large amplitude vibrations of parabolic cables the non linear equations of motion for the coupled transverse vertical vibrations of parabolic cables are presented approximate solutions are developed by using the method of multiple scales solutions and numerical results are obtained and discussed for some special cases

a hybrid pseudo force laplace transform method for non linear transient response of a suspended cable a hybrid numerical scheme involving the combination of the laplace transform technique and the pseudo force method is proposed to analyze the non linear transient response of a suspended cable subjected to arbitrary dynamic loading a theoretical model of the cable with multi degree of freedom is first obtained through discretization of the partial differential equations by finite difference approximation the non linear governing equations take into account the effects of quadratic and cubic geometric non linearities the proposed method deals with the non linear effects as pseudo forces and then establishes an iterative solution scheme in the alternating laplace time domain by means of fast numerical laplace transform this method eschews a time stepping process and therefore is computationally efficient it also readily deals with the viscoelastic damping with frequency dependent model parameters and the hysteresis damping in terms of complex stiffness models numerical examples are presented to evaluate the dynamic responses of suspended cables under a concentrated sinusoidal force and a distributed random excitation and to identify the non linear response properties by comparison with the linear vibration the validity and accuracy of the proposed method is also verified by comparing the results with those obtained by using the direct time integration

regular subspaces of a quaternionic hilbert space from quaternionic hermite polynomials and associated coherent states we define quaternionic hermite polynomials by analogy with two families of complex hermite polynomials as in the complex case these polynomials constitute orthogonal families of vectors in ambient quaternionic l2 spaces using these polynomials we then define regular and anti regular subspaces of these l2 spaces the associated reproducing kernels and the ensuing quaternionic coherent states

non linear galloping of sagged cables in 1 2 internal resonance the aeroelastic behaviour of a flexible elastic suspended cable driven by mean wind speed blowing perpendicularly to the cable s plane is investigated by applying the galerkin procedure to the partial differential equations of motion and using an in plane and an out of plane mode as shape functions a two d o f model is derived the discrete equations are coupled through quadratic and cubic terms arising both from geometric and aerodynamic effects the associated linear frequencies are assumed to be in an almost 1 2 ratio so that internal resonance occurs the multiple scale perturbation method is employed to obtain a set of three amplitude modulation equations whose coefficients depend on the mean wind speed which is assumed as control parameter two perturbative solutions are developed each based on a different assumption about the order of magnitude of the static displacements produced by steady state wind forces analytical results are then compared with direct numerical integrations of discrete non linear equations by performing a bifurcation analysis the existence of several equilibrium branches is proved the relative importance of geometric and aerodynamic non linearities is discussed through simplified models the influence on critical and postcritical behaviour of several parameters including geometrical cable parameters detuning and non symmetric flow effects is investigated the important role played by the steady state forces is highlighted

left symmetric algebras from linear functions abstract in this paper some left symmetric algebras are constructed from linear functions they include a kind of simple left symmetric algebras and some examples appearing in mathematical physics their complete classification is also given which shows that they can be regarded as generalization of certain two dimensional left symmetric algebras

finite element analysis of a three dimensional underwater cable with time dependent length three dimensional underwater vibrations of a geometrically non linear cable with a weight at the lower end are investigated the length of the cable is time dependent a set of non linear time varying differential equations describing this system is derived by hamilton s principle and the variable domain finite element method the results of numerical simulation are presented for constant speed and sinusoidal axial motions of the cable the vibration responses of three initial conditions are shown the effects of initial displacements initial tensions due to gravity and the hydrodynamic forces on the non linear longitudinal and transverse amplitudes are presented finally some conclusions are drawn

new complex function space related to both entangled state representation and spin coherent state a new complex function space whose basis is the single variable hermite polynomial h2j 2 is constructed which is related to both entangled state representation and spin coherent state in schwinger bosonic realization new binomial theorem involving two variable hermite polynomial is derived which helps to constitute the new complex function space we also present a new integration transformation of the basis h2j 2 with its reciprocal transformation which is useful to deriving some operator identities

squeezed states and hermite polynomials in a complex variable following the lines of the recent paper of j p gazeau and f h szafraniec j phys a math theor 44 495201 2011 we construct here three types of coherent states related to the hermite polynomials in a complex variable which are orthogonal with respect to a non rotationally invariant measure we investigate relations between these coherent states and obtain the relationship between them and the squeezed states of quantum optics we also obtain a second realization of the canonical coherent states in the bargmann space of analytic functions in terms of a squeezed basis all this is done in the flavor of the classical approach of v bargmann commun pure appl math 14 187 1961

