some non compact quasi variational inequalities abstract we present a generalized version of a quasi variational inequality for maps defined on non compact sets and satisfying generalized concavity and coercivity conditions several quasi variational inequalities obtained in the literature can be extended by our result

some properties of a random walk on a comb structure abstract we analyze transport properties of a random walk on a comb structure which serves as a model for a random walk on the backbone of a percolation cluster it is shown that the random walk along the x axis which is the analog of the backbone exhibits anomalous diffusion in that x 2 n n 1 2 and the expected number of x sites visited is proportional to n 1 4 for large n the distribution function is found to be a two dimensional gaussian if a field in the x direction so that diffusion is asymmetric the expected displacement is found to be asymptotically proportional to n 1 2

a reference free cuscore chart for dynamic mean change detection and a unified framework for charting performance comparison to detect and estimate nonconstant time varying mean shifts statistical process control spc tools such as the cumulative score cuscore and generalized likelihood ratio test glrt charts have recently been proposed however their efficiency is based on previous and exact knowledge of a reference pattern in this article a reference free cuscore rfcuscore chart is proposed that can trace and detect dynamic mean changes quickly without knowing the reference pattern in addition a unified framework that contains most of the control charts is presented and applied for a theoretical comparison of the rfcuscore cuscore glrt and cusum charts in detecting dynamic mean changes moreover numerical simulations and a real example are used to illustrate and verify the results both theoretical analysis and numerical results show that the rfcuscore chart performs not only robustly but also quickly in detecting both small and large dynamic mean changes

fox h functions in fractional diffusion the h functions introduced by fox in 1961 are special functions of a very general nature which allow one to treat several phenomena including anomalous diffusion in a unified and elegant framework in this paper we express the fundamental solutions of the cauchy problem for the space time fractional diffusion equation in terms of proper fox h functions based on their mellin barnes integral representations we pay attention to the particular cases of space fractional time fractional and neutral fractional diffusion

retarding subdiffusion and accelerating superdiffusion governed by distributed order fractional diffusion equations we propose diffusionlike equations with time and space fractional derivatives of the distributed order for the kinetic description of anomalous diffusion and relaxation phenomena whose diffusion exponent varies with time and which correspondingly cannot be viewed as self affine random processes possessing a unique hurst exponent we prove the positivity of the solutions of the proposed equations and establish their relation to the continuous time random walk theory we show that the distributed order time fractional diffusion equation describes the subdiffusion random process that is subordinated to the wiener process and whose diffusion exponent decreases in time retarding subdiffusion this process may lead to superslow diffusion with the mean square displacement growing logarithmically in time we also demonstrate that the distributed order space fractional diffusion equation describes superdiffusion phenomena with the diffusion exponent increasing in time accelerating superdiffusion

subdiffusion on a fractal comb subdiffusion on a fractal comb is considered a mechanism of subdiffusion with a transport exponent different from 1 2 is suggested it is shown that the transport exponent is determined by the fractal geometry of the comb

surveillance of nonhomogeneous poisson processes the use of varying sample size monitoring techniques for poisson count data has drawn a great deal of attention in recent years specifically these methods have been used in public health surveillance manufacturing and safety monitoring a number of approaches have been proposed from the traditional shewhart charts to cumulative sum cusum and exponentially weighted moving average ewma methods it is convenient to use techniques based on statistics that are invariant to the units of measurement since in most cases these units are arbitrarily selected a few of the methods reviewed in our expository article are not inherently invariant but most are easily modified to be invariant most importantly if methods are invariant to the choice of units of measurement they can be applied in situations where the in control poisson mean varies over time even if there is no associated varying sample size several examples are discussed to highlight the promising uses of invariant poisson control charting me

