existence uniqueness and comparison results for a differential equation with discontinuous nonlinearities abstract in this paper we shall show that the initial value problem x q x g t x x 0 x o has on an interval j 0 t t 0 a unique solution which is increasing and right continuous with respect to x o and g under hypotheses which allow measurable discontinuities for q and g z and left hand side discontinuities for g t if g t is also increasing the solution is obtained by a method of successive approximations

finite dimensional schwinger basis deformed symmetries wigner function and an algebraic approach to quantum phase schwinger s finite d dimensional periodic hilbert space representations are studied on the toroidal lattice with specific emphasis on the deformed oscillator subalgebras and the generalized representations of the wigner function these subalgebras are shown to be admissible endowed with the non negative norm of hilbert space vectors hence they provide the desired canonical basis for the algebraic formulation of the quantum phase problem certain equivalence classes in the space of labels are identified within each subalgebra and connections with area preserving canonical transformations are examined the generalized representations of the wigner function are examined in the finite dimensional cyclic schwinger basis these representations are shown to conform to all fundamental conditions of the generalized phase space wigner distribution as a specific application of the schwinger basis the number phase unitary operator pair in is studied and based on the admissibility of the underlying q oscillator subalgebra an algebraic approach to the unitary quantum phase operator is established this being the focus of this work connections with the susskind glogower carruthers nieto phase operator formalism as well as standard action angle wigner function formalisms are examined in the infinite period limit the concept of continuously shifted fock basis is introduced to facilitate the fock space representations of the wigner function

a weak formulation of roe s approximate riemann solver abstract this paper presents a weak formulation of roe s approximate riemann solver based on a notion of weak solution to nonlinear hyperbolic systems in nonconservative form this weak formulation is applied to the euler equations for real gases and the homogeneous equilibrium two phase flow model numerical results for a two phase flow heat addition problem are given

generalized holstein primakoff realizations and quantum group theoretic coherent states a set of deformed k boson operators are defined and it is shown that the nonlinear transformations from the usual deformed oscillator operators to the deformed k boson operators form an abelian group it is shown that the multiboson operators satisfy quantum weyl heisenberg group the generalized holstein primakoff realizations in terms of these multibosons operators are used to define the quantum group theoretic coherent states of suq 1 1 and suq 2 the uncertainties x k q and p k q with respect to those group theoretic and generalized coherent states are computed explicitly and the results show that these coherent states are squeezed

a godunov type method for the shallow water equations with discontinuous topography in the resonant regime abstract we investigate the riemann problem for the shallow water equations with variable and possibly discontinuous topography and provide a complete description of the properties of its solutions existence uniqueness in the non resonant regime multiple solutions in the resonant regime this analysis leads us to a numerical algorithm that provides one with a riemann solver next we introduce a godunov type scheme based on this riemann solver which is well balanced and of quasi conservative form finally we present numerical experiments which demonstrate the convergence of the proposed scheme even in the resonance regime except in the limiting situation when riemann data precisely belong to the resonance hypersurface

on quantization of simple harmonic oscillators a general framework is presented of quantizing the system of a simple harmonic oscillator various methods of quantization so far proposed are accommodated here in a unified form some remarks are also made on quantization for the case of more than one oscillator

generalized q bosons and their squeezed states generalized q boson operators associated with the simultaneous creation of several q bosons are introduced these operators give rise to a realization of the quantum weyl heisenberg algebra and are applied to the construction of corresponding holstein primakoff realizations of the quantum algebras suq 2 and suq 1 1 coherent states of these algebras are defined in the various ways suggested by the equivalent definitions of the harmonic oscillator coherent states and some of their properties are studied particular attention is devoted to the squeezing properties of the quadrature of the electromagnetic field in these states

