stability and convergence of the difference methods for the space time fractional advection diffusion equation abstract in this paper we consider a space time fractional advection dispersion equation stfade on a finite domain the stfade is obtained from the standard advection dispersion equation by replacing the first order time derivative by the caputo fractional derivative of order 0 1 and the first order and second order space derivatives by the riemman liouville fractional derivatives of order 0 1 and of order 1 2 respectively for the space fractional derivatives d x u x t and d x u x t we adopted the grunwald formula and the shift grunwald formula respectively we propose an implicit difference method idm and an explicit difference method edm to solve this equation stability and convergence of these methods are discussed using mathematical induction we prove that the idm is unconditionally stable and convergent but the edm is conditionally stable and convergent numerical results are in good agreement with theoretical analysis

exact solutions for the unsteady rotating flows of a generalized maxwell fluid with oscillating pressure gradient between coaxial cylinders this paper deals with the unsteady rotating flow of a generalized maxwell fluid with fractional derivative model between two infinite straight circular cylinders where the flow is due to an infinite straight circular cylinder rotating and oscillating pressure gradient the velocity field and the adequate shear stress are determined by means of the combine of the sequential fractional derivatives laplace transform and finite hankel transform the exact solutions are presented by integral and series form in terms of the generalized g and mittag leffler functions the similar solutions can be easily obtained for ordinary maxwell and newtonian fluids as limiting cases finally the influence of the relaxation time and the fractional parameter on the fluid dynamic characteristics as well as a comparison between models is shown by graphical illustrations

generalized baire category and differential inclusions in banach spaces soit e un espace de banach separable reflexif et on considere le probleme de cauchy x t f x t x 0 x 0 e ou f est une fonction multiforme continue de hausdorff a valeurs bornees fermees on demontre l existence locale d une solution en supposant que la fermeture convexe de f x 0 a une codimension finie

unsteady flow of a generalized maxwell fluid with fractional derivative due to a constantly accelerating plate the velocity field and the adequate shear stress corresponding to the unsteady flow of a generalized maxwell fluid are determined using fourier sine and laplace transforms they are presented as a sum of the newtonian solutions and the corresponding non newtonian contributions the similar solutions for maxwell and newtonian fluids performing the same motion are obtained as limiting cases of our general results graphical illustrations show that the velocity profiles corresponding to a generalized maxwell fluid are going to that for an ordinary maxwell fluid if a 1

the canonical syzygy conjecture for ribbons green s canonical syzygy conjecture asserts a simple relationship between the clifford index of a smooth projective curve and the shape of the minimal free resolution of its homogeneous ideal in the canonical embedding we prove the analogue of this conjecture formulated by bayer and eisenbud for a class of non reduced curves called ribbons our proof uses the results of voisin and hirschowitz ramanan on green s conjecture for general smooth curves

the analytical solution and numerical solution of the fractional diffusion wave equation with damping fractional partial differential equations have been applied to many problems in physics finance and engineering numerical methods and error estimates of these equations are currently a very active area of research in this paper we consider a fractional diffusionwave equation with damping we derive the analytical solution for the equation using the method of separation of variables an implicit difference approximation is constructed stability and convergence are proved by the energy method finally two numerical examples are presented to show the effectiveness of this approximation

selections and their absolutely continuous invariant measures abstract let i 0 1 and let p be a partition of i into a finite number of intervals let 1 2 i i be two piecewise expanding maps on p let g i i be the region between the boundaries of the graphs of 1 and 2 any map i i that takes values in g is called a selection of the multivalued map defined by g there are many results devoted to the study of the existence of selections with specified topological properties however there are no results concerning the existence of selection with measure theoretic properties in this paper we prove the existence of selections which have absolutely continuous invariant measures acim by our assumptions we know that 1 and 2 possess acims preserving the distribution functions f 1 and f 2 the main result shows that for any convex combination f of f 1 and f 2 we can find a map with values between the graphs of 1 and 2 that is a selection such that f is the invariant distribution function examples are presented we also study the relationship of the dynamics of our multivalued maps to random maps

