that the long range component of random fields leads to the appearance of a new compared to the white noise case fixed point in the renormalisation group equations the critical exponents and oscillating corrections corresponding to the new fixed point are calculated

nonlinear bayesian filtering using the unscented linear fractional transformation model for nonlinear state space model involving random variables with arbitrary probability distributions the state estimation given a sequence of observations is based on an appropriate criterion such as the minimum mean square error mmse this leads to linear approximation in the state space of the extended kalman filter ekf and the unscented kalman filter ukf which work reasonably well only for mildly nonlinear systems we propose a bayesian filtering technique based on the mmse criterion in the framework of the virtual linear fractional transformation lft model which is characterized by a linear part and a simple nonlinear structure in the feedback loop lft is an exact representation for any differentiable nonlinear mapping so the virtual lft model is amenable to a wide range of nonlinear systems simulation results demonstrate that the proposed filtering technique gives better approximation and tracking performance than standard methods like the ukf furthermore for highly nonlinear systems where ukf diverges the lft model estimates the conditional mean with reasonable accuracy

integral transforms between tomogram and quasi probability functions based on quantizer dequantizer operators formalism an application of a quantizer dequantizer method as a unifying description for representations of states in quantum mechanics is considered well known quasi distributions and tomograms are rewritten in terms of the dequantizer and quantizer operators using this description of the tomographic probability function and its symbol we construct the invertible integral transforms between the tomogram and the quasi probability distributions such as wigner kirkwood rihaczek choi williams p and q functions and others