on the laplace transform of the frechet distribution we calculate exactly the laplace transform of the frechet distribution in the form x 1 exp x 0 0 x for arbitrary rational values of the shape parameter i e for l k with l k 1 2 the method employs the inverse mellin transform the closed form expressions are obtained in terms of meijer g functions and their graphical illustrations are provided a rescaled frechet distribution serves as a kernel of frechet integral transform it turns out that the frechet transform of one sided levy law reproduces the frechet distribution

coherency of su 1 1 barut girardello type and entanglement for spherical harmonics barut girardello coherent states corresponding to the l m and l m integer discrete irreducible representations of su 1 1 lie algebra are calculated by the spherical harmonics ylm their explicit compact forms and also to realize the resolution of the identity their corresponding positive definite measures on the complex plane are obtained in terms of the known functions it is also shown that coherent states of both positive and negative representations separately lead us to construct new representation bases for su 1 1 lie algebra then it is shown that the su 1 1 barut girardello coherent states corresponding to two particles containing the spatial parity symmetries of a bipartite quantum system can be entangled in ten different ways

nonclassical properties of semi coherent quantum states we study the properties of semi coherent quantum states introduced by mathews and eswaran in 1973 establishing relations between them and other families of nonclassical states such as displaced number states and multiphoton states we also analyse the photon number distribution photon statistics the wigner and marginal distribution functions and show the ways for possible further generalizations

comments with reply on the controllability of planar bilinear systems by d e koditschek and k s narendra in the above titled study ibid vol ac 30 p 87 89 jan 1985 two classes of bilinear systems in the plane are examined and it is claimed that necessary and sufficient conditions for complete controllability of both classes are derived the commenter shows that the conditions for one of these classes are only sufficient a counterexample is given the authors briefly review their work and concede that the relevant theorem is incorrect

new q deformed coherent states with an explicitly known resolution of unity we construct a new family of q deformed coherent states zq where 0 q 1 these states are normalizable on the whole complex plane and continuous in their label z they allow the resolution of unity in the form of an ordinary integral with a positive weight function obtained through the analytic solution of the associated stieltjes power moment problem and expressed in terms of one of the two jacksons s q exponentials they also permit exact evaluation of matrix elements of physically relevant operators we use this to show that the photon number statistics for the states is sub poissonian and that they exhibit quadrature squeezing as well as an enhanced signal to quantum noise ratio over the conventional coherent state value finally we establish that they are the eigenstates of some deformed boson annihilation operator and study some of their characteristics in deformed quantum optics

on a decomposition of fuzzy automata the purpose of the present work is to obtain a unique decomposition of a fuzzy automaton possibly with infinite state set as a union of a regular closed decomposable subautomaton and a source splitting subautomaton

necessary and sufficient condition for global controllability of planar affine nonlinear systems in this correspondence we will investigate the global controllability of general planar affine nonlinear systems and present a simple necessary and sufficient condition for global controllability the analysis is carried out in detail which is based on some basic facts in planar topology such as the jordan curve theorem and in the geometrical theory of ordinary differential equations including the poincare bendixson theorem furthermore we will also discuss the global controllability for higher dimensional affine nonlinear system with a triangular like structure

quantum algebraic structures compatible with the harmonic oscillator newton equation we study some of the algebraic structures that are compatible with the quantization of the harmonic oscillator through its newton equation examples of such structures are given they include undeformed and q deformed oscillators as well as the su 2 and the deformed suq 2 lie algebras which appear in a variety of physical models

difference ladder operators for a harmonic schrodinger oscillator using unitary linear lattices the formalism of raising and lowering operators is developed for the difference operator analogue of a quantum harmonic oscillator which acts on functions on a discrete support the grid under consideration is a mixed version of an equidistant lattice and a q linear grid several properties of the grid are described the grids under consideration are referred to by the name unitary linear lattices the ladder difference operators are derived and compared with the continuum situation the arising spectral problems for these operators are dealt by using the theory of bilateral jacobi operators in weighted l2 z spaces eventual applications to mathematical physics and numerical schrodinger theory are briefly discussed

