covariance and geometrical invariance in quantization several notions of invariance and covariance for products with respect to lie algebras and lie groups are investigated some examples including the poincare group are given the passage from the lie algebra invariance to the lie group covariance is performed the compact and nilpotent cases are treated

central limit theorems for infinite series of queues and applications to simple exclusion we prove that a tagged particle in asymmetric simple exclusion satisfies a central limit theorem when properly rescaled to obtain this result we derive several results of positive or negative correlation for occupation times of a server in a series of queues which imply various central limit theorems

star quantization on the cylinder star product quantization as an autonomous quantum theory is reviewed with emphasis on its relation to path integral and hilbert space formulations quantization of the usual heisenberg group is used as an example when phase space is the cylinder this group is replaced by e 2 the euclidean group in two dimensions this case is worked out in detail in doing so polarizations on the cylinder are discussed and a phase space path integral is constructed

a globally convergent estimator for n frequencies in this paper we propose a solution to the well known problem of ensuring a simultaneous globally convergent online estimation of the state and the frequencies of a sinusoidal signal composed of n sinusoidal terms we present an estimator which guarantees global boundedness and convergence of both the state estimation and the frequency estimation for all initial conditions and frequency values

w covariance of the weyl wigner groenewold moyal quantization the differential structure of operator bases used in various forms of the weyl wigner groenewold moyal wwgm quantization is analyzed and a derivative based approach alternative to the conventional integral based one is developed thus the fundamental quantum relations follow in a simpler and unified manner an explicit formula for the ordered products of the heisenberg weyl algebra is obtained the w covariance of the wwgm quantization in its most general form is established it is shown that the group action of w that is realized in the classical phase space induces on bases operators in the corresponding hilbert space a similarity transformation generated by the corresponding quantum w which provides a projective representation of the former w explicit expressions for the algebra generators in the classical phase space and in the hilbert space are given it is made manifest that this w covariance of the wwgm quantization is a genuine property of the operator bases

quantization of poisson lie groups and applications letg be a connected poisson lie group we discuss aspects of the question of drinfel d can g be quantized and give some answers wheng is semisimple a case where the answer isyes we introduce quantizable poisson subalgebras ofc g related to harmonic analysis ong they are a generalization of f r t models of quantum groups and provide new examples of quantized poisson algebras

moyal quantization of 2 1 dimensional galilean systems stratonovich weyl kernels are constructed for some of the coadjoint orbits of the two dimensional extended galilean group g 2 1 as an intermediate step the unitary irreducible representations associated with a given group orbit are obtained by using the kirillov mackey theory star products are defined in the sense of moyal for functions on each of these orbits the central extension of g 2 1 with parameter k is also analyzed which results from the commutator between the generators of boosts to conclude that it originates a sort of nonrelativistic remainder of the thomas precession

quantum algebras as quantizations of dual poisson lie groups a systematic computational approach for the explicit construction of any quantum hopf algebra uz g z starting from the lie bialgebra g that gives the first order deformation of the coproduct map z is presented the procedure is based on the well known quantum duality principle namely the fact that any quantum algebra can be viewed as the quantization of the unique poisson lie structure g g on the dual group g which is obtained by exponentiating the lie algebra g defined by the dual map from this perspective the coproduct for uz g is just the pull back of the group law for g and the poisson analogues of the quantum commutation rules for uz g are given by the unique poisson lie structure g on g whose linearization is the poisson analogue of the initial lie algebra g this approach is shown to be a very useful technical tool in order to solve the lie bialgebra quantization problem explicitly since once a lie bialgebra g is given the full dual poisson lie group g can be obtained either by applying standard poisson lie group techniques or by implementing the algorithm presented here with the aid of symbolic manipulation programs as a consequence the quantization of g will give rise to the full uz g quantum algebra provided that ordering problems are appropriately fixed through the choice of certain local coordinates on g whose coproduct fulfils a precise quantum symmetry property the applicability of this approach is explicitly demonstrated by reviewing the construction of several instances of quantum deformations of physically relevant lie algebras such as the 2 1 anti de sitter algebra so 2 2 and the poincare algebra in 3 1 dimensions