anomalous diffusion and charge relaxation on comb model exact solutions abstract the random walks on the comb structure are considered it is shown that due to fingers a diffusion has an anomalous character that is an r m s displacement depends on time by a power way with exponent 1 2 the generalized diffusion equation for an anomalous case is deduced it essentially differs from a usual diffusion equation in the continuity equation form instead of the first time derivative the time derivative of fractal order 1 2 appears in the second part the charge relaxation on the comb structure is studied a non maxwell character is established the reason is that the electric field has three components but a charge may relax only along some conducting lines

likelihood based ewma charts for monitoring poisson count data with time varying sample sizes many applications involve monitoring incidence rates of the poisson distribution when the sample size varies over time recently a couple of cumulative sum and exponentially weighted moving average ewma control charts have been proposed to tackle this problem by taking the varying sample size into consideration however we argue that some of these charts which perform quite well in terms of average run length arl may not be appealing in practice because they have rather unsatisfactory run length distributions with some charts the specified in control ic arl is attained with elevated probabilities of very short and very long runs as compared with a geometric distribution this is reflected in a larger run length standard deviation than that of a geometric distribution and an elevated probability of false alarms with short runs which in turn hurt an operator s confidence in valid alarms furthermore with many charts the ic arl exhibits considerable variations with different patterns of sam

generalized langevin equation with a three parameter mittag leffler noise abstract the relaxation functions for a given generalized langevin equation in the presence of a three parameter mittag leffler noise are studied analytically the results are represented by three parameter mittag leffler functions exact results for the velocity and displacement correlation functions of a diffusing particle are obtained by using the laplace transform method the asymptotic behavior of the particle in the short and long time limits are found by using the tauberian theorems it is shown that for large times the particle motion is subdiffusive for 1 and superdiffusive for many previously obtained results are recovered due to the many parameters contained in the noise term the model considered in this work may be used to improve the description of data and to model anomalous diffusive processes in complex media

a comparison of weighted cusum procedures that account for monotone changes in population size the cusum procedure has been popularly used for detecting a shift in the incidence rate of a rare health event many cusum methods are developed based on a poisson model with a constant mean number of events in practice the expected number of events is likely to vary over time as the population size at risk is not constant but often grows over time an increase in the baseline incidence rate tends to be masked by the population growth to efficiently detect an increase in the baseline incidence rate it is appealing to assign more weight to recent observations and less weight to older observations this paper compares weighted cusum wcusum and conventional cusum procedures in the presence of monotone changes in population size the simulation results show that the wcusum method may be more efficient than the conventional cusum methods in detecting increases in the incidence rate especially for small shifts an example based on mortality data from new mexico is used to illustrate the implementation of the wcusum method copyright 2010 john wiley sons ltd

the performance of exponentially weighted moving average charts with estimated parameters the exponentially weighted moving average ewma control chart is typically designed assuming that standards are given for the process parameters in practice the parameters are rarely known and control charts are constructed using estimates in place of the parameters this practice can affect the control chart s run length performance in both in and out of control situations specifically estimation can lead to substantially more frequent false alarms and yet reduce the sensitivity of the chart to detecting process changes in this article the run length distribution of the ewma chart with estimated parameters is derived the effect of estimation on the performance of the chart is discussed in a variety of practical scenarios

fractional time quantum dynamics application of the fractional calculus to quantum processes is presented in particular the quantum dynamics is considered in the framework of the fractional time schr odinger equation se which differs from the standard se by the fractional time derivative ensuremath partial ensuremath partial t ensuremath rightarrow ensuremath partial ensuremath alpha ensuremath partial t ensuremath alpha it is shown that for ensuremath alpha 1 2 the fractional se is isospectral to a comb model an analytical expression for the green s functions of the systems are obtained the semiclassical limit is discussed

time dependent schrodinger like equation with nonlocal term we investigate a time dependent schrodinger like equation in presence of a nonlocal term by using the method of variable separation and the green function approach we analyze the green function for different forms of the memory kernel and the nonlocal term results for delta potential energy function are presented distributed order memory kernels are also considered and the asymptotic behaviors of the green function are derived by using tauberian theorem the obtained results for the green function for the considered schrodinger like equation may be transformed to those for the probability distribution function of a diffusion like equation with memory kernel and can be used to explain various anomalous diffusive behaviors