a well balanced approach for flows over mobile bed with high sediment transport in this paper we deal with the numerical computation of one dimensional unsteady free surface flows over mobile bed we focus on flows characterized by high concentration of sediments and strong interaction between flow and bottom dynamics as in hyper concentrated and debris flows these features are fully considered in the adopted system of equations challenging in its numerical approximation is the preservation of the coupling and the treatment of a non conservative flux in the momentum equation in order to devise a new godunov type approach we analyzed in detail the riemann problem associated with the mobile bed phenomena and the peculiar features of its wave relations the scheme we developed is based on two supports well balanced treatment of the variable updating at the new time level and flux evaluation by three wave approximations of the intercell riemann problem that without any split embody the effect of the non conservative term the properties of the new numerical strategy named awb are assessed by comparison with exact solutions of riemann problems built by handling an inverse technique finally awb has been applied to cases of practical interest where wave interaction and friction effects makes the flow more complex the obtained results point out that the new method is able to predict faithfully the overall behaviour of the solution and of any type of waves the use of awb in this one dimensional frame is therefore fostered in representing rapid transients in river torrent flows with movable bed

the riemann problem for the one dimensional free surface shallow water equations with a bed step theoretical analysis and numerical simulations in this paper the solution of the riemann problem for the one dimensional free surface shallow water equations over a bed step is analyzed both from a theoretical and a numerical point of view particular attention has been paid to the wave that is generated at the location of the bed discontinuity starting from the classical shallow water equations considering the bed level as an additional variable and adding to the system an equation imposing its time invariance we show that this wave is a contact wave across which one of the riemann invariants namely the energy is not constant this is due to the fact that the relevant problem is nonconservative we demonstrate that in this type of system riemann invariants do not generally hold in contact waves furthermore we show that in this case the equations that link the flow variables across the contact wave are the generalized rankine hugoniot relations and we obtain these for the specific problem from the numerical point of view we present an accurate and efficient solver for the step riemann problem to be used in a finite volume godunov type framework through a two step predictor corrector procedure the solver is able to provide solutions with any desired accuracy the predictor step uses a well balanced generalized roe solver while the corrector step solves the exact nonlinear system of equations that consitutes the problem by means of an iterative procedure that starts from the predictor solution in order to show the effectiveness and the accuracy of the proposed approach we consider several step riemann problems and compare the exact solutions with the numerical results obtained by using a standard roe approach far from the step and the novel two step algorithm for the fluxes over the step achieving good results

exact solution of the riemann problem for the shallow water equations with discontinuous bottom geometry in this paper we present the exact solution of the riemann problem for the non linear shallow water equations with a step like bottom the solution has been obtained by solving an enlarged system that includes an additional equation for the bottom geometry and then using the principles of conservation of mass and momentum across the step the resulting solution is unique and satisfies the principle of dissipation of energy across the shock wave we provide examples of possible wave patterns numerical solution of a first order dissipative scheme as well as an implementation of our riemann solver in the second order upwind method are compared with the proposed exact riemann problem solution a practical implementation of the proposed exact riemann solver in the framework of a second order upwind tvd method is also illustrated

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

a realization of generalized deformed oscillators with cyclic symmetry the algebra of generalized deformed oscillators that possess cyclic symmetry is studied the general set of multilinear operator relations is presented which characterizes the multilinear part of the algebra of cyclic extended deformed oscillators the realization scheme of generalized deformed oscillators with cyclic symmetry in terms of those without cyclic symmetry is established it is shown that all generalized deformed oscillators with cyclic symmetry constructed by the scheme are actually equivalent in the viewpoint of mathematics though each generalized deformed oscillator admits its own particular cyclic extended counterpart examples are given to illustrate this peculiar realization scheme

