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

equivalence of q bosons using the exponential phase operator various forms of the q boson are explained and their hidden symmetry revealed by transformations using the exponential phase operator both the one component and the multicomponent q bosons are discussed as a byproduct we obtain a new boson algebra having a shifted vacuum structure and define a global operator u 1 gauge transformation

a symplectic analytical wave based method for the wave propagation and steady state forced vibration of rectangular thin plates abstract a semi analytical method is used to investigate the wave propagation characteristics and steady state forced vibration response for rectangular thin plates by way of a rigorous but simple derivation the governing differential equations for transverse vibration of rectangular thin plates are first converted into hamiltonian canonical equations following the method of separation of variables a symplectic eigenproblem is formed whose solution gives analytically the dispersion equation and the wave mode shape using the wave modes i e the wave propagation parameters and wave shapes and combining the directly excited waves the wave propagation within the plate and the wave reflection at the boundary the forced response of the plate can be computed in the wave domain with high precision and high efficiency the present method is based on the basic elasticity equations of the plate and can give the symplectic analytical solutions for the wave modes for any combination of simple boundary conditions along the plate edges the present method eliminates the limitation of the traditional analytical wave propagation method which can only obtain wave modes for plates with two opposite edges simply supported in contrast to numerical wave propagation methods the present method provides symplectic analytical solutions for the wave modes and hence the computations are of high precision and well conditioned also continuously distributed external forces can be easily considered in the numerical examples the wave propagation characteristics are analyzed for plates with three different combinations of boundary conditions i e with two opposite edges either both simply supported or both clamped or one simply supported and the other clamped the steady state forced responses are also computed for plates excited by point forces as well as for line and area distributed forces for the three combinations of boundary conditions comparison of the present results with analytical results wave finite element and finite element results validates the high accuracy and high efficiency of the present method

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

finite permutation groups with a transitive minimal normal subgroup a finite permutation group is said to be innately transitive if it contains a transitive minimal normal subgroup in this paper we give a characterisation and structure theorem for the finite innately transitive groups as well as describing those innately transitive groups which preserve a product decomposition the class of innately transitive groups contains all primitive and quasiprimitive groups

complementarity of suq 3 and uq 2 and q boson realization of the suq 3 irreducible representations the complementarity relationship also termed duality that arises between the irreps of the su 3 and u 2 lie algebras when their direct sum su 3 u 2 is embedded into a larger u 6 algebra and single row irreps of the latter are considered is extended to the corresponding q algebras suq 3 and uq 2 it is demonstrated by explicitly constructing the unique q boson state that is simultaneously maximal in suq 3 and uq 2 for a given u q 2 weight in addition the relations between the suq 3 and uq 2 casimir operators resulting from their complementarity are explicitly found together with the q bargmann representation of q boson operators the complementarity relationship is then used to construct a gel fand tseitlin basis for arbitrary suq 3 irreps in terms of q boson operators

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

modelling turbulence induced vibration of pipes with a spectral finite element method the vibration of pipes is studied here using the arnold warburton theory for thin shells and a simplified theory valid in a lower frequency regime the vibrational response is described numerically with the spectral finite element method sfem which uses the exact solutions of the equations of motion as basis functions for turbulence excitation the set of basis functions was extended to include particular solutions which model a spatially distributed excitation an efficient numerical solution to homogeneous random excitation is presented and the results compare favourably with wind tunnel measurements

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

on locally semiprimitive graphs and a theorem of weiss abstract in this paper we investigate graphs that admit a group acting arc transitively such that the local action is semiprimitive with a regular normal nilpotent subgroup this type of semiprimitive group is a generalisation of an affine group we show that if the graph has valency coprime to six then there is a bound on the order of the vertex stabilisers depending on the valency alone we also prove a detailed structure theorem for the vertex stabilisers in the remaining case this is a contribution to an ongoing project to investigate the validity of the potocnik spiga verret conjecture