self starting monitoring scheme for poisson count data with varying population sizes in this article we consider the problem of monitoring poisson rates when the population sizes are time varying and the nominal value of the process parameter is unavailable almost all previous control schemes for the detection of increases in the poisson rate in phase ii are constructed based on assumed knowledge of the process parameters for example the expectation of the count of a rare event when the process of interest is in control in practice however this parameter is usually unknown and not able to be estimated with a sufficiently large number of reference samples a self starting exponentially weighted moving average ewma control scheme based on a parametric bootstrap method is proposed the success of the proposed method lies in the use of probability control limits which are determined based on the observations during rather than before monitoring simulation studies show that our proposed scheme has good in control and out of control performance under various situations in particular

generalized space time fractional diffusion equation with composite fractional time derivative abstract we investigate the solution of space time fractional diffusion equations with a generalized riemann liouville time fractional derivative and riesz feller space fractional derivative the laplace and fourier transform methods are applied to solve the proposed fractional diffusion equation the results are represented by using the mittag leffler functions and the fox h function special cases of the initial and boundary conditions are considered numerical scheme and grunwald letnikov approximation are also used to solve the space time fractional diffusion equation the fractional moments of the fundamental solution of the considered space time fractional diffusion equation are obtained many known results are special cases of those obtained in this paper we investigate also the solution of a space time fractional diffusion equations with a singular term of the form x t 1 0

time dependent solutions for a fractional schrodinger equation with delta potentials we investigate for an arbitrary initial condition the time dependent solutions for a fractional schrodinger equation in the presence of delta potentials by using the green function approach the solutions obtained show an anomalous spreading asymptotically characterized by a power law behavior which is governed by the order of the fractional spatial operator present in the schrodinger equation

unified continuum description for sub diffusion random walks on multi dimensional comb model abstract the anisotropic sub diffusion random walks on multi dimensional comb structure model have been studied in the continuum approximation the problem is that in the considered model mean square displacements on different directions have different power temporal dependencies so this case essentially differs from usual anisotropic diffusion case and it is not obviously how to describe such a diffusion by a unified way nevertheless the unified continuum description for such random walks has been developed as result the new generalization of fick s law for diffusion current has been obtained for anisotropic anomalous sub diffusion random walks in multi dimensional case namely it has been shown that the effective diffusion coefficient in the generalized fick s law has new operator form components of diffusion tensor instead of constant values have the fractional order temporal derivatives

diffusion on random comb structure effective medium approximation abstract the random walks on comb model of percolation clusters are studied the generalized diffusion equations in the form of fractal temporal derivatives are deduced the random distributions of fingers over lengths gaussian and power are studied in the effective medium approximation

levy walks and scaling in quenched disordered media we study levy walks in quenched disordered one dimensional media with scatterers spaced according to a long tailed distribution by analyzing the scaling relations for the random walk probability and for the resistivity in the equivalent electric problem we obtain the asymptotic behavior of the mean square displacement as a function of the exponent characterizing the scatterers distribution we demonstrate that in quenched media different average procedures can display different asymptotic behavior in particular we estimate the moments of the displacement averaged over processes starting from scattering sites our results are compared with numerical simulations with excellent agreement

occupation times on a comb with ramified teeth we investigate occupation time statistics for random walks on a comb with ramified teeth this is achieved through the relation between the occupation time and the first passage times statistics of occupation times in half space follows lamperti s distribution i e the generalized arcsine law holds transitions between different behaviors are observed which are controlled by the size of the backbone and teeth of the comb as well as bias occupation time on a nonsimply connected domain is analyzed with a mean field theory and numerical simulations in that case the generalized arcsine law is not valid

