some quantum lie algebras of type dn positive a quantum lie algebra is constructed within the positive part of the drinfeld jimbo quantum group of type dn our quantum lie algebra structure includes a generalized antisymmetry property and a generalized jacobi identity closely related to the braid equation a generalized universal enveloping algebra of our quantum lie algebra of type dn positive is proved to be the drinfeld jimbo quantum group of the same type the existence of such a generalized lie algebra is reduced to an integer programming problem moreover when the integer programming problem is feasible we show by means of the generalized jacobi identity that the poincare birkhoff witt theorem basis is still true

classification of bicovariant differential calculi on quantum groups suppose thatq is not a root of unity we classify all bicovariant differential calculi of dimension greater than one on the quantum groupsgl q n o q n andsp q n for which the differentials du of the matrix entriesu generate the left module of first order forms our first classification theorem asserts that there are precisely two one parameter families of such calculi ongl q n forn 3 in the limitq 1 only two of these calculi give the ordinary differential calculus ongl n our second main theorem states that apart from finitely manyq there exist precisely two differential calculi with these properties ono q n andsp q n forn 4 this strengthens the corresponding result proved in our previous paper ss2 there are four such calculi ono q 3 we introduce two new 4 dimensional bicovariant differential calculi ono q 3

model reduction of nonlinear systems with external periodic excitations via construction of invariant manifolds abstract a methodology for determining reduced order models of periodically excited nonlinear systems with constant as well as periodic coefficients is presented the approach is based on the construction of an invariant manifold such that the projected dynamics is governed by a fewer number of ordinary differential equations due to the existence of external and parametric periodic excitations however the geometry of the manifold varies with time as a result the manifold is constructed in terms of temporal and dominant state variables the governing partial differential equation pde for the manifold is nonlinear and contains time varying coefficients an approximate technique to find solution of this pde using a multivariable taylor fourier series is suggested it is shown that in certain cases it is possible to obtain various reducibility conditions in a closed form the case of time periodic systems is handled through the use of lyapunov floquet l f transformation application of the l f transformation produces a dynamically equivalent system in which the linear part of the system is time invariant however the nonlinear terms get multiplied by a truncated fourier series containing multiple parametric excitation frequencies this warrants some structural changes in the proposed manifold but the solution procedure remains the same two examples namely a 2 dof mass spring damper system and an inverted pendulum with periodic loads are used to illustrate applications of the technique for systems with constant and periodic coefficients respectively results show that the dynamics of these 2 dof systems can be accurately approximated by equivalent 1 dof systems using the proposed methodology

nonlinear model identification and spectral submanifolds for multi degree of freedom mechanical vibrations in a nonlinear oscillatory system spectral submanifolds ssms are the smoothest invariant manifolds tangent to linear modal subspaces of an equilibrium amplitude frequency plots of the dynamics on ssms provide the classic backbone curves sought in experimental nonlinear model identification we develop here a methodology to compute analytically both the shape of ssms and their corresponding backbone curves from a data assimilating model fitted to experimental vibration signals this model identification utilizes taken s delay embedding theorem as well as a least square fit to the taylor expansion of the sampling map associated with that embedding the ssms are then constructed for the sampling map using the parametrization method for invariant manifolds which assumes that the manifold is an embedding of rather than a graph over a spectral subspace using examples of both synthetic and real experimental data we demonstrate that this approach reproduces backbone curves with high accuracy

normal modes for non linear vibratory systems a methodology is presented which extends to non linear systems the concept of normal modes of motion which is well developed for linear systems the method is constructive for weakly non linear systems and provides the physical nature of the normal modes along with the non linear differential equations which govern their dynamics it also provides the non linear co ordinate transformation which relates the original system co ordinates to the modal co ordinates using this transformation we demonstrate how an approximate non linear version of superposition can be employed to reconstruct the overall motion from the individual non linear modal dynamics the results presented herein for non linear systems reduce to modal analysis for the linearized system when non linearities are neglected even though the approach is entirely different from the traditional one the tools employed are from the theory of invariant manifolds for dynamical systems and were inspired by the center manifold reduction technique in this paper the basic ideas are outlined a few examples are presented and some natural extensions and applications of the method are briefly described in the conclusions

