dna breathing dynamics analytic results for distribution functions of relevant brownian functionals we investigate dna breathing dynamics by suggesting and examining several brownian functionals associated with bubble lifetime and reactivity bubble dynamics is described as an overdamped random walk in the number of broken base pairs the walk takes place on the poland scheraga free energy landscape we suggest several probability distribution functions that characterize the breathing process and adopt the recently studied backward fokker planck method and the path decomposition method as elegant and flexible tools for deriving these distributions in particular for a bubble of an initial size x 0 we derive analytical expressions for i the distribution p t f x 0 of the first passage time t f characterizing the bubble lifetime ii the distribution p a x 0 of the area a until the first passage time providing information about the effective reactivity of the bubble to processes within the dna iii the distribution p m of the maximum bubble size m attained before the first passage time and iv the joint probability distribution p m t m of the maximum bubble size m and the time t m of its occurrence before the first passage time these distributions are analyzed in the limit of small and large bubble sizes we supplement our analytical predictions with direct numerical simulations of the related langevin equation and obtain a very good agreement in the appropriate limits the nontrivial scaling behavior of the various quantities analyzed here can in principle be explored experimentally

quantitative weights and aggregation based on the strong idempotency of aggregation operators quantitative weights are incorporated into the fusion process our general method is compared with some previous specific cases more details about weighted aggregation based on some penalty function is given further weighted integral based aggregation linked to quantifier based fuzzy measures is investigated especially weighted owa operators several examples are included

feedback stabilization of magnetohydrodynamic equations we prove the local exponential stabilizability for the magnetohydrodynamic mhd system in space dimension 3 with internally distributed feedback controllers these controllers take values in a finite dimensional space which is the unstable manifold of the elliptic part of the linearized operator the stabilization of the linear system is derived using a unique continuation property for systems of parabolic and elliptic equations as well as the equivalence between controllability and feedback stabilizability in the case of finite dimensional systems the feedback that stabilizes the linearized system is also stabilizing the nonlinear system in a certain interpolation space

om3 ordered maxitive minitive and modular aggregation operators axiomatic and probabilistic properties in an arity monotonic setting the recently introduced om3 aggregation operators fulfill three appealing properties they are simultaneously minitive maxitive and modular among the instances of om3 operators we find e g owmax and owmin operators the famous hirsch h index and all its natural generalizations in this paper the basic axiomatic and probabilistic properties of extended i e in an arity dependent setting om3 aggregation operators are studied we illustrate the di culties one is inevitably faced with when trying to combine the quality and quantity of numeric items into a single number the discussion on such aggregation methods is particularly important in the information resources producers assessment problem which aims to reduce the negative e ects of information overload it turns out that the hirsch like indices of impact do not fulfill a set of very important properties which puts the sensibility of their practical usage into question moreover thanks to the probabilistic analysis of the operators in an i i d model we may better understand the relationship between the aggregated items quality and their producers productivity

mean exit times for particles driven by weakly colored noise consider a particle whose velocity is an ornstein uhlenbeck process with correlation time varepsilon 2 frac dx dt frac sigma z varepsilon qquad frac dz dt frac z varepsilon 2 frac sqrt 2 xi t varepsilon where xi t is gaussian white noise this represents brownian motion with memory i e a non markovian brownian motion singular perturbation techniques reduce the mean exit time problem to a boundary layer problem which turns out to be the half range expansion problem for the fokker planck operator this is solved via complex variable theory it is found that the spatial density has a milne extrapolation length varepsilon sigma zeta tfrac 1 2 varepsilon sigma 1 46035 cdots where zeta is the riemann zeta function it is also found that the average time at which x t first escapes an interval a 0 b ven that it starts at x 0 0 and z 0 z 0 is e t text ex frac 1 2 sigma 2 left a varepsilo

