invariants of 3 manifolds via link polynomials and quantum groups the aim of this paper is to construct new topological invariants of compact oriented 3 manifolds and of framed links in such manifolds our invariant of a link in a closed oriented 3 manifold is a sequence of complex numbers parametrized by complex roots of 1 for a framed link in s 3 the terms of the sequence are equale to the values of the suitably parametrized jones polynomial of the link in the corresponding roots of 1 in the case of manifolds with boundary our invariant is a sequence of finite dimensional complex linear operators this produces from each root of unity q a 3 dimensional topological quantum field theory

higher dimensional abelian chern simons theories and their link invariants the role played by deligne beilinson cohomology in establishing the relation between chern simons theory and link invariants in dimensions higher than three is investigated deligne beilinson cohomology classes provide a natural abelian chern simons action non trivial only in dimensions 4l 3 whose parameter k is quantized the generalized wilson 2l 1 loops are observables of the theory and their charges are quantized the chern simons action is then used to compute invariants for links of 2l 1 loops first on closed 4l 3 manifolds through a novel geometric computation then on r4l 3 through an unconventional field theoretic computation

stability analysis of discrete time fuzzy model based control systems with time delay time delay independent approach this paper presents the stability analysis of discrete time fuzzy model based control systems with time delays to facilitate the stability analysis the t s fuzzy model is employed to represent the discrete time nonlinear system due to the multiplication property of the fuzzy model based control system the number of lmi based stability conditions is p p 1 2 where p is the number of rules for the fuzzy model and fuzzy controller consequently the computational demand for solving the solution to the stability conditions is very expensive especially when the value of p is large the problem becomes much worse when the relaxed stability conditions are formulated as huge matrices the huge matrices incorporate the information of all the closed loop subsystems which may cause the solution of the lmi based stability conditions difficult or even impossible to obtain owing to the limited computer power in this paper to reduce the computational demand the fuzzy model based control system is divided into parts which the control input will handle separately as a result the multiplication property of the fuzzy model based control system can be removed which effectively reduces the number of stability conditions to p and the computational demand for finding the solution can be reduced lmi based delay independent stability conditions are derived using the lyapunov based approach simulation examples are given to illustrate the effectiveness of the proposed approach

dynamic response of non linear systems to poisson distributed random impulses abstract the dynamic response of non linear systems to external excitations in form of a poisson distributed train of random impulses is considered the state vector of the dynamical system under consideration is a poisson driven markov vector process the equations governing its joint statistical moments are obtained by making use of a generalized ito s differential rule the resulting infinite hierarchy of equations is truncated with the help of a cumulant neglect closure of different orders for a duffing oscillator the time histories of the mean value the variance and the skewness coefficient of the response are evaluated analytically and compared with those obtained from monte carlo simulations it is found that if the departure of the poisson driven excitation process from gaussianity ranges from small to moderately large i e the expected arrival rate of impulses is not very low the application of the fourth order cumulant neglect closure technique i e neglecting the cumulants above the fourth order yields very good estimates of the response mean values and variances

response of nonlinear systems in probability domain using stochastic averaging determination of probability density function pdf of the response for strongly nonlinear single degree of freedom system subjected to both multiplicative and additive random excitations using stochastic averaging technique is faced with few difficulties firstly the size of excitations should be small such that the response of the system converges weakly to a markov process secondly the excitations should preferably be broad banded so that the analytical results are reasonably accurate and finally the nonlinear functions should be integrable if closed formed expressions for the result are desired the above issues are examined in the paper with a view to show a limiting values of the size parameter of excitations for which stochastic averaging technique can be applied to obtain reasonable estimates of pdf and mean square value of response b the effect of the nature of the frequency contents of excitation on the response and c the use of the stochastic averaging method employing generalized harmonic functions for nonintegrable functions representing the dynamic system it is shown that the stochastic averaging procedure provides results which compare very well with those obtained from simulation analysis not only for wide band excitations but also for narrow band excitations for a wide range of the size parameter of excitation further the procedure can be easily implemented for highly irregular functions by employing a numerical scheme with fft

abelian bf theory and turaev viro invariant the u 1 bf quantum field theory is revisited in the light of deligne beilinson cohomology we show how the u 1 chern simons partition function is related to the bf one and how the latter on its turn coincides with an abelian turaev viro invariant significant differences compared to the non abelian case are highlighted

three manifold invariant from functional integration we give a precise definition and produce a path integral computation of the normalized partition function of the abelian u 1 chern simons field theory defined in a general closed oriented 3 manifold we use the deligne beilinson formalism we sum over the inequivalent u 1 principal bundles over the manifold and for each bundle we integrate over the gauge orbits of the associated connection 1 forms the result of the functional integration is compared with the abelian u 1 reshetikhin turaev surgery invariant

statistical linearization of the duffing oscillator under non gaussian external excitation the duffing oscillator under external non gaussian excitations is investigated by means of statistical linearization the input process is modelled as a polynomial of a gaussian process or as a renewal driven impulse process four criteria of statistical linearization are considered the interarrival times of the renewal process are distributed according to a pearson type iii law predictions of the stationary variance are compared with monte carlo simulations