barut girardello and klauder perelomov coherent states for the kravchuk functions the barut girardello and klauder perelomov coherent states for the kravchuk functions are constructed it is shown that the resolution of unity condition is satisfied for both of the coherent states also in the n 1 dimensional hilbert space spanned by the kravchuk eigenstates the appropriate measure and analytic function are obtained

algebraic properties of l fuzzy finite automata fuzzy automata theory on lattice ordered monoids was introduced by li and pedrycz dropping the distributive laws fuzzy finite automata l ffas for short based on a more generalized structure l named a po monoid are presented and investigated from the view of algebra in this paper the notions of strong successor and source operators fuzzy successor and source operators which are shown to be closure operators on certain conditions are introduced and discussed in detail using the weak primary submachines a unique decomposition theorem of a fuzzy finite automaton based on a lattice ordered monoid is obtained taking l as a quantale fuzzy subsystems are proved to be the same as fuzzy submachines of an l ffa in particular intrinsic connections between algebraic properties of l and properties of some operators of an l ffa are discovered it is shown that the join preserving property of fuzzy successor and source operators can be fully characterized by the right and left distributive laws respectively and the idempotence of successor operator can be characterized equivalently by the nonexistence of zero divisors when l is a lattice ordered monoid

a class of vector coherent states defined over matrix domains a general scheme is proposed for constructing vector coherent states in analogy with the well known canonical coherent states and their deformed versions when these latter are expressed as infinite series in powers of a complex variable z in the present scheme the variable z is replaced by matrix valued functions over appropriate domains as particular examples we analyze the quaternionic extensions of the canonical coherent states and the gilmore perelomov and barut girardello coherent states arising from representations of su 1 1 possible physical applications are indicated

generalized coherent states for associated hypergeometric type functions we introduce a right inverse for the annihilation operator which appears in the factorization of associated hypergeometric type operators this makes possible the definition of generalized coherent states for the associated eigenfunctions these generalized coherent states satisfy the relevant properties i e label continuity overcompleteness temporal stability and action identity required to establish a close connection between the quantum and classical formulations of a given physical system

canonical commutation relations on the interval on the hilbert space h l 2 0 l where 0 l is a bounded interval of r1 the domain for the canonical commutation relation ccr and the ccr quasi algebra is constructed it is shown that the bogolubov inequality for a bose gas in a box is fulfilled

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

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

coherent states and hermite polynomials on quaternionic hilbert spaces coherent states similar to the canonical coherent states of the harmonic oscillator labeled by quaternions are established on the right and left quaternionic hilbert spaces on the left quaternionic hilbert space reproducing kernels are established as was claimed by adler and millard j math phys 1997 38 2117 26 it is proved that these coherent states cannot be realized as a group action on a quaternionic hilbert space as an extension of the complex hermite polynomials quaternionic hermite polynomials are defined and these polynomials are associated with an operator as eigenfunctions

new generalized coherent states we construct a new family of boson coherent states using a specially designed function which is a solution of a functional equation de q x dx e q qx with 0 q 1 and e q 0 1 we use this function in place of the usual exponential to generate new coherent states q z from the vacuum which are normalized and continuous in their label z these states allow the resolution of unity and a corresponding weight function is furnished by the exact solution of the associated stieltjes moment problem they also permit exact evaluation of matrix elements of an arbitrary polynomial given as a normally ordered function of boson operators we exemplify this by showing that the photon number statistics for these states is sub poissonian for any q 1 the states q z are squeezed we obtain and discuss their signal to quantum noise ratio the function e q x allows a natural generation of multiboson coherent states of arbitrary multiplicity which is impossible for the usual coherent states for q 1 all the above resul

general displaced su 1 1 number states revisited the most general displaced number states based on the bosonic and an irreducible representation of the lie algebra symmetry of su 1 1 and associated with the calogero sutherland model are introduced here we utilize the barut girardello displacement operator instead of the klauder perelomov counterpart to construct new kind of the displaced number states which can be classified in nonlinear coherent states regime too with special nonlinearity functions they depend on two parameters and can be converted into the well known barut girardello coherent and number states respectively depending on which of the parameters equal to zero a discussion of the statistical properties of these states is included significant are their squeezing properties and anti bunching effects which can be raised by increasing the energy quantum number depending on the particular choice of the parameters of the above scenario we are able to determine the status of compliance with flexible statistics major parts of the