topological proof for the alexander orbach conjecture this paper advocates an unconventional analytical approach to studying the fractal geometry of percolation at the threshold which is based on the most general methods of the differential topology our particular interest concentrates on the alexander orbach ao conjecture j phys france lett 43 l625 1982 which assigns the universal mean field value 4 3 to the spectral fractal dimension stackrel ifmmode tilde else fi d at the percolation threshold for all embedding euclidean dimensions n greater than one i e ng 2 using the topological arguments we show that the ao conjecture might be improved for the relatively low embedding dimensions 2l nl 5 for which the analytical result stackrel ifmmode tilde else fi d 1 327 ifmmode pm else textpm fi 0 001 is proposed instead of the original ao estimate 4 3 meanwhile we assume that the exact value stackrel ifmmode tilde else fi d 4 3 holds for all ng 6 as it follows directly from the well known mean field theory the improved value of stackrel ifmmode tilde else fi d ensuremath approx 1 327 for 2l nl 5 is obtained from an analysis of the basic topological properties of the percolating fractal sets at the threshold of percolation we show that these properties could be investigated fruitfully with the introduction of the concept of the fractal manifold which might serve as an effective instrument when considering the topology of the fractal objects our results indicate that the proposed value of stackrel ifmmode tilde else fi d ensuremath approx 1 327 for the spectral dimension at the percolation threshold has the fundamental topological origin related to the most general features of the fractal geometry of percolation at criticality we argue that the constraint 2l nl 5 on the topological dimension n of the embedding euclidean space is the direct consequence of the famous whitney theorem which establishes the embedding properties of manifolds from the viewpoint of their dimensionality a simple topological condition that identifies the threshold of percolation is obtained for 2l nl 5 the particular topological restrictions implied throughout the present study are discussed and the important issue of contractibility of the fractal manifolds is pointed out

quasi variational inequalities with non compact sets in this paper we first generalize a foundational quasi variational inequality theorem 3 which plays a key role throughout this paper by relaxing the compactness condition then we set up general forms of generalized quasi variational inequalities and obtain a series of existence theorems without the compactness assumption also since many other quasi variational inequalities in the literature are special cases of ours they can be generalized by our results

mesoscopic description of random walks on combs combs are a simple caricature of various types of natural branched structures which belong to the category of loopless graphs and consist of a backbone and branches we study continuous time random walks on combs and present a generic method to obtain their transport properties the random walk along the branches may be biased and we account for the effect of the branches by renormalizing the waiting time probability distribution function for the motion along the backbone we analyze the overall diffusion properties along the backbone and find normal diffusion anomalous diffusion and stochastic localization diffusion failure respectively depending on the characteristics of the continuous time random walk along the branches and compare our analytical results with stochastic simulations

anomalous diffusion on a fractal mesh we present exact analytical results for properties of anomalous diffusion on a fractal mesh the fractal mesh structure is a direct product of two fractal sets one belonging to a main branch of backbones the other to the side branches of fingers both fractal sets are constructed on the entire infinite y and x axes we suggest a special algorithm in order to construct such sets out of standard cantor sets embedded in the unit interval the transport properties of the fractal mesh are studied in particular subdiffusion along the backbones is obtained with the dispersion relation x 2 t t where the transport exponent 1 has been observed as well when the environment is controlled by means of a memory kernel

sequential changepoint detection in quality control and dynamical systems after a brief survey of a large variety of sequential detection procedures that are widely scattered in statistical references on quality control and engineering references on fault detection and signal processing we study some open problems concerning these procedures and introduce a unified theory of sequential changepoint detection this theory leads to a class of sequential detection rules which are not too demanding in computational and memory requirements for on line implementation and yet are nearly optimal under several performance criteria

nonparametric profile monitoring by mixed effects modeling in some applications the quality of a process is characterized by the functional relationship between a response variable and one or more explanatory variables profile monitoring is for checking the stability of this relationship over time control charts for monitoring nonparametric profiles are useful when the relationship is too complicated to be described parametrically most existing control charts in the literature are for monitoring parametric profiles they require the assumption that within profile measurements are independent of each other which is often invalid in practice this article focuses on nonparametric profile monitoring when within profile data are correlated a novel control chart is suggested which incorporates local linear kernel smoothing into the exponentially weighted moving average ewma control scheme in this method within profile correlation is described by a nonparametric mixed effects model our proposed control chart is fast to compute and convenient to use numeric

