a constructive representation for the fourier dual of the zadoff chu sequences in this paper a complex matrix c consisting of a set of perfect sequences is studied the matrix c is constructed by taking the inverse discrete fourier transform idft of a diagonal matrix in which the diagonal elements comprise an arbitrary periodically perfect sequence gamma properties of the matrix c are presented in addition the fourier dual e of the matrix c is investigated when gamma is a zadoff chu sequence for the case of n even m 1 and g 0 an explicit representation for the matrix e is derived

generalization of the darboux transformation and generalized harmonic oscillators the darbroux transformation is generalized for time dependent hamiltonian systems which include a term linear in momentum and a time dependent mass the formalism for the n fold application of the transformation is also established and these formalisms are applied for a general quadratic system a generalized harmonic oscillator and a quadratic system with an inverse square interaction up to n 2 among the new features found it is shown for the general quadratic system that the shape of potential difference between the original system and the transformed system could oscillate according to a classical solution which is related to the existence of coherent states in the system

fully implicit methodology for the dynamics of biomembranes and capillary interfaces by combining the level set and newton methods abstract this framework is concerned with the numerical modeling of the dynamics of individual biomembranes and capillary interfaces in a surrounding newtonian fluid a level set approach helps to follow the interface motion our method features the use of high order fully implicit time integration schemes that enable to overcome stability issues related to the explicit discretization of the highly non linear bending force or capillary force at each time step the tangent systems are derived and the resulting nonlinear problems are solved by a newton raphson method based on the signed distance assumption several inexact newton strategies are employed to solve the capillary and vesicle problems and guarantee the second order convergence behavior we address in detail the main features of the proposed method and we report several experiments in the two dimensional case with the aim of illustrating its accuracy and efficiency comparative investigations with respect to the fully explicit scheme depict the stabilizing effect of the new method which allows to use significantly larger time step sizes

holomorphic quantization on the torus and finite quantum mechanics we explicitly construct the quantization of classical linear maps of on toroidal phase space of arbitrary modulus using the holomorphic chiral version of the metaplectic representation we show that finite quantum mechanics fqm on tori of arbitrary integer discretization is a consistent restriction of the holomorphic quantization of to the subgroup being the principal congruent subgroup on a finite dimensional hilbert space the generators of the rotation group for arbitrary values of l are determined as well as their quantum mechanical eigenvalues and eigenstates

finite analogues of euclidean space graphs are attached to fqn where fq is the field with q elements q odd using an analogue of the euclidean distance the graphs are shown to be asymptotically ramanujan for large q better than ramanujan in half the cases comparisons are made with finite upper half planes constructed in a similar way using an analogue of poincare s non euclidean distance the eigenvalues of the adjacency operators of the finite euclidean graphs are shown to be kloosterman sums

dual state vector of nonlinear coherent state and its application in complex p representation we introduce the dual vector z f n of a single mode nonlinear coherent state ncs by using the contour integral form of function and the explicit form of z f n is obtained in enlarged hilbert space the nonlinear fock states and their contour representation are deduced a new completeness relation composed of z f n and ncs in contour integral form is derived and its application in constructing a complex p representation of density operators is shown

lyapunov theory for 2 d nonlinear roesser models application to asymptotic and exponential stability this technical note deals with a general class of discrete 2 d possibly nonlinear systems based on the roesser model we first motivate the introduction of lyapunov type definitions of asymptotic and exponential stability this will allow us to introduce and discuss several particularities that cannot be found in 1 d systems once this background has been carefully designed we develop different lyapunov theorems in order to check asymptotic and exponential stability of nonlinear 2 d systems finally we propose the first converse lyapunov theorem in the case of exponential stability

a problem of time in the multiplicative scheme for the n site hopper quantum measure theory qmt is an approach to quantum mechanics based on the path integral in which quantum theory is conceived of as a generalised stochastic process one of the postulates of qmt is that events with zero quantum measure do not occur however this is not sufficient to give a full picture of the quantum world determining the other postulates is a work in progress and this paper investigates a proposal called the multiplicative scheme for qmt in which the physical world corresponds essentially to a set of histories from the path integral this scheme is applied to sorkin s n site hopper a discrete unitary model of a single particle on a ring of n sites motivated by free schrodinger propagation it is shown that the multiplicative scheme s global features lead to the conclusion that no non trivial time finite event can occur

a partitioned strongly coupled fluid structure interaction method to model heart valve dynamics a new method for the calculation of fluid structure interaction fsi of highly flexible bodies is presented this innovative algorithm demonstrates the strong coupling of a commercial computational fluid dynamics code with an in house coded structural solver the strong response of the pressure distribution to the displacement can be approximated by a reduced order model for the fluid solver the jacobian of this reduced order model is then used in the structural solver to obtain a stable and full implicit iteration scheme the method is demonstrated on a 2d model of a flexible aortic valve during the cardiac cycle furthermore the model is able to calculate shear stresses on the leaflet