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

the riemann problem for the shallow water equations with discontinuous topography the wet dry case abstract in this paper we consider riemann problems for the shallow water equations with discontinuous topography whose initial conditions correspond to a wet dry front at time t 0 there is vacuum on the right or on the left of the step besides the theoretical interest of this analysis the results may be useful to design numerical methods and or to produce reference solutions to compare different schemes we show that depending on the state at the wet side 0 1 or 2 self similar solutions can be constructed by composing simple waves in problems with 0 solutions the step acts as an obstacle for the fluid and physically meaningful solutions can be constructed by interpreting the problem as a partial riemann problems for the homogeneous shallow water system some numerical results are shown where different numerical methods are compared in particular it is shown that in the non uniqueness cases the numerical solutions can converge to one or to the other solution what is the reason that explains the huge differences observed when different numerical methods are applied to the shallow water system with abrupt changes in the bottom moreover problems with zero solutions will be reinterpreted as partial riemann problems for the homogeneous system what will allow us to build a physically solution when one side of the step is wet and the other one is dry we will specify the regions where we can find zero one or two solutions giving the form of the solution when it is possible and giving an alternative when it is not possible

self adjusting grid methods for one dimensional hyperbolic conservation laws it is shown how to automatically adjust the grid to follow the dynamics of the numerical solution of hyperbolic conservation laws the grid motion is determined by averaging the local characteristic velocities of the equations with respect to the amplitudes of the signals the resulting algorithm is a simple extension of many currently popular godunov type methods computer codes using one of these methods can be easily modified to add the moving mesh as an option numerical examples are given that illustrate the improved accuracy of godunov s and roe s methods on a self adjusting mesh

on the cauchy problem for first order discontinuous ordinary differential equations abstract we prove the existence of extremal caratheodory solutions for the initial value problem x t f t x t for a e t 0 1 x 0 0 under weak conditions over f 0 1 r r

unified approach to the analogues of single photon and multiphoton coherent states for generalized bosonic oscillators a large class of bosonic coherent states known in the literature have been constructed in a unified way by shanta et al 1994 it is shown that this method can be easily extended to generalized bosonic oscillator systems

hypergeometric states and their nonclassical properties hypergeometric states which are a one parameter generalization of binomial states of the single mode quantized radiation field are introduced and their nonclassical properties are investigated their limits to the binomial states and to the coherent and number states are studied the ladder operator formulation of the hypergeometric states is found and the algebra involved turns out to be a one parameter deformation of su 2 algebra these states exhibit highly nonclassical properties like sub poissonian character antibunching and squeezing effects the quasiprobability distributions in phase space namely the q and the wigner functions are studied in detail these remarkable properties seem to suggest that the hypergeometric states deserve further attention from theoretical and applicational sides of quantum optics

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

reliability of first order numerical schemes for solving shallow water system over abrupt topography we compare some first order well balanced numerical schemes for shallow water system with special interest in applications where there are abrupt variations of the topography we show that the space step required to obtain a prescribed error depends on the method moreover the solutions given by the numerical scheme can be significantly different if not enough space resolution is used we shall pay special attention to the well known hydrostatic reconstruction technique where it is shown that the effect of large bottom discontinuities might be missed and a modification is proposed to avoid this problem

the uniqueness of the exact solution of the riemann problem for the shallow water equations with discontinuous bottom abstract the riemann problem for the shallow water equations with discontinuous topography is considered in a general case the exact solution of this problem is not unique which complicates the application of an exact riemann solver in numerical methods since it is not clear which solution should be chosen in the present work it is shown that involving an additional physical assumption makes it possible to prove the existence and uniqueness of the solution the assumption is that the discharge at the bottom discontinuity should continuously depend on the initial conditions the proven uniqueness opens up a possibility to use an exact riemann solver for a numerical solution of the shallow water equations with complex discontinuous topography