generalized fractional diffusion equations for accelerating subdiffusion and truncated levy flights fractional diffusion equations are widely used to describe anomalous diffusion processes where the characteristic displacement scales as a power of time for processes lacking such scaling the corresponding description may be given by diffusion equations with fractional derivatives of distributed order such equations were introduced in a v chechkin r gorenflo and i sokolov phys rev e 66 046129 2002 for the description of the processes getting more anomalous in the course of time decelerating subdiffusion and accelerating superdiffusion here we discuss the properties of diffusion equations with fractional derivatives of the distributed order for the description of anomalous relaxation and diffusion phenomena getting less anomalous in the course of time which we call respectively accelerating subdiffusion and decelerating superdiffusion for the former process by taking a relatively simple particular example with two fixed anomalous diffusion exponents we show that the proposed equation effectively describes the subdiffusion phenomenon with diffusion exponent varying in time for the latter process we demonstrate by a particular example how the power law truncated levy stable distribution evolves in time to the distribution with power law asymptotics and gaussian shape in the central part the special case of two different orders is characteristic for the general situation in which the extreme orders dominate the asymptotics

green s function for the time dependent scattering problem in the fractional quantum mechanics we study the green s function of the time dependent 3d space fractional schrodinger equation for the scattering problem in the fractional quantum mechanics the green s function is expressed in terms of fox s h function and in a computable series form we get the asymptotic formula of the green s function and apply it to obtain the approximate wave function for the fractional quantum scattering problem

levy processes on a generalized fractal comb comb geometry constituted of a backbone and fingers is one of the most simple paradigm of a two dimensional structure where anomalous diffusion can be realized in the framework of markov processes however the intrinsic properties of the structure can destroy this markovian transport these effects can be described by the memory and spatial kernels in particular the fractal structure of the fingers which is controlled by the spatial kernel in both the real and the fourier spaces leads to the levy processes levy flights and superdiffusion this generalization of the fractional diffusion is described by the riesz space fractional derivative in the framework of this generalized fractal comb model levy processes are considered and exact solutions for the probability distribution functions are obtained in terms of the fox h function for a variety of the memory kernels and the rate of the superdiffusive spreading is studied by calculating the fractional moments for a special form of the memory kernels we also observed a competition between long rests and long jumps finally we considered the fractal structure of the fingers controlled by a weierstrass function which leads to the power law kernel in the fourier space this is a special case when the second moment exists for superdiffusion in this competition between long rests and long jumps

generalized time dependent schrodinger equation in two dimensions under constraints we investigate a generalized two dimensional time dependent schrodinger equation on a comb with a memory kernel a dirac delta term is introduced in the schrodinger equation so that the quantum motion along the x direction is constrained at y 0 the wave function is analyzed by using green s function approach for several forms of the memory kernel which are of particular interest closed form solutions for the cases of dirac delta and power law memory kernels in terms of fox h function as well as for a distributed order memory kernel are obtained further a nonlocal term is also introduced and investigated analytically it is shown that the solution for such a case can be represented in terms of infinite series in fox h functions green s functions for each of the considered cases are analyzed and plotted for the most representative ones anomalous diffusion signatures are evident from the presence of the power law tails the normalized green s functions obtained in this work are of broader interest

time fractional schrodinger equation the schrodinger equation is considered with the first order time derivative changed to a caputo fractional derivative the time fractional schrodinger equation the resulting hamiltonian is found to be non hermitian and nonlocal in time the resulting wave functions are thus not invariant under time reversal the time fractional schrodinger equation is solved for a free particle and for a potential well probability and the resulting energy levels are found to increase over time to a limiting value depending on the order of the time derivative new identities for the mittag leffler function are also found and presented in an appendix