deformations of lie group and lie algebra representations a complete study of deformations of lie group and lie algebra representations including differentiability and integrability results is given adapted results are given in the semisimple case a notion of induced deformations is introduced various examples are given including deformations of indecomposable representations

from geometric quantization to moyal quantization it is shown how the moyal product of phase space functions and the weyl correspondence between symbols and operator kernels may be obtained directly using the procedures of geometric quantization applied to the symplectic groupoid constructed by doubling the phase space

equipartition of the eigenfunctions of quantized ergodic maps on the torus we give a simple proof of the equipartition of the eigenfunctions of a class of quantized ergodic area preserving maps on the torus examples are the irrational translations the skew translations the hyperbolic automorphisms and some of their perturbations

geometric quantization of the brst charge in the first half of this paper sects 1 4 we generalise the standard geometric quantization procedure to symplectic supermanifolds in the second half sects 5 6 we apply this to two examples that exhibit classical brst symmetry i e we quantize the brst charge and the ghost number more precisely in the first example we consider the reduced symplectic manifold obtained by symplectic reduction from a free group action with ad equivariant moment map in the second example we consider a foliated configuration space whose cotangent bundle admits the construction of a brst charge associated to this foliation we show that the classical brst symmetry can be described in terms of a hamiltonian supergroup action on the extended phase space and that geometric quantization gives us a super unitary representation of this supergroup finally we point out how these results are related to reduction at the quantum level as compared with the reduction at the classical level

q exchangeability via quasi invariance for positive q is not 1 the q exchangeability of an infinite random word is introduced as quasi invariance under permutations of letters with a special cocycle which accounts for inversions in the word this framework allows us to extend the q analog of de finetti s theorem for binary sequences see gnedin and olshanski electron j combin 16 2009 r78 to general real valued sequences in contrast to the classical case of exchangeability q 1 the order on plays a significant role for the q analogs an explicit construction of ergodic q exchangeable measures involves random shuffling of 1 2 by iteration of the geometric choice connections are established with transient markov chains on q pascal pyramids and invariant random flags over the galois fields

mixing times of the biased card shuffling and the asymmetric exclusion process consider the following method of card shuffling start with a deck of n cards numbered 1 through n fix a parameter p between 0 and 1 in this model a shuffle consists of uniformly selecting a pair of adjacent cards and then flipping a coin that is heads with probability p if the coin comes up heads then we arrange the two cards so that the lower numbered card comes before the higher numbered card if the coin comes up tails then we arrange the cards with the higher numbered card first in this paper we prove that for all p 1 2 the mixing time of this card shuffling is o n 2 as conjectured by diaconis and ram 2000 our result is a rare case of an exact estimate for the convergence rate of the metropolis algorithm a novel feature of our proof is that the analysis of an infinite asymmetric exclusion process plays an essential role in bounding the mixing time of a finite process

an extended weyl wigner transformation for special finite spaces abstract we extend the weyl wigner transformation to those particular degrees of freedom described by a finite number of states using a technique of constructing operator bases developed by schwinger discrete transformation kernels are presented instead of continuous coordinate momentum pair system and systems such as the one dimensional canonical continuous coordinate momentum pair system and the two dimensional rotation system are described by special limits expressions are explicitly given for the spin one half case

quantum mechanics on p adic numbers a quantum system with positions in and momenta in is studied displacement operators in the phase space of this system and the corresponding heisenberg weyl group are studied it is shown that such a system can be constructed from a semi infinite chain of spins which are coupled in a particular way

semiclassical analysis of wigner 3j symbol we analyse the asymptotics of the wigner 3j symbol as a matrix element connecting eigenfunctions of a pair of integrable systems obtained by lifting the problem of the addition of angular momenta into the space of schwinger s oscillators a novel element is the appearance of compact lagrangian manifolds that are not tori due to the fact that the observables defining the quantum states are noncommuting these manifolds can be quantized by generalized bohr sommerfeld rules and yield all the correct quantum numbers the geometry of the classical angular momentum vectors emerges in a clear manner efficient methods for computing amplitude determinants in terms of poisson brackets are developed and illustrated