asymptotic solution of the wang uhlenbeck recurrence time problem a langevin particle is initiated at the origin with positive velocity its trajectory is terminated when it returns to the origin in 1945 wang and uhlenbeck posed the problem of finding the joint probability density function pdf of the recurrence time and velocity naming it the recurrence time problem we show that the short time asymptotics of the recurrence pdf is similar to that of the integrated brownian motion solved in 1963 by mckean we recover the long time t ensuremath 3 2 decay of the first arrival pdf of diffusion by solving asymptotically an appropriate variant of mckean s integral equation

bouncing ball with a finite restitution chattering locking and chaos we study the dynamic evolution of a bouncing ball on a vibrating platform such as the membrane of a loudspeaker as a function of its coefficient of restitution ensuremath alpha and demonstrate primarily that the presence of chaos in this system is by no means inevitable and its development is by no means obvious indeed we show that generic trajectories starting under experimental conditions terminate in a region of chattering where the memory of earlier dynamics is lost before repeating themselves in a periodic way as a consequence except possibly for the strictly elastic case ensuremath alpha 1 the evolution to chaos via a period doubling route will not be observed our arguments are corroborated by numerical studies concerning especially the divergence of the mean period of generic trajectories as the elastic limit is approached ensuremath alpha ensuremath rightarrow 1

a first passage time distribution for a discrete version of the ornstein uhlenbeck process the probability of the first entrance to the negative semi axis for a one dimensional discrete ornstein uhlenbeck o u process is studied in this work the discrete o u process is a simple generalization of the random walk and many of its statistics may be calculated using essentially the same formalism in particular the case in which sparre andersen s theorem applies for normal random walks is considered and it is shown that the universal features of the first passage probability do not extend to the discrete o u process finally an explicit expression for the generating function of the probability of first entrance to the negative real axis at step n is calculated and analysed for a particular choice of the step distribution

magnetohydrodynamic state estimation with boundary sensors we present a pde observer that estimates the velocity pressure electric potential and current fields in a magnetohydrodynamic mhd channel flow also known as hartmann flow this flow is characterized by an electrically conducting fluid moving between parallel plates in the presence of an externally imposed transverse magnetic field the system is described by the inductionless mhd equations a combination of the navier stokes equations and a poisson equation for the electric potential under the so called inductionless mhd approximation in a low magnetic reynolds number regime we identify physical quantities measurable on the wall of the channel that are sufficient to generate convergent estimates of the velocity pressure and electric potential field away from the walls our observer consists of a copy of the linearized mhd equations combined with linear injection of output estimation error with observer gains designed using backstepping pressure skin friction and current measurements from one of the walls are used for output injection for zero magnetic field or nonconducting fluid the design reduces to an observer for the navier stokes poiseuille flow a benchmark for flow control and turbulence estimation we show that for the linearized mhd model the estimation error converges to zero in the l 2 norm despite being a subject of practical interest the problem of observer design for nondiscretized 3 d mhd or navier stokes channel flow has so far been an open problem

brownian simulations and unidirectional flux in diffusion the prediction of ionic currents in protein channels of biological membranes is one of the central problems of computational molecular biophysics existing continuum descriptions of ionic permeation fail to capture the rich phenomenology of the permeation process so it is therefore necessary to resort to particle simulations brownian dynamics bd simulations require the connection of a small discrete simulation volume to large baths that are maintained at fixed concentrations and voltages the continuum baths are connected to the simulation through interfaces located in the baths sufficiently far from the channel average boundary concentrations have to be maintained at their values in the baths by injecting and removing particles at the interfaces the particles injected into the simulation volume represent a unidirectional diffusion flux while the outgoing particles represent the unidirectional flux in the opposite direction the classical diffusion equation defines net diffusion flux but not unidirectional fluxes the stochastic formulation of classical diffusion in terms of the wiener process leads to a wiener path integral which can split the net flux into unidirectional fluxes these unidirectional fluxes are infinite though the net flux is finite and agrees with classical theory we find that the infinite unidirectional flux is an artifact caused by replacing the langevin dynamics with its smoluchowski approximation which is classical diffusion the smoluchowski approximation fails on time scales shorter than the relaxation time 1 ensuremath gamma of the langevin equation we find that the probability of brownian trajectories that cross an interface in one direction in unit time ensuremath delta t equals that of the probability of the corresponding langevin trajectories if ensuremath gamma ensuremath delta t 2 that is we find the unidirectional flux source strength needed to maintain average boundary concentrations in a manner consistent with the physics of brownian particles this unidirectional flux is proportional to the concentration and inversely proportional to sqrt ensuremath delta t to leading order we develop a bd simulation that maintains fixed average boundary concentrations in a manner consistent with the actual physics of the interface and without creating spurious boundary layers

