invariant subspaces of the dirichlet shift and pseudocontinuations in this paper we study extremal functions for invariant subspaces x of the dirichlet shift i e solutions v of the extremal problem sup if n 0 1 1f lid f e x f o here n is the smallest nonnegative integer such that the sup is positive it is known that such a function v generates x we show that the derivative z o has a pseudocontinuation to the exterior disc this pseudocontinuation is an analytic continuation exactly near those points of the unit circle where 0 is bounded away from zero we also show that the radial limit of the absolute value of an extremal function exists at every point of the unit circle some of our results are valid for all functions that are orthogonal to a nonzero invariant subspace

a representation theorem for cyclic analytic two isometries a bounded linear operator t on a complex separable hilbert space z is called a 2 isometry if t 2t2 2t t i o we say that t is analytic if nn 0 tnt 0 in this paper we show that every cyclic analytic 2 isometry can be represented as multiplication by z on a dirichlet type space d 8 here ze denotes a finite positive borel measure on the unit circle for two measures u and v the 2 isometries obtained as multiplication by z on d 8 and d v are unitarily equivalent if and only if u v we also investigate similarity and quasisimilarity of these 2 isometries and we apply our results to the invariant subspaces of the dirichlet shift

cyclicity and invariant subspaces in dirichlet spaces let be a positive finite measure on the unit circle and d the associated dirichlet space the generalized brown shields conjecture asserts that an outer function f d is cyclic if and only if c z f 0 where c is the capacity associated with d and z f is the zero set of f in this paper we prove that this conjecture is true for measures with countable support we also give in this case a complete and explicit characterization of invariant subspaces

non stationary processes of rotor bearing system in bifurcations non stationary processes of a rotor bearing system were dealt with by taking the rotating angular speed increases or decreases linearly at different levels of acceleration as control parameter the stationary bifurcation diagrams show that the period doubling bifurcation or quasi periodic bifurcation corresponding to the system with larger or smaller level of mass imbalance respectively occurs smoothly as the control parameter is increased or decreased in stationary manner then the non stationary processes of these two types of bifurcation were investigated by constructions of the non stationary bifurcation diagrams using non stationary bifurcation map technique in the non stationary bifurcation diagrams penetrations can be easily observed during the forward and reverse transitions and their absolute values increase with that of accelerations in all cases jumps exist only in forward period doubling transitions which indicate the quick increases of the amplitudes of motion time flows and orbit trajectories are also presented to illustrate the non stationary transition processes visually

perturbation of a hopf bifurcation by an external time periodic forcing contenrs i introduction ii the mathematical model iii dynamics of the poincark map in the non resonant and weakly resonant cases iv dynamics of the poincark map in the p l resonant case v dynamics of the poincart map in the p 2 resonant case vi dynamics of the poincark map in the p 3 resonant case

kernel and capacity estimates in dirichlet spaces abstract we study the capacity in the sense of beurling deny associated with the dirichlet space d where is a finite positive borel measure on the unit circle first we obtain a sharp asymptotic estimate of the norm of the reproducing kernel of d it allows us to give an estimate of the capacity of points and arcs of the unit circle we also provide new conditions on closed sets to be polar our method is based on sharp estimates of norms of some outer functions which allow us to transfer these problems to an estimate of the reproducing kernel of an appropriate weighted sobolev space

maximum entropy principle and classical evolution equations with source terms abstract we devise a maximum entropy technique to construct approximate time dependent solutions to evolution equations endowed with source terms and consequently not preserving normalization in some special cases the method yields exact solutions it is shown that the present implementation of the maximum entropy prescription always even in the case of approximate solutions preserves the exact functional relationship between the time derivative of the entropy and the time dependent solutions of the evolution equation other properties of the maximum entropy solutions and some illustrative examples are also discussed