the moyal bracket and the dispersionless limit of the kp hierarchy a new lax equation is introduced for the kp hierarchy which avoids the use of pseudo differential operators as used in the sate approach this lax equation is closer to that used in the study of the dispersionless kp hierarchy and is obtained by replacing the poisson bracket with the moyal bracket the dispersionless limit under which the moyal bracket collapses to the poisson bracket is particularly simple

quantization and the uniqueness of invariant structures we determine and classify certain algebraic structures defined on the space of all complex valued polynomials in 2n real variables which admitaffine contact transformations as automorphisms these are the structures which have the minimum symmetry necessary to define the basic linear and angular momentum observables of classical and quantum mechanics the results relate to the so called dirac problem of finding an appropriate mathematical characterization of the canonical quantization procedure

quantum symmetries and the weyl wigner product of group representations in the usual formulation of quantum mechanics groups of automorphisms of quantum states have ray representations by unitary and antiunitary operators on complex hilbert space in accordance with wigner s theorem in the phase space formulation they have real true unitary representations in the space of square integrable functions on phase space each such phase space representation is a weyl wigner product of the corresponding hilbert space representation with its contragredient and these can be recovered by factorizing the weyl wigner product however not every real unitary representation on phase space corresponds to a group of automorphisms so not every such representation is in the form of a weyl wigner product and can be factorized the conditions under which this is possible are examined examples are presented

ordered products w algebra and two variable definite parity orthogonal polynomials it has been shown that the cartan subalgebra of w algebra is the space of the two variable definite parity polynomials explicit expressions of these polynomials and their basic properties are presented it also has been shown that they carry the infinite dimensional irreducible representation of the su 1 1 algebra having the spectrum bounded from below a realization of this algebra in terms of difference operators is also obtained for particular values of the ordering parameter s they are identified with the classical orthogonal polynomials of a discrete variable such as the meixner meixner pollaczek and askey wilson polynomials with respect to variable s they satisfy a second order eigenvalue equation of hypergeometric type exact scattering states with zero energy for a family of potentials are expressed in terms of these polynomials it has been put forward that it is the inonu wigner contraction and its inverse that form a bridge between the difference and differential calculus

entanglement swapping between multi qudit systems we generalize the entanglement swapping scheme originally proposed for two pairs of qubits to an arbitrary number q of systems composed from an arbitrary number mj of qudits each of the systems is supposed to be prepared in a maximally entangled state of mj qudits while different systems are not correlated at all we show that when a set of qj 1 aj particles from each of the q systems aj particles are measured is subjected to a generalized bell type measurement the resulting set of qj 1 mj aj particles will collapse into a maximally entangled state

a general theory of phase space quasiprobability distributions we present a general theory of quasiprobability distributions on phase spaces of quantum systems whose dynamical symmetry groups are finite dimensional lie groups the family of distributions on a phase space is postulated to satisfy the stratonovich weyl correspondence with a generalized traciality condition the corresponding family of the stratonovich weyl kernels is constructed explicitly in the presented theory we use the concept of generalized coherent states that brings physical insight into the mathematical formalism

a globally convergent frequency estimator online estimation of the frequency of a sinusoidal signal is a classical problem in systems theory that has many practical applications in this paper the authors provide a solution to the problem of ensuring a globally convergent estimation more specifically they propose a new adaptive notch filter whose dynamic equations exhibit the following remarkable features 1 all signals are globally bounded and the estimated frequency is asymptotically correct for all initial conditions and all frequency values 2 the authors obtain a simple tuning procedure for the estimator design parameters which trades off the adaptation tracking capabilities with noise sensitivity ensuring exponential stability of the desired orbit and 3 transient performance is considerably enhanced even for small or large frequencies as witnessed by extensive simulations to reveal some of the stability instability mechanisms of the existing algorithms and motivate our modifications the authors make appeal to a novel nonlinear state dependent time scaling the main advantage of working in the new time scale is that they remove the coupling between the parameter update law and the filter itself decomposing the system into a feedback form where the required modifications to ensure stability become apparent even though they limit their attention here to the simplest case of a single constant frequency without noise the algorithm is able to track time varying frequencies preserve local stability in the presence of multiple sinusoids and is robust with respect to noise

