not necessary but sufficient condition for the positivity of generalized wigner functions many authors both in quantum mechanics and signal theory are concerned with a condition of positivity for the generalized wigner functions they give and use as necessary and sufficient the condition that the kernel be the characteristic function of another wigner function it is shown that the condition is not necessary but only sufficient

levy walk with multiple internal states levy walk with multiple internal states can effectively model the motion of particles that don t immediately move back to the directions or areas which they come from when the levy walk behaves superdiffusion it is discovered that the non immediately repeating property characterized by the constructed transition matrix has no influence on the particle s mean square displacement msd or pearson coefficient this is a kind of stable property of levy walk however if the levy walk shows the dynamical behaviors of normal diffusion then the effect of non immediately repeating emerges for the levy walk with some particular transition matrices it may display nonsymmetric dynamics in these cases the behaviors of their variances are detailedly discussed especially some comparisons with the ones of the continuous time random walks are made a striking difference is the changes of the exponents of the variances the first passage time distribution and its average of levy walks are simulated the results of which turn out that the first passage time can distinguish levy walks with different transition matrices while the msd can not

linear response in complex systems ctrw and the fractional fokker planck equations abstract we consider the linear response of systems modelled by continuous time random walks ctrw and by fractional fokker planck equations under the influence of time dependent external fields we calculate the corresponding response functions explicitly the ctrw curve exhibits aging i e it is not translationally invariant in the time domain this is different from what happens under fractional fokker planck conditions

phase space functions and correspondence rules it is shown that positive quantum joint distributions in phase space lead to quantum mechanical operators depending on the state to be considered it is also shown that a simple requirement of canonical invariance leads to the weyl correspondence rule as the only allowed one

kahler einstein metrics and the kahler ricci flow on log fano varieties we prove the existence and uniqueness of kahler einstein metrics on q fano varieties with log terminal singularities and more generally on log fano pairs whose mabuchi functional is proper we study analogues of the works of perelman on the convergence of the normalized kahler ricci flow and of keller rubinstein on its discrete version ricci iteration in the special case of non singular fano manifolds our results on ricci iteration yield smooth convergence without any additional condition improving on previous results our result for the kahler ricci flow provides weak convergence independently of perelman s celebrated estimates

linear chevalley estimates a chevalley estimate for a germ of an analytic mapping is a function n n such that if the composite with of a germ of an analytic function on the target vanishes to order at least l k then it vanishes on the image to order at least k work of izumi revealed the equivalence between reg ularity of a mapping in the sense of gabrielov see 1 and the existence of a linear chevalley estimate l k bierstone and milman showed that uniformity of the chevalley estimate is fundamental to several analytic and geometric prob lems on the images of mappings the central topic of this article is uniformity of linear chevalley estimates for regular mappings we first establish the equivalence between uniformity of a linear chevalley estimate and uniformity of a linear product estimate on the image a linear product estimate on a local analytic ring or equivalently on a germ of an ana lytic space means a bound on the order of vanishing of a product of elements which is linear with respect to the sum of the orders of its factors we study the linear product estimate in the central case of a hypersurface i e the zero set of an analytic function our results show that a linear product estimate is equivalent to an explicit estimate concerning resultants in the special case of hypersurfaces of multiplicity 2 this allows us to prove uniformity of linear product estimates

levy statistics in a hamiltonian system enhanced diffusion in a hamiltonian system is studied in terms of the continuous time random walk formulation for l evy walks the previous l evy walk scheme is extended i to include interruptions by periods of temporal localization and ii to describe motion in two dimensions we analyze a case of conservative motion in a two dimensional periodic potential numerical calculations of the mean squared displacements and the propagators for intermediate energies are consistent with the l evy walk description

the quantum normal form and its equivalents a quantum analog called the quantum normal form of the classical birkhoff gustavson normal form is presented the algebraic relationship between the quantum and birkhoff gustavson normal forms has been established by developing the latter using lie transforms it is shown that the birkhoff gustavson normal form can be obtained from the quantum normal form using an anharmonic oscillator and a henon heiles system as test cases the equivalence between the quantum normal form and the rayleigh schrodinger perturbation method is shown this equivalence provides an algebraic connection between the birkhoff gustavson normal form and the rayleigh schrodinger perturbation approach the question of weyl and torus quantizations of the birkhoff gustavson normal form is discussed in the light of the quantum normal form

lemme d artin rees theoreme d izumi et fonction de artin abstract we interpret the artin rees lemma and the izumi theorem in term of artin function and we obtain a stable version of the artin rees lemma we present different applications of these interpretations first we show that the artin function of x 1 x 2 x 3 x 4 as a polynomial in the ring of power series in more than three variables is not bounded by an affine function then we prove that the artin functions of a class of polynomials are bounded by affine functions and we use this to compute approximated integral closures of ideals