an exactly solvable periodic schrodinger operator the authors explicitly determine the band spectrum of a periodically strongly singular schrodinger operator in l2 r associated with the differential expression d2 dx2 s2 1 4 cos2 x s 2 1 4 sin2 x x epsilon r x epsilon pi z 2 0 s s 1 the corresponding density of states is calculated analytically

generation of coherent states of photon added type via pathway of eigenfunctions we obtain and investigate the regular eigenfunctions of simple differential operators xr dr 1 dxr 1 r 1 2 with the eigenvalues equal to 1 with the help of these eigenfunctions we construct a non unitary analogue of a boson displacement operator which will be acting on the vacuum in this way we generate collective quantum states of the fock space which are normalized and equipped with the resolution of unity with the positive weight functions that we obtain explicitly these states are thus coherent states in the sense of klauder they span the truncated fock space without first r lowest lying basis states 0 1 r 1 these states are squeezed sub poissonian in nature and reminiscent of photon added states in agarwal and tara 1991 phys rev a 43 492

nonlinear semi coherent states their nonclassical features and phase properties semi coherent states semi css were previously introduced and their nonclassical properties studied in this paper we first propose a general formalism for the construction of nonlinear semi css as an extension of semi css and then their explicit form in the number state basis is generally deduced next as some physical appearances of the formalism after choosing two well known nonlinearity functions nonclassical features and quantum statistical properties of the associated states are studied by evaluating quadrature squeezing higher order squeezing and the mandel parameter as well as their phase properties and number and phase squeezing of the introduced states finally the results are compared with the properties of semi css

on the completeness of photon added coherent states we demonstrate explicitly the completeness of photon added coherent states pacss introduced by agarwal and tara agarwal g s and tara k 1991 phys rev a 43 492 and defined up to normalization by m z m 0 1 2 where is the boson creation operator and z are conventional glauber klauder coherent states we find the analytical form of the positive weight function in their resolution of unity by solving the associated stieltjes power moment problem we furnish an example of generation of another set of pacss which are complete

on relationships among fuzzy approximation operators fuzzy topology and fuzzy automata the fuzzy approximation operator associated with an approximation space x r turns out to be a saturated kuratowski fuzzy closure operator on x precisely when the relation r on x is reflexive and transitive it is shown that all the level topologies of the fuzzy topology so obtained on x coincide these observations are then applied to fuzzy automata

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

q graded heisenberg algebras and deformed supersymmetries the notion of q grading on the enveloping algebra generated by products of q deformed heisenberg algebras is introduced for q complex number in the unit disk within this formulation we consider the extension of the notion of supersymmetry in the enveloping algebra we recover the ordinary z2 grading or grassmann parity for associative superalgebra and a modified version of the usual supersymmetry as a specific problem we focus on the interesting limit q 1 for which the arik and coon deformation j math phys 17 524 1976 of the heisenberg algebra allows one to map fermionic modes to bosonic ones in a modified sense different algebraic consequences are discussed

on category of l fuzzy automata coalgebras and dialgebras abstract this paper is towards the study of l fuzzy automata from the categorical point of view where l is a complete residuated lattice we introduce a functor having both the left right adjoint from the category of l fuzzy semiautomata lfsa to the category lftcrl a category of complete residuated lattices corresponding to l fuzzy semiautomata the l fuzzy response map of an l fuzzy automaton leads us to provide a characterization of an l fuzzy regular language interestingly we show that the category lfsa is a category of t 1 coalgebras t 2 t 3 dialgebras moreover we establish a relationship between the category of t 1 coalgebras and the category of t 2 t 3 dialgebras

the controllability of planar bilinear systems recent results concerning the controllability of planar bilinear systems are summarized the results are then used to characterize the controllability behavior of the homogeneous and general bilinear system in r 2