response of stochastic dynamical systems driven by additive gaussian and poisson white noise solution of a forward generalized kolmogorov equation by a spectral finite difference method abstract a numerical method is given for the solution of the probability density function of the response process of memoryless one and two state dynamical systems having polynomial restoring forces and which are subjected to a combination of gaussian and poisson white noises the method employs the fourier transformed forward generalized kolmogorov equation to arrive at an initial boundary value problem for the characteristic function which is solved using a high order finite difference procedure the probability density function is recovered by numerical inverse fourier transformation several examples are given the results of which are compared with analytical solutions where available and with simulation otherwise

the de rham federer theory of differential characters and character duality the theory of differential characters is developed completely from a de rham federer viewpoint characters are defined as equivalence classes of special currents called sparks which appear naturally in the theory of singular connections as in de rham federer cohomology many different spaces of currents are shown to yield the character groups the fundamental exact sequences are derived and a multiplication of de rham federer characters is defined using new transversality intersection results for flat and rectifiable currents an equivalence of de rham federer characters with the classical cheeger simons characters is given as in de rham cohomology via integration this discussion rounds out the approach to characters introduced by gillet soule and harris the groups of differential characters have a natural topology and smooth pontrjagin duals introduced here which fit into fundamental exact sequences a principal result is the formulation and proof of duality for characters on oriented manifolds it is shown that the pairing a b inline graphic xmlns xlink http www w3 org 1999 xlink xlink href 01i a b x defined by multiplication and evaluation on the fundamental cycle gives an isomorphism of the group of differential characters of degree k with the dual to characters in degree n k 1 where n dim x thom homomorphisms which refine the usual ones in de rham theory and integral cohmology are established for differential characters gysin maps for characters are similarly established new examples namely morse sparks and hodge sparks are introduced and examined in detail

stochastic response of vibro impact duffing oscillators under external and parametric gaussian white noises abstract this study presents a solution procedure for the stationary probability density function pdf of the response of vibro impact duffing oscillators under external and parametric gaussian white noises first the zhuravlev non smooth coordinate transformation is adopted to convert a vibro impact oscillator into an oscillator without barriers the stationary pdf of the converted oscillator is governed by the fokker planck fp equation the fp equation is solved by the exponential polynomial closure epc method illustrative examples are presented with vibro impact duffing oscillators under external and parametric gaussian white noises to show the effectiveness of the solution procedure the parametric excitation is acting in displacement and the constraint is a unilateral zero offset barrier the restitution coefficient of impacts is taken as 0 90 comparison with the simulated results shows that the proposed solution procedure can provide good approximate pdfs for displacement and velocity although a little difference exists in the tail of these pdfs this difference may be due to the weak approximation on the response of the vibro impact oscillators using a continuous markov process when the restitution coefficient is not very close to unity

exact stationary probability density for second order non linear systems under external white noise excitation abstract in this paper exact stationary solutions are constructed for non linear dynamical systems subjected to stochastic excitation the solution of the equations 6 7 in this paper is demonstrated to be unique and then the results of references 10 11 are shown to be generalized therefore new exact stationary solutions that satisfies the fokker plank kolmogorov fpk equation is obtainable

abelian link invariants and homology we consider the link invariants defined by the quantum chern simons field theory with compact gauge group u 1 in a closed oriented 3 manifold m the relation of the abelian link invariants with the homology group of the complement of the links is discussed we prove that when m is a homology sphere or when a link in a generic manifold m is homologically trivial the associated observables coincide with the observables of the sphere s3 finally we show that the u 1 reshetikhin turaev surgery invariant of the manifold m is not a function of the homology group only nor a function of the homotopy type of m alone

probabilistic solution of nonlinear oscillators excited by combined gaussian and poisson white noises abstract the stationary probability density function pdf solution of the stochastic response of nonlinear oscillators is investigated in this paper the external excitation is assumed to be a combination of gaussian and poisson white noises the pdf solution is governed by the generalized kolmogorov equation which is solved by the exponential polynomial closure epc method in order to evaluate the effectiveness of the epc method different nonlinear oscillators are considered in numerical analysis nonlinearity exists either in displacement or in velocity for these nonlinear oscillators the impulse arrival rate mono modal pdf and bi modal pdf are also considered in this study compared to the pdf given by monte carlo simulation the epc method presents good agreement with the simulated result which can also be observed in the tail region of the pdf solution

response of dynamic systems to poisson white noise abstract a method is developed for finding response statistics and reliability for a non linear system subjected to poisson white noise the poisson white noise can be viewed as a sequence of independent indentically distributed pulses arriving in time according to a poisson counting process the method is based on the observation that the system experiences free vibrations between consecutive pulses of the input two algorithms are used for analysis the first uses the definition of the poisson white noise and the second is based on an approximate representation of the poisson white noise referred to as binomial white noise the binomial white noise is an independent time series with a fixed time step that can be zero with a finite probability the time step of the first and second algorithms are random and deterministic respectively the algorithms are used to calculate transition probabilities and estimate response statistics numerical examples are presented to demonstrate the proposed method of response and reliability analysis