on one controversy about the smoothed wigner function abstract we give a simple proof that the smoothed wigner function in the general case cannot be non negative whenever the smoothing function is zero outside a finite phase space region our proof is not based on whatever assumptions about the behavior of the smoothing function in the non zero region and on its boundary in this way the long lasted conjecture claiming the opposite is refuted

statistics of the occupation time of renewal processes we present a systematic study of the statistics of the occupation time and related random variables for stochastic processes with independent intervals of time according to the nature of the distribution of time intervals the probability density functions of these random variables have very different scalings in time we analyze successively the cases where this distribution is narrow where it is broad with index 1 and finally where it is broad with index 1 2 the methods introduced in this work provide a basis for the investigation of the statistics of the occupation time of more complex stochastic processes see joint paper by g de smedt c godreche and j m luck 26

aging ballistic levy walks aging can be observed for numerous physical systems in such systems statistical properties like probability distribution mean square displacement msd first passage time depend on a time span t a between the initialization and the beginning of observations in this paper we study aging properties of ballistic levy walks and two closely related jump models wait first and jump first we calculate explicitly their probability distributions and msds it turns out that despite similarities these models react very differently to the delay t a aging weakly affects the shape of probability density function and msd of standard levy walks for the jump models the shape of the probability density function is changed drastically moreover for the wait first jump model we observe a different behavior of msd when t a t and t a t

energy momentum tensor in phase space a connection between schrodinger energy momentum tensor and terletsky distribution function schrodinger energy momentum tensor for a matter field interacting with an external electromagnetic field is represented in phase space by means of terletsky distribution function the explicit form of this distribution function in the case of a hydrogen type atom is found the structure of the schrodinger energy momentum tensor in phase space is compared with the structure of a real fluid and its local pressure and local energy are presented in the fundamental state of a hydrogen type atom the negative values of the terletsky distribution function are not rejected in view of their participation in the phase space energy momentum tensor the negative part of the quantum distribution function could be interpreted as phase space density for anti constituents in a hypothetical sub quantum level of the matter

scaling breakdown a signature of aging we prove that the levy walk is characterized by bilinear scaling this effect mirrors the existence of a form of aging that does not require the adoption of nonstationary conditions

on the probability density interpretation of smoothed wigner functions it has been conjectured that averages of the wigner function over phase space volumes larger than those of minimum uncertainty are always positive this is true for gaussian averaging so that the husimi distribution is positive however the authors provide a specific counterexample for the averaging with a discontinuous hat function the analysis of the specific system of a one dimensional particle in a box also elucidates the respective advantages of the wigner and the husimi functions for the study of the semiclassical limit the falsification of the averaging conjecture is shown not to depend on the discontinuities of the hat function by considering the latter as the limit of a sequence of analytic functions

homomorphisms of local algebras in positive characteristic we study some properties of regularity of homomorphisms of local rings of positive equicharacteristic in particular we extend a theorem of izumi about the linear equivalence of topologies in this case the main tool we use is a monomialization theorem for homomorphisms of power series in positive characteristic

minimizing normalized volumes of valuations for any mathbb q gorenstein klt singularity x o we introduce a normalized volume function widehat mathrm vol that is defined on the space of real valuations centered at o and consider the problem of minimizing widehat mathrm vol we prove that the normalized volume has a uniform positive lower bound by proving an izumi type estimate for any mathbb q gorenstein klt singularity furthermore by proving a properness estimate we show that the set of real valuations with uniformly bounded normalized volumes is compact and hence reduce the existence of minimizers for widehat mathrm vol to a conjectural lower semicontinuity property for a smooth point we use an inequality of de fernex ein musta to show that the divisorial valuation associated to the exceptional divisor of the standard blow up is a minimizer of widehat mathrm vol finally the relation to fujita s work on divisorial stability is pointed out

aging two state process with levy walk and brownian motion with the rich dynamics studies of single state processes the two state processes are attracting more interest since they are widely observed in complex system and have effective applications in diverse fields such as foraging behavior of animals this paper builds the theoretical foundation of the process with two states levy walk and brownian motion having been proved to be an efficient intermittent search process the sojourn time distributions in two states are both assumed to be heavy tailed with exponents 0 2 the dynamical behaviors of this two state process are obtained through analyzing the ensemble averaged and time averaged mean squared displacements msds in weak and strong aging cases it is discovered that the magnitude relationship of decides the fraction of two states for long times playing a crucial role in these msds according to the generic expressions of msds some inherent characteristics of the two state process are detected the effects of the fraction on these observables are presented in detail for six different cases the key of getting these results is to calculate the velocity correlation function of the two state process the techniques of which can be generalized to other multistate processes

