isotropic gauss markov currents a natural definition of the markov property for multi parameter random processes random fields is the following let xt t n be a multiparameter process for any set d in n let d denote the field generated by x t t d the field xt t d is said to be markov or markov of degree 1 6 or sharp markov if for any bounded open set d with smooth boundary d and d c are conditionally independent given d it has been known for some time that to find interesting examples of markov processes under this definition it is necessary to consider generalized random functions in this paper we show that a natural framework for the markov property of multiparameter processes is a class of generalized random differential forms i e random currents our principal objective is to relate the markovian nature of an isotropic gaussian current to its spectral properties

on the curvature of piecewise flat spaces we consider analogs of the lipschitz killing curvatures of smooth riemannian manifolds for piecewise flat spaces in the special case of scalar curvature the definition is due to t regge considerations in this spirit date back to j steiner we show that if a piecewise flat space approximates a smooth space in a suitable sense then the corresponding curvatures are close in the sense of measures

classical dirichlet forms on topological vector spaces the construction of the associated diffusion process given a minimal classical dirichlet form onl 2 e we construct the associated diffusion process heree is a locally convex topological vector space and is a not necessarily quasi invariant probability measure one the construction is carried out under certain assumptions one and which can be easily verified in many examples in particular we explicitly apply our results to time zero and space time quantum fields with or with out cut off

construction of convergent simplicial approximations of quantum fields on riemannian manifolds we construct simplicial approximations of random fields on riemannian manifolds of dimensiond we prove convergence of the fields to the continuum limit for arbitraryd in the gaussian case and ford 2 in the non gaussian case in particular we obtain convergence of the simplicial approximation to the continuum limit for quantum fields on riemannian manifolds with exponential interaction

friction induced vibration in periodic linear elastic media for a one dimensional finite elastic continuum with distributed contacts and periodic boundary conditions the presence of unstable waves is investigated the stability of the waves is evaluated and explanations for instabilities under a constant coefficient of friction are provided a negative slope in the coefficient of friction as a function of sliding speed is not a necessary condition for the occurrence of dynamic instability dynamic instability occurs in the form of self excited unstable travelling waves the stabilizing effects of external and internal damping were studied low and high frequency terms of the travelling waves are stabilized by adding external and internal damping respectively responses corresponding to unstable eigenvalues can dominate the system response it is presumed that this can lead to squeaking or squealing noise in applications

a geometrically non linear model of rotating shafts with internal resonance and self excited vibration a geometrically non linear model of the rotating shaft is introduced which includes karman non linearity non linear curvature effects large displacements and rotations as well as gyroscopic effects through applying timoshenko type assumptions the shear effects are also included in the model convenient matrix descriptions are used in order to facilitate the analysis based on galerkin and continuation methods the model is used to analyze the phenomenon of internal resonance the influence of some of the system s parameters on the amplitude and frequency of self excited vibration is investigated

hopf bifurcation at 1 1 resonance on etudie un probleme concernant la bifurcation de hopf pour une famille a 1 parametre d equations differentielles dans un cas de resonance

instabilities and bifurcations in a rotating shaft abstract flexural vibrations of a slender balanced rotating shaft are considered the shaft is of circular cross section it rotates at a constant rate about its longitudinal axis of symmetry and is made of a viscoelastic material the effects of large transverse displacements and external sources of dissipation are also included the resulting non linear model is analyzed for stability and bifurcations of the trivial shaft configuration the undeformed straight position the instabilities are predicted by using the linearized shaft model and the post critical behaviors are determined by applying center manifold theory to the full non linear equations of motion the bifurcations encountered are simple hopf double hopf and double zero eigenvalues it is determined that synchronous whirl non synchronous whirl and competing mode types of behavior are possible for various ranges of the parameter values the results obtained prove that the modal truncations typically used when analyzing continuous shaft instabilities are mathematically justifiable

representation and construction of multiplicative noise 251 the basic assumption in this paper in which we continue expand and in certain respects bring to conclusion the investigations from 2 is as follows we consider exclusively noise with values in some topological monoid semigroup which are multiplicative in distribution at dif ferent points since multiplication of independent random variables with values in a monoid corresponds to convolution it is clear that this is an invariance assumption we will now give a brief discussion of our results generally speaking one should look upon them as generalizations to random fields and therefore to a more general time parameter of the classical levy khinchin formulae and their consequences section 3 corresponds to processes with stationary and independent increments otherwise stationarity is not assumed in section 1 we prove a kind of daniell kolmogorov theorem to settle the relevant questions on consistency and existence furthermore support properties are discussed we introduce an additional basic assumption our noise is continuous on its support in the sense that it is non atomic in section 2 we restrict ourselves to noise with values in an abelian group a complete characterisation via the fourier transform is afforded by theorem 2 5 in section 3 we assume a general kind of invariance not necessarily given by translations also in the domain of definition then at least formally our random field is of the form x p where x t