the analytic solutions of some boundary layer problems in the theory of brownian motion the authors give analytic solutions of the generalised albedo and milne problems for the uhlenbeck ornstein process and discuss the relation between these and the original wang uhlenbeck 1945 problem of determining the distribution of first passage times

on the analyticity of the semigroup generated by the stokes operator with neumann type boundary conditions on lipschitz subdomains of riemannian manifolds we study the analyticity of the semigroup generated by the stokes operator equipped with neumann type boundary conditions on l p spaces in lipschitz domains our strategy is to regularize this operator by considering the hodge laplacian which has the additional property that it commutes with the leray projection

stability of weighted penalty based aggregation functions in many practical applications the need arises to aggregate data of varying dimension following from the self identity property some recent studies have looked at the stability of aggregation operators in terms of their behavior as the dimensionality is increased from n 1 to n we use the penalty based representation of aggregation functions in order to investigate the conditions for weighting vectors associated with some important weighted families extending on the results already established for quasi arithmetic means in particular we obtain results for quasi medians and functions that involve a reordering of the inputs such as the owa and order statistics

a generalization of stability for families of aggregation operators abstract in this paper we extend the notion of stability of each aggregation function as presented in a previous paper of the authors where an aggregation function was denominated family of aggregation operators fao in order to stress that aggregation operators within an aggregation function should be consistent we will show that the previous definition presents certain problems when dealing with a fao that is not idempotent or continuous meanwhile the previous definition was based on the study of fixed points without taking into account the environment of each point as many applications demand the new approach we propose now is more flexible and at the end allows a more appropriate definition of the consistency of a fao it will be shown that under certain conditions our new proposal is equivalent to the previous definition of strict stability but the new definition covers families of aggregation operators that are not strictly stable but intuitively stable and vice versa in short we will see that our new proposal fits much better the intuition of stability of a fao this reformulation of stability is based upon the concept of penalty function as a measure of proximity between a value and an array of values

the analytic structure of the stationary kinetic boundary layer for brownian particles near an absorbing wall a method for solving kinetic boundary layer problems for the 1d klein kramers equation the kinetic equation for brownian particles was proposed a few years ago by marshall and watson 1987 for the special case of particles moving under the influence of a constant or zero external force in this paper the authors apply this method to a number of classical stationary boundary layer problems for completely or partially absorbing walls these are the milne problem in which a current flows towards the wall from infinity and the albedo problem in which particles are injected into the system at the wall with a prescribed velocity distribution the solutions are known to be non analytic at the wall for zero normal velocity the authors pay particular attention to the nature of this singularity for several special cases the results are compared with results obtained by approximate methods

the convex hull for a random acceleration process in two dimensions we compute exactly the mean perimeter l t and the mean area a t of the convex hull of a random acceleration process of duration t in two dimensions we use an exact mapping that relates via cauchy s formulae the computation of the perimeter and the area of the convex hull of an arbitrary two dimensional stochastic process x t y t to the computation of the extreme value statistics of the associated one dimensional component process x t the latter can be computed exactly for the one dimensional random acceleration process even though the process is non markovian physically our results are relevant in describing the average shape of a semi flexible ideal polymer chain in two dimensions