maximum entropy approach to the collisional vlasov equation exact solutions we show that the maximum entropy approach proposed by el wakil elhanbaly and abdou from now on eea in s a el wakil a elhanbaly m a abdou physica a 323 2003 213 for solving approximately the collisional vlasov equation actually can provide exact solutions if properly implemented we consider here two alternative procedures for obtaining exact maximum entropy solutions of the aforementioned equation on the one hand after identifying an appropriate set of relevant mean values moments we show that there are exact maximum entropy solutions associated with that set of moments these solutions can be studied focusing either on the equations of motion of the moments themselves or on the equations of motion of the corresponding lagrange multipliers on the other hand it is possible to find exact solutions of the reduced equation considered by eea if one takes explicitly into account the zeroth order moment of the solutions

hopf bifurcation analysis of a rotor seal system abstract the hopf bifurcation behaviour of a symmetric rotor seal system was investigated using muszynska s non linear seal fluid dynamic force model for a perfectly balanced system the instability from certain critical equilibrium positions is proved to be the result of hopf bifurcation and only the supercritical type is found for a specific rotor system using poore s algebraic criteria hence a stable periodic orbit bifurcates from the critical equilibrium position after the threshold speed is exceeded due to the dimensionless whirl frequency being found to be close to 1 2 over quite a large range of system parameters the periodically perturbed hopf bifurcation in 1 2 subharmonic resonance is dealt with for an imbalanced rotor system the bifurcation of the averaged system obtained using the centre manifold procedure and averaging method is analyzed the results show that non synchronized whirl of the imbalanced rotor can either be a quasi periodic motion resulting from a hopf bifurcation or a half frequency whirl from period doubling bifurcation determined by the structure parameters of the system and operation conditions numerical simulation verifies the analytical results

well posedness and maximum entropy approximation for the dynamics of quantitative traits abstract we study the fokker planck equation derived in the large system limit of the markovian process describing the dynamics of quantitative traits the fokker planck equation is posed on a bounded domain and its transport and diffusion coefficients vanish on the domain s boundary we first argue that despite this degeneracy the standard no flux boundary condition is valid we derive the weak formulation of the problem and prove the existence and uniqueness of its solutions by constructing the corresponding contraction semigroup on a suitable function space then we prove that for the parameter regime with high enough mutation rate the problem exhibits a positive spectral gap which implies exponential convergence to equilibrium next we provide a simple derivation of the so called dynamic maximum entropy dynmaxent method for approximation of observables moments of the fokker planck solution which can be interpreted as a nonlinear galerkin approximation the limited applicability of the dynmaxent method inspires us to introduce its modified version that is valid for the whole range of admissible parameters finally we present several numerical experiments to demonstrate the performance of both the original and modified dynmaxent methods we observe that in the parameter regimes where both methods are valid the modified one exhibits slightly better approximation properties compared to the original one

on the brown shields conjecture for cyclicity in the dirichlet space abstract let d be the dirichlet space namely the space of holomorphic functions on the unit disk whose derivative is square integrable we establish a new sufficient condition for a function f d to be cyclic i e for p f p a polynomial to be dense in d this allows us to prove a special case of the conjecture of brown and shields that a function is cyclic in d iff it is outer and its zero set defined appropriately is of capacity zero

a generalization of the kullback leibler divergence and its properties a generalized kullback leibler relative entropy is introduced starting with the symmetric jackson derivative of the generalized overlap between two probability distributions the generalization retains much of the structure possessed by the original formulation we present the fundamental properties including positivity metricity concavity bounds and stability in addition a connection to shift information and behavior under liouville dynamics are discussed

dynamic analysis of a self excited hysteretic system the dynamic behaviour of a self excited system with hysteretic non linearity is investigated in this paper the averaging method is applied to the autonomous system and the resulting bifurcation equation of the self excited response is analyzed using the singularity theory the study of the bifurcation diagrams reveals the multivalued and jumping phenomena due to the effect of the hysteretic non linearity secondly the steady state response of the averaged system of the non autonomous oscillator in primary resonance is investigated due to the effect of the hysteretic non linearity the system exhibits softening spring behaviour a stability analysis shows that the steady state periodic response exists over a limited excitation frequency range it loses its stability outside the frequency range through hopf bifurcation and then the system undergoes quasi periodic motion finally by using circle maps to get winding numbers various orders of super and subharmonic resonance and mode locking are investigated the mode locking alternating with the quasi periodic responses takes place according to the farey number tree as revealed in many other systems the increase of the hystereticity can improve the stability of subharmonic resonance