extended pseudo fermions from non commutative bosons we consider some modifications of the two dimensional canonical commutation relations leading to non commutative bosons and we show how biorthogonal bases of the hilbert space of the system can be obtained out of them our construction extends those recently introduced by one of us f b modifying the canonical anticommutation relations we also briefly discuss how bicoherent states producing a resolution of the identity can be defined

non linear oscillations of a four degree of freedom model of a suspended cable under multiple internal resonance conditions abstract a four degree of freedom model able to capture the main phenomena which are likely to occur in the non planar finite dynamics of an elastic suspended cable subjected to external forcings and support motions is developed from the continuum equations it contains two in plane and two out of plane components one symmetric and one antisymmetric an order two multiple time scales solution is obtained for the case of primary external resonance and three simultaneous internal resonances cable at crossover frequency possible classes of steady state planar non planar unimodal multimodal regular motions of the system are identified and their linearized stability analysis is performed some results are presented to highlight the role played by key perturbations on the onset of various classes the rich behaviour of the system and the influence of some control parameters on the response

space time numerical simulation and validation of analytical predictions for nonlinear forced dynamics of suspended cables abstract this paper presents space time numerical simulation and validation of analytical predictions for the finite amplitude forced dynamics of suspended cables the main goal is to complement analytical and numerical solutions accomplishing overall quantitative qualitative comparisons of nonlinear response characteristics by relying on an approximate kinematically non condensed planar modeling a simply supported horizontal cable subject to a primary external resonance and a 1 1 or 1 1 vs 2 1 internal resonance is analyzed to obtain analytical solution a second order multiple scales approach is applied to a complete eigenfunction based series of nonlinear ordinary differential equations of cable damped forced motion accounting for both quadratic cubic geometric nonlinearities and multiple modal contributions local scenarios of cable uncoupled coupled responses and associated stability are predicted based on chosen reduced order models as a cross checking tool numerical simulation of the associated nonlinear partial differential equations describing the dynamics of the actual infinite dimensional system is carried out using a finite difference technique employing a hybrid explicit implicit integration scheme based on system control parameters and initial conditions cable amplitude displacement and tension responses are numerically assessed thoroughly validating the analytically predicted solutions as regards the actual existence the meaningful role and the predominating internal resonance of coexisting competing dynamics some methodological aspects are noticed along with a discussion on the kinematically approximate versus exact as well as planar versus non planar cable modeling

a unified algebraic approach to the classical yang baxter equation in this paper the different operator forms of the classical yang baxter equation are given in the tensor expression through a unified algebraic method it is closely related to left symmetric algebras which play an important role in many fields in mathematics and mathematical physics by studying the relations between left symmetric algebras and the classical yang baxter equation we can construct left symmetric algebras from certain classical r matrices and conversely there is a natural classical r matrix constructed from a left symmetric algebra which corresponds to a parakahler structure in geometry moreover the former in a special case gives an algebraic interpretation of the left symmetry as a lie bracket left twisted by a classical r matrix

generalized 2d laguerre polynomials and their quaternionic extensions a class of orthogonal polynomials in two quaternionic variables is introduced this class serves as an analogous to the classical zernike polynomials z m n z z arxiv 1502 07256 2014 a number of interesting properties such as the orthogonality condition recurrence relations raising and lowering operators are discussed in detail particularly the ladder operators realized as differential operators in terms of the so called cullen derivatives for these quaternionic polynomials are also studied some physically interesting summation and integral formulas are also proved and their physical relevance briefly discussed

squeezing of arbitrary order the ups and downs we show how using classical von neumann index theory makes possible a universal treatment of squeezing of arbitrary order universal means that the same approach applied to displacement order 1 a

the dynamic analysis of a suspended cable due to a moving load the dynamic behaviour of a saggy suspension cable under a moving load was investigated first of all the updated lagrangian formulation and the finite element method were used to derive the property matrices of a saggy suspension cable in order to define the discretized equations of motion then the jacobi method was applied to the determination of the natural frequencies and the mode shapes of the suspended cable the moving load induced dynamic responses of the saggy suspended cable were obtained by using the newmark direct integration method incorporated with the newton raphson iteration technique the influence of some pertinent factors such as speed of moving load ratio of axial rigidity to total cable weight ae 0mg0l and ratio of moving load mass to total cable mass is the key point of the dynamic analysis