quantum mechanics of non linear systems a generalisation of weyl s correspondence rule and the associated moyal bracket for systems with non linear phase spaces that admit symplectic transitive group actions is presented this provides a simple account with explicit constructions of some of the general results of bayen et al 1978

optimal tradeoff between instantaneous and delayed neighbor information in consensus algorithms we consider a distributed consensus problem over a network where at each time instant every node receives two pieces of information from disjoint neighboring sets a weighted average of current st

sorting processes with energy constrained comparisons we study very simple sorting algorithms based on a probabilistic comparator model in this model errors in comparing two elements are due to 1 the energy or effort put in the comparison and 2 the difference between the compared elements such algorithms repeatedly compare and swap pairs of randomly chosen elements and they correspond to natural markovian processes the study of these markov chains reveals an interesting phenomenon namely in several cases the algorithm that repeatedly compares only adjacent elements is better than the one making arbitrary comparisons in the long run the former algorithm produces sequences that are better sorted the analysis of the underlying markov chain poses interesting questions as the latter algorithm yields a nonreversible chain and therefore its stationary distribution seems difficult to calculate explicitly we nevertheless provide bounds on the stationary distributions and on the mixing time of these processes in several restrictions

matrix cartan superdomains super toeplitz operators and quantization we present a general theory of non perturbative quantization of a class of hermitian symmetric supermanifolds the quantization scheme is based on the notion of a super toeplitz operator on a suitable z2 graded hilbert spaces of super holomorphic functions the quantized supermanifold arises as the c algebra generated by all such operators we prove that our quantization framework reproduces the invariant super poisson structure on the classical supermanifold as planck s constant tends to zero

on one controversy about the smoothed wigner function abstract we give a simple proof that the smoothed wigner function in the general case cannot be non negative whenever the smoothing function is zero outside a finite phase space region our proof is not based on whatever assumptions about the behavior of the smoothing function in the non zero region and on its boundary in this way the long lasted conjecture claiming the opposite is refuted

the stratonovich weyl correspondence for one dimensional kinematical groups the stratonovich weyl correspondence is a restatement of the moyal quantization where the phase space is a manifold and where a group of transformations acts on it transitively the first and most important step is to define a mapping from the manifold into the set of self adjoint operators on a hilbert space under suitable conditions this mapping is called a stratonovich weyl kernel the construction of this mapping is discussed on coadjoint orbits of the one dimensional galilei poincare and newton hooke groups as well as the two dimensional euclidean group

classification of real three dimensional poisson lie groups all real three dimensional poisson lie pl groups are explicitly constructed and fully classified under group automorphisms by making use of their one to one correspondence with the complete classification of real three dimensional lie bialgebras given in gomez 2000 j math phys 41 4939 many of these 3d pl groups are non coboundary structures whose poisson brackets are given here for the first time casimir functions for all three dimensional pl groups are given and some features of several pl structures are commented

the proper quantum analogue of the birkhoff gustavson method of normal forms a deformation approach resolves problems concerning the ordering of operators and the commutation of quantization with canonical transformation this completes the programme of robnik 1984 to develop a purely algebraic method for the quantization of non integrable hamiltonian systems about a point of stable equilibrium

energy momentum tensor in phase space a connection between schrodinger energy momentum tensor and terletsky distribution function schrodinger energy momentum tensor for a matter field interacting with an external electromagnetic field is represented in phase space by means of terletsky distribution function the explicit form of this distribution function in the case of a hydrogen type atom is found the structure of the schrodinger energy momentum tensor in phase space is compared with the structure of a real fluid and its local pressure and local energy are presented in the fundamental state of a hydrogen type atom the negative values of the terletsky distribution function are not rejected in view of their participation in the phase space energy momentum tensor the negative part of the quantum distribution function could be interpreted as phase space density for anti constituents in a hypothetical sub quantum level of the matter