on the completeness of coherent states generated by binomial distribution we demonstrate the completeness of boson and spin coherent states generated by binomial distribution by furnishing the exact analytical form of their respective positive weight functions in resolution of unity these weight functions are solutions of the associated truncated stieltjes power moment problem we elaborate on the non unique character of these solutions

controllability in codimension one abstract local and global controlability of analytic affine control systems with an arbitrary number of controls are studied assuming strong accessibility of and codimension one of the lie algebra t generated by the input vector fields i e dim t p n 1 at every p m controls are assumed to have no a priori bound from the study of the set h where a necessary condition for local controllability at a point is verified and assuming some transversality relations an easy to verify geometric condition is proved h is a submanifold and is locally controllable at every point of h outside a codimension one submanifold a geometric sufficient condition for global controllability on simply connected manifolds is then obtained if every leaf of t intersects the manifold h and some transversality relations including those involved in the local condition are verified is globally controllable

nonlinear conserved charge coherent state and its relation to nonlinear entangled state by suitably averaging over u 1 group action on a two mode nonlinear coherent state we derive the nonlinear conserved charge coherent state based on it a new nonlinear entangled state f g and its deductive state are introduced their completeness relation is proved a new two mode nonlinear squeezing operator in f g representation is obtained which in turn leads to a nonlinear negative binomial state

deformed photon added nonlinear coherent states and their non classical properties in this paper we will try to present a general formalism for the construction of deformed photon added nonlinear coherent states dpancss f m which in a special case lead to the well known photon added coherent state pacs m some algebraic structures of the introduced dpancss are studied and particularly the resolution of the identity as the most important property of generalized coherent states is investigated meanwhile it will be demonstrated that the introduced states can also be classified in the f deformed coherent states with a special nonlinearity function next we will show that these states can be produced through a simple theoretical scheme a discussion on the dpancss with negative values of m i e f m is then presented our approach has the potentiality to be used for the construction of a variety of new classes of dpancss corresponding to any nonlinear oscillator with known nonlinearity function as well as arbitrary solvable quantum system with known discrete non degenerate spectrum finally after applying the formalism to a particular physical system known as the poschl teller p t potential and the nonlinear coherent states corresponding to a specific nonlinearity function some of the non classical properties such as the mandel parameter second order correlation function in addition to first and second order squeezing of the corresponding states will be investigated numerically

lie algebras for systems with mixed spectra i the scattering poschl teller potential starting from an n body quantum space we consider the lie algebraic framework where the poschl teller hamiltonian 1 2 2 c sech2 s csch2 is the single sp 2 r casimir operator the spectrum of this system is mixed it contains a finite number of negative energy bound states and a positive energy continuum of free states it is identified with the clebsch gordan series of the d d representation coupling the wave functions are the sp 2 r clebsch gordan coefficients of that coupling in the parabolic basis using only lie algebraic techniques we find the asymptotic behavior of these wave functions for the special pure trough potential s 0 we derive thus the transmission and reflection amplitudes of the scattering matrix

photon added coherent states as nonlinear coherent states the states m defined as up to a normalization constant and where m is a non negative integer are shown to be the eigenstates of where is a nonlinear function of the number operator the explicit form of is constructed the eigenstates of this operator for negative values of m are introduced the properties of these states are discussed and compared with those of the state m the eigenstates corresponding to the positive and negative values of m are shown to be the result of nonunitarily deforming the number states m and 0 respectively

local controllability of nonlinear systems abstract the local controllability of control systems with an arbitrary number of controls is considered first on an open set and then at a given point necessary conditions are derived concerning the lie algebra t generated by the input vector fields and applied to gradient systems the main results are a geometric sufficient condition for local controllability at a point and an equivalent condition based on the computation of lie brackets assuming t to be n 1 dimensional

