quantum algebraic description of the pairing correlations in a single j nuclear shell pairing in a single j shell is described in terms of two q oscillators one describing the j 0 fermion pairs and the other corresponding to the j not 0 pairs the deformation parameter t ln q being related to the inverse of the size of the shell using these two oscillators an suq 2 algebra is constructed while a pairing hamiltonian giving the correct energy eigenvalues up to terms of first order in the small parameter can be written in terms of the casimir operators of the algebras appearing in the uq 2 contains implies uq 1 chain thus exhibiting a quantum algebraic dynamical symmetry the additional terms introduced by the q oscillator are found to improve the agreement with the experimental data for the neutron pair separation energies of the sn isotopes with no extra parameter introduced

non variational effects in a domain wall model equation abstract we study in two dimensions a ginzburg landau equation for a complex amplitude with broken phase invariance the addition of non variational terms breaks the chiral symmetry of the equation and leads to striking effects a non variational term is provided by an external complex field with time dependence our results which are for two dimensional systems can be phrased in the language of domain walls we investigate how these walls move when a weak complex magnetic field is applied there occurs spiral type behavior around stationary points where the amplitude is zero and there exists a critical radius above which circular domains grow

the clebsch gordan coefficients for the two parameter quantum algebra sup q 2 in the lowdin shapiro approach the structure of the irreducible representations of the two parameter quantum algebra sup q 2 is studied the projection operators for this algebra are constructed in the lowdin shapiro form the explicit analytical expressions for the sup q 2 clebsch gordan coefficients are obtained with the help of these projection operators there are clear perspectives to elaborate the theory of tensor operators universal r matrix 6j 9j symbols etc for the sup q 2 algebra using the same tools

a p q oscillator realization of two parameter quantum algebras it is noted that the study of a quantum algebra sup q 2 with two independent deformation parameters p q leads to a p q oscillator realization for it the analysis is extended to the p q analogues of su 1 1 osp 2 1 and the centreless virasoro algebra the standard single parameter q deformations are obtained in the limit p q

a two parameter deformation of the jaynes cummings model path integral representation a two parameter p q deformation of the jaynes cummings model is obtained using a recently developed p q deformed oscillator in the rotating wave approximation rwa the dynamical symmetry of the model is the quantum superalgebra up q 1 mod 1 the partition function of the model is obtained as a path integral over generalized perelomov coherent states corresponding to the quantum algebra up q 1 mod 1 the complete spectrum of the model is extracted for both the case when the coupling constants are grassman valued and when they are c number valued it is noted that a relaxation of the rwa extends the dynamical symmetry to the quantum superalgebra ospp q 2 mod 2

algebraic structure of green s ansatz and its q deformed analogue the algebraic structure of green s ansatz 1953 is analysed in such a way that its generalization to the case of q deformed para bose and para fermi operators becomes evident to this end the underlying lie super algebraic properties of the parastatistics are essentially used

finite dimensional representations of the quantum analog of the enveloping algebra of a complex simple lie algebra let g be a complex simple lie algebra we show that whent is not a root of 1 all finite dimensional representations of the quantum analogu t g are completely reducible and we classify the irreducible ones in terms of highest weights in particular they can be seen as deformations of the representations of the classical u g

generalized boson algebra and its entangled bipartite coherent states starting with a given generalized boson algebra known as the bosonized version of the quantum super hopf algebra we employ the hopf duality arguments to provide the dually conjugate function algebra with both the hopf algebras being finitely generated we produce a closed form expression of the universal matrix that caps the duality and generalizes the familiar exponential map relating a lie algebra with its corresponding group subsequently using an inverse mellin transform approach the coherent states of single node systems subject to the symmetry are found to be complete with a positive definite integration measure the nonclassical coalgebraic structure of the algebra is found to generate naturally entangled coherent states in bipartite composite systems