deformation of algebras and related quantizations weak bose and fermi type quantizations are defined via deformations of algebras generated by characters from linear topological spaces into commutative or grassmann algebras respectively this yields an inherent symmetrization and antisymmetrization respectively of deformed products with respect to undeformed products combining both quantizations one obtains a weak supersymmetric quantization of a 2 graded algebra for bose type quantizations a hilbert space representation based on quasi invariant measures is outlined

the wigner transformation is of finite order the wigner integral transformation which intertwines the twisted product and the composition of kernels is of order 24 indeed it commutes with and its sixth power equals the fourier cotransformation

quantum systems with finite hilbert space galois fields in quantum mechanics a galois quantum system in which the position and momentum take values in the galois field gf pl is considered it is comprised of l component systems which are coupled in a particular way and is described by a certain class of hamiltonians displacements in the gf pl gf pl phase space and the corresponding heisenberg weyl group are studied symplectic transformations are shown to form the sp 2 gf pl group wigner and weyl functions are defined and their properties are studied frobenius symmetries which are based on frobenius automorphisms in the theory of galois fields are a unique feature of these systems for l 2 if they commute with the hamiltonian there are constants of motion which are discussed an analytic representation in the l sheeted complex plane provides an elegant formalism that embodies the properties of frobenius transformations the difference between a galois quantum system and other finite quantum systems where the position and momentum take values in the ring is discussed

quantum normal forms moyal star product and bohr sommerfeld approximation a normal form transformation is carried out on one dimensional quantum hamiltonians that transforms them into functions of the quantum harmonic oscillator the method works with the weyl transform or symbol of the hamiltonian the moyal star product is used to carry out the normal form transformation at the level of symbols diagrammatic techniques are developed for handling the expressions that result from higher order terms in the moyal series once the normal form is achieved the bohr sommerfeld formula for the eigenvalues including higher order corrections follows easily

the constrained rayleigh quotient with a general orthogonality constraint and an eigen balanced laplacian matrix the greatest lower bound and applications in cooperative control problems mathematically the rayleigh quotient is defined as the quadratic function of a symmetric matrix and a nonzero usually unconstrained variable vector in this paper we consider the constrained rayleigh quotient in which the variable vector has the orthogonality constraint i e it is constrained to be orthogonal to a nonzero vector this nonzero vector is called the orthogonality constraint vector or abbreviated as the oc vector for the variable vector the matrix for the rayleigh quotient is an eigen balanced eb laplacian matrix a tighter lower bound of the constrained rayleigh quotient has many implications in mathematics as well as in cooperative control problems the main contributions in this paper are as follows first we provide the greatest lower bound or the infimum of the constrained rayleigh quotient with respect to a general oc vector and the eb laplacian matrix whose results are novel and better than the existing results then we interpret the physical meaning of our results in an insightful geometric form and characterize the properties of the results finally as an example to illustrate the merit of the tighter lower bound of the constrained rayleigh quotient we consider the scale of the agents driving by a fundamental consensus protocol and show that the convergence rate of the agents scale is characterized by the greatest lower bound of the constrained rayleigh quotient

phase uniqueness for the mallows measure on permutations for a positive number q the mallows measure on the symmetric group is the probability measure on sn such that pn q is proportional to q to the power inv where inv equals the number of inversions inv equals the number of pairs i j one may consider this as a mean field model from statistical mechanics the weak large deviation principle may replace the gibbs variational principle for characterizing equilibrium measures in this sense we prove the absence of phase transition i e phase uniqueness

on the probability density interpretation of smoothed wigner functions it has been conjectured that averages of the wigner function over phase space volumes larger than those of minimum uncertainty are always positive this is true for gaussian averaging so that the husimi distribution is positive however the authors provide a specific counterexample for the averaging with a discontinuous hat function the analysis of the specific system of a one dimensional particle in a box also elucidates the respective advantages of the wigner and the husimi functions for the study of the semiclassical limit the falsification of the averaging conjecture is shown not to depend on the discontinuities of the hat function by considering the latter as the limit of a sequence of analytic functions