mittag leffler coherent states we create a family of boson coherent states using the functions of mittag leffler ml e z 0 and their generalizations e z 0 instead of exponentials these states are shown to satisfy the usual requirements of normalizability continuity in the label and the resolution of unity with a positive weight function this last quantity is found for arbitrary 0 as a solution of an associated stieltjes moment problem in addition for m 1 2 3 and 1 corresponding to em z we propose and analyse special q deformations 0 q1 of the functions em z which serve as a tool to define q deformed coherent states of ml type we provide the expressions for expectation values of physical quantities for all the above states we discuss physical properties of these states noting that they are squeezed the ml coherent states are sub poissonian in nature whereas the q deformed ml states can be sub and super poissonian depending on q all these states are shown to be eigenstates of deformed boson operators whose commutation relations are given

new p q μ ν f deformed states we construct a new family of deformed states these states are normalizable on the whole complex plane and continuous in their label z under fixed values of parameters they allow the resolution of unity in the form of an ordinary integral with a positive weight function obtained through the analytic solution of the associated stieltjes power moment problem in addition to the mathematical characteristics the quantum statistical properties of these states are analytically and numerically discussed in detail in the context of conventional as well as deformed quantum optics we find that for non deformed photons the states exhibit quadrature squeezing and their photon number statistics is sub poissonian on the other hand for deformed photons the states are super poissonian and no quadrature squeezing occurs

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

on the controllability of piecewise linear hypersurface systems this paper investigates the global controllability of piecewise linear hypersurface systems which are defined as control systems that are subject to affine dynamics on each of the components of a finite polyhedral partition various new tools are developed for the study of the problem including a classification of the facets of the polyhedra in the partition necessary and sufficient conditions for complete controllability are obtained via the study of a suitably defined controllability connection matrix of polyhedra

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

n dimensional controllability with n 1 controls let m be a connected real analytic n dimensional manifold f g 1 g n 1 be complete real analytic vector fields on m which are linearly independent at some point of m and u 1 u n 1 be real valued controls consider the controllability of the system dot x t f x t sum min i 1 max n 1 u i t g i x t x 0 x 0 in m necessary and sufficient conditions are given so that this system is controllable on any simply connected domain d contained in m on which g 1 g n 1 are linearly independent these conditions depend on the computation of lie brackets at those points where f g 1 g n 1 are linearly dependent

on factorized l fuzzy automaton and its l fuzzy topological characterization abstract this paper is towards the study of l fuzzy automata via theory of factorizations where l is a complete residuated lattice we study the concept of factorization of l fuzzy sets and factorization of collection of l fuzzy sets such factorizations are used i to study the concept of minimal l fuzzy automaton and ii to introduce l fuzzy topologies for the study of concepts associated with an l fuzzy automaton specifically we introduce the notion of factorized l fuzzy automaton corresponding to a given l fuzzy automaton and study the minimality of such automaton further we associate l fuzzy topologies for factorized l fuzzy automaton and use these to characterize some algebraic concepts

photon added squeezed vacuum one photon state as an even odd nonlinear coherent state we show that the photon added squeezed vacuum a m s z 0 and the photon added squeezed one photon state a m s z 1 where m is a non negative integer may be regarded as even and odd nonlinear coherent states respectively to achieve this we derive an operator valued function f n m of the number operator n a a such that a m s z i i 0 1 are eigenstates of f n m a 2 based on this and using the unified method developed by shanta et al we find that a m s z i can be equivalently expressed in exponential forms the eigenstates of f n m a 2 are also constructed and their nonclassical features are studied in detail

local controllability along a reference trajectory abstract local controllability along a reference trajectory of analytic and smooth affine single input control systems without any a priori bounds on the control is considered and a geometric proof of a version of the hermes conjecture is given

reachability of a set of facets for linear affine systems with n 1 inputs this note provides new necessary and sufficient conditions for an n dimensional linear affine system with n 1 inputs to reach an exit facet or set of exit facets of a simplex the conditions reduce the original np hard necessary and sufficient conditions to a set of at most n lp problems