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

generalized heisenberg algebras and fibonacci series we have constructed a heisenberg type algebra generated by the hamiltonian the step operators and an auxiliary operator this algebra describes quantum systems having eigenvalues of the hamiltonian depending on the eigenvalues of the two previous levels this happens for example for systems having the energy spectrum given by a fibonacci sequence moreover the algebraic structure depends on the two functions f x and g x when these two functions are linear we classify analysing the stability of the fixed points of the functions the possible representations for this algebra

stability boundary and collisions of two dimensional solitons in pt symmetric couplers with the cubic quintic nonlinearity we introduce one and two dimensional 1d and 2d models of parity time mathcal pt symmetric couplers with the mutually balanced linear gain and loss applied to the two cores and cubic quintic cq nonlinearity acting in each one the 2d and 1d models may be realized in dual core optical wave guides in the spatiotemporal and spatial domains respectively stationary solutions for mathcal pt symmetric solitons in these systems reduce to their counterparts in the usual coupler the most essential problem is the stability of the solitons which become unstable against symmetry breaking with the increase of the energy norm and retrieve the stability at still larger energies the boundary value of the intercore coupling constant above which the solitons are completely stable is found by means of an analytical approximation based on the cw zero dimensional counterpart of the system the approximation demonstrates good agreement with numerical findings for the 1d and 2d solitons numerical results for the stability limits of the 2d solitons are obtained by means of the computation of eigenvalues for small perturbations and verified in direct simulations although large parts of the soliton families are unstable the instability is quite weak collisions between 2d solitons in the mathcal pt symmetric coupler are studied by means of simulations outcomes of the collisions are inelastic but not destructive as they do not break the mathcal pt symmetry

stochastic scheduling on parallel machines subject to random breakdowns to minimize expected costs for earliness and tardy jobs this paper addresses a stochastic scheduling problem in which a set of independent jobs are to be processed by a number of identical parallel machines under a common deadline each job has a processing time which is a random variable with an arbitrary distribution each machine is subject to stochastic breakdowns which are characterized by a poisson process the deadline is an exponentially distributed random variable the objective is to minimize the expected costs for earliness and tardiness where the cost for an early job is a general function of its earliness while the cost for a tardy job is a fixed charge optimal policies are derived for cases where there is only a single machine or are multiple machines the decision maker can take a static policy or a dynamic policy and job preemptions are allowed or forbidden in contrast to their deterministic counterparts which have been known to be np hard and are thus intractable from a computational point of view we find that optimal solutions for many cases of the stochastic problem can be constructed analytically

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

on the clebsch gordan coefficients for the two parameter quantum algebra su 2 p q we show that the clebsch gordan coefficients for the su 2 p q algebra depend on a single parameter q square root pq contrary to the explicit calculation of smirnov and wehrhahn 1992

q analogues of the parabose and parafermi oscillators and representations of quantum algebras deformations of the one dimensional parabose oscillators are presented they are shown to provide fock representations of the quantum sp q 2 algebra and ospq 1 2 superalgebra the representations of suq 2 are used to define the q analogues of the parafermi oscillators

a note on p q oscillators and bibasic hypergeometric functions the authors examine the relation between the representation theory of a two parameter deformation of the oscillator algebra and certain bibasic laguerre functions and polynomials

an analogue of the unitary displacement operator for the q oscillator using the concept of a non standard hilbert space over the quantum complex plane recently introduced by kowalski et al 1993 we construct a unitary q analogue of the weyl displacement operator we investigate the q displaced vacuum states and show that they exhibit properties analogous to coherent states in the undeformed theory they are however distinct from any q coherent states previously found in the literature

energy spectrum potential and inertia functions of a generalized f oscillator we consider a generalized four parameter q algebra aa q a a q n n a a n a a associating with operators a and a the nonlinear f oscillator operators defined in terms of the usual harmonic oscillator operators as a af n and a f n a where a and a are operators of the weyl heisenberg algebra and n a a the function f n is determined from the commutation relations we write the hamiltonian for the free f oscillator and obtain its energy spectrum besides expressing the hamiltonian in terms of coordinate and momentum we determine the potential and inertia functions coordinate dependent mass and analyse their behaviour by varying the parameters

double squeezing in generalized q coherent states using a generalization of the q commutation relations we develop a formalism in which we define generalized q bosonic operators this formalism includes both types of the usual q deformed bosons as special cases the coherent states of these operators show interesting and novel noise reduction properties including simultaneous squeezing in both field components unlike the conventional case in which squeezing is permitted in only one component this also contrasts with the usual quantum group deformation which also only permits one component squeezing