decentralized estimation of laplacian eigenvalues in multi agent systems in this paper we present a decentralized algorithm to estimate the eigenvalues of the laplacian matrix that encodes the network topology of a multi agent system we consider network topologies modeled by undirected graphs the basic idea is to provide a local interaction rule among agents so that their state trajectory is a linear combination of sinusoids oscillating only at frequencies function of the eigenvalues of the laplacian matrix in this way the problem of decentralized estimation of the eigenvalues is mapped into a standard signal processing problem in which the unknowns are the finite number of frequencies at which the signal oscillates

quantum canonical invariance a moyal approach the quasiclassical generalised moyal quantisation procedure is applied to the problem of quantum canonical invariance simple new formulae for the moyal bracket corresponding to various correspondence rules are given and are used to calculate the additional potential terms arising from a point canonical transformation made on a free hamiltonian the status of canonical transformations in other equivalent quantum phase space formulations is also reviewed

toeplitz quantization of kahler manifolds ang gl n n limits for general compact kahler manifolds it is shown that both toeplitz quantization and geometric quantization lead to a well defined by operator norm estimates classical limit this generalizes earlier results of teh authors and klimek and lesniewski obtained for the tours and higher genus riemann surfaces respectively we thereby arrive at an approximation of the poisson algebra by a sequence of finitedimensional matrix algebrasgl n n

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

the hidden group structure of quantum groups strong duality rigidity and preferred deformations a notion of well behaved hopf algebra is introduced reflexivity for strong duality between hopf algebras of drinfeld type and their duals algebras of coefficients of compact semi simple groups is proved a hidden classical group structure is clearly indicated for all generic models of quantum groups moyal product like deformations are naturally found for all frt models on coefficients andc functions strong rigidity hbi2 0 under deformations in the category of bialgebras is proved and consequences are deduced

remarks on a paper of olver some disparate ideas in the literature are drawn together the work of p j olver and his associates on lagrangians which vanish for arbitrary variations the so called null lagrangians is viewed as a parallel development to witten s study of topological field theories a theorem of olver that all hyperjacobians are expressible as divergences and are thus candidates for the construction of null lagrangians is shown to follow directly from the observation that such entities appear in a power series development of the general associative product and this technique facilitates the construction of multi dimensional examples

a su 3 wigner function for three dimensional systems we derive a wigner function with su 3 symmetry for three dimensional systems exemplified by the polarization of three dimensional electromagnetic fields

deformation quantization of heisenberg manifolds form a smooth manifold equipped with a poisson bracket we formulate ac algebra framework for deformation quantization including the possibility of invariance under a lie group of diffeomorphisms preserving the poisson bracket we then show that the much studied non commutative tori give examples of such deformation quantizations invariant under the usual action of ordinary tori going beyond this the main results of the paper provide a construction of invariant deformation quantizations for those poisson brackets on heisenberg manifolds which are invariant under the action of the heisenberg lie group and for various generalizations suggested by this class of examples interesting examples are obtained of simplec algebras on which the heisenberg group acts ergodically

a semiclassical egorov theorem and quantum ergodicity for matrix valued operators we study the semiclassical time evolution of observables given by matrix valued pseudodifferential operators and construct a decomposition of the hilbert space l2 open image in new windowd open image in new windown into a finite number of almost invariant subspaces for a certain class of observables that is preserved by the time evolution we prove an egorov theorem we then associate with each almost invariant subspace of l2 open image in new windowd open image in new windown a classical system on a product phase space t open image in new windowd open image in new window where open image in new window is a compact symplectic manifold on which the classical counterpart of the matrix degrees of freedom is represented for the projections of eigenvectors of the quantum hamiltonian to the almost invariant subspaces we finally prove quantum ergodicity to hold if the associated classical systems are ergodic