stochastic multiplicative measures generalized markov semigroups and group valued stochastic processes and fields abstract we extend the well known relation between markov semigroups and processes with independent increments to the case of generalized group valued semigroups indexed by some measurable space and stochastic multiplicative measures we give a kolmogorov type theorem and a classification theorem connecting the stochastic multiplicative measures with vector valued levy khinchine fields the results have applications to the study of stochastic connections and differential equations for forms on lie groups

parametric stabilization of a gyroscopic system this paper studies the stabilization of a gyroscopic system using parametric stabilization near a combination resonance the gyroscopic system is near its primary instability i e the bifurcation parameter is such that the system possesses a double zero eigenvalue the stability of the system is studied for the linear hamiltonian system the damped linear system the forced linear hamiltonian system and finally the damped and forced linear system the addition of the periodic excitation near the critical combination resonance provides the system with an extended stability region when the excitation frequency is slightly above the combination resonance a non linear numerical example shows that these results may persist for the non linear problem the results of this work are then discussed in relation to an example gyroscopic problem a rotating shaft with periodically perturbed rotation rate

convergence of u 1 3 lattice gauge theory to its continuum limit it is shown that in three space time dimensions the pure u 1 lattice gauge theory with villain action and fixed coupling constant converges to the free electromagnetic field as the lattice spacing approaches zero the same holds for the wilson action on the electric sector

lattice systems with a continuous symmetry iii low temperature asymptotic expansion for the plane rotator model we prove that the expansion in powers of the temperature t of the correlation functions and the free energy of the plane rotator model on a d dimensional lattice is asymptotic to all orders in t the leading term in the expansion is the spin wave approximation and the higher powers are obtained by the usual perturbation series we also prove the inverse power decay of the pair correlation at low temperatures for d 3

on the minimum spectral radius of matrices of zeros and ones abstract we consider the minimum spectral radius for an n n matrix of 0 s and 1 s having a specified number of 0 s we determine this minimum spectral radius when n 2 n 2 and bound it between two consecutive integers for all other values of

abelian chern simons theory and linking numbers via oscillatory integrals a rigorous mathematical model of abelian chern simons theory based on the theory of infinite dimensional oscillatory integrals developed by albeverio and ho egh krohn is introduced a gauge fixed chern simons path integral is constructed as a fresnel integral in a certain hilbert space wilson loop variables are defined as fresnel integrable functions and it is shown in this context that the expectation value of products of wilson loops with respect to the chern simons path integral is a topological invariant which can be computed in terms of pairwise linking numbers of the loops as conjectured by witten furthermore a lattice chern simons action is proposed which converges to the continuum limit

the maximum determinant of an n n lower hessenberg 0 1 matrix abstract let a aij be an n n 0 1 matrix which is lower hessenberg i e aij 0 for j i 1 there are 2n 1 possibly nonzero terms in the determinant of an n n lower hessenberg 0 1 matrix so this is a triavial upper bound for the determinant we define an n n 0 1 matrix dn and show that this upper bound is det d n 1 5 1 5 2 n 1 5 2 n here det dn is the nth filbonacci number i e det d n det d n 1 det d n 2 and det d 1 det d 2 1 one has det dn as n this answers positively a question due to w w barrett

convergence of theu 1 4 lattice gauge theory to its continuum limit it is shown that in four space time dimensions the compactu 1 lattice gauge theory with general energy function converges to a renormalized free electromagnetic field on the current sector as the lattice spacing approaches zero provided the coupling constant is sufficiently large for the wilson energy function it is possible by judicious choice of the gibbs state to get convergence for arbitrary coupling strengths furthermore for all but a countable number of values of the coupling constant the limit exists and is independent of the particular state chosen to define the lattice model