representations of two parameter quantum algebras and p q special functions abstract in this paper the connection between p q analogue of special functions and representations of certain two parameter quantum algebras has been developed the realizations of the representations of these quantum algebras are in terms of p q derivative operators the matrix elements of these representations are computed in terms of the generalized p q hypergeometric series this leads to the developments in the theory of p q special functions

on up q gl 2 and a p q virasoro algebra the quantum algebra up q gl 2 with two independent deformation parameters p q is studied and in particular its universal r matrix is constructed using reshetikhin s method a contraction procedure then leads to the p q deformed heisenberg algebra up q h 1 and its universal r matrix using a sugawara construction employing an infinite number of copies of these heisenberg modes a p q deformed virasoro algebra is obtained the closure property of the p q virasoro algebra necessitates two parameters alpha beta for the generators lm alpha beta while the parameter alpha may be taken as an integer the parameter beta is continuous on a complex path and imparts an integral equation structure to the p q deformed virasoro algebra

on the new algebra related to the non standard r matrix the authors demonstrate that the new algebra associated to the non standard r matrix investigated previously by fei and yue 1993 is related to the su 2 q algebra by a simple transformation criteria which identify equivalent quantum algebra are given

on the combinatorics of normal ordering bosonic operators and deformations of it recently some combinatorial aspects for the normal ordering of powers of arbitrary monomials of boson operators were discussed in particular it was shown that the resulting formulae lead to generalizations of the usual bell and stirling numbers in this paper these considerations are generalized to the q deformed case in particular it is shown that the simplest example of this generalization leads to q deformed lah numbers the connection between generalized stirling and bell numbers and matrix elements of the above mentioned operators with respect to the usual fock space basis and coherent states is discussed

proof of quasi adaptivity for the m measurement feedback class of stochastic control policies it is shown that the m measurement feedback mm policy for nonlinear stochastic control performs as well or better than the open loop optimal policy and hence becomes one of only a few suboptimal policies presently known to be quasi adaptive in the sense of witsenhausen

stirling number identities interconsistency of q analogues q analogues of stirling number identities are formulated and the interconsistency among the q analogues of the stirling numbers and of the binomial coefficients is investigated the close relation with the normal ordering problem for arik coon type q bosons plays a central role in the derivations presented

nondistributive algebraic structures derived from nonextensive statistical mechanics we propose a two parametric nondistributive algebraic structure that follows from q q logarithm and q q exponential functions properties of generalized q q operators are analyzed we also generalize the proposal into a multiparametric structure generalization of logarithm and exponential functions and the corresponding algebraic operators all n parameter expressions recover n 1 generalization when the corresponding qn 1 nonextensive statistical mechanics has been the source of successive generalizations of entropic forms and mathematical structures in which this work is a consequence

unified p q α β ν γ deformed oscillator algebra irreducible representations and induced deformed harmonic oscillator a new deformed canonical commutation relation generalizing various known deformations is defined together with its structure function of deformation then the related irreducible representations are characterized and classified finally the discrete spectrum of the corresponding deformed harmonic oscillator hamiltonian is investigated and discussed

a solution of the generalised non linear schrodinger equation the author first presents a non linear schrodinger equation that describes wave propagation in fluids and plasmas with sharp boundaries and dissipation then the author shows that an exact solution can be found

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

a forward method for optimal stochastic nonlinear and adaptive control a computational approach is taken to solve the optimal partially observed nonlinear stochastic control problem the approach is to systematically solve the stochastic dynamic programming equations forward in time using a nested stochastic approximation technique although computationally intensive this provides a straightforward numerical solution for this class of problems and provides an alternative to the usual curse of dimensionality associated with solving the dynamic programming equation backwards in time in particular the curse is seen to take a new form where the amount of computation depends on the amount of uncertainty in the problem and the length of the horizon as a matter of more practical interest it is shown that the cost degrades monotonically as the complexity of the algorithm is reduced this provides a strategy for suboptimal control with clear performance computation trade offs a numerical study focusing on a generic optimal stochastic adaptive control example is included to demonstrate the feasibility of the method

parabosons virasoro type algebras and their deformations two parameter p q deformation of a parabosonic algebra underlying the two particle calogero model is considered the fock space representation bargmann fock representation coherent states spectrum generating algebra and a hidden supersymmetry are discussed the paraboson algebra induces a centreless virasoro type algebra with a doubling of the space of generators a two parameter deformation of this virasoro type algebra is studied