domain number distribution in the nonequilibrium ising model we study domain distributions in the one dimensional ising model subject to zero temperature glauber and kawasaki dynamics the survival probability of a domain s t t and an unreacted domain q1 t t are characterized by two independent nontrivial exponents we develop an independent interval approximation that provides close estimates for many characteristics of the domain length and number distributions including the scaling exponents

differential calculus on compact matrix pseudogroups quantum groups the paper deals with non commutative differential geometry the general theory of differential calculus on quantum groups is developed bicovariant bimodules as objects analogous to tensor bundles over lie groups are studied tensor algebra and external algebra constructions are described it is shown that any bicovariant first order differential calculus admits a natural lifting to the external algebra so the external derivative of higher order differential forms is well defined and obeys the usual properties the proper form of the cartan maurer formula is found the vector space dual to the space of left invariant differential forms is endowed with a bilinear operation playing the role of the lie bracket commutator generalized antisymmetry relation and jacobi identity are proved

matrix element bialgebras determined by quadratic coordinate algebras abstract we develop the theory of manin s construction of quantum groups from finitely generated quadratic algebras in general this construction yields a bialgebra with matrix comultiplication we give formulae for the relations in the algebra and sufficient conditions for the existence of an antipode and for polynomiality of the algebra these are more systematic than the calculational approach of previous treatments

quantum lie algebras associated to and quantum lie algebras are non associative algebras which are embedded into the quantized enveloping algebras of drinfeld and jimbo in the same way as ordinary lie algebras are embedded into their enveloping algebras the quantum lie product on is induced by the quantum adjoint action of we construct the quantum lie algebras associated to and we determine the structure constants and the quantum root systems which are now functions of the quantum parameter q they exhibit an interesting duality symmetry under

a note on the generalized lie algebra in a recent paper dobrev and sudbery classified the highest weight and lowest weight finite dimensional irreducible representations of the quantum lie algebra introduced by lyubashenko and sudbery the aim of this note is to add to this classification all the finite dimensional irreducible representations which have no highest weight and or no lowest weight in the case when q is a root of unity for this purpose we give a description of the enlarged centre

order reduction of nonlinear systems with time periodic coefficients using invariant manifolds abstract the basic problem of order reduction of nonlinear systems with time periodic coefficients is considered first the equations of motion are transformed using the lyapunov floquet transformation such that the linear parts of new set of equations are time invariant at this stage the linear order reduction technique can be applied in a straightforward manner a nonlinear order reduction methodology is also suggested through a generalization of the invariant manifold technique via time periodic center manifold theory a reducibility condition is derived to provide conditions under which a nonlinear order reduction is possible unlike perturbation or averaging type approaches the parametric excitation term is not assumed to be small an example consisting of two parametrically excited coupled pendulums is given to show potential applications to real problems order reduction possibilities and results for various cases including parametric internal true internal and combination resonances are discussed

nonlinear normal modes for vibratory systems under harmonic excitation this paper considers the use of numerically constructed invariant manifolds to determine the response of nonlinear vibratory systems that are subjected to harmonic excitation the approach is an extension of the nonlinear normal mode nnm formulation previously developed by the authors for free oscillations wherein an auxiliary system that models the excitation is used to augment the equations of motion in this manner the excitation is simply treated as an additional system state yielding a system with an extra degree of freedom dof whose response is known a reduced order model for the forced system is then determined by the usual nnm procedure and an efficient galerkin based solution method is used to numerically construct the attendant invariant manifolds the technique is illustrated by determining the frequency response for a simple 2 dof mass spring system with cubic nonlinearities and for a discretized beam model with 12 dof the results show that this method provides very accurate responses over a range of frequencies near resonances

generalized lie algebras of type an it is shown that the quantized enveloping algebra of sl n contains a generalized lie algebra defined by means of axioms similar to woronowicz s this gives rise to lie algebra like generators and relations for the locally finite part of the quantized enveloping algebra and suggests a canonical poincare birkhoff witt basis