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

on the uniqueness of the moyal structure of phase space functions uniqueness up to isomorphism of the moyal product and bracket of functions on as associative and lie deformations of the ordinary product and poisson bracket is known to follow under additional hypotheses using an integral formalism we show here that this result holds without these hypotheses

distributed estimation of laplacian eigenvalues via constrained consensus optimization problems from the recent literature we know that some consecutive measurements of the consensus protocol can be used to compute the exact average of the initial condition in this paper we show that these measurements can also be used for estimating the laplacian eigenvalues of the graph representing the network as recently shown in the literature by solving the factorization of the averaging matrix the laplacian eigenvalues can be inferred herein the problem is posed as a constrained consensus problem formulated two fold the first formulation direct approach yields a non convex optimization problem solved in a distributed way by means of the method of lagrange multipliers the second formulation indirect approach is obtained after an adequate re parameterization the problem is then convex and is solved by using the distributed subgradient algorithm and the alternating direction method of multipliers admm the proposed algorithms allow estimating the actual laplacian eigenvalues with high accuracy

the oriented swap process particles labelled 1 n are initially arranged in increasing order subsequently each pair of neighboring particles that is currently in increasing order swaps according to a poisson process of rate 1 we analyze the asymptotic behavior of this process as n oo we prove that the space time trajectories of individual particles converge when suitably scaled to a certain family of random curves with two points of non differentiability and that the permutation matrix at a given time converges to a certain deterministic measure with absolutely continuous and singular parts the absorbing state where all particles are in decreasing order is reached at time 2 o 1 n the finishing times of individual particles converge to deterministic limits with fluctuations asymptotically governed by the tracy widom distribution

the wigner function the basic relations of the weyl wigner representation of quantum mechanics are reviewed it is stressed that this representation is unique and based on a phase space operator which corresponds to an observable in dirac s sense

the yang baxter equation and invariants of links on considere le fait que l on peut construire des invariants d isotopie p et f pour des liens en utilisant certaines solutions des equations de yang baxter

an integral transform related to quantization ii some mathematical properties we study in more detail the mathematical properties of the integral transform relating the matrix elements between coherent states of a quantum operator to the corresponding classical function explicit families of hilbert spaces are constructed between which the integral transform is an isomorphism

distributed optimal coordination for multiple heterogeneous euler lagrangian systems abstract in this paper we consider the distributed optimal coordination doc problem for multi agent systems with the agents in the form of euler lagrangian el dynamics we propose two different distributed protocols for the heterogeneous continuous time el agents to achieve the optimization task by constructing suitable lyapunov functions we prove the global convergence to the optimal coordination of the el systems in the case with parametric uncertainties and the global exponential convergence in the case without parametric uncertainties furthermore we estimate the regret bound for an uncertain doc problem with time varying cost functions and inexact gradients finally we provide a numerical example to validate the theoretical results

h control design for synchronisation of identical linear multi agent systems in this paper we study the state synchronization problem of multi agent systems subject to external additive perturbations we consider high order linear time invariant multi agent systems whose communication topology is encoded by an undirected and connected graph we propose an h control design technique based on a decentralized output feedback controller we give sufficient conditions to ensure state synchronization with bounded l2 gain using a lyapunov based approach these conditions are characterized in terms of matrix inequalities since these matrix inequality conditions are nonconvex and can not be solved straightforwardly we propose a relaxation technique and an effective numerical procedure to design a suitable controller with guaranteed performance on the multi agent distributed closed loop

q deformed star products and moyal brackets the standard and antistandard ordered operators acting on two dimensional q deformed phase space are shown to satisfy algebras which can be called q w q star products and q moyal brackets corresponding to these algebras are constructed some applications like defining q classical mechanics and q path integrals are discussed

weyl underhill emmrich quantization and the stratonovich weyl quantizer weyl underhill emmrich wue quantization and its generalization are considered it is shown that an axiomatic definition of the stratonovich weyl quantizer leads to severe difficulties quantization on the cylinder within the wue formalism is discussed