a convergent lattice approximation for nonlinear electromagnetic fields in four dimensions a discrete version of the quaternionic cauchy riemann equation a f where f is gauss poisson white noise is discussed on the lattice z4 random variables f n and a n are constructed which approximate the corresponding random fields f and a respectively in the limit 0 in the gaussian case the random variables a n can be interpreted as the lattice approximation of the free electromagnetic euclidean potential field whereas in the non gaussian case one obtains an approximation of nonlinear interacting electromagnetic quantum fields convergence to the continuum limit is proven

lattice systems with a continuous symmetry we prove that the expansion in powers of the temperature t of the correlation functions and the free energy of the plane rotator model on a d dimensional lattice is asymptotic to all orders in t the leading term in the expansion is the spin wave approximation and the higher powers are obtained by the usual perturbation series we also prove the inverse power decay of the pair correlation at low temperatures for d 3

ferromagneticity of simplicial fields on two dimensional compact manifolds smooth triangulations of a compact smooth connected two dimensional riemannian manifold m are considered the q simplicial fields are defined with values in the space of q cochains and a natural gaussian measure is defined giving their distribution with covariance defined essentially in terms of the combinatorial laplacian c in the continuum limit this measure for q 0 is the free quantum field measure over m in this case it is shown that for a certain collection of triangulations there exists a sequence of subdivisions of each triangulation such that the corresponding measure is ferromagnetic it is also shown that for sufficiently fine subdivisions m2i m 0 has nonpositive off diagonal elements the proofs are obtained by a result on triangulations by simplexes with acute angles it is also proven that the probability measures describing quantum fields on m with polynomial trigonometric or exponential interactions satisfy fkg inequalities

random fields as solutions of the inhomogeneous quaternionic cauchy riemann equation i invariance and analytic continuation we consider random fieldsa satisfying the quaternionic cauchy riemann equation a f wheref is white noise under appropriate conditions onf a is invariant under the proper euclidean group in four dimensions but in general not under time reflection the schwinger functions can be analytically continued to wightman functions satisfying the relativistic postulates on invariance specrral property and locality

uniqueness and the global markov property for euclidean fields the case of general exponential interaction the uniqueness and the global markov property for the regular gibbs measure corresponding to the interaction u lambda varphi lambda int limits lambda d 2 x int d varrho alpha e alpha varphi 0 x for 0 d a probability measure with support in 2 sqrt pi 2 sqrt pi is proved

on hessenberg and pentadiagonal determinants related with fibonacci and fibonacci like numbers in this paper we establish several new connections between the generalizations of fibonacci and lucas sequences and hessenberg determinants we also give an interesting conjecture related to the determinant of an infinite pentadiagonal matrix with the classical fibonacci and gaussian fibonacci numbers

three dimensional gravity capillary waves on water small surface tension case abstract this paper considers three dimensional gravity capillary waves on water of finite depth which are uniformly translating in a horizontal propagating direction and periodic in a transverse direction the exact euler equations are formulated as a spatial dynamic system in which the variable used for the propagating direction is a time like variable the existence of the solutions of the system is determined by two non dimensional constants the bond number b and the froude number f which in turn give the number of eigenvalues on the imaginary axis of the complex plane for the corresponding linearized operator around a uniform flow assume that f 2 c 1 is the curve in the b plane on which the first two eigenvalues for three dimensional waves collide at the imaginary axis and the intersection point of c 1 with 1 is b 1 0 in this paper the case for 0 b b 1 and b near c 1 is considered a center manifold reduction technique and a normal form analysis are applied to show that the dynamical system can be reduced to a system of ordinary differential equations using the existence of a homoclinic orbit connecting to a two dimensional periodic called generalized solitary wave thereafter solution for the reduced system it is shown that such a generalized solitary wave solution persists for the original system by applying a perturbation method and adjusting some appropriate constants

a simple global characterization for normal forms of singular vector fields we derive a new global characterization of the normal forms of amplitude equations describing the dynamics of competing order parameters in degenerate bifurcation problems using an appropriate scalar product in the space of homogeneous vector polynomials we show that the resonant terms commute with the group generated by the adjoint of the original critical linear operator this leads to a very efficient constructive method to compute both the nonlinear coefficients and the unfolding of the normal form explicit examples and results obtained when there are additional symmetries are also presented

amplitude equations for systems with competing instabilities we describe how to derive ordinary differential equations to predict the time dependence of a system governed by partial differential equations when that system is near to the polycritical condition for the onset of several instabilities the method is illustrated for the general case of two competing instabilities and then a specific physical example of this case is worked out in detail the basic idea is to extend the krylov bogolyubov mitropolsky method of nonlinear mechanics to bifurcation problems