semiflexible polymer in the half plane and statistics of the integral of a brownian curve a continuum model of a polymer with non zero bending energy fluctuating without overhangs in the half plane is considered the exact partition function is obtained from the marshall watson solution of the klein kramers equation for brownian motion in the half space the partition function contains information on probabilities associated with the integral of a brownian curve and reproduces sinai s t 5 4 result for the asymptotic first passage time density the t 5 2 dependence of a different passage probability implies a first order polymer adsorption transition for short range pinning potentials

dynamics of absorption of a randomly accelerated particle consider a randomly accelerated particle moving on the half line x 0 with a boundary condition at x 0 that respects the scale invariance of the equations of motion under x 3x v v t 2t if the boundary condition leads to absorption of the particle at x 0 and if the probability q x v t that the particle has not yet been absorbed at time t decays for long times as a power law with exponent then the power law must have the specific form q x v t cx2 3u 2 3 2 3 v3 9x t this is a consequence of scale invariance and the fokker planck equation here c is a constant and u a b z is a confluent hypergeometric function the persistence exponents for several boundary conditions of physical interest follow directly from this result

handbook of brownian motion facts and formulae i theory i stochastic processes in general ii linear diffusions iii stochastic calculus iv brownian motion v local time as a markov process vi differential systems associated to brownian motion appendix 1 briefly on some diffusions ii tables of distributions of functionals of brownian motion and related processes 1 brownian motion 2 brownian motion with drift 3 reflecting brownian motion 4 bessel process of order 5 bessel process of order 1 2 6 bessel process of order zero 7 ornstein uhlenbeck process 8 radial ornstein uhlenbeck process 9 geometric brownian motion appendix 2 special functions appendix 3 inverse laplace transforms appendix 4 differential equations and their solutions appendix 5 formulae for n fold differentiation

aggregation functions based on penalties this article studies a large class of averaging aggregation functions based on minimizing a distance from the vector of inputs or equivalently minimizing a penalty imposed for deviations of individual inputs from the aggregated value we provide a systematization of various types of penalty based aggregation functions and show how many special cases arise as the result we show how new aggregation functions can be constructed either analytically or numerically and provide many examples we establish connection with the maximum likelihood principle and present tools for averaging experimental noisy data with distinct noise distributions

the exact distribution of the oscillation period in the underdamped one dimensional sinai model we consider the newtonian dynamics of a massive particle in a one dimensional random potential which is a brownian motion in space this is the zero temperature nondamped sinai model as there is no dissipation the particle oscillates between two turning points where its kinetic energy becomes zero the period of oscillation is a random variable fluctuating from sample to sample of the random potential we compute the probability distribution of this period exactly and show that it has a power law tail for large period p t t 5 3 and an essential singularity p t exp 1 t as t 0 our exact results are confirmed by numerical simulations and also via a simple scaling argument

exact controllability of partial integrodifferential equations with mixed boundary conditions in this work the exact controllability of linear parabolic integrodifferential equations with mixed boundary conditions are studied carleman estimate for the linearized problem providing the observability results is fundamental to the analysis and by duality it provides exact global controllability

universal first passage properties of discrete time random walks and levy flights on a line statistics of the global maximum and records abstract in these lecture notes i will discuss the universal first passage properties of a simple correlated discrete time sequence x 0 0 x 1 x 2 x n up to n steps where x i represents the position at step i of a random walker hopping on a continuous line by drawing independently at each time step a random jump length from an arbitrary symmetric and continuous distribution it includes e g the levy flights i will focus on the statistics of two extreme observables associated with the sequence i its global maximum and the time step at which the maximum occurs and ii the number of records in the sequence and their ages i will demonstrate how the universal statistics of these observables emerge as a consequence of pollaczek spitzer formula and the associated sparre andersen theorem