pbh tests for nonlinear systems abstract recently concepts of nonlinear eigenvalues and eigenvectors are introduced in this paper we establish connections between the nonlinear eigenvalues and nonlinear accessibility observability in particular we provide a generalization of popov belevitch hautus pbh controllability observability test to nonlinear accessibility observability our pbh accessibility observability test is equivalent to the accessibility observability rank condition under a stranded assumption

quantization on the virasoro group the quantization of the virasoro group is carried out by means of a previously established group approach to quantization we explicitly work out the two cocycles on the virasoro group as a preliminary step in our scheme the carrier space for all the virasoro representations is made out of polarized functions on the group manifold it is proved that this space does not contain null vector states even forc 1 although it is not irreducible the full reduction is achieved in a striaghtforward way by just taking a well defined invariant subspace c h the orbit of the enveloping algebra through the vacuum which is irreducible for any value ofc andh c h is a proper subspace of the space of polarized functions for those values ofc andh for which the kac determinant is zero we give the local version of these group representations as well as the associated classical phase space structures i e symplectic form and noether invariants

non coboundary poisson lie structures on the book group all possible poisson lie pl structures on the 3d real lie group generated by a dilation and two commuting translations are obtained their classification is fully performed by relating these pl groups to the corresponding lie bialgebra structures on the corresponding book lie algebra by construction all these poisson structures are quadratic poisson hopf algebras for which the group multiplication is a poisson map in contrast to the case of simple lie groups it turns out that most of the pl structures on the book group are non coboundary ones moreover from the viewpoint of poisson dynamics the most interesting pl book structures are just some of these non coboundaries which are explicitly analysed in particular we show that the two different q deformed poisson versions of the sl 2 r algebra appear as two distinguished cases in this classification as well as the quadratic poisson structure that underlies the integrability of a large class of 3d lotka volterra equations finally the quantization problem for these pl groups is sketched

symplectic groupoids and poisson manifolds on definit la notion de groupoide symplectique on donne la variete de poisson de ce groupoide symplectique on presente une construction

quantum groups and deformation quantization explicit approaches and implicit aspects deformation quantization which gives a development of quantum mechanics independent of the operator algebra formulation and quantum groups which arose from the inverse scattering method and a study of yang baxter equations share a common idea abstracted earlier in algebraic deformation theory that algebraic objects have infinitesimal deformations which may point in the direction of certain continuous global deformations i e quantizations in deformation quantization the algebraic object is the algebra of observables functions on symplectic phase space whose infinitesimal deformation is the poisson bracket and global deformation a star product in quantum groups it is a hopf algebra generally either of functions on a lie group or often its dual in the topological vector space sense as we briefly explain a completed universal enveloping algebra of a lie algebra with for infinitesimal a matrix satisfying the modified classical yang baxter equation mcybe frequently existence proofs are known but explicit formulas useful for physical applications have been difficult to extract one success here comes from universal deformation formulas udfs expressions built from a lie algebra which deform any algebra on which the lie algebra operates as derivations the most famous of these is the moyal product a special case of a class in which the lie algebra is abelian another comes from recognition that the belavin drinfel d solutions to the mcybe are in fact infinitesimal deformations for which in the case of the special linear groups it is possible to give explicit formulas for the corresponding quantum yang baxter equations this review paper discusses necessarily in brief these and related topics including twisting as a form of udf and finding formulas for preferred deformations of hopf algebras in which the multiplication or comultiplication is rigid and must be preserved in the course of deformation

step size sequence design for finite time average consensus in secure wireless sensor networks this paper concerns the study of average consensus in wireless sensor networks with aim of providing a way to reach consensus in a finite number of steps in particular we investigate the design of consensus protocols when for security reasons for instance the underlying graph is constrained to be strongly regular or distance regular the proposed design method is based on parameters of the intersection array characterizing the underlying graph with this protocol at execution time average consensus is achieved in a number of steps equal to the diameter of the graph i e the smallest possible number of steps to achieve consensus

discrete wigner function by symmetric informationally complete positive operator valued measure we construct a version of the discrete wigner function making use of symmetric informationally complete positive operator valued measure we will show that this version is the natural discrete analog of continuous wigner function in addition to this discrete wigner function has many properties of the continuous wigner function