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

application of the dynamic stiffness method to the free and forced vibrations of aircraft panels abstract the free and forced vibrations of a row of rectangular panels which are stiffened transversely and simply supported along the longitudinal edges is considered the equations of motion of the component parts are derived by using a dynamic stiffness formulation which enables the standard techniques of the finite element method to be applied to the assembly and solution of the equations which govern the complete system distributed loading is accounted for by using particular integrals which allows the forced response of the system to be calculated simply without recourse to modal methods expressions are derived for the mean power flow through the system and the mean energy which is stored in the component parts the method is applied to a single panel a six panel row and an infinite panel row

representations of the quadratic algebra and partially asymmetric diffusion with open boundaries we consider the one dimensional partially asymmetric exclusion model with open boundaries the model describes a system of hard core particles that hop stochastically in both directions with different rates at both boundaries particles are injected and extracted by means of the method of derrida et al the stationary probability measure can be expressed as a matrix product state involving two matrices forming a fock like representation of a general quadratic algebra we obtain the representations of this algebra which were unknown in the mathematical literature and use the two dimensional one to derive exact expressions for the density profile and correlation functions using the correspondence between the stochastic model and a quantum spin chain we obtain exact correlation functions for a spin heisenberg xxz chain with non diagonal boundary terms generalizations to other reaction diffusion models are discussed

quantum groups and lie admissible time evolution the time evolution of operators for q oscillators is derived for the first time by exploiting the connection between q deformation algebras and lie admissible algebras

on groups with every normal subgroup transitive or semiregular we investigate finite solvable permutation groups in which all normal subgroups are transitive or semiregular the motivation comes from universal algebra such groups are examples of collapsing transformation monoids

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

free vibration of two elastically coupled rectangular plates with uniform elastic boundary restraints abstract an analytical method is derived for determining the vibrations of two plates which are generally supported along the boundary edges and elastically coupled together at an arbitrary angle the interactions of all four wave groups bending waves out of plane shearing waves in plane longitudinal waves and in plane shearing waves have been taken into account at the junction via four types of coupling springs of arbitrary stiffnesses each of the transverse and in plane displacement functions is expressed as the superposition of a two dimensional 2 d fourier cosine series and several supplementary functions which are introduced to ensure and improve the convergence of the series representation by removing the discontinuities that the original displacement and its derivatives will potentially exhibit at the edges when they are periodically expanded onto the entire x y plane as mathematically implied by a 2 d fourier series the unknown expansions coefficients are calculated using the rayleigh ritz procedure which is actually equivalent to solving the governing equation and the boundary and coupling conditions directly when the assumed solutions are sufficiently smooth over the solution domains numerical examples are presented for several different coupling configurations a good comparison is observed between the current results and the fea models although this study is specifically focused on the coupling of two plates the proposed method can be directly extended to structures consisting of any number of plates

compact matrix pseudogroups the compact matrix pseudogroup is a non commutative compact space endowed with a group structure the precise definition is given and a number of examples is presented among them we have compact group of matrices duals of discrete groups and twisted deformed su n groups the representation theory is developed it turns out that the tensor product of representations depends essentially on their order the existence and the uniqueness of the haar measure is proved and the orthonormality relations for matrix elements of irreducible representations are derived the form of these relations differs from that in the group case this is due to the fact that the haar measure on pseudogroups is not central in general the corresponding modular properties are discussed the haar measures on the twistedsu 2 group and on the finite matrix pseudogroup are found

time quantization and q deformations we extend to quantum mechanics the technique of stochastic subordination by means of which one can express any semi martingale as a time changed brownian motion as examples we considered two versions of the q deformed harmonic oscillator in both ordinary and imaginary time and show how these various cases can be understood as different patterns of time quantization rules

quantum and classical mechanics of q deformed systems quantum and classical mechanics of a system of q deformed bosonic oscillators are considered the q deformed heisenberg weyl algebra of creation and destruction operators is realized by differential operators in a space of functions of real commutative variables the corresponding hilbert space is constructed in this approach the deformation parameter turns out to be a function of the planck constant an oscillator frequency and a parameter with dimension of length the hamiltonian path integral is derived and its semiclassical approximation is investigated to obtain the corresponding q deformed classical theory the phase space spanned by the usual commutative coordinates is shown to be a cylinder in classical theory the dimensional parameter introduced determines its radius it is argued that the q deformation can be associated with a special non canonical transformation the principle of least action for the classical q deformed system is formulated a representation of uq m in a space of functions on a phase space spanned by commutative coordinates is constructed

three dimensional quantum groups from contractions of su 2 q contractions of lie algebras and of their representations are generalized to define new quantum groups an explicit and complete exposition is made for the one dimensional heisenberg h 1 q and the two dimensional euclidean quantum group e 2 q obtained by contracting su 2 q

a new method of analyzing wave propagation in periodic structures applications to periodic timoshenko beams and stiffened plates a response function is found for an infinite uniform one dimensional structure which is subjected to an array of harmonic forces or moments spaced equidistantly and which have a constant phase or ratio between any adjacent pair receptance functions are derived for these phased arrays they are used to set up a general determinantal equation for the propagation constants of the infinite structure when it is made periodic by the addition of an infinite set of regular constraints they are also used to set up equations for the response of the structure to a convected harmonic pressure field the method enables the equations for the propagation constants and for the response to convected loading to be set up with much greater facility than by earlier methods it only requires a knowledge of the response function of the infinite uninterrupted structure under a single point harmonic force or moment the general equation for the propagation constants is used to study a a simply supported periodic timoshenko beam and b a parallel plate with periodic beam type stiffeners some calculated propagation constants are presented and discussed the periodic plate results are relevant to integrally stiffened skins of the type used in aeroplanes