field induced drift and trapping in percolation networks the authors study the effects of a bias producing external field on a random walk on the infinite cluster in the percolation problem there are two competing physical effects drift and trapping which result in a drift velocity nu which rises and then falls as the field increases they study these effects on a one dimensional lattice with random length branches and on the diluted bethe lattice they calculate nu in the first model with a maximum allowed length for each branch in the limit that this cutoff length becomes infinite they find that the velocity vanishes identically above a finite critical value of the field for the bethe lattice they derive an upper bound on the critical field which varies as p pc 1 2 as the percolation concentration pc is approached in the one dimensional model they also investigate the anomalous regime in which the velocity vanishes they discuss the distribution of steady state times required to traverse n sites and find that it can be described in terms of a stable distribution of index x with superimposed oscillations the index x of the stable distribution is given by l xi where xi is a characteristic branch length and l is a bias induced length which describes the exponential buildup of the steady state density of particles towards the end of a branch

continuous time random walk as a guide to fractional schrodinger equation we argue that the continuous time random walk approach may be a useful guide to extend the schrodinger equation in order to incorporate nonlocal effects avoiding the inconsistencies raised by jeng et al j math phys 51 062102 2010 as an application we work out a free particle in a half space obtaining the time dependent solution by considering an arbitrary initial condition

generalized quasi variational inequalities with non compact sets in this paper we will present several results concerning generalized quasi variational inequalities with non compact sets at first we generalize foundational quasi variational inequalities which play a key role throughout this paper by relaxing the compactness condition several generalized quasi variational inequalities can be extended by our results

surveillance strategies for detecting changepoint in incidence rate based on exponentially weighted moving average methods surveillance is a major issue in the today s world the need to develop adequate surveillance strategies is genuine in many spheres of human activity in this article we focus on a specific problem of surveillance and discuss some related statistical issues this specific problem deals with a possible change in the incidence rate of an event to a higher value when a system is studied at discrete time points we apply the exponentially weighted moving average methods for detecting an increased incidence rate per exposure unit of an event different measures of evaluation suitable in different types of applications such as the expected delay out of control average run length and probability of successful detection are studied analytical bounds are provided for those measures of evaluation results from intensive simulations indicate that the analytical bounds perform fairly well when the weight parameter is large

scaling properties of diffusion on comb like structures the authors study the scaling properties of the probability density of random walks on comb like structures they find that in contrast to the first passage time in which several exponents are needed to characterise their distribution the probability density can be described by a single exponent

fractional schrodinger equation some properties of the fractional schrodinger equation are studied we prove the hermiticity of the fractional hamilton operator and establish the parity conservation law for fractional quantum mechanics as physical applications of the fractional schrodinger equation we find the energy spectra of a hydrogenlike atom fractional bohr atom and of a fractional oscillator in the semiclassical approximation an equation for the fractional probability current density is developed and discussed we also discuss the relationships between the fractional and standard schrodinger equations

random walks on bundled structures bundled structures bs are discrete structures obtained joining to each point of a base graph a copy of a fiber graph in condensed matter physics bs are used as realistic models for the geometry and dynamics of nontranslationally invariant systems polymers inhomogeneous systems etc we present an analytical solution for the random walk problem on these structures which is possible when we know the solution for base and fiber separately we obtain an expression for the spectral dimension of the bs as a function of the spectral dimensions of its components moreover we discuss some applications of these results concerning anomalous diffusion laws proving the existence of nondisordered structures with logarithmic and sublogarithmic diffusion laws due only to geometric features

fractional diffusion and levy stable processes anomalous diffusion in which the mean square distance between diffusing quantities increases faster than linearly in time has been observed in all manner of physical and biological systems from macroscopic surface growth to dna sequences herein we relate the cause of this nondiffusive behavior to the statistical properties of an underlying process using an exact statistical model this model is a simple two state process with long time correlations and is shown to produce a random walk described by an exact fractional diffusion equation fractional diffusion equations describe anomalous transport and are shown to have exact solutions in terms of fox functions including l evy ensuremath alpha stable processes in the superdiffusive domain 1 21