on p q μ ν ϕ1 ϕ2 generalized oscillator algebra and related bibasic hypergeometric functions this paper provides the generalization of the work by floreanini et al 1993 j phys a math gen 26 611 4 who generated bibasic hypergeometric functions from p q oscillators we consider a six parameter deformed oscillator algebra realized from the p q deformed boson oscillators we build the corresponding fock space representation in an infinite dimensional subspace of the hilbert space of a harmonic oscillator we also discuss the properties of a discrete spectrum of the hamiltonian of the deformed harmonic oscillator corresponding to this system we then define a realization of the deformed algebra in terms of a generalized derivative and investigate the relation between this representation and generalized bibasic laguerre functions and polynomials

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

on models of certain p q algebra representations the p q oscillator algebra we construct one and two variable models of the p q oscillator algebra in terms of ladder operators by using two p q analogs of the exponential function mapping we show that matrix elements of these operators can be represented in terms of p q special functions further we exhibit that these matrix elements satisfy certain biorthogonality relations

some approximation results by p q analogue of bernstein stancu operators in this paper we introduce a new analogue of bernstein stancu operators based on p q integers which we call as p q bernstein stancu operators we study approximation properties for these operators based on korovkin s type approximation theorem and also study some direct theorems furthermore we give comparisons and some illustrative graphics for the convergence of operators to some function

breathing and randomly walking pulses in a semilinear ginzburg landau system abstract we consider a system consisting of the cubic complex ginzburg landau equation which is linearly coupled to an additional linear equation the model is known in the context of dual core nonlinear optical fibers with one active and one passive cores by means of systematic simulations we find new types of stable localized excitations which exist in the system in addition to the earlier found stationary pulses the new localized excitations include pulses existing on top of a small amplitude background that may be regular or chaotic above the threshold of instability of the zero solution and breathers into which stationary pulses are transformed through a hopf bifurcation below the aforementioned threshold a sharp border between stable stationary pulses and breathers which precludes their coexistence is identified stable bound states of two breathers with a phase shift 1 2 between their internal vibrations are found too above the threshold the pulse is standing if the background oscillations are regular if the background is chaotic the pulse is randomly walking with the increase of the system s size additional randomly walking pulses are spontaneously generated the random walk of different pulses in a multi pulse state is partly synchronized due to their mutual repulsion at a large overcriticality the multi pulse state goes over into a spatiotemporal chaos

the cubic complex ginzburg landau equation for a backward bifurcation abstract the one dimensional complex ginzburg landau equation cgle with a destabilizing cubic nonlinearity and no saturating higher order terms has stable bounded solutions we consider a simple pedagogical model exhibiting qualitatively the mechanism which may suppress the divergence of the solutions then we investigate the functional form of the blow up collapse solutions immediately before the divergence from this analysis we find analytic boundaries for the existence of collapse solutions in the parameter space of the cgle a comparison with numerical simulations demonstrates that for parameters without collapse solutions the solutions of the cgle remain bounded for all times finally we discuss the implications of our results for the solutions of the cgle when saturating higher order terms are included

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

deformation of the askey wilson algebra with three generators a most general algebra with three generators and with ladder and duality properties gaw 3 is considered it is shown that the obtained algebra corresponds to p q deformation of the askey wilson algebra for the new algebra gaw 3 the ladder representation is constructed and the overlap problem is discussed

three dimensional quadratic algebras some realizations and representations four classes of three dimensional quadratic algebra of the type q0 q q q q aq02 bq0 c where a b c are constants or central elements of the algebra are constructed using a generalization of the well known two mode bosonic realizations of su 2 and su 1 1 the resulting matrix representations and single variable differential operator realizations are obtained some remarks on the mathematical and physical relevance of such algebras are given

on models of certain p q algebra representations the quantum euclidean algebra e p q 2 abstract we construct one and two variable models of the p q algebra e p q 2 in terms of ladder operators we define two p q analogues of the exponential function mapping and using these show that matrix elements of these operators can be represented in terms of p q series further we exhibit that these matrix elements satisfy certain biorthogonality relations