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

new deformed heisenberg oscillator the discrete spectrum of a deformed oscillator is calculated here for the first time according to the noncanonical heisenberg algebra the spectrum extends from omega 2 1 mu to omega mu where mu is a positive deformation parameter

a theory of semiprimitive groups abstract a transitive permutation group is semiprimitive if each of its normal subgroups is transitive or semiregular interest in this class of groups is motivated by two sources problems arising in universal algebra related to collapsing monoids and the graph restrictive problem for permutation groups here we develop a theory of semiprimitive groups which encompasses their structure their quotient actions and a method by which all finite semiprimitive groups are constructed we also extend some results from the theory of primitive groups to semiprimitive groups and conclude with open problems of a similar nature

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

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

approach of spherical harmonics to the representation of the deformed su 1 1 algebra the m shifting generators of su 2 algebra together with a pair of l shifting ladder symmetry operators have been used in the space of all spherical harmonics ylm in order to introduce a new set of operators expressing the transitions between them it is shown that the space of spherical harmonics whose l 2m or l 2m is given presents negative and positive irreducible representations of a deformed su 1 1 algebra respectively these internal symmetries also suggest new algebraic methods to construct the spherical harmonics in the framework of the spectrum generating algebras

an elastic wave technique for the free vibration analysis of plate assemblies abstract a method is presented for the free vibration analysis of a class of plate assembly which includes an orthogonally stiffened flat plate as a special case the method is based on the analysis of free elastic wave propagation through the structure and consists of applying the relevant wave transmission and reflection coefficients at the structural discontinuities regardless of the structural complexity the problem of calculating the natural frequencies is reduced to that of solving two simultaneous non linear algebraic equations in the case of a periodic plate assembly the method yields closed form solutions for the propagation constants it is shown that the method is basically a reformulation of bolotin s asymptotic method and the relative simplicity of the approach is illustrated by application to a number of example structures

random vibration analysis of axially compressed cylindrical shells under turbulent boundary layer in a symplectic system a random vibration analysis of an axially compressed cylindrical shell under a turbulent boundary layer tbl is presented in the symplectic duality system by expressing the cross power spectral density psd of the tbl as a fourier series in the axial and circumferential directions the problem of structures excited by a random distributed pressure due to the tbl is reduced to solving the harmonic response function which is the response of structures to a spatial and temporal harmonic pressure of unit magnitude the governing differential equations of the axially compressed cylindrical shell are derived in the symplectic duality system and then a symplectic eigenproblem is formed by using the method of separation of variables expanding the excitation vector and unknown state vector in symplectic space decoupled governing equations are derived and then the analytical solution can be obtained in contrast to the modal decomposition method mdm the present method is formulated in the symplectic duality system and does not need modal truncation and hence the computations are of high precision and efficiency in numerical examples harmonic response functions for the axially compressed cylindrical shell are studied and a comparison is made with the mdm to verify the present method then the random responses of the shell to the tbl are obtained by the present method and the convergence problems induced by fourier series expansion are discussed finally influences of the axial compression on random responses are investigated

a study of representations of the algebra of functions on the quantum group glq n a q analogue of the root system is constructed for this algebra which is similar to the root system of classical lie algebras it is then used to construct in detail a class of representations of the algebra of functions on the quantum group glq n and a q boson realization of the generators of glq n is given i also construct infinite dimensional hilbert space representations of this algebra the main result of this paper is stated in proposition 8

suq h cross to 0 2 and suq h cross 2 the classical and quantum q deformations of the su 2 algebra ii the hopf algebra the yang baxter equation and multi deformed algebraic structures for pt i see ibid vol 23 p 4185 1990 the suq 2 algebra is realized by means of both the poisson brackets in classical mechanics and commutators in quantum mechanics in a system with q deformed oscillators of two different types the structures of the hopf algebra and the quantum yang baxter equation are also discussed on a quantum level a set of j representations of the quantum algebra suq 2 is constructed based on the type ii q oscillators multi deformations of the oscillators of the two types and multi deformed algebras expressed in poisson brackets as well as in lie brackets are proposed