explicit solutions of the time dependent schrodinger equation the darboux transformation is used to generate explicit solutions of the time dependent schrodinger equation in one dimension the potentials are a reflectionless potential and certain asymmetric double well potentials if explicit solutions of a second order ordinary differential equation are known then the darboux transformation generates explicit solutions of a related differential equation deift and trubowitz 1979 lamb 1980 when applied to the time indepen dent schrodinger equation this method gives a new equation with a different potential function the purpose of this paper is to apply the procedure to the time dependent schrodinger equation in one dimension a number of new explicit solutions are thereby obtained given by closed formulae which do not require knowledge of the eigenfunc tions

geometrical description of quantal state determination under the assumption that every quantal measurement may give data about the post measurement state of the inspected ensemble the problem of the state determination is reconsidered it is shown that orthogonal decomposition of the set of complex n n hermitian matrices into the commutative subsets allows operators to be found such that post measurement information on these observables allows a partial in some cases total determination of the pre measurement state to be effected

new families of isospectral hydrogen like potentials by applying algebraic techniques we construct a two parametric family of strictly isospectral hydrogen like potentials as well as some of its one parametric limits an additional one parametric almost isospectral family of hydrogen like potentials is also investigated it is argued that the construction of a susy partner hamiltonian using a factorization energy less than the ground state energy of the departure hamiltonian is unnecessarily restrictive

bipartite and tripartite entanglement of truncated harmonic oscillator coherent states via beam splitters we introduce a special class of truncated weyl heisenberg algebra and discuss the corresponding hilbertian and analytical representations subsequently we study the effect of a quantum network of beam splitting on coherent states of this nonlinear class of harmonic oscillators we particularly focus on quantum networks involving one and two beam splitters and examine the degree of bipartite as well as tripartite entanglement using the linear entropy

factorization little or great algorithm the progress of the factorization method since the 1935 work of dirac is briefly reviewed though linked with older mathematical theories the factorization seems an autonomous driving force offering substantial support to the present day darboux and backlund approaches

darboux transformations of coherent states of the time dependent singular oscillator darboux transformation of both barut girardelo and perelomov coherent states for the time dependent singular oscillator is studied in either case a measure that realizes the resolution of the identity operator in terms of coherent states is found and a corresponding holomorphic representation is constructed for the particular case of the free particle moving with the fixed value of the square of angular momentum equal to 2 it is shown that the barut giriardelo coherent states are more localized at the initial time moment while the perelomov coherent states are more stable with respect to time evolution it is also illustrated that darboux transformation may keep unchanged this different time behaviour

asymptotic and exponential stability of nonlinear two dimensional continuous discrete roesser models abstract sufficient conditions guaranteeing lyapunov stability asymptotic stability and exponential stability of nonlinear two dimensional continuous discrete systems are proposed special attention is paid to neutrally stable systems such as some two dimensional system descriptions of vehicle platoons which may be stable or asymptotically stable but never exponentially stable our conditions for lyapunov stability and asymptotic stability only require the corresponding two dimensional lyapunov function to have a negative semidefinite divergence they are thus suitable for the analysis of non exponential versions of 2d stability examples are given to illustrate the results

refined factorizations of solvable potentials a generalization of the factorization technique is shown to be a powerful algebraic tool to discover further properties of a class of integrable systems in quantum mechanics the method is applied in the study of radial oscillator morse and coulomb potentials to obtain a wide set of raising and lowering operators and to show clearly the connection that links these systems

the barut girardello coherent states it is shown that the completeness problem of the sl 2 r coherent states proposed by barut and girardello leads to a moment problem not a mellin transform this moment problem which also appears in the theory of para bose oscillators has been solved following the sharma mehta mukunda sudarshan solution of the problem the matrix element of finite transformation in the coherent state basis is shown to satisfy a quasiorthogonality condition analogous to the orthogonality condition of the matrix element in the canonical basis finally the barut girardello hilbert space of entire analytic functions of growth 1 1 turns out to be only a subspace of bargmann s well known hilbert space of analytic functions this subspace which has been called the reduced bargmann space in a previous paper is an invariant subspace of sl 2 r with this identification the generators of the group in this realization turn out to be the well known boson operators of holman and biedenharn

factorization method and new potentials with the oscillator spectrum a one parameter family of potentials in one dimension is constructed with the energy spectrum coinciding with that of the harmonic oscillator this is a new derivation of a class of potentials previously obtained by abraham and moses with the help of the gelfand levitan formalism