on the representations of glp q 2 glp q 1 mod 1 and non commutative spaces explicit realizations of the quantum groups glp q 2 and glp q 1 mod 1 corresponding to unimodular values of the deformation parameters p and q are given in terms of the canonically conjugate x p operators using the heisenberg weyl commutation relations matrix representations are also discussed some observations are made on similar realizations of the non commutative coordinate spaces on which the quantum groups act as endomorphisms

a holstein primakoff and a dyson realization for the quantum algebra the known holstein primakoff and dyson realizations of the lie algebra in terms of bose operators are generalized to the class of the quantum algebras for any n it is shown how the elements of can be expressed via n pairs of bose creation and annihilation operators

on boson algebras as hopf algebras certain types of generalized undeformed and deformed boson algebras which admit a hopf algebra structure are introduced together with their fock type representations and their corresponding r matrices it is also shown that a class of generalized heisenberg algebras including those underlying physical models such as that of calogero sutherland is isomorphic with one of the types of boson algebra proposed and can be formulated as a hopf algebra

relations for clebsch gordan and racah coefficients in suq 2 and yang baxter equations relations are exploited among clebsch gordan cg and racah coefficients in the algebra suq 2 known as a deformation of su 2 these are used to show that the yang baxter yb relation for the irf interaction round a face model results from one of the symmetry relations for the 9 j symbol specific to suq 2 and that in an asymptotic limit this yb relation becomes the yb relation for the two dimensional vertex model the racah coefficient which has a particularly simple dependence on q is efficiently used such that an asymptotic limit of the racah coefficient is the cg coefficient and another limit gives the factorized s matrix of the vertex model

characterization of mathcal r p q deformed rogers szego polynomials associated quantum algebras deformed hermite polynomials and relevant properties this paper addresses a new characterization of deformed rogers szego polynomials by providing their three term recurrence relation and the associated quantum algebra built with corresponding creation and annihilation operators the whole construction is performed in a unified way generalizing all known relevant results which are straightforwardly derived as particular cases continuous deformed hermite polynomials and their recurrence relation are also deduced novel relations are provided and discussed

boson para boson and boson fermion representations of some graded lie algebras some graded lie algebras with the lie algebras so 3 so 2 1 so 4 so 3 1 and so 2 2 as their bose sectors are realized in terms of bosons para bosons and certain bilinear combinations of bosons and fermions

recursively minimally deformed oscillators a recursive deformation of the boson commutation relation is introduced each step consists of a minimal deformation of a commutator a a fk n into a a qk 1 fk n where stands for the set of deformation parameters that fk depends on followed by a transformation into the commutator a a fk 1 qk 1 n to which the deformed commutator is equivalent within the fock space starting from the harmonic oscillator commutation relation a a 1 we obtain the arik coon and macfarlane biedenharn oscillators at the first and second steps respectively followed by a sequence of multiparameter generalizations several other types of deformed commutation relations related to the treatment of integrable models and to parastatistics are also obtained the generic form consists of a linear combination of exponentials of the number operator and the various recursive families can be classified according to the number of free linear parameters involved that depends on the form of the initia

consistent multiparameter quantisation of gl n the author describes a manifold of quantum group structures on the vector space of the universal enveloping algebra of gl n and on its dual the space of polynomials in n2 variables the dimension of the manifold is n2 n 2 2

cole hopf like transformation for schrodinger equations containing complex nonlinearities we consider systems which conserve the particle number and are described by schrodinger equations containing complex nonlinearities in the case of canonical systems we study their main symmetries and conservation laws we introduce a cole hopf like transformation both for canonical and noncanonical systems which changes the evolution equation into another one containing purely real nonlinearities and reduces the continuity equation to the standard form of the linear theory this approach allows us to treat in a unifying scheme a wide variety of canonical and noncanonical nonlinear systems some of them already known in the literature

generalized q fermion oscillators and q coherent states the algebra of q fermion operators developed earlier by two of the present authors is re examined it is shown that these operators represent particles that are distinct from usual spacetime fermions except in the limit q 1 it is shown that it is possible to introduce generalized q oscillators defined for infinity q or 1 in the range infinity q 0 these coincide with the q boson operators and for 0 q or 1 they coincide with q fermions the ordinary bosons and fermions may be identified with the limits q 1 and 1 respectively generalized q fermion coherent states are constructed by utilizing a nonlinear shift automorphism of the algebra of q fermion operators these are compared with the coherent states defined as eigenstates of annihilation operator matrix elements of the shift operator in the fock space basis are evaluated