modelling the transition between fixed and mobile bed conditions in two phase free surface flows in a two phase free surface flow the transition from a mobile bed condition to a fixed bed one and vice versa occurs at a sharp interface across which the relevant system of partial differential equations changes abruptly this leads to the possibility of conceiving a new type of riemann problem rp which we have called composite riemann problem crp where not only the initial constant values of the variables but also the system of equations change from left to right of a discontinuity in this paper we present a strategy for solving a crp by reducing it to a standard rp of a single composite system of equations this can be obtained by combining the two original systems by means of a suitable weighting function namely the erodibility variable and the introduction of an appropriate differential equation for this quantity in this way the crp problem can be analyzed theoretically with standard methods and the features of the solutions can be clearly identified in particular a stationary contact wave is able to correctly describe the sharp transition between mobile and fixed bed conditions a finite volume scheme based on the multiple averages generalized roe approach rosatti and begnudelli 2013 22 was used to numerically solve the fixed mobile crp several test cases demonstrate the effectiveness exact well balanceness and high accuracy of the scheme when applied to problems that fall within the physical range of applicability of the relevant mathematical model

study of quommutators of quantum variables and generalized derivatives a general deformation of the heisenberg algebra is introduced with two deformed operators instead of just one this is generalized to many variables and permits the simultaneous existence of coherent states and the transposition of creation operators

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

a simple difference realization of the heisenberg q algebra a realization of the heisenberg q algebra whose generators are first order difference operators on the full real line is discussed herein the eigenfunctions of the corresponding q oscillator hamiltonian are given explicitly in terms of the q 1 hermite polynomials the nonuniqueness of the measure for these q oscillator states is also studied

a closure independent generalized roe solver for free surface two phase flows over mobile bed several different natural phenomena can be studied in the framework of free surface two phase flows over mobile bed mathematically they can be described by the same set of highly nonlinear hyperbolic nonconservative pdes but they differ in the possible algebraic closure relations these affect significantly the relevant eigenvalues and consequently all finite volume numerical methods based on upwind godunov type fluxes in this work the generalized roe solver introduced in 29 for the case of a specific closure is reformulated in a complete closure independent way this gives the solver a quite general applicability to the class of problems previously mentioned moreover the new method maintains all the desirable features shown by the original one full two dimensionality and exact well balanceness this result is made possible thanks to the development of a novel multiple averages mas approach that allows a straightforward determination of the matrices required by the solver several tests show the capabilities of the proposed numerical strategy

a godunov type scheme for the isentropic model of a fluid flow in a nozzle with variable cross section we present a godunov type scheme for the isentropic model of a fluid flow in a nozzle with variable cross section the model is of nonconservative form making it hard for standard numerical discretizations of the nonconservative term in particular the error for a standard numerical scheme with a usual discretization of the nonconservative term may become larger as the mesh size gets smaller we first re investigate the riemann problem of the model pointing out several interesting properties of the wave curves and establishing specific existence domain for each type of solutions then we incorporate local riemann solutions to build a godunov type scheme for the model the scheme is constructed in subsonic and supersonic regions where the system is strictly hyperbolic tests show that our scheme can capture standing waves so that it is well balanced furthermore tests also show that our godunov type scheme can give a good accuracy for numerical approximations of exact solutions our godunov type scheme can resolve the difficulty of other existing schemes for similar models of fluid flows with nonconservative terms

the construction of the q analogues of the harmonic oscillator operators from ordinary oscillator operators the q analogues of boson operators are constructed from ordinary boson operators by an embedding approach accordingly the q deformed quantum algebras su n q can be obtained straightforwardly from corresponding universal enveloping algebras of lie algebra su n

isospectral susy potentials the authors introduce a new linear transformation in order to construct isospectral potentials within the framework of supersymmetric quantum mechanics under this transformation the adjoint character of the ladder operator is destroyed but with preservation of the energy spectrum leading to some interesting consequences such as the concept of pseudo partnership of the two components connection with the darboux theorem as well as with some other recent methods of construction is analysed