sensitivity of spin glass order to temperature changes by a loop expansion around parisi s mean field theory for an ising spin glass it is shown that the overlap of the magnetization patterns belonging to two different temperatures t and t vanishes to any order si t si t 0 while the correlation overlap sisj t sisj t calculated to first loop order and for technical reasons for dimensions d 8 only is found to decay exponentially with a characteristic length approximately t t 1

on lipschitz properties of generated aggregation functions this article discusses lipschitz properties of generated aggregation functions such generated functions include triangular norms and conorms quasi arithmetic means uninorms nullnorms and continuous generated functions with a neutral element the lipschitz property guarantees stability of aggregation operations with respect to input inaccuracies and is important for applications we provide verifiable sufficient conditions to determine when a generated aggregation function holds the k lipschitz property and calculate the lipschitz constants of power means we also establish sufficient conditions which guarantee that a generated aggregation function is not lipschitz we found the only 1 lipschitz generated function with a neutral element email protected 0 1

exact internal controllability for the two dimensional magnetohydrodynamic equations in this paper we establish the local exact internal controllability for the two dimensional magnetohydrodynamic equations the needed carleman estimate for the adjoint linearized magnetohydrodynamic equations is also obtained here

dynamics of inelastic collapse we consider a particle randomly accelerated by gaussian white noise on the half line xg0 the collisions of the particle with the wall at x 0 are inelastic the velocities just before and after reflection are related by v f ensuremath mathrm rv i where r is the coefficient of restitution cornell swift and bray have shown that for rl r c e ensuremath ensuremath pi sqrt 3 0 163 there is inelastic collapse i e boundary collisions localize the particle at x 0 the probability that the particle is not yet absorbed at the boundary after a time t decays for long times as t ensuremath ensuremath theta r the exponent ensuremath theta r is calculated exactly we also consider the case of partial survival boundary conditions i e elastic reflection with probability p and absorption with probability 1 ensuremath p and derive the analogous persistence exponent ensuremath varphi p the exact exponents satisfy the swift bray conjecture ensuremath theta r ensuremath varphi r 2 ensuremath theta r

connectives and quantifiers in fuzzy sets abstract we discuss some of the issues involved in the selection of appropriate operators for implementing the union and intersection of fuzzy subsets we discuss the extension principles used in extending operators to fuzzy subsets we provide a structure for aggregating linguistic variables in the theory of approximate reasoning we look at mean operators on fuzzy subsets as well as the inclusion of importances in aggregation we discuss non monotone set operators we introduce the concept of linguistic quantifiers and look at some applications of these structures we are particularly concerned with their application to linguistic summarizers syllogistic reasoning and multi criteria decision making

on the area under a continuous time brownian motion till its first passage time the area swept out under a one dimensional brownian motion till its first passage time is analysed using a fokker planck technique we obtain an exact expression for the area distribution for the zero drift case and provide various asymptotic results for the nonzero drift case emphasizing the critical nature of the behaviour in the limit of vanishing drift the results offer important insights into the asymptotic behaviour of a number of discrete models we also provide a succinct derivation for the distribution of the maximum displacement observed during a first passage

the distribution of exit times for weakly colored noise we analyze the exit time first passage time problem for the ornstein uhlenbeck model of brownian motion specifically consider the positionx t of a particle whose velocity is an ornstein uhlenbeck process with amplitude and correlation time e2 dx dt sigma z varepsilon dz dt z varepsilon 2 2 1 mathord left vphantom 1 2 right kern nulldelimiterspace 2 xi t varepsilon where t is gaussian white noise let the exit timetex be the first time the particle escapes an interval a t by directly solving the fokker planck equation in brief after taking a laplace transform we use singular perturbation methods to reduce the fokker planck equation to a boundary layer problem this boundary layer problem turns out to be a half range expansion problem which we solve via complex variable techniques this yields the laplace transform off t to within a transcendentally smallo e a e e b e error we then obtainf t by inverting the transform order by order in e in particular by lettingb we obtain the solution to wang and uhlenbeck s unsolved problem b througho e2 2 a1 this solution is f t erf left frac a varepsilon sigma alpha varepsilon sigma z 0 2 sigma t varepsilon 2 kappa 1 mathord left vphantom 1 2 right kern nulldelimiterspace 2 right for frac t varepsilon 2 1 andf 1 otherwise here 1 2 1 4603 where is the riemann zeta function and the constant is 0 22749