a measure free approach to coherent states in the process of generalizing coherent states the situation when the measure which is customarily incorporated in their definition is indeterminate becomes unavoidable a more dramatic situation may occur if there is no measure which makes the reproducing kernel hilbert space involved in the construction of coherent states isometrically included in an space therefore it appears that there is a need to redefine coherent states making the definition measure free starting out with the reproducing kernel property we ensure the basic feature of coherent states resolution of the identity to be maintained cf 15 and remark 2 the only investment in the whole undertaking is a sequence n dn 0 satisfying 4 the rest including the aforesaid resolution of the identity is a consequence of our choice the approach is supported by examples which make the circumstances clear under which the sequence n dn 0 appears moment problems or rather orthogonal polynomials are one of them this article is part of a special issue of journal of physics a mathematical and theoretical devoted to coherent states mathematical and physical aspects

non abelian phase spaces for a vector space v its phase space t v is the vector space v v together with the canonical symplectic form on it since the vector space is the same as an abelian lie algebra the natural question is given a lie algebra g does there exist a phase space t g in general the answer is negative below for a large class of lie algebras g the phase space t g is constructed three examples are treated in detail g gl v g d rn the lie algebra of vector fields on rn and current algebras

new orthogonality relations for the hermite polynomials and related hilbert spaces the hermite polynomials give rise to orthonormal bases in bagmann like hilbert spaces xa 0 a 1 consisting of entire functions these hilbert spaces are related to the gelfand shilov space s1212 viz s1212 0 a 1 xa

complex and real hermite polynomials and related quantizations it is known that the anti wick or standard coherent state quantization of the complex plane produces both canonical commutation rule and quantum spectrum of the harmonic oscillator up to the addition of a constant in this work we show that these two issues are not necessarily coupled there exists a family of separable hilbert spaces including the usual fock bargmann space and in each element in this family there exists an overcomplete set of unit norm states resolving the unity with the exception of the fock bargmann case they all produce non canonical commutation relation whereas the quantum spectrum of the harmonic oscillator remains the same up to the addition of a constant the statistical aspects of these non equivalent coherent state quantizations are investigated we also explore the localization aspects in the real line yielded by similar quantizations based on real hermite polynomials

dynamic and energetic analyses of a string slider non linear coupling system by variable grid finite difference in this paper a string slider non linear coupling system with time dependent boundary condition is considered one partial differential equation pde describing the transverse small amplitude vibration of the string non linearly coupled with one ordinary differential equation ode describing the horizontal displacement of the slider are derived by hamilton s principle this is a moving boundary problem since the unknown position of the slider has to be determined as a part of the solutions a transformation of the variable that converts the original non stationary boundary conditions to a set of fixed boundary conditions is proposed to avoid the increased complication and loss of accuracy associated with unequal space intervals near the moving boundary the finite difference method with variable grid is employed to show the numerical results of the coupling effect between the string and slider finally some periodic motions of the moving boundary are assigned to show the divergence of the string vibrations

from rota baxter algebras to pre lie algebras rota baxter algebras were introduced to solve some analytic and combinatorial problems and have appeared in many fields in mathematics and mathematical physics rota baxter algebras provide a construction of pre lie algebras from associative algebras in this paper we give all rota baxter operators of weight 1 on complex associative algebras in dimension 3 and their corresponding pre lie algebras

holomorphic hermite polynomials and a non commutative plane one more coherent state quantization of a complex plane is presented although the complex plane is equipped with a non rotationally invariant measure we still obtain a canonical commutation rule up to a simple rescaling we explain how the involved coherent states built from holomorphic continuations of hermite polynomials are related to the non commutative plane

modules and morita theorem for operads associative rings a b are called morita equivalent when the categories of left modules over them are equivalent we call two classical linear operads p q morita equivalent if the categories of algebras over them are equivalent we transport a part of morita theory to the operadic context by studying modules over operads as an application of this philosophy we consider an operadic version of the sheaf of linear differential operators on a super manifold m and give a comparison theorem between algebras over this sheaf on m and m red

the automorphisms of novikov algebras in low dimensions novikov algebras were introduced in connection with poisson brackets of hydrodynamic type and hamiltonian operators in the formal variational calculus they also correspond to a class of vertex algebras an automorphism of a novikov algebra is a linear isomorphism satisfying xy x y which keeps the algebraic structure the set of automorphisms of a novikov algebra is a lie group whose lie algebra is just the novikov algebra s derivation algebra the theory of automorphisms plays an important role in the study of novikov algebras in this paper we study the automorphisms of novikov algebras we get some results on their properties and classification in low dimensions these results are fundamental in a certain sense and they will serve as a guide for further development moreover we apply these results to classify gel fand dorfman bialgebras and novikov poisson algebras these results also can be used to study certain phase spaces and geometric classical r matrices