on the limitations of the birkhoff gustavson normal form approach recently the birkhoff gustavson normal form bgnf approach has been used in both classical and semiclassical calculations the authors consider the limitations associated with this approach using as an illustration the anharmonic oscillator at the classical level they emphasise the need to properly take into account the divergence properties of the bgnf series by reviewing an earlier work they demonstrate that this divergence problem may in some cases be resolved however after considering several standard quantisation rules they find that it is not possible to obtain the correct quantisation of a system via the bgnf as a result they maintain that care should be used when working with the bgnf

optimizing the encounter rate in biological interactions levy versus brownian strategies an important application involving two species reaction diffusion systems relates to the problem of finding the best statistical strategy for optimizing the encounter rate between organisms we investigate the general problem of how the encounter rate depends on whether organisms move in levy or brownian random walks by simulating a limiting generalized searcher target model e g predator prey mating partner pollinator flower we find that levy walks confer a significant advantage for increasing encounter rates when the searcher is larger or moves rapidly relative to the target and when the target density is low

on the uniqueness of the moyal structure of phase space functions uniqueness up to isomorphism of the moyal product and bracket of functions on as associative and lie deformations of the ordinary product and poisson bracket is known to follow under additional hypotheses using an integral formalism we show here that this result holds without these hypotheses

the wigner function the basic relations of the weyl wigner representation of quantum mechanics are reviewed it is stressed that this representation is unique and based on a phase space operator which corresponds to an observable in dirac s sense

optimum smoothing of the wigner ville distribution a compromise is found between the different requirements that we would like to be fulfilled by a time frequency distribution namely positivity and obtention of a distribution close to the dirac one for the unimodular signal s t exp i phi t the fulfillment of the marginal conditions being of less interest in signal theory starting from the usual wigner ville distribution we define an optimum smoothing by minimizing the width of the different functions approximating the desired dirac distribution the smoothing is obtained by a convolution through a double gaussian of width t and such that t 1 2 two possibilities appear in the first one we do not introduce any correlation between t and in the convolution kernel and obtain a simple result in the second one extrapolating the frequency variation and still using a gaussian we obtain a better result although the smoothing process becomes more complex these results to be physically meaningful impose inequalities on the successive derivatives of which are equivalent to those used for the obtention of the classical limit for the corresponding quantum problem

the algebraic quantisation of the birkhoff gustavson normal form the author develops an algebraic quantisation method for the birkhoff gustavson normal form for this purpose the weyl quantisation rule is used the method developed here for multidimensional systems allows one to calculate the energy levels and the transition probabilities the author gives a brief review of the normal form derives some of its general properties and finds a general analytic solution for the fourth degree normal form for hamiltonians of two degrees of freedom in particular this includes the henon heiles system the author compares the results of specific examples with other works the question of canonically invariant quantisation the relation to the quantum mechanical perturbation theory and the question of chaotic behaviour and quantum stochasticity are discussed the author shows that the operators corresponding to the formal integrals of the motion are also quantum mechanical integrals if the normal form accidentally terminates so that the classical system is integrable then this implies quantum integrability of the normal form hamiltonian

the volume of an isolated singularity we introduce a notion of volume of a normal isolated singularity that gener alizes wahl s characteristic number of surface singularities to arbitrary dimensions we prove a basic monotonicity property of this volume under finite morphisms we draw sev eral consequences regarding the existence of non invertible finite endomorphisms fixing an isolated singularity using a cone construction we deduce that the anticanonical di visor of any smooth projective variety carrying a non invertible polarized endomorphism is pseudoeffective our techniques build on shokurov s b divisors we define the notion of nef weil b divisors and of nef envelopes of b divisors we relate the latter notion to the pull back of weil divisors introduced by de fernex and hacon using the subadditivity theorem for multiplier ideals with respect to pairs recently obtained by takagi we carry over to the isolated singularity case the intersection theory of nef weil b divisors formerly developed by boucksom favre and jonsson in the smooth case

the parametrisation of quantisation rules equivalent to operator orderings and the effect of different rules on the physical spectrum the author recalls the problem of choosing an ordering for the terms in a hamiltonian of the form h p q of finite dimension in p q he demonstrates that most orderings which provide one with a hermitian operator are in fact redundant and he gives a general form for ordering rules in terms of arbitrary parameters he concludes that differences in the choice of an ordering contribute differences to the physics which are only of order 2 and higher he provides an example of a hamiltonian for which the spectrum is explicitly dependent on the choice of quantisation rule operator ordering he compares the method of characterising operator ordering rules with that of cohen 1966 1970 finally he generalises cohen s method to the case of all linear quantisation rules and shows how his rule is a special case

dynamically generated enhanced diffusion the stationary state case abstract we investigate the dynamics generated by iterated maps and analyze the motion in terms of the probabilistic continuous time levy walk approach we consider the case of particles which move randomly with a constant velocity between points of halt and study the mean squared displacement r 2 t and the propagator p r t the probability to be at location r at time t having started at the origin at t 0 we emphasize the importance of the stationary state and demonstrate it in the case of enhanced diffusion