persistence of a continuous stochastic process with discrete time sampling we introduce the concept of discrete time persistence which deals with zero crossings of a continuous stochastic process x t measured at discrete times t n delta t for a gaussian markov process with relaxation rate mu we show that the persistence no crossing probability decays as rho a n for large n where a exp mu delta t and we compute rho a to high precision we also define the concept of alternating persistence which corresponds to a 1 corresponding to motion in an unstable potential mu 0 there is a nonzero probability of having no zero crossings in infinite time and we show how to calculate it

controllability and observability theory of certain parabolic integrodifferential equations the exact null controllability of linear and nonlinear parabolic integrodifferential equations with space periodic boundary conditions are studied carleman estimate for the linearized problem providing the observability results is fundamental to the analysis and by duality also provides exact global controllability local exact controllability for the nonlinear problem is obtained using the kakutani fixed point theorem

local exact boundary controllability of the boussinesq equation we study the local exact boundary controllability problem for the boussinesq equations that describe an incompressible fluid flow coupled to thermal dynamics the result that we get in this paper is as follows suppose that hat y t x is a given solution of the boussinesq equation where t in 0 t x in omega omega is a bounded domain with c infty boundary partial omega let y 0 x be a given initial condition and vert hat y 0 cdot y 0 vert epsilon where epsilon epsilon hat y is small enough then there exists boundary control u such that the solution y t x of the boussinesq equations satisfying y vert 0 t times partial omega u qquad y vert t 0 y 0 coincides with hat y t x at the instant t y t x equiv hat y t x

escape by diffusion from a parabolic well across a parabolic barrier abstract the problem of escape of a particle by diffusion from a parabolic potential well across a parabolic barrier adjacent to free space is studied on the basis of the one dimensional smoluchowski equation for the space and time dependent probability distribution for the model potential the smoluchowski equation is solved exactly by a laplace transform with respect to time for the initial condition that at time zero the probability distribution is given by a thermal equilibrium distribution in the well in the limit of a high barrier the rate of escape is given by an asymptotic result due to kramers for a potential barrier of moderate height there are significant corrections to the asymptotic result the probability that the particle resides in the well barrier region at time t decays with a 1 t long time tail

probability distribution functions for a single particle vibrating in one dimension experimental study and theoretical analysis abstract we consider the form of the rebound velocity 0 particle velocity and height h probability density functions pdfs for the one dimensional motion of a single particle on a sinusoidally oscillating base the motion is considered in the limit of high excitation vibration frequency collision rate experimentally we find that these pdfs are well approximated by p 0 0 0 exp 0 2 a gaussian p exp 2 and a boltzmann type function p h h exp 2 gh where is a constant and g is the acceleration due to gravity we develop an analytical model which accurately predicts the general form for the rebound velocity pdf the other two pdfs are then analytically shown to follow as a consequence scaling laws for the particle granular temperature with peak base velocity and particle base restitution coefficient determined from previous work can also be predicted from the pdf a fine scale spiky structure in the rebound velocity pdf is found using numerical simulations to be a consequence of resonance phenomena between the particle and vibrating base good agreement between scaling laws from the theory and simulation is found but insufficient data is obtainable to derive accuracy exponents experimentally

noncommutative self identity aggregation abstract we introduce a number of properties associated with the aggregation of scores notable among these is the property of self identity the property of commutativity is discussed and a number of situations in which this is an inappropriate condition to assume are presented motivated by these examples we consider a linear class of noncommutative aggregation operators we show how the requirement of self identity imposes a useful restriction on the weights associated with this aggregation a number of special families of this class are investigated