holonomy and parallel transport for abelian gerbes in this paper we establish a one to one correspondence between u 1 gerbes with connections on the one hand and their holonomies for simply connected manifolds or their parallel transports in the general case on the other hand this result is a higher order analogue of the familiar equivalence between bundles with connections and their holonomies for connected manifolds the holonomy of a gerbe with group u 1 on a simply connected manifold m is a group morphism from the thin second homotopy group to u 1 satisfying a smoothness condition where a homotopy between maps from 0 1 2 to m is thin when its derivative is of rank 2 for the non simply connected case holonomy is replaced by a parallel transport functor between two special lie groupoids which we call lie 2 groups the reconstruction of the gerbe and connection from its holonomy is carried out in detail for the simply connected case

maximum entropy principle and nonlinear stochastic oscillators abstract the principle of maximum entropy introduced first in physics and successfully applied in many other fields e g statistics reliability estimation simulation has recently been developed to analyze the systems governed by stochastic differential equations in this paper we extend the maximum entropy method to the general class of stochastic nonlinear systems and apply it to stochastic nonlinear oscillators to indicate the effectiveness of the method a comparison of the results with predictions of the known procedures is shown graphically the analysis presented in this paper indicates that the maximum entropy principle can serve as a general method for determining the probability distributions of a wide class of stochastic systems when we have only a partial information in the form of moments or equations for moments

deligne beilinson cohomology and abelian link invariants torsion case for the abelian chern simons field theory we consider the quantum functional integration over the deligne beilinson cohomology classes and present an explicit path integral nonperturbative computation of the chern simons link invariants in so 3 rp3 a toy example of a 3 manifold with torsion

an improved path integration method for nonlinear systems under poisson white noise excitation abstract in order to overcome some unsatisfactory trends and limitations of the traditional path integration pi method for poisson white noise a novel pi method is proposed in this paper which includes two improved schemes the first one is a new transition probability density function tpdf approximation which considers the randomness of the impulse happening time during each time intervals the second one is a transformation of chapman kolmogorov ck equation by a variable substitution instead of directly using it whose numerical calculation is based on the back stepping runge kutta scheme and the triangulation based interpolation monte carlo simulations mcs are utilized to measure the accuracy of the improved algorithm with three illustrative nonlinear systems the results show that compared with the traditional pi method the improved pi method can give a more accurate description of the tpdf values and provide more precise stationary probability density function pdf results whenever the mean arrival rate is large or small the improved algorithm has a wider range of choices in time interval values to maintain the accuracy of stationary pdf results besides it is discovered that cubic interpolation deserves to be applied in the improved pi method more than linear and natural interpolations

reliability of non linear oscillators subject to poisson driven impulses abstract the reliability problem of a sdof non linear and non hysteretic oscillator subject to a stationary poisson driven train of impulses is considered in the first passage time problem of the oscillator time invariant double barriers with a deterministic start in the safe domain are assumed initially the kolmogorov feller backwards equation for the reliability function along with associated initial and boundary conditions is specified next a petrov galerkin approach with shape and weighting functions matching all differentiability and continuity requirements of the weak formulation is applied to solve the consequent partial differential equation as an example a duffing oscillator with linear damping is considered

extreme value prediction for non linear stochastic oscillators via numerical solutions of the stationary fpk equation abstract the accuracy of two well established numerical methods is demonstrated and the importance of bandwidth examined for computationally efficient markov based extreme value predictions associated with finite duration stationary sample paths of a non linear oscillator driven by gaussian white noise by making the poisson assumption of independent upcrossings extreme exceedance probabilities are predicted via the mean threshold crossing rate using numerical solutions of the stationary fokker planck fpk equation with bandwidth initially ignored predicted exceedances using the weighted residual methods of bhandari and sherrer soize and kunert and the finite element method of langley are compared with nominally exact predictions for a heavily damped duffing type model obtained by using an explicit fpk solution the fe method being established as superior predictions via fe solutions are then compared with very long monte carlo simulations in which bandwidth effects are included two lightly damped non linear oscillator models are examined both with cubic stiffness but different damping mechanisms one model again being of simple duffing type with linear damping the other being appropriate to single co ordinate random vibration of a clamped clamped beam with wholly non linear damping the realistic damping parameter values assigned to the beam model are statistically equivalent to the linear damping level chosen for the simple model at just above 1 at this overall damping level results clearly demonstrate that for the probability levels and durations considered bandwidth is only important for the linearly damped model for the beam model with non linear damping bandwidth can be ignored allowing accurate extreme exceedance predictions by using only the stationary fpk equation the paper also demonstrates that the limiting decay rate of the first passage probability advocated by crandall roberts and others as a criterion for deciding the barrier height above which first passage times can be assumed independent proves grossly over conservative as a corresponding criterion for deciding the independence level for use in stationary extreme value prediction