low correlation sequences from linear combinations of characters pairs of binary sequences formed using linear combinations of multiplicative characters of finite fields are exhibited that when compared with a random sequence pairs simultaneously achieve significantly lower mean square autocorrelation values for each sequence in the pair and significantly lower mean square crosscorrelation values if we define crosscorrelation merit factor analogously to the usual merit factor for autocorrelation and if we define demerit factor as the reciprocal of merit factor then randomly selected binary sequence pairs are known to have an average crosscorrelation demerit factor of 1 our constructions provide sequence pairs with a crosscorrelation demerit factor significantly less than 1 and at the same time the autocorrelation demerit factors of the individual sequences can also be made significantly less than 1 which also indicates better than average performance the sequence pairs studied here provide combinations of autocorrelation and crosscorrelation performance that are not achievable using sequences formed from single characters such as maximal linear recursive sequences m sequences and legendre sequences in this paper exact asymptotic formulae are proved for the autocorrelation and crosscorrelation merit factors of sequence pairs formed using linear combinations of multiplicative characters data is presented that shows that the asymptotic behavior is closely approximated by sequences of modest length

efficient computation of root numbers and class numbers of parametrized families of real abelian number fields let k m be a parametrized family of simplest real cyclic cubic quartic quintic or sextic number fields of known regulators e g the so called simplest cubic and quartic fields associated with the polynomials p m x x3 mx2 m 3 x 1 and p m x x 4 mx 3 6x 2 mx 1 we give explicit formulas for powers of the gaussian sums attached to the characters associated with these simplest number fields we deduce a method for computing the exact values of these gaussian sums these values are then used to efficiently compute class numbers of simplest fields finally such class number computations yield many examples of real cyclotomic fields q p of prime conductors p 3 and class numbers h p greater than or equal to p however in accordance with vandiver s conjecture we found no example of p for which p divides h p

variations on a theme of heisenberg pauli and weyl the parentage between weyl pairs the generalized pauli group and the unitary group is investigated in detail we start from an abstract definition of the heisenberg weyl group on the field and then switch to the discrete heisenberg weyl group or generalized pauli group on a finite ring the main characteristics of the latter group an abstract group of order d3 noted pd are given conjugacy classes and irreducible representation classes or equivalently lie algebra of dimension d3 associated with pd leaving the abstract sector a set of weyl pairs in dimension d is derived from a polar decomposition of su 2 closely connected to angular momentum theory then a realization of the generalized pauli group pd and the construction of generalized pauli matrices in dimension d are revisited in terms of weyl pairs finally the lie algebra of the unitary group u d is obtained as a subalgebra of the lie algebra associated with pd this leads to a development of the lie algebra of u d in a basis consisting of d2 generalized pauli matrices in the case where d is a power of a prime integer the lie algebra of su d can be decomposed into d 1 cartan subalgebras

distortion of a phase space under the darboux transformation the darboux transformation operator technique is applied to construct exactly solvable anharmonic singular oscillator potentials and to study their coherent states classical system corresponding to a transformed quantum system is constructed with the help of the coherent states technique it is shown that at classical level the darboux transformation may be treated as a transformation of kahler potential which leads to a distortion of the initial phase space

exponential stability of discrete linear repetitive processes repetitive processes are a distinct class of 2d systems of both practical and theoretical interest their essential characteristic is repeated sweeps termed passes through a set of dynamics defined over a finite duration with explicit interaction between the outputs or pass profiles produced as the process evolves experience has shown that these processes cannot be studied controlled by direct application of existing theory in all but a few very restrictive special cases this fact and the growing list of applications areas has prompted an on going research programme into the development of a mature systems theory for these processes for onward translation into reliable generally applicable controller design algorithms in this paper we develop the concept of exponential stability for the very important sub class of so called discrete linear repetitive processes and relate the results obtained to those already in both the general 2d linear systems and repetitive process literature

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

coherent states for anharmonic oscillator hamiltonians with equidistant and quasi equidistant spectra two kinds of transformation for the time dependent schrodinger equation i e the differential and integral transformations are introduced if one considers only stationary solutions of this equation both transformations reduce to the well known darboux transformation for the stationary schrodinger equation when applied to non stationary solutions they give different results both transformations are invertible in appropriate spaces with the help of these transformations alternative systems of coherent states to those in the literature are obtained for isospectral hamiltonians with equidistant spectra these transformations are also applied to the construction of coherent states for hamiltonians whose spectrum consists of an equidistant part and one separately disposed level with an energy gap equal to the k skipped levels

on one dimensional schrodinger problems allowing polynomial solutions we discuss the explicit construction of the schrodinger equations admitting a representation through some family of general polynomials almost all solvable quantum potentials are shown to be generated by this approach some generalization has also been performed in higher dimensional problems

necessary and sufficient lmi conditions for stability and performance analysis of 2 d mixed continuous discrete time systems this paper proposes necessary and sufficient conditions for stability and performance analysis of 2 d mixed continuous discrete time systems that can be checked with convex optimization in particular linear matrix inequalities lmis specifically the first contribution of the paper is a condition for exponential stability based on the introduction of a complex lyapunov function depending polynomially on a parameter and on the use of the gram matrix method it is shown that this condition is sufficient for any chosen degree of the complex lyapunov function and necessary for an a priori known degree the second contribution is a non lyapunov condition for exponential stability based on eigenvalue products this condition is necessary and sufficient and has the advantage of requiring a significantly smaller computational burden for achieving necessity lastly the third contribution is to show how upper bounds on the h norm of 2 d mixed continuous discrete time systems can be obtained through a semidefinite program based on complex lyapunov functions a necessary and sufficient condition is provided for establishing the tightness of the found upper bounds