exact internal controllability for the two dimensional navier stokes equations with the navier slip boundary conditions abstract a new result of exact internal controllability for the two dimensional navier stokes equations with the navier slip boundary conditions is established here the authors give an analogue of their previous three dimensional result which improves the known two dimensional result due to imanuvilov

the ultimate planar convex hull algorithm we present a new planar convex hull algorithm with worst case time complexity o n log h where n is the size of the input set and h is the size of the output set i e the number of vertices found to be on the hull we also show that this algorithm is asymptotically worst case optimal on a rather realistic model of computation even if the complexity of the problem is measured in terms of input as well as output size the algorithm relies on a variation of the divide and conquer paradigm which we call the marriage before conquest principle and which appears to be interesting in its own right

penalty based aggregation of multidimensional data abstract research in aggregation theory is nowadays still mostly focused on algorithms to summarize tuples consisting of observations in some real interval or of diverse general ordered structures of course in practice of information processing many other data types between these two extreme cases are worth inspecting this contribution deals with the aggregation of lists of data points in r d for arbitrary d 1 even though particular functions aiming to summarize multidimensional data have been discussed by researchers in data analysis computational statistics and geometry there is clearly a need to provide a comprehensive and unified model in which their properties like equivariances to geometric transformations internality and monotonicity may be studied at an appropriate level of generality the proposed penalty based approach serves as a common framework for all idempotent information aggregation methods including componentwise functions pairwise distance minimizers and data depth based medians it also allows for deriving many new practically useful tools

inelastic collapse of a ball bouncing on a randomly vibrating platform a theoretical study is undertaken of the dynamics of a ball which is bouncing inelastically on a randomly vibrating platform of interest are the distributions of the number of flights n f and the total time ensuremath tau c until the ball has effectively collapsed i e coalesced with the platform in the strictly elastic case both distributions have power law tails characterized by exponents that are universal i e independent of the detail of the platform noise distribution however in the inelastic case both distributions have exponential tails p n f ensuremath sim mathrm exp ensuremath ensuremath theta 1 n f and p ensuremath tau c ensuremath sim mathrm exp ensuremath ensuremath theta 2 ensuremath tau c the decay exponents ensuremath theta 1 and ensuremath theta 2 depend continuously on the coefficient of restitution and are nonuniversal however as one approaches the elastic limit they vanish in a manner which turns out to be universal an explicit expression for ensuremath theta 1 is provided for a particular case of the platform noise distribution

a drop of ink falls from my pen it comes to earth i know not when the authors obtain for a brownian particle in a uniform force field the mean and asymptotic first passage times as functions of the particle s initial position and velocity with the recurrence times given as a special case they discuss the region of phase space for which the diffusion model of brownian motion provides an adequate approximation and conclude that there is no possibility of obtaining the recurrence times within that model they find that the nature of the boundary value problem is profoundly altered when the motion is treated as a process in phase rather than configuration space because the time development operator is then parabolic rather than elliptic they argue that such a change in the treatment of brownian motion places it within the sphere of transport theory rather than diffusion theory and that consequently results such as ours have relevance to the study of phenomena such as radiative transfer and neutron transport

half range expansion analysis for langewin dynamics in the high friction limit with a singular absorbing boundary condition noncharacteristic case we consider the dynamics of a brownian particle given by the langevin equation in a strip under the effects of a deterministic force the trajectories of particles originate at a source whose spatial location in the phase space coincides with the location of adsorbing boundaries this leads to singular behavior of trajectories in the high friction limit we use the half range expansion technique and systematic asymptotics to solve a boundary value problem for the fokker planck operator and to calculate the steady state transition probability density the mean time to absorption and the distribution of exit points we do not make assumptions about other parameters in the problem except that they areo 1 relative to the friction coefficient we calculate explicitly the correct location of the milne type extrapolation for absorbing boundary conditions for the smoluchowski approximation to the langevin equation