a robust numerical method for approximating solutions of a model of two phase flows and its properties the objective of the present paper is to extend our earlier works on simpler systems of balance laws in nonconservative form such as the model of fluid flows in a nozzle with variable cross section to a more complicated system consisting of seven equations which has applications in the modeling of deflagration to detonation transition in granular materials first we transform the system into an equivalent one which can be regarded as a composition of three subsystems then depending on the characterization of each subsystem we propose a convenient numerical treatment of the subsystem separately precisely in the first subsystem of the governing equations in the gas phase stationary waves are used to absorb the nonconservative terms into an underlying numerical scheme in the second subsystem of conservation laws of the mixture we can take a suitable scheme for conservation laws for the third subsystem of the compaction dynamics equation the fact that the velocities remain constant across solid contacts suggests us to employ the technique of engquist osher s scheme then we prove that our method possesses some interesting properties it preserves the positivity of the volume fractions in both phases and in the gas phase our scheme is capable of capturing equilibrium states preserves the positivity of the density and satisfies the numerical minimum entropy principle numerical tests show that our scheme can provide reasonable approximations for data the supersonic regions but the results are not satisfactory in the subsonic region however the scheme is numerically stable and robust

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

on the q oscillator and the quantum algebra suq 1 1 the authors discuss some problems of the q deformed harmonic oscillator different q bosonisations of the quantum suq 1 1 algebra are given and the corresponding infinite dimensional representations of discrete series are analysed

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

the resonant cases and the riemann problem for a model of two phase flows abstract the resonant cases in the riemann problem for a model of two phase flows with resonance are investigated which complete the construction of riemann solutions the model is given by a nonconservative hyperbolic system of balance laws the phase decomposition method is developed to construct solutions in each phase in a relatively separated way but still glued to each other via the contact discontinuities composite wave curves can be built and intersections of wave curves in each phase plane help to determine various configurations of riemann solutions in particular solutions containing multiple waves propagating with the same shock speed are constructed

constructing a godunov type scheme for the model of a general fluid flow in a nozzle with variable cross section a godunov type scheme for the model of a general fluid flow in a nozzle with variable cross section is presented the model has the form of a nonconservative system of balance laws which poses many challenging questions for study first exact riemann solvers in computing form are described in both subsonic and supersonic regions second the computable exact solutions of local riemann problem are incorporated into a godunov type scheme third the scheme is shown to be well balanced in the sense that it can capture exactly stationary waves finally numerical tests for data belong to both subsonic and supersonic regions are presented these tests show that the scheme has a very fine accuracy especially the scheme can give very good approximations to the exact solutions even in the resonant phenomenon where the solution contains three waves of the same speed

generally deformed oscillator isospectral oscillator system and hermitian phase operator the generally deformed oscillator gdo and its multiphoton realization as well as the coherent and squeezed vacuum states are studied we discuss in particular the gdo depending on a complex parameter q therefore we call it q gdo together with the finite dimensional cyclic representations as a realistic physical system of a gdo the isospectral oscillator system is studied and it is found that its coherent and squeezed vacuum states are closely related to those of the oscillator it is pointed out that starting from the q gdo with q root of unity one can define the hermitian phase operators in quantum optics consistently and algebraically the new creation and annihilation operators of the pegg barnett type phase operator theory are defined by using the cyclic representations and these operators degenerate to those of the ordinary oscillator in the classical limit

uniqueness and existence results for ordinary differential equations we establish some uniqueness and existence results for first order ordinary differential equations with constant signed discontinuous nonlinear parts several examples are given to illustrate the applicability of our work

coherent states on the m sheeted complex plane coherent states on the m sheeted complex plane are introduced and properties like overcompleteness and resolution of the identity are studied operators am am which create and annihilate clusters of m particles are considered and it is shown that the properties of our coherent states with respect to them are analogous to the properties of the ordinary glauber coherent states with respect to a a an extended bargmann representation in the m sheeted complex plane and p and q representations with respect to our coherent states are studied applications of this formalism in the study of hamiltonians that describe m particle clustering are also considered