quasi variational inequality problems with non compact valued constraint maps abstract quasi variational inequality problems correspond to variational inequality problems in which the constraint set depends on the variable they are playing nowadays an increasing role in the modelization of real life problem in particular because they provide a perfect framework for the reformulation of generalized nash equilibrium problems our aim in this work is to establish the existence of solutions for quasi variational inequalities defined by a non monotone map and a constraint map which possibly admits unbounded values the key tools are the use of coercivity conditions and himmelberg fixed point theorem applications to existence of generalized nash equilibrium is also considered

generalized quasi variational inequalities on non compact sets with pseudo monotone operators abstract in this paper we first generalize a ky fan minimax inequality then we obtain two foundational quasi variational inequalities which play a key role throughout this paper we shall use these results to obtain some general theorems on solutions of the generalized quasi variational inequalities gqvi on a paracompact set x in a hausdorff locally convex space e where the set valued operator t x 2 e is either strongly pseudo monotone or pseudo monotone

exponentially weighted moving average control schemes properties and enhancements roberts 1959 first introduced the exponentially weighted moving average ewma control scheme using simulation to evaluate its properties he showed that the ewma is useful for detecting small shifts in the mean of a process the recognition that an ewma control scheme can be represented as a markov chain allows its properties to be evaluated more easily and completely than has previously been done in this article we evaluate the properties of an ewma control scheme used to monitor the mean of a normally distributed process that may experience shifts away from the target value a design procedure for ewma control schemes is given parameter values not commonly used in the literature are shown to be useful for detecting small shifts in a process in addition several enhancements to ewma control schemes are considered these include a fast initial response feature that makes the ewma control scheme more sensitive to start up problems a combined shewhart ewma that provides protection against both larg

an approximate cusum procedure for surveillance of health events the cusum method is frequently used by epidemiologists for detecting a shift in the incidence of rare health events an exact solution for a poisson process has been proposed by other works but potential applications have been limited by the fact that the size the structure of the at risk population and the baseline rate may not be constant during the period of surveillance furthermore for practical use tables of critical values are available only for some expected values and in any case less then 9 this paper proposes an approximate cusum procedure based on the normal approximation to a poisson process which may be an efficient solution of the problems previously pointed out analyses of simulated and actual data sets illustrate the usefulness of the proposed procedure an application to mortality data for respiratory diseases in a north tuscany area characterized by the presence of chemical plants is showed no shift in the mortality rate during the 1980 1989 period was detected compared with the 1970 1979 period in contrast with the result obtained with the standard cusum method for a poisson variate

localized states on comb lattices complex networks and graphs provide a general description of a great variety of inhomogeneous discrete systems these range from polymers and biomolecules to complex quantum devices such as arrays of josephson junctions microbridges and quantum wires we introduce a technique based on the analysis of the motion of a random walker that allows us to determine the density of states of a general local hamiltonian on a graph when the potential differs from zero on a finite number of sites we study in detail the case of the comb lattice and we derive an analytic expression for the elements of the resolvent operator of the hamiltonian giving its complete spectrum

fractional diffusion equation with a generalized riemann liouville time fractional derivative in this paper the solution of a fractional diffusion equation with a hilfer generalized riemann liouville time fractional derivative is obtained in terms of mittag leffler type functions and fox s h function the considered equation represents a quite general extension of the classical diffusion heat conduction equation the methods of separation of variables laplace transform and analysis of the sturm liouville problem are used to solve the fractional diffusion equation defined in a bounded domain by using the fourier laplace transform method it is shown that the fundamental solution of the fractional diffusion equation with a generalized riemann liouville time fractional derivative defined in the infinite domain can be expressed via fox s h function it is shown that the corresponding solutions of the diffusion equations with time fractional derivative in the caputo and riemann liouville sense are special cases of those diffusion equations with the hilfer generalized riemann liouville time fractional derivative the asymptotic behaviour of the solutions are found for large values of the spatial variable the fractional moments of the fundamental solution of the fractional diffusion equation are obtained the obtained results are relevant in the context of glass relaxation and aquifer problems