a solvable lie algebra condition for stability of linear multidimensional systems this note analyzes exponential stability of a class of linear discrete multidimensional systems using a multidimensional comparison principle for estimating the system componentwise exponential convergence and a solvable lie algebra condition a sufficient condition for exponential stability of linear multidimensional systems is presented the stability condition can be easily examined by computing the system matrices in finite steps this is demonstrated by an example

distorted heisenberg algebra and coherent states for isospectral oscillator hamiltonians the dynamical algebra associated with a family of isospectral oscillator hamiltonians is studied through the analysis of its representation in the basis of energy eigenstates it is shown that this representation becomes similar to that of the standard heisenberg algebra and it is dependent on a parameter omega or 0 we call it the distorted heisenberg algebra where omega is the distortion parameter the corresponding coherent states for an arbitrary omega are derived and some particular examples are discussed in detail a prescription to produce the squeezing by adequately selecting the initial state of the system is given

temporally stable coherent states for infinite well and poschl teller potentials this article is a direct illustration of a construction of coherent states which has been recently proposed by two of us jpg and jk we have chosen the example of a particle trapped in an infinite square well and also in poschl teller potentials of the trigonometric type in the construction of the corresponding coherent states we take advantage of the simplicity of the solutions which ultimately stems from the fact they share a common su 1 1 symmetry a la barut girardello many properties of these states are then studied both from mathematical and from physical points of view

supersymmetry and potentials with bound states at arbitrary energies ii for pt i see ibid vol 19 p 2297 1986 it has been shown previously that a potential v0 chi in one dimension which supports no bound states may be used as a reference potential from which by successive applications of the concept of a supersymmetric partner to a given hamiltonian it is possible to find a potential vn chi which supports any specified number n of bound states at any chosen energies ej j 1 n the reflection coefficient of vn is related to the reflection coefficient of v0 various alternative representations of the potentials constructed by this procedure are presented an illustrative example in which vn is constructed by using a sech2 chi barrier as the reference potential is discussed

lossless h synthesis for 2d systems special issue jcw abstract we study 2d systems with a continuous and discrete time axis we embed known results about the stability and h performance properties of such systems into multiplier theory from robust control it is shown that this opens the way for applying recently developed gain scheduled controller synthesis techniques in order to solve the h design problem for 2d systems without any conservatism this is presented if the discrete time axis is either one or two sided the latter leading to non conservative h synthesis result for infinite string interconnections of identical linear time invariant systems

phase operators phase states and vector phase states for su3 and su2 1 this paper focuses on phase operators phase states and vector phase states for the sl3 lie algebra we introduce a one parameter generalized oscillator algebra a 2 which provides a unified scheme for dealing with su3 for 0 and h4 h4 for 0 symmetries finite and infinite dimensional representations of a 2 are constructed for 0 and 0 respectively phase operators associated with a 2 are defined and temporally stable phase states as well as vector phase states are constructed as eigenstates of these operators finally we discuss a relation between quantized phase states and a quadratic discrete fourier transform and show how to use these states for constructing mutually unbiased bases

exponential stability of 2 d systems exponential stability of 2 d systems is defined and characterized the definition of exponential stability works also with unbounded data as for the case of 1 d systems we show in particular that exponential stability and asymptotic stability are equivalent properties

an angular momentum approach to quadratic fourier transform hadamard matrices gauss sums mutually unbiased bases the unitary group and the pauli group the construction of unitary operator bases in a finite dimensional hilbert space is reviewed through a nonstandard approach combining angular momentum theory and representation theory of su 2 a single formula for the bases is obtained from a polar decomposition of su 2 and is analyzed in terms of cyclic groups quadratic fourier transforms hadamard matrices and generalized gauss sums weyl pairs generalized pauli operators and their application to the unitary group and the pauli group naturally arise in this approach

higher order susy linearized nonlinear heisenberg algebras and coherent states using an iterative construction of the first order intertwining technique we find k parametric families of exactly solvable anharmonic oscillators whose spectra consist of a part isospectral to the oscillator plus k additional levels at arbitrary positions below e0 it is seen that the natural ladder operators for these systems give place to polynomial nonlinear algebras and it is shown that these algebras can be linearized the coherent states construction is performed in the nonlinear and linearized cases

on the asymptotic connection between two exponential sums the relation between the exponential sums sn x p n 0n 1exp ixnp and t0 t0 x n p n 1 e n nexp ixnpe pn n where x 0 and p 0 is investigated it is demonstrated that there is an asymptotic connection as n which is found numerically to be valid provided the variable x satisfies the restriction xnp o n when p 1 the sum t0 is shown to be associated with a zeta function defined by z s n 1 exp i e an n s for real and a 0