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

two parameter deformation of virasoro algebra in this paper the two parameter deformation of virasoro algebra is derived two parameter deformation of central charge is also obtained the operator product expansion for p q deformed virasoro algebra is derived

q μ and p q ζ exponential functions rogers szegő polynomials and fourier gauss transform from the realization of q oscillator algebra in terms of generalized derivative we compute the matrix elements from deformed exponential functions and deduce generating functions associated with rogers szeg polynomials as well as their relevant properties we also compute the matrix elements associated with the p q oscillator algebra a generalization of the q one and perform the fourier gauss transform of a generalization of the deformed exponential functions

on the generation of dispersive shock waves abstract we review various methods for the analysis of initial value problems for integrable dispersive equations in the weak dispersion or semiclassical regime some methods are sufficiently powerful to rigorously explain the generation of modulated wavetrains so called dispersive shock waves as the result of shock formation in a limiting dispersionless system they also provide a detailed description of the solution near caustic curves that delimit dispersive shock waves revealing fascinating universal wave patterns

thermodynamic equilibrium and its stability for microcanonical systems described by the sharma taneja mittal entropy it is generally assumed that the thermodynamic stability of equilibrium states is reflected by the concavity of entropy we inquire in the microcanonical picture about the validity of this statement for systems described by the two parametric entropy s kappa r of sharma taneja and mittal we analyze the composability rule for two statistically independent systems a and b described by the entropy s kappa r with the same set of the deformation parameters it is shown that in spite of the concavity of the entropy the composability rule modifies the thermodynamic stability conditions of the equilibrium state depending on the values assumed by the deformation parameters when the relation s kappa r a union b s kappa r a s kappa r b holds superadditive systems the concavity condition does imply thermodynamics stability otherwise when the relation s kappa r a union b s kappa r a s kappa r b holds subadditive systems the concavity condition does not imply thermodynamical stability of the equilibrium state

the q boson realizations of the quantum groups uq dn we give explicit realization for the quantum enveloping algebras uq dn to obtain recurrence formulae we simply extend the algebra uq dn to uq n for which uq dn is a subalgebra in these formulae the generators of the algebra are expressed by means of 2n 2 canonical q boson pairs and one auxiliary representation of uq n 1

bose realization of a non canonical heisenberg algebra the authors find out the bose realization of a generalized heisenberg algebra in which the bracket of the annihilation and creation operators is proportional to a polynomial function of the number operator the eigenvalues of the corresponding oscillator are derived in a special case they stress also the connection between non canonical commutation relations and q algebras

equivalence of deformed fermionic algebras generalized deformations of the fermionic algebra are studied the polynomial representations of these algebras are constructed all the deformation schemes can be realized by the same polynomial basis using the bargmann representation thus proving that all deformed fermionic algebras are isomorphically equivalent to the non deformed fermionic algebra

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

quantization of set theory and generalization of the fermion algebra the quantum states of a d dimensional fermion algebra are in one to one correspondence with the subsets of a d element universal set in this paper we use this set theoretical motivation to construct a one parameter deformation of the fermion algebra and extend it to a d dimensional generalization which is invariant under the group u d this discrete fermionic oscillator system is extended to the continuous case we also show that the q deformation of these systems is related to supercovariant q oscillators

the q t gaussian process the q t fock space fq t h introduced in this paper is a deformation of the q fock space of bozejko and speicher the corresponding creation and annihilation operators now satisfy the commutation relation aq t f aq t g qaq t g aq t f f g htn turn mathjax off a defining relation of the chakrabarti jagannathan deformed quantum oscillator algebra the moments of the deformed gaussian element sq t h aq t h aq t h are encoded by the joint statistics of crossings and nestings in pair partitions the q 0 t specialization yields a natural single parameter deformation of the full boltzmann fock space of free probability with the corresponding semicircular measure variously encoded via the rogers ramanujan continued fraction the t airy function the t catalan numbers of carlitz riordan and the first order statistics of the reduced wigner process

bosonic quasideterminants and eigenvalue problems of generalized spin orbit operators this paper deals with an extension of the applications of the paper by gelfand and retakh funct anal appl 25 91 1991 on quasideterminant qsd algebraic method to eigenvalue problems in quantum mechanics using relevant identities on the free 1 mode bosonic algebra we build characteristic qsds associated with generalized spin orbit hamiltonians with a well defined representation which allows us to explicitly and straightforwardly compute analytical expressions of eigenenergies specific instances are provided on f deformed generalized jaynes cummings models and other hamiltonian classes widely used in condensed matter physics