nth even order minimum uncertainty products this paper considers the problem of finding the quantum states that minimize the products of the even nth order fluctuation of two canonically conjugate operators the problem is first attacked in an abstract form and an equation derived for the desired states a consideration of the n 2 case then leads to a connection with the new concept of squeezed states of the electromagnetic field and the usual exact solution involving the coherent state the concept of higher order squeezing is touched on to motivate the further discussion the cases n 4 6 and 8 are then taken up and approximate solutions to them found via a new numerical technique during these calculations it is noted that only the first few terms in the expansion in number states figure in the solution this observation is then exploited to find an approximate closed solution to the problem valid for all n

the construction of some important classes of generalized coherent states the nonlinear coherent states method considering some important classes of generalized coherent states known in the literature we demonstrated that all of them can be created via conventional methods i e the lowering operator eigenstate and the displacement operator techniques using the nonlinear coherent states approach as a result we obtained a unified method to construct a large class of coherent states which have already been introduced by different prescriptions

q ν deformation of generalized basic hypergeometric states we provide with a q deformation of the generalized hypergeometric coherent states defined such that the normalization function is given by generalized basic hypergeometric functions these states are eigenstates of suitably defined deformed lowering operators we study the domain of convergence of the corresponding normalization function on the basis of these states we investigate generalized basic hypergeometric husimi distributions and corresponding phase distributions as well as new analytic basis representations of arbitrary quantum states in bargmann and hardy spaces the quantum statistical properties of the states such as photon counting statistics and quadrature squeezing are analytically and numerically discussed in the framework of conventional quantum optics

new physics in landau levels the most general displaced number coherent states based on the heisenberg su 2 and su 1 1 lie algebras symmetries are constructed they depend on two parameters and can be converted into the well known photon added two variable glauber coherent states and displaced number states respectively depending on which of the parameters is equal to zero the relations of the weyl heisenberg algebra guarantee a corresponding resolution of the identity conditions a discussion of the statistical properties of these states is included significant are their squeezing properties which can be raised by increasing the energy and angular momentum quantum numbers n and m the maximum squeezing is obtained for bext 0 depending on the particular choice of parameters in the above scenarios we are able to determine the status of compliance with poissonian statistics in the limiting case we obtain a major result about the non classical properties of the glauber minimum uncertainty coherent states in other words in addition to the requirement to minimize uncertainty conditions they carry non classical features too finally a theoretical framework is proposed to generate them

global transformations of nonlinear systems recent results have established necessary and sufficient conditions for a nonlinear system of the form dot x t f x t u t g x t with f 0 0 to be locally equivalent in a neighborhood of the origin in rnto a controllable linear system we combine these results with several versions of the global inverse function theorem to prove sufficient conditions for the transformation of a nonlinear system to a linear system in doing so we introduce a technique for constructing a transformation under the assumptions that g ldot f dotg ad n 1 f ldotg span an n dimensional space and that g ldot f ldot g ad n 2 f ldotg is an involutive set

spherical harmonics coherent states constructed by the second lowest and second highest bases of su 1 1 lie algebra the second lowest and second highest bases of the discrete positive and negative irreducible representations of su 1 1 lie algebra via spherical harmonics are used to construct generalized coherent states depending on whether the representation label is an even or odd integer each of the new coherent states is separated into two different classes they are constituted by appropriate superpositions of the increasing and decreasing infinite sequences with respect to the m index of the spherical harmonics ym2j m m j 1 and ym2k m 1 m k 2 and converge to the known functions also the non oscillating measures to realize the resolution of the identity condition on the unit disk are calculated

the truncated stieltjes moment problem solved by using kernel density functions in this work the problem of the approximate numerical determination of a semi infinite supported continuous probability density function pdf from a finite number of its moments is addressed the target space is carefully defined and an approximation theorem is proved establishing that the set of all convex superpositions of appropriate kernel density functions kdfs is dense in this space a solution algorithm is provided based on the established approximate representation of the target pdf and the exploitation of some theoretical results concerning moment sequence asymptotics the solution algorithm also permits us to recover the tail behavior of the target pdf and incorporate this information in our solution a parsimonious formulation of the proposed solution procedure based on a novel sequentially adaptive scheme is developed enabling a very efficient moment data inversion the whole methodology is fully illustrated by numerical examples