exactly solvable hydrogen like potentials and the factorization method a set of factorization energies is introduced giving rise to a generalization of the schrodinger or infeld and hull factorization for the radial hydrogen like hamiltonian an algebraic intertwining technique involving such factorization energies leads us to derive n parametric families of potentials which in general are almost isospectral to the hydrogen like radial hamiltonians the construction of susy partner hamiltonians with ground state energies greater than the corresponding ground state energy of the initial hamiltonian is also explicitly performed

feynman s path integral and mutually unbiased bases our previous work on quantum mechanics in hilbert spaces of finite dimension n is applied to elucidate the deep meaning of feynman s path integral pointed out by g svetlichny he speculated that the secret of the feynman path integral may lie in the property of mutual unbiasedness of temporally proximal bases we confirm the corresponding property of the short time propagator by using a specially devised n n approximation of quantum mechanics in applied to our finite dimensional analogue of a free quantum particle

generalized coherent and intelligent states for exact solvable quantum systems the so called gazeau klauder and perelomov coherent states are introduced for an arbitrary quantum system we give also the general framework to construct the generalized intelligent states which minimize the robertson schrodinger uncertainty relation as illustration the poschl teller potentials of trigonometric type will be chosen we show the advantage of the analytical representations of gazeau klauder and perelomov coherent states in obtaining the generalized intelligent states in analytical way

comments on on stabilization of 2 d roesser models in this note we clarify the statement given in the above paper claiming that the condition for state feedback stabilisation tends to necessity actually it is possible to find examples for which the above mentioned condition introduces a very weak conservatism and hence is not necessary the source of the conservatism has been identified furthermore we also realized that the condition could be substantially improved in terms of computation time therefore both the analysis and synthesis conditions are improved

about two trigonometric matrices abstract let r s be coprime integers s 1 and odd the characteristic polynomials of the matrices sin rmn s 0 and sin rmn s 0 mn s 1 are determined

robust stability and performance analysis of 2d mixed continuous discrete time systems with uncertainty this paper investigates 2d mixed continuous discrete time systems whose coefficients are polynomial functions of an uncertain vector constrained into a semialgebraic set it is shown that a nonconservative linear matrix inequality lmi condition for ensuring robust stability can be obtained by introducing complex lyapunov functions depending polynomially on the uncertain vector and a frequency moreover it is shown that nonconservative lmi conditions for establishing upper bounds of the robust h and h 2 norms can be obtained by introducing analogous lyapunov functions depending rationally on the frequency some numerical examples illustrate the proposed methodology

structural stability asymptotic stability and exponential stability for linear multidimensional systems the good the bad and the ugly abstractin this paper we investigate three concepts of stability for linear two dimensional systems the good structural stability an algebraic property linked to the location of the roots of a certain characteristic polynomial the bad asymptotic stability roughly the trajectory converges to the equilibrium point and the ugly exponential stability the rate of convergence is at least exponential more precisely we show that for a usual set of boundary conditions taken along the positive semi axes structural stability and exponential stability are equivalent notions for this particular set of boundary conditions we further prove that structural stability implies asymptotic stability but a counterexample shows that asymptotic stability does not imply structural stability which is a major difference compared to the one dimensional case this also highlights the importance of the boundary conditions when one works with multidimensional systems

phase operators temporally stable phase states mutually unbiased bases and exactly solvable quantum systems we introduce a one parameter generalized oscillator algebra that covers the case of the harmonic oscillator algebra and discuss its finite and infinite dimensional representations according to the sign of the parameter we define an hamiltonian operator associated with and examine the degeneracies of its spectrum for the finite when 0 and the infinite when 0 representations of we construct the associated phase operators and build temporally stable phase states as eigenstates of the phase operators to overcome the difficulties related to the phase operator in the infinite dimensional case and to avoid the degeneracy problem for the finite dimensional case we introduce a truncation procedure which generalizes the one used by pegg and barnett for the harmonic oscillator this yields a truncated generalized oscillator algebra where s denotes the truncation order we construct two types of temporally stable states for as eigenstates of a phase operator and as eigenstates of a polynomial in the generators of two applications are considered in this paper the first concerns physical realizations of and in the context of one dimensional quantum systems with finite morse system or infinite poschl teller system discrete spectra the second deals with mutually unbiased bases used in quantum information

coherent states for transparent potentials the darboux transformation operator method is applied to the investigation of coherent states of transparent multisoliton potentials an isometric correspondence between hilbert spaces of the states of a free particle and a particle moving in the soliton potential is established it is shown that the darboux transformation operator being unbounded and closed cannot realize an isometric mapping between hilbert spaces a quasispectral representation of transformation operators in terms of continuous basis sets is obtained different families of coherent states of the multisoliton potential are introduced measures that realize the resolution of the unity in terms of the projectors on the coherent states vectors are calculated these measures are defined by ordinary smooth functions for the states obtained with the help of bounded transformation operators and by generalized ones otherwise