cohomology of metacyclic groups group n by a finite cyclic group k using homological perturbation theory we introduce the beginning of a free resolution of the integers z over the group ring zg of g in such a way that the resolution reflects the structure of g as an extension of n by k and we use this resolution to compute the additive structure of the integral cohomology of g in many cases we proceed by first establishing a number of special cases thereafter constructing suitable cohomology classes thereby obtaining a lower bound then computing characteristic classes introduced in an earlier paper and finally exploiting these classes obtaining upper bounds for the cohomology via the integral cohomology spectral sequence of the extension e the calculation is then completed by comparing the two bounds

limits on inferring the past here we define and study the properties of retrodictive inference we derive equations relating retrodiction entropy and thermodynamic entropy and as a special case show that under equilibrium conditions the two are identical we demonstrate relations involving the kullback leibler divergence and retrodiction probability and bound the time rate of change of retrodiction entropy as a specific case we invert various langevin processes inferring the initial condition of n particles given their final positions at some later time we evaluate the retrodiction entropy for langevin dynamics exactly for special cases and find that one s ability to infer the initial state of a system can exhibit two possible qualitative behaviors depending on the potential energy landscape either decreasing indefinitely or asymptotically approaching a fixed value we also study how well we can retrodict points that evolve based on the logistic map we find singular changes in the retrodictivity near bifurcations counterintuitively the transition to chaos is accompanied by maximal retrodictability

experimental verification of jeffcott rotor model with preloaded snubber ring abstract this paper describes the experimental verification of a nonlinear jeffcott rotor model with a preloaded snubber ring the nonlinearity in the form of a discontinuous stiffness is caused by the radial clearance between rotor and the snubber ring the rotor is placed eccentrically within the snubber ring and the eccentricity can be varied for purpose of clarity the mathematical model of the rotor system with the preloaded snubber ring developed in pavlovskaia et al nonlinear dynamics of a jeffcott rotor with a preloaded snubber ring journal of sound and vibration 276 2004 361 379 is presented briefly theoretical results obtained from analytical approximate solutions and numerical simulations of the model are verified by the experimental study a detailed description of the experimental rig and the data acquisition system developed are presented along with the experimental procedures used to investigate the dynamical responses of the system the results concentrate on the dynamic responses caused by interactions between the whirling rotor and the massless snubber ring which has much higher support stiffness than the rotor bifurcation diagrams poincare maps and phase plane diagrams are used to compare the results obtained from the experiment and the theory good correlation between the experimental and theoretical results is found

periodically perturbed hopf bifurcation in this paper the influence of small periodic perturbations on systems exhibiting hopf bifurcation is studied in detail in two dimensional systems that ordinarily exhibit hopf bifurcation the addition of small periodic parametric excitation gives rise to interesting secondary phenomena explicit results for various primary and secondary bifurcations along with their stabilities are obtained in this work the ideas related to method of averaging poincare birkhoff normal forms and center manifold theorem are used appropriately at different stages it is found that various results obtained using these techniques agree in their common regions of validity

quasi equilibrium closure hierarchies for the boltzmann equation abstract after boltzmann and gibbs the notion of disorder in statistical physics relates to ensembles not to individual states this disorder is measured by the logarithm of ensemble volume the entropy but recent results about measure concentration effects in analysis and geometry allow us to return from the ensemble based point of view to a state based one at least partially in this paper the order disorder problem is represented as a problem of relation between distance and measure the effect of strong order disorder separation for multiparticle systems is described the phase space could be divided into two subsets one of them set of disordered states has almost zero diameter the second one has almost zero measure the symmetry with respect to permutations of particles is responsible for this type of concentration dynamics of systems with strong order disorder separation has high average acceleration squared which can be interpreted as evolution through a series of collisions acceleration dominated dynamics the time arrow direction from order to disorder follows from the strong order disorder separation but inverse for systems in space of symmetric configurations with sticky boundaries the way back from disorder to order is typical natural selection recommendations for mining of molecular dynamics results are also presented