a deformed oscillator with coulomb energy spectrum a deformed oscillator with eigenvalues equal to the eigenvalues of the schrodinger equation with the coulomb potential is constructed the deformed oscillator algebra has a polynomial realization and the associate deformed operations of integration and differentiation are studied

generalized deformed oscillator and nonlinear algebras the harmonic oscillator is deformed arbitrarily and the properties of the deformed oscillator algebra are studied the eigenstates and eigenvalues of the deformed oscillator are calculated this generalized deformed oscillator algebra is used to create nonlinear deformation of the classical su 2 algebra the deformed boson realizations of an arbitrary nonlinear su 2 algebra are calculated the algebra of the q deformed oscillator is a special case of the generalized deformed oscillator algebra

coherent states for nonlinear harmonic oscillator and some of its properties a one dimensional nonlinear harmonic oscillator is studied in the context of generalized coherent states we develop a perturbative framework to compute the eigenvalues and eigenstates for the quantum nonlinear oscillator and construct the generalized coherent states based on gazeau klauder formalism we analyze their statistical properties by means of mandel parameter and second order correlation function our analysis reveals that the constructed coherent states exhibit super poissonian statistics moreover it is shown that the coherent states mimic the phenomena of quantum revivals and fractional revivals during their time evolution the validity of our results has been discussed in terms of various parametric bounds imposed by our computational scheme

on global controllability of planar affine nonlinear systems with a singularity this paper is concerned with the global controllability of planar affine nonlinear systems with a singular point by using some recent developed methods a necessary and sufficient condition is obtained which can also be viewed as a generalization of the corresponding result in the book by nikitin s nikitin global controllability and stabilization of nonlinear systems world scientific publishing co pte ltd singapore 1994

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

dynamical symmetry approach to periodic hamiltonians we show that dynamical symmetry methods can be applied to hamiltonians with periodic potentials we construct dynamical symmetry hamiltonians for the scarf potential and its extensions using representations of su 1 1 and so 2 2 energy bands and gaps are readily understood in terms of representation theory we compute the transfer matrices and dispersion relations for these systems and find that the complementary series plays a central role as well as nonunitary representations

new nonlinear coherent states based on hypergeometric type operators the main goal of this paper is to present an alternative method to construct new kinds of nonlinear coherent states to do this we first establish a class of hypergeometric type of generalized displacement operators 1fr 0 0 1 r 1 za act on the vacuum state of the harmonic oscillator and generate normalized quantum states of the fock space which admit a resolution of the identity through a positive definite measure on the complex plane furthermore realization of the compact form of these states as functions of the position coordinate x for r 2 leads to a generating function of the hermite polynomials in terms of the modified bessel function finally studying some statistical characters reveals that they have indeed non classical features such as squeezing an anti bunching effect and sub poissonian statistics too

the quantum mechanical schrodinger picture of a q oscillator a q deformed version of standard quantum mechanics in the coordinate schrodinger picture is obtained by replacing the ordinary coordinate derivative by the so called q discrete derivative as the representative of the momentum operator the chosen q discrete derivative is symmetric with respect to the exchange of q and q 1 under the usually adopted assumptions a q deformed schrodinger equation is derived for a harmonic oscillator the complete set of eigenfunctions can be explicitly constructed as special q functions and the corresponding energy eigenvalues are identical to those obtained by biedenharn in his pioneering work 1989 this q deformed oscillator exhibits a rich novel structure including dynamical symmetry and in the limit q to 1 it reveals some hitherto unknown features of the harmonic oscillator eigenfunctions

one dimensional schrodinger operators with interactions singular on a discrete set on etudie le caractere auto adjoint des operateurs de schrodinger sur y u j i x j y j ou on suppose y j x j 1

generalized deformed oscillator corresponding to the modified poschl teller energy spectrum a generalized deformed oscillator with eigenvalues equal to the eigenvalues of the schrodinger equation with the modified poschl teller potential is constructed for special values of the potential depth the deformed oscillator algebra has a finite dimensional irreducible representation the polynomial representation and the associate deformed operations of integration and differentiation are studied the results of this study are general and they can be applied directly to the case of the q deformed oscillator with q being a root of unity

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