coherent states for isospectral oscillator hamiltonians coherent states for a family of isospectral oscillator hamiltonians are derived from a suitable choice of annihilation and creation operators the fock bargmann representation is also considered

factorization of analytic representations in the unit disc and number phase statistics of a quantum harmonic oscillator the inner outer part factorization of analytic representations in the unit disc is used for an effective characterization of the number phase statistical properties of a quantum harmonic oscillator it is shown that the factorization is intimately connected with the number phase weyl semigroup and its properties in the barut girardello analytic representation the factorization is implemented as a convolution several examples are given which demonstrate the physical significance of the factorization and its role for quantum statistics in particular we study the effect of phase space interference on the factorization properties of a superposition state

eulerian finite element method for the numerical modeling of fluid dynamics of natural and pathological aortic valves we present a finite element methodology tailored for the simulation of pulsatile flow in the full aorta and sinus of valsalva interacting with highly deformable thin leaflets we describe an extension of the so called resistive immersed surface method to circumvent stability issues resulting from the bad conditioning of the linear system especially when flow and geometry become complex after the inclusion of the aorta we use a lagrange multiplier technique that couples the dynamics of valve and flow a banded level set variant allows to address the singularity of the resulting linear system while featuring in addition to the parallel implementation higher accuracy and an affordable computational burden high fidelity computational geometries are built and simulations are performed under physiological conditions several numerical experiments illustrate the ability of the model to capture the basic fluidic phenomena in both healthy and pathological configurations we finally examine numerically the flow dynamics in the sinus of valsalva after transcatheter aortic valve implantation we show numerically that flow may be subject to stagnation in the lower part of the sinuses we highlight the far reaching implications of this phenomenon and we hope inciting adequate studies to further investigate its potential clinical consequences display omitted hemodynamics in full aorta and aortic sinuses coupled with highly deformable valve an exact lagrange multiplier technique couples the dynamics of valve and flow a damped newton strategy allows more stability for relatively large reynolds numbers numerical examples in 2d and 3d with healthy and pathological valves numerical investigations pinpoint a risk of blood stagnation after tavi

a fluid structure interaction method with solid rigid contact for heart valve dynamics a computational method is proposed for problems where fluid structure interaction is combined with solid rigid contact this combination is particularly important for the dynamics and impact of heart valves the navier stokes equation in an eulerian setting is coupled to a neo hookean solid model using a lagrangian description a fictitious domain method extended with a local mesh adaptation algorithm provides the required flexibility with respect to the motion and deformation of the valve in addition it ensures the solids ability of sustaining pressures present in the fluid making use of the fact that the fluid and solid mesh are not required to be connected conformingly it is shown that the model can be extended with a contact algorithm without introducing meshing complications near the contact surfaces

coherent states for systems with discrete and continuous spectrum for a system with one degree of freedom coherent states that are parametrized by classical canonical action angle variables are introduced these states also possess continuity of labelling a resolution of unity and temporal stability the insistence on canonical action angle variables strongly restricts any remaining arbitrariness in the coherent state definition such states are introduced for semibounded hamiltonian operators having either a discrete or a continuous spectrum hamiltonians that have both discrete and continuous parts in their spectrum are also discussed

generalizes darboux transformations classification of inverse scattering methods for the radial schrodinger equation a wide class of darboux transformations of a sturm liouville equation providing a unified treatment of exactly solvable models in quantum scattering theory is considered systematically a classification of darboux transformations is given and the relations between darboux transformations and standard inverse scattering procedures for the radial schrodinger equation including the matrix method of newton sabatier are studied in particular the definitions properties and matrix generalizations of darboux transformations associated with marchenko type integral equations are studied in detail

linking forms reciprocity for gauss sums and invariants of 3 manifolds we study invariants of 3 manifolds derived from finite abelian groups equipped with quadratic forms these invariants arise in turaev s theory of modular categories and generalize those of h murakami t ohltsuki and m okada the crucial algebraic tool is a new reciprocity formula for gauss sums generalizing classical formulas of cauchy kronecker krazer and siegel we use this reciprocity formula to give an explicit formula for the invariants and to generalize them to higher dimnensions

cal h _ infty and cal h _ 2 norms of 2 d mixed continuous discrete time systems via rationally dependent complex lyapunov functions this paper addresses the problem of determining the cal h infty and cal h 2 norms of 2 d mixed continuous discrete time systems the first contribution is to propose a novel approach based on the use of complex lyapunov functions with even rational parametric dependence which searches for upper bounds on the sought norms via linear matrix inequalities lmis the second contribution is to show that the upper bounds provided are nonconservative by using lyapunov functions in the chosen class with sufficiently large degree the third contribution is to provide conditions for establishing the tightness of the upper bounds the fourth contribution is to show how the numerical complexity of the proposed approach can be significantly reduced by proposing a new necessary and sufficient lmi condition for establishing positive semidefiniteness of even hermitian matrix polynomials this result is also exploited to derive an improved necessary and sufficient lmi condition for establishing exponential stability of 2 d mixed continuous discrete time systems some numerical examples illustrate the proposed approach it is worth remarking that nonconservative lmi methods for determining the cal h infty and cal h 2 norms of 2 d mixed continuous discrete time systems have not been proposed yet in the literature