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

verma module of the quantum group gl n q and its q boson and heisenberg weyl relation realizations the structure and verma module of the quantum matrix element algebra a n q of the quantum group gl n q are studied the method used here is similar to that for studying the structure and verma module of semisimple lie algebras the concept of the cartan subalgebra raising and lowering operators and their pairs is defined the q boson and the corresponding heisenberg weyl relation realizations are generally studied and the cyclic representations of a n q are obtained the explicit examples a 2 q and a 3 q are discussed in detail

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

specular and diffuse reflections of rays in coupled thin plates at high frequencies the flexural energy distribution in two right angled point excited thin plates at high frequencies is investigated by means of an integral energy flow approach the fields of energy averaged over time and frequency are described by the superposition of uncorrelated cylindrical waves stemming from both boundaries and direct sources specular and diffuse laws are considered for the reflection and transmission of rays giving rise to two kinds of energy equations the diffuse law leads to a fredholm integral equation over the boundary sources while the specular law is shown to allow an image source solution when the plates have identical propagation properties the algorithm for computing the image position magnitude and directivities is described then some comparisons between the results from the both energy formulations and also from the statistical energy analysis and the numerical solution of the equations of motion are performed with two damped plates at high frequency the non diffuse pattern of the averaged flexural energy fields is well described by the energy flow approaches

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

a modal spectral model for flanking transmissions abstract a model for the prediction of direct and indirect flanking sound transmissions is presented it can be applied to geometries with extrusion symmetry the structures are modelled with spectral finite elements the acoustic domains are described by means of a modal expansion of the pressure field and must be cuboid shaped these reasonable simplifications in the geometry allow the use of more efficient numerical methods consequently the coupled vibroacoustic problem in structures such as junctions is efficiently solved the vibration reduction index of t junctions with acoustic excitation and with point force excitation is compared the differences due to the excitation type obey quite general trends that could be taken into account by prediction formulas however they are smaller than other uncertainties not considered in practice the model is also used to check if the sound transmissions of a fully vibroacoustic problem involving several flanking paths can be reproduced by superposition of independent paths there exist some differences caused by the interaction between paths which are more important at low frequencies

application of the spectral finite element method to turbulent boundary layer induced vibration of plates the spectral finite element method and equally the dynamic stiffness method use exponential functions as basis functions thus it is possible to find exact solutions to the homogeneous equations of motion for simple rod beam plate and shell structures normally this restricts the analysis to elements where the excitation is at the element ends this study removes the restriction for distributed excitation that in particular has an exponential spatial dependence by the inclusion of the particular solution in the set of basis functions these elementary solutions in turn build up the solution for an arbitrary homogeneous random excitation a numerical implementation for the vibration of a plate excited by a turbulent boundary layer flow is presented the results compare favourably with results from conventional modal analysis

exact spectral elements for follower tension buckling by power series the spectral dynamic stiffness method using exact solutions of the governing equations as shape functions has been popular for vibration and dynamic stability analyses of framed structures consisting of uniform members since non uniform members do not generally have closed form solutions special cases only have been considered however exact solutions are still possible for generally non uniform members using power series the paper studies the exact dynamic stability of columns with distributed axial force by power series both uniform and distributed compression and tension and conservative and non conservative axial forces are considered interaction diagrams of various kinds of axial loads on the natural frequencies including different intensities of the distributed loads and degree of tangency are given follower tension buckling is reported for the first time it is found that the power series outperforms the dynamic stiffness method in terms of versatility in applications and numerical stability at the very low and high ends of the frequency spectrum

variability of the coupling loss factor between two coupled plates abstract within statistical energy analysis sea the coupling loss factor clf is a statistical quantity defined in terms of the average behaviour of an ensemble of similar systems thus the effective clf for a given realization may differ from the ensemble average the effective clf of two coupled plates with low modal density and low modal overlap fluctuates significantly compared with the ensemble average clf accordingly the clf is the main parameter expected to determine the confidence intervals in the sea prediction the aim of the present paper is to quantify the variability of the effective clf for the case of two finite rectangular plates extensive parameter investigations have been performed by using the dynamic stiffness method dsm and a numerical power injection method pim using the sea power balance equations the effects of frequency bandwidth and the number of modes in a band were separated by using frequency averages at a series of constant bandwidths rather than one third octave averages while the modal overlap is made independent of frequency by setting the damping loss factor to be inversely proportional to frequency finally an improved empirical model for the variability of the clf is derived from these numerical results in terms of the modal overlap factor and the number of modes in a frequency band this model can subsequently be used to evaluate the uncertainty of the clf of such a system

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