dynamics of non stationary processes that follow the maximum of the renyi entropy principle we propose dynamics equations which describe the behaviour of non stationary processes that follow the maximum renyi entropy principle the equations are derived on the basis of the speed gradient principle originated in the control theory the maximum of the renyi entropy principle is analysed for discrete and continuous cases and both a discrete random variable and probability density function pdf are used we consider mass conservation and energy conservation constraints and demonstrate the uniqueness of the limit distribution and asymptotic convergence of the pdf for both cases the coincidence of the limit distribution of the proposed equations with the renyi distribution is examined

numerical analysis of nonlinear rotor seal system abstract the seal characteristic is an important factor affecting the performance of the rotor system the nonlinear model of the rotor seal system is established using muszynska s nonlinear seal forces an efficient and high precision direct integration scheme is presented based on the 2 n type algorithm for the computation of exponential matrices the nonlinear phenomena in the unbalanced rotor seal system are investigated using the adopted model and numerical integration method the influence of the seal on the nonlinear characteristics of the rotor system is analyzed by the bifurcation diagrams and poincare maps various nonlinear phenomena in the rotor seal system such as periodic motion double periodic motion quasi periodic motion and hopf bifurcation are investigated and the stability is judged by floquet theory and bifurcation theorem the influence of parameters on the critical instability speed of the balanced rotor seal system is also included the high precision direct integration method is effectively applied to the nonlinear numerical analysis of the rotor seal system the scheme has high precision and a large time step may be adopted to save computing resources

cyclic vectors in the dirichlet space we study the hilbert space of analytic functions with finite dinchlet integral in the open unit disc we try to identify the functions whose polynomial multiples are dense in this space theorems 1 and 2 confirm a special case of the following conjecture if ij z i ig z l at all points and if g is cyclic thenjis cyclic theorems 3 5 give a sufficient condition t is an outer function with some smoothness and the boundary zero set is at most countable and a necessary condition the radial limit can vanish only for a set of loganthmic capacity zero for a function j to be cyclic introduction in this paper we shall study the hilbert space of analytic functions in the open unit disc a in the complex plane that have a finite dirichlet integral jj if t12 dx dy g z l for some cyclic g and all z question 4 asks if f must be cyclic whenever f and l f are both in the space no examples are known where either of these questions has a negative answer in 2 we begin the study of cyclic vectors in the dirichlet space d theorems 1 and 2 give a partial answer to question 3 above for this space this section also contains 2 propositions 10 11 and 4 questions 7 10 proposition 11 says that if f and g are bounded functions in d whose product is cyclic then bothf and g must be cyclic theorem 2 gives a partial converse we require that gl be dini continuous on received by the editors july 21 1983 1980 mathematics subject classification primary 30h05 secondary 46e15 46e20 47b37

information gain within nonextensive thermostatistics we discuss the information theoretical foundations of the kullback information gain recently generalized within a nonextensive thermostatistical formalism general properties are studied and in particular a consistent test for measuring the degree of correlation between random variables is proposed in addition minimum entropy distributions are discussed and the h theorem is proved within the generalized context

toeplitz operators on harmonically weighted bergman spaces and applications to composition operators on dirichlet spaces abstract in this paper we consider toeplitz operators acting on bergman spaces associated with harmonic weights we give a complete description of those operators which belong to p schatten classes we also obtain an upper estimate for the reproducing kernel of these spaces applications to composition operators on dirichlet spaces are given

maximum entropy approach to stretched exponential probability distributions we introduce a nonextensive entropy functionals whose optimization under simple constraints mean values of some standard quantities yields stretched exponential probability distributions which occur in many complex systems the new entropy functional is characterized by a parameter the stretching exponent such that for d 1 the standard logarithmic entropy is recovered we study its mathematical properties showing that the basic requirements for a well behaved entropy functional are verified i e s possesses the usual properties of positivity equiprobability concavity and irreversibility and verifies khinchin axioms except the one related to additivity since s is nonextensive the entropys is shown to be superadditive for 1