a sufficient condition on the exponential stability of two dimensional 2 d shift variant systems in this paper we consider a class of two dimensional 2 d shift variant systems based on the bound on the deviation of parameters a sufficient condition is derived which ensures exponential stability with different decaying rates along the two directions an example is presented to illustrate the result

reply to the comment on generalization of the darboux transformation and generalized harmonic oscillators in the comment on our paper schulze halberg introduces a gauge transformation to gauge away the linear term in momentum he explicitly shows that the gauge transformation works for n fold darboux transformed system the comment is however entirely on the formalism of the darboux transformation while most pages of our paper are devoted to the applications of the formalism in this reply we add some considerations so that his gauge transformation method can be used to reproduce the solvable hermitian hamiltonian systems given in our paper

littlewood polynomials with small l4 norm abstract littlewood asked how small the ratio f 4 f 2 where denotes the l norm on the unit circle can be for polynomials f having all coefficients in 1 1 as the degree tends to infinity since 1988 the least known asymptotic value of this ratio has been 7 6 4 which was conjectured to be minimum we disprove this conjecture by showing that there is a sequence of such polynomials derived from the fekete polynomials for which the limit of this ratio is less than 22 19 4

bosonic and k fermionic coherent states for a class of polynomial weyl heisenberg algebras the aim of this paper is to construct coherent states la perelomov and la barut girardello for a polynomial weyl heisenberg algebra this generalized weyl heisenberg algebra denoted by depends on r real parameters and is an extension of the one parameter algebra daoud and kibler 2010 j phys a math theor 43 115303 which covers the cases of the su 1 1 algebra for 0 the su 2 algebra for 0 and the h4 ordinary weyl heisenberg algebra for 0 for finite dimensional representations of and where is a truncation of order s of in the sense of pegg barnett a connection is established with k fermionic algebras or quon algebras this connection makes it possible to use generalized grassmann variables for constructing certain coherent states coherent states of the perelomov type are derived for infinite dimensional representations of and for finite dimensional representations of and through a fock bargmann analytical approach based on the use of complex or bosonic variables the same approach is applied for deriving coherent states of the barut girardello type in the case of infinite dimensional representations of in contrast the construction of coherent states la barut girardello for finite dimensional representations of and can be achieved solely at the price of replacing complex variables by generalized grassmann or k fermionic variables some of the results are applied to su 2 su 1 1 and the harmonic oscillator in a truncated or not truncated form this article is part of a special issue of journal of physics a mathematical and theoretical devoted to coherent states mathematical and physical aspects

nonlinear coherent states for nonlinear systems in this work we construct nonlinear coherent states for hamiltonians with linear and quadratic terms in the number operator by the generalization of two definitions as eigenstates of a deformed annihilation operator and as those states obtained by the application of a deformed displacement operator on the vacuum state we evaluate their temporal dependence analyze its dispersion relations and some of their statistical properties for two model hamiltonians one supporting a finite number of bound states and the other supporting an infinite number of bound states

fock bargmann representation of the distorted heisenberg algebra the dynamical algebra associated with a family of isospectral oscillator hamiltonians named distorted heisenberg algebra because of its dependence on a distortion parameter has recently been studied the connection of this algebra with the hilbert space of entire analytic functions of growth is analysed

control systems analysis for the fornasini marchesini 2d systems model progress after four decades the development of a control systems theory for multidimensional linear systems i e systems with more than one independent variable is an area where a very significant volume of research is based

comments on 2 d descriptor systems abstract this paper discusses general 2 d descriptor systems of the form ex i 1 j 1 ax i j bx i 1 j cx i j 1 d 0 u i j d 1 u i 1 j d 2 u i j 1 solution formula and structural forms are developed for several large classes of 2 d descriptor systems the idea of a recursive chain is introduced it is shown that these systems include several types of behavior not discussed elsewhere in the literature

application of nonlinear deformation algebra to a physical system with poschl teller potential nonlinear deformation algebra are realized in a physical system with p schl teller potential the raising and lowering operators satisfying this algebra are constructed from which the eigenproblem of the system can be exactly solved by the operator method the physical meaning of two deforming functions involved in this algebra is also found in addition algebra is obtained naturally and discussions on the coherent state are also made

polynomial heisenberg algebras polynomial deformations of the heisenberg algebra are studied in detail some of their natural realizations are given by the higher order susy partners and not only by those of first order as is already known of the harmonic oscillator for even order polynomials here it is shown that the susy partners of the radial oscillator play a similar role when the order of the polynomial is odd moreover it will be proved that the general systems ruled by such kinds of algebras in the quadratic and cubic cases involve painleve transcendents of types iv and v respectively