spread measures and their relation to aggregation functions abstract the theory of aggregation most often deals with measures of central tendency however sometimes a very different kind of a numeric vector s synthesis into a single number is required in this paper we introduce a class of mathematical functions which aim to measure spread or scatter of one dimensional quantitative data the proposed definition serves as a common abstract framework for measures of absolute spread known from statistics exploratory data analysis and data mining e g the sample variance standard deviation range interquartile range iqr median absolute deviation mad etc additionally we develop new measures of experts opinions diversity or consensus in group decision making problems we investigate some properties of spread measures show how are they related to aggregation functions and indicate their new potentially fruitful application areas

generalized bonferroni mean operators in multi criteria aggregation in this paper we provide a systematic investigation of a family of composed aggregation functions which generalize the bonferroni mean such extensions of the bonferroni mean are capable of modeling the concepts of hard and soft partial conjunction and disjunction as well as that of k tolerance and k intolerance there are several interesting special cases with quite an intuitive interpretation for application

exact controllability for the magnetohydrodynamic equations we study the local exact controllability of the steady state solutions of the magnetohydrodynamic equations the main result of the paper asserts that the steady state solutions of these equations are locally controllable if they are smooth enough we reduce the local exact controllability of the steady state solutions of the magnetohydrodynamic equations to the global exact controllability of the null solution of the linearized magnetohydrodynamic system via a x ed point argument the treatment of the reduced problem relies on two carleman type inequalities for the backward adjoint system c 2003 wiley periodicals inc

some mathematical questions related to the mhd equations some questions relating to the large time behavior of the solutions of mhd equations for a viscous incompressible resistive fluid are investigated the physical system is briefly described and the functional setting of the equations a flow in a bounded domain or in whole space with a space periodicity property in all directions the main existence and uniqueness results for weak and strong solutions of the mhd equations are recalled regularity properties and bounds on the solutions to the equations which are valid for all time are established and the concept of functional invariant sets is introduced which is contained in the space of smooth functions if the data are sufficiently regular the squeezing property of the trajectories are stated and it is shown that any functional invariant set for the mhd equations and in particular any attractor has a finite haussdorf dimension the flow is found to be totally determined for large dimensions by a finite number of parameters 26 references

a numerical approach to study the kramers equation for finite geometries boundary conditions and potential fields the kramers equation for the phase space function which models the dynamics of an underdamped brownian particle is the subject of our study numerical solutions of this equation for natural boundaries unconfined geometries have been well reported in the literature but not much has been done on the kramers equation for finite confining geometries which require a set of additional constraints imposed on the phase space function at physical boundaries in this paper we present numerical solutions for the kramers equation with a variety of potential fields namely constant linear harmonic and periodic in the presence of fully absorbing and fully reflecting boundary conditions bcs the choice of the numerical method and its implementation take into consideration the type of bcs in order to avoid the use of ghost points or artificial conditions we study and assess the conditions under which the numerical method converges various aspects of the solutions for the phase space function are presented with figures and discussed in detail

integrated brownian motion conditioned to be positive we study the two dimensional process of integrated brownian motion and brownian motion where integrated brownian motion is conditioned to be positive the transition density of this process is derived from the asymptotic behavior of hitting times of the unconditioned process explicit expressions for the transition density in terms of confluent hypergeometric functions are derived and it is shown how our results on the hitting time distributions imply previous results of isozaki watanabe and goldman the conditioned process is characterized by a system of stochastic differential equations sdes for which we prove an existence and unicity result some sample path properties are derived from the sdes and it is shown that t to t 9 10 is a critical curve for the conditioned process in the sense that the expected time that the integral part of the conditioned process spends below any curve t to t alpha is finite for alpha 9 10 and infinite for alpha geq 9 10