a novel sensitivity based method for damage detection of structures under unknown periodic excitations abstract this paper presents a technique for damage detection in structures under unknown periodic excitations using the transient displacement response the method is capable of identifying the damage parameters without finding the input excitations we first define the concept of displacement space as a linear space in which each point represents displacements of structure under an excitation and initial condition roughly speaking the method is based on the fact that structural displacements under free and forced vibrations are associated with two parallel subspaces in the displacement space considering this novel geometrical viewpoint an equation called kernel parallelization equation kpe is derived for damage detection under unknown periodic excitations and a sensitivity based algorithm for solving kpe is proposed accordingly the method is evaluated via three case studies under periodic excitations which confirm the efficiency of the proposed method

stochastic aggregation scaling properties we study the scaling properties of stochastic aggregation processes in one dimension numerical simulations for both diffusive and ballistic transport show that the mass distribution is characterized by two independent non trivial exponents corresponding to the survival probability of particles and monomers the overall behaviour agrees qualitatively with the mean field theory this theory also provides a useful approximation for the decay exponents as well as the limiting mass distribution

bicovariant differential calculus on quantum groups su q n and so q n following woronowicz s proposal the bicovariant differential calculus on the quantum groupssu q n andso q n is constructed a systematic construction of bicovariant bimodules by using the hat r q matrix is presented the relation between the hopf algebras generated by the linear functionals relating the left and right multiplication of these bicovariant bimodules and theq deformed universal enveloping algebras is given imposing the conditions of bicovariance and consistency with the quantum group structure the differential algebras and exterior derivatives are defined as an application the maurer cartan equations and theq analogue of the structure constants are formulated

on quantum lie algebras and quantum root systems as a natural generalization of ordinary lie algebras we introduce the concept of quantum lie algebras we define these in terms of certain adjoint submodules of quantized enveloping algebras endowed with a quantum lie bracket given by the quantum adjoint action the structure constants of these algebras depend on the quantum deformation parameter q and they go over into the usual lie algebras when q 1 the notions of q conjugation and q linearity are introduced q linear analogues of the classical antipode and cartan involution are defined and a generalized killing form q linear in the first entry and linear in the second is obtained these structures allow the derivation of symmetries between the structure constants of quantum lie algebras the explicitly worked out examples of and illustrate the results

reaction kinetics of cluster impurities we study the density of clustered immobile reactants in the diffusion controlled single species annihilation an initial state in which these impurities occupy a subspace of codimension d leads to a substantial enhancement of their survival probability the smoluchowski rate theory suggests that the codimensionality plays a crucial role in determining the long time behavior the system undergoes a transition at d 2 for d 2 above this critical codimension d 2 the subspace decays indefinitely at the critical codimension inverse logarithmic decay occurs ni t log t a d d above the critical codimension the decay is algebraic ni t t a d d in general the exponents governing the long time behavior depend on the dimension as well as the codimension

a poincare birkhoff witt theorem for generalized lie color algebras a proof of the poincare birkhoff witt theorem is given for a class of generalized lie algebras closely related to the gurevich s lie algebras as concrete examples we construct the positive negative parts of the quantized universal enveloping algebras of type an and mp q e n k which is a nonstandard quantum deformation of gl n in particular we get for both algebras a unified proof of the poincare birkhoff witt theorem and we show that they are genuine universal enveloping algebras of certain generalized lie algebras

first passage and first exit times of a bessel like stochastic process we study a stochastic process x t which is a particular case of the rayleigh process and whose square is the bessel process with various applications in physics chemistry biology economics finance and other fields the stochastic differential equation is dx t nd x t dt 2d dw t where w t is the wiener process the drift term can arise from a logarithmic potential or from taking x t as the norm of a multidimensional random walk due to the singularity of the drift term for x t 0 different natures of boundary at the origin arise depending on the real parameter n entrance exit and regular for each of them we calculate analytically and numerically the probability density functions of first passage times or first exit times nontrivial behavior is observed in the case of a regular boundary