symmetrization of the hurwitz zeta function and dirichlet l functions we consider the hurwitz zeta function z s a and form two parts zc and zk by symmetric and antisymmetric combinations of z s a a ndz s 1ka we consider the properties of zc and zk and then show that each may be decomposed into parts denoted by p and n each of which obeys a functional equation of the dirichlet l type with a multiplicative factor of k1 for the functions n we show the results of this procedure for rational az p q with qz1 2 3 4 5 6 7 8 10 and demonstrate that the functions p and n have some of the key properties of dirichlet l functions

a three dimensional computational analysis of fluid structure interaction in the aortic valve numerical analysis of the aortic valve has mainly been focused on the closing behaviour during the diastolic phase rather than the kinematic opening and closing behaviour during the systolic phase of the cardiac cycle moreover the fluid structure interaction in the aortic valve system is most frequently ignored in numerical modelling the effect of this interaction on the valve s behaviour during systolic functioning is investigated the large differences in material properties of fluid and structure and the finite motion of the leaflets complicate blood valve interaction modelling this has impeded numerical analyses of valves operating under physiological conditions a numerical method known as the lagrange multiplier based fictitious domain method is used to describe the large leaflet motion within the computational fluid domain this method is applied to a three dimensional finite element model of a stented aortic valve the model provides both the mechanical behaviour of the valve and the blood flow through it results show that during systole the leaflets of the stented valve appear to be moving with the fluid in an essentially kinematical process governed by the fluid motion

on generalized coherent states with maximal symmetry for the harmonic oscillator generalized coherent states for the one dimensional harmonic oscillator with maximal symmetry i e admitting the semidirect sum so 2 1 h 2 as the largest invariance lie algebra pointed out by niederer are constructed the normalization of such states as well as their completeness property are determined and discussed they are also analyzed in the subcontexts of the so 2 1 algebra and of the heisenberg h 2 algebra general considerations on heisenberg relations on minimal dispersions and on quantum mechanical entropies are presented in connection with the uncertainty principle

complementarity and phases in su 3 phase operators and phase states are introduced for irreducible representations of the lie algebra using a polar decomposition of ladder operators in contradistinction with it is found that the polar decomposition does not uniquely determine a hermitian phase operator we describe two possible ways of proceeding one based on imposing su 2 invariance and the other based on the idea of complementarity the generalization of these results to su n is sketched this article is part of a special issue of journal of physics a mathematical and theoretical devoted to coherent states mathematical and physical aspects

q extension of mehta s eigenvectors of the finite fourier transform for q a root of unity it is shown that the continuous q hermite polynomials for q a root of unity have simple transformation properties with respect to the classical fourier transform this result is then used to construct q extended eigenvectors of the finite fourier transform in terms of these polynomials

analysis of quantum walks with time varying coin on d dimensional lattices in this paper we present a study of discrete time quantum walks whose underlying graph is a d dimensional lattice the dynamical behavior of these systems is of current interest because of their applications in quantum information theory as tools to design quantum algorithms we assume that at each step of the walk evolution the coin transformation is allowed to change so that we can use it as a control variable to drive the evolution in a desired manner we give an exact description of the possible evolutions and of the set of possible states that can be achieved with such a system in particular we show that it is possible to go from a state where there is probability 1 for the walker to be found in a vertex to a state where all the vertices have equal probability we also prove a number of properties of the set of admissible states in terms of the number of steps needed to obtain them we provide explicit algorithms for state transfer in low dimensional cases as well as results that allow to reduce algorithms on two dimensional lattices to algorithms on the one dimensional lattice the cycle

quantum mechanics on p adic fields a formulation of quantum mechanics on p adic number fields is presented quantum amplitudes are taken as complex functions of p adic variables and it is shown how the weyl approach to quantum mechanics can be generalized to the p adic case the p adic analogs of simple one dimensional systems free particle compact and noncompact oscillators are defined by a group of motion which is an abelian subgroup of sl 2 qp in each case the evolution operator is a unitary representation of the appropriate group its spectrum is given by characters and its eigenstates are calculated

generalized coherent squeezed and intelligent states for exactly solvable quantum systems and the analogue of the displacement and squeezing operators using an algebraic approach we construct purely coherent and squeezed states for a set of exactly solvable quantum confined systems assuming a generalization of both the ladder operator and the displacement operator methods showing the equivalence between the two procedures we obtain the analogue of the displacement and the squeeze operators and study their basic relations and their connections with the properties of the purely coherent and squeezed states that they produce in a second approach we construct generalized squeezed coherent and intelligent states for these systems considering the successive action of the displacement and the squeeze operators in the first case and the combined action of these operators in the second case we apply the generalized approach for shape invariant systems with potential parameters related by a translation and by a scaling and show that the presence of the generalizing functionals of the potential parameters in the formalism opens a large number of possibilities in the construction of these special quantum states