fractional diffusion on a fractal grid comb a grid comb model is a generalization of the well known comb model and it consists of n backbones for n 1 the system reduces to the comb model where subdiffusion takes place with the transport exponent 1 2 we present an exact analytical evaluation of the transport exponent of anomalous diffusion for finite and infinite number of backbones we show that for an arbitrarily large but finite number of backbones the transport exponent does not change contrary to that for an infinite number of backbones the transport exponent depends on the fractal dimension of the backbone structure

generalized quasi variational inequalities in locally convex topological vector spaces abstract let e be a hausdorff topological vector space and x e an arbitrary nonempty set denote by e the dual space of e and the pairing between e and e by w x for w e and x e given a point to set map s x 2x and a point to set map t x 2e the generalized quasi variational inequality problem gqvi is to find a point y s y and a point u t y such that re u y x 0 for all x s y by using the ky fan minimax principle or its generalized version as a tool some general theorems on solutions of the gqvi in locally convex hausdorff topological vector spaces are obtained which include a fixed point theorem due to ky fan and i l glicksberg and two different multivalued versions of the hartman stampacchia variational inequality

fixed points theorems for mappings with non compact and non convex domains this note gives some fixed point theorems for lower and upper semi continuous mappings and mappings with open lower sections defined on non compact and non convex sets it will be noted that the conditions of our theorems are not only sufficient but also necessary also our theorems generalize some well known fixed point theorems such as the kakutani fixed point theorem and the brouwer schauder fixed point theorem by relaxing the compactness and convexity conditions

the restaurant at the end of the random walk recent developments in the description of anomalous transport by fractional dynamics fractional dynamics has experienced a firm upswing during the past few years having been forged into a mature framework in the theory of stochastic processes a large number of research papers developing fractional dynamics further or applying it to various systems have appeared since our first review article on the fractional fokker planck equation metzler r and klafter j 2000a phys rep 339 1 77 it therefore appears timely to put these new works in a cohesive perspective in this review we cover both the theoretical modelling of sub and superdiffusive processes placing emphasis on superdiffusion and the discussion of applications such as the correct formulation of boundary value problems to obtain the first passage time density function we also discuss extensively the occurrence of anomalous dynamics in various fields ranging from nanoscale over biological to geophysical and environmental systems

application of hyperbolic scaling for calculation of reaction subdiffusion front propagation a technique of hyperbolic scaling is applied to calculate a reaction front velocity in an irreversible autocatalytic conversion reaction a b 2a under subdiffusion the method based on the geometric optics approach is a technically elegant observation of the propagation front failure obtained in phys rev e 78 011128 2008

constrained quantum motion in δ potential and application of a generalized integral operator abstract a quantum motion of a particle along the x direction constrained at y 0 in presence of the dirac potential is considered the green s function approach is applied for solving the corresponding two dimensional schrodinger equation the exact results for the green s function are presented in terms of the fox h function and a generalized integral operator which contains the mittag leffler function in the kernel

generalized games and non compact quasi variational inequalities abstract in this paper by developing an approximation approach which is originally due to tuleca in 1986 we prove the existence of equilibria for generalized games in which constraint mappings correspondences are lower resp upper semicontinuous instead of having lower resp upper open sections or open graphs in infinite dimensional topological spaces then existence theorems of solutions for quasi variational inequalities and non compact generalized quasi variational inequalities are also established finally existence theorems of constrained games with non compact strategy sets are derived our results unify and generalize many well known results given in the existing literature in particular we answer the question raised by yannelis and prabhakar in 1983 in the affirmative under more weaker conditions