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

representations of the quantum algebra uq su1 1 all irreducible representations of the quantum group uq su1 1 are given they are determined by two complex numbers infinitesimally unitary representations are separated from the set of irreducible representations it is shown that the symmetric operators of irreducible infinitesimally unitary representations corresponding to generators of the lie algebra su1 1 admit self adjoint extensions

example of infinite statistics i give a second quantized example of infinite statistics in which any representation of the symmetric group can occur for identical particles and discuss the properties of the example

bfv brst analysis of the classical and quantum q deformations of the sl 2 algebra bfv brst charge for quantum algebras is not unique different constructions of it in classical and quantum phase space for the universal enveloping algebra of the q deformed sl 2 are discussed in the quantum framework a positive definite scalar product is used to introduce a co bfv brst charge to study the cohomology problem by means of the techniques of the non deformed case moreover deformation of the phase space without deforming the generators of sl 2 is considered h cross q deformation of the phase space is shown to yield the witten s second deformation for sl 2 to study the bfv brst cohomology problem when both the quantum phase space and the group are deformed a two parameter deformation of sl 2 is proposed and its bfv brst charge is given

a completeness relation for the coherent states of the p q oscillator by p q integration p q integration is defined for the p q oscillator this is used to prove a completeness relation for the coherent states of the p q oscillator the p q analogue of the bargmann fock representation is also discussed

tensorial structure of a q deformed sp 4 r superalgebra a supersymmetric quantum algebra is generated by irreducible tensor operators with respect to the algebra suq 2 the even generators are realized as tensor products of q boson creation and annihilation operators transforming as suq 2 spinors and acting as odd generators in this way the transformation properties of all the algebra s generators with respect to the q deformed algebra of the angular momentum are simultaneously preserved which is important in view of future applications in physics in the limit q to 1 the classical lie superalgebra sp 4 r or the algebra osp 1 mod 4 is recovered

a p q deformed virasoro algebra a conformal dimension delta dependent p q deformed virasoro p q virasoro algebra with two independent deformation parameters p q is constructed the comultiplication rule for the generating functional for the delta 0 1 case is established and found to be depending on p and q individually the central charge term for the p q virasoro algebra is described a p q deformed nonlinear equation p q kdv corresponding to p q virasoro algebra for delta 0 1 case is obtained

multistable pulselike solutions in a parametrically driven ginzburg landau equation department of interdisciplinary studies faculty of engineering tel aviv university tel aviv 69978 israel dated february 8 2008 it is well known that pulse like solutions of the cubic complex ginzburg landau equation are un stable but can be stabilised by the addition of quintic terms in this paper we explore an alternativemechanism where the role of the stabilising agent is played by the parametric driver our analysis isbased on the numerical continuation of solutions in one of the parameters of the ginzburg landauequation the di usion coe cient c starting from the nonlinear schr odinger limit for which c 0 the continuation generates recursively a sequence of coexisting stable solutions with increasingnumber of humps the sequence converges to a long pulse which can be interpreted as a boundstate of two fronts with opposite polarities i introduction

normal ordering for nonlinear deformed ladder operators and the f generalization of the stirling and bell numbers we resolve the normal ordering problem for symmetric d d n and asymmetric d rd n strings of the nonlinear deformed ladder operators d for supersymmetric and shape invariant potential systems where r and n are positive integers we provide exact and explicit expressions for their normal forms n d d n and n d rd n where in n all d are at the right side we find that the solutions involve sequence of expansion coefficients which for r n 1 corresponds to the f deformed generalization of the classical stirling and bell numbers of the second kind we apply the general formalism for the translational shape invariant potential systems as well as for the particular case of the harmonic oscillator potential system we show that these numbers are obtained for families of polynomial expressions generated with the deformations parameters and the parameters related to the forms of the supersymmetric partner potentials

fronts pulses sources and sinks in generalized complex ginzberg landau equations an important clement in the long time dynamics of pattern forming systems is a class of solutions we will call coherent structures these are states that are either themselves localized or that consist of domains of regular patterns connected by localized defects or interfaces this paper summarizes and extends recent work on such coherent structures in the one dimensional complex ginzburg landau equation and its generalizations for which rather complete information can be obtained on the existence and competition of fronts pulses sources and sinks for the special subclass of uniformly translating structures the solutions are derived from a set of ordinary differential equations that can be interpreted as a flow in a three dimensional phase space fixed points of the flow correspond to the two basic building blocks of coherent structures uniform amplitude states and evanescent waves whose amplitude decreases smoothly to zero a study of the stability of the fixed points under the flow leads to results on the existence and multiplicity of the different coherent structures the dynamical analysis of the original partial differential equation focusses on the competition between pulses and fronts and is expressed in terms of a set of conjectures for front propagation that generalize the marginal stability and pinch point approaches of earlier authors these rules together with an exact front solution whose dynamics plays an important role in the selection of patterns yield an analytic expression for the upper limit of the range of existence of pulse solutions as well as a determination of the regions of parameter space where uniformly translating fron t solutions can exist extensive numerical simulations show consistency with these rules and conjectures for the existence of fronts and pulses in the parameter ranges where no uniformly translating fronts can exist examples are shown of irregularly spreading fronts that generate strongly chaotic regions as well as nonuniformly translating fronts that lead to uniform amplitude states recent perturbative treatments based on expansions about the nonlinear schr6dinger equation are generalized to perturbations of the cubic quintic and derivative schr idinger equations for which both pulses and fronts exist in the unperturbed system comparison of the results with the exact solutions shows that the perturbation theory only yields a subset of the relevant solutions nevertheless those that are obtained are found to be consistent with the general conjectures and in particular they provide an analytic demonstration of front pulse competition while the discussion of the competition between fronts and pulses focusses on the complex ginzburg landau equation with quintic terms and a subcritical bifurcation a number of results are also presented for the cubic equation in particular the existence of a family of moving source solutions derived by bekki and nozaki for this equation contradicts the naive counting arguments we attribute this contradiction to a hidden symmetry of the solution but have not been able to show explicitly how this symmetry affects the phase space orbits

evolution of nonsoliton and quasi classical wavetrains in nonlinear schro dinger and korteweg de vries equations with dissipative perturbations abstract nonlinear schrodinger equations with attraction and with repulsion nse and nse and the korteweg de vries equation perturbed by small dissipative terms are considered near the linear instability threshold where nonlinear and spatially nonuniform dissipations dominate explicit solutions expressing the local amplitude and occupation numbers of a nonsoliton dispersive wavetrain in terms of arbitrary initial data are obtained at sufficiently large times in the logarithmic approximation for nse the particular case of the wavetrain near the soliton birth threshold is also considered the influence of the dissipation on the evolution of a quasi classical strongly nonlinear wavetrain is studied it is demonstrated that for nse the dissipation can be taken into account within the framework of the eikonal approximation while for the nse a perturbation theory based on the inverse scattering transform is relevant

quasi fibonacci oscillators we study the properties of the sequences of the energy eigenvalues for some generalizations of q deformed oscillators including the p q oscillator and the three four and five parameter deformed oscillators given in the literature it is shown that most of the considered models belong to the class of so called fibonacci oscillators for which any three consecutive energy levels satisfy the relation en 1 en en 1 with real constants on the other hand for a certain oscillator known since 1993 we prove its non fibonacci nature possible generalizations of the three term fibonacci relation are discussed among which for the oscillator we choose as the most adequate the so called quasi fibonacci or local fibonacci property of the energy levels the property is encoded in the three term quasi fibonacci qf relation with the non constant n dependent coefficients and various aspects of the qf relation are elaborated for the oscillator and some of its extensions

two parametric solution to graded yang baxter equation and two parametric uuvgl 1 mod 1 algebra as a hopf algebra the authors discuss a two parametric solution of the graded yang baxter equation ybe and perform the yang baxterization to obtain the solution to the quantum ybe in the formalism developed previously they present the two parametric quantized superalgebra uuvgl 1 mod 1 and prove that this algebra is a hopf algebra with the hopf operations explicitly provided