flow heat and mass transfer of three dimensional fractional maxwell fluid over a bidirectional stretching plate with fractional fourier s law and fractional fick s law abstract this paper investigates the flow heat and mass transfer of fractional maxwell fluid over a bidirectional stretching sheet and research is carried out for the three dimensional case by analogy with the constitutive equation of fractional maxwell fluid fractional derivative is introduced into fourier s law and fick s law meanwhile the magnetic field and chemical reaction are considered furthermore the stretching speeds are not only power law dependent on time but also power law dependent on the distance of each space direction combining with l1 algorithm a newly finite difference method is developed to solve the governing equations and convergence of the method is verified by constructing a numerical example the influences of various physical parameters on velocity temperature and concentration are analyzed through three dimensional graphs the velocity fractional parameter presents an interesting effect on the velocity when the powers of each space direction coincide the smaller the velocity fractional parameter is the thinner the velocity boundary layer is on the contrary larger velocity fractional parameter results in decreasing velocity at first and then increasing for different powers of each space direction furthermore fractional fourier s law leads to more obvious heat transfer phenomena which is similar with the effect of fractional fick s law on the mass transfer

analytical and numerical solutions of the unsteady 2d flow of mhd fractional maxwell fluid induced by variable pressure gradient abstract the nonlocal property of the fractional derivative can supply more precise mathematical models for depicting flow dynamics of complex fluid which cannot be modelled appropriately by normal integer order differential equations this paper studies the analytical and numerical methods of unsteady 2d flow of magnetohydrodynamic mhd fractional maxwell fluid in a rectangular pipe driven by variable pressure gradient the governing equation is formulated with caputo time dependent fractional derivatives whose orders are distributed in interval 0 2 a challenge is to firstly obtain the exact solution by combining modified separation of variables method with mikusinski type operational calculus meanwhile the numerical solution is also obtained by the implicit finite difference method whose validity has been confirmed by the comparison with the exact solution constructed different to the most classical works both the stability and convergence analysis of two dimensional multi term time fractional momentum equation are derived based on numerical analysis the results show that the velocity increases with the rise of the fractional parameter and relaxation time while an increase in the values of hartmann number leads to a slower velocity in the rectangular pipe

relaxation theorem for the evolution differential inclusions abstract in this paper we use an improved version of baire category method to prove the existence of solutions to the evolution differential inclusion ax ext f t x under the hausdorff noncompactness measure condition we also obtain a density result for the evolution differential inclusion

periodic unidirectional flows of a viscoelastic fluid with the fractional maxwell model exact analytic solutions for the flows of viscoelastic fluids are constructed the flows are induced by general periodic oscillations of a plate based on the flow conditions described three flow situations are solved by fourier transform further the fractional calculus approach is taken into account in the constitutive relationship of viscoelastic fluid model finally some interesting flows caused by certain special oscillations are also established

harmonic averages and new explicit constants for invariant densities of piecewise expanding maps of the interval the statistical behavior of families of maps is important in studying the stability properties of chaotic maps for a piecewise expanding map whose slope 2 in magnitude much is known about the stability of the associated invariant density however when the map has slope magnitude 2 many different behaviors can occur as shown in keller in monatsh math 94 4 313 333 1982 for w maps the main results of this note use a harmonic average of slopes condition to obtain new explicit constants for the upper and lower bounds of the invariant probability density function associated with the map as well as a bound for the speed of convergence to the density since these constants are determined explicitly the results can be extended to families of approximating maps

continuous selections for vector measures a vector measure is a many to one map it maps many measurable sets onto the same point a selection for a vector measure is a function which assigns to each point in the range of the vector measure only one measurable set which is mapped onto the point the existence of a continuous selection for nonatomic vector measures is proved where the distance in the field is the measure for a given scalar measure of the symmetric difference a stronger version of continuous selection exists for strictly convex ranges

computing graded betti tables of toric surfaces we present various facts on the graded betti table of a projectively embedded toric surface expressed in terms of the combinatorics of its defining lattice polygon these facts include explicit formulas for a number of entries as well as a lower bound on the length of the quadratic strand that we conjecture to be sharp and prove to be so in several special cases we also present an algorithm for determining the graded betti table of a given toric surface by explicitly computing its koszul cohomology and report on an implementation in sagemath it works well for ambient projective spaces of dimension up to roughly 25 depending on the concrete combinatorics although the current implementation runs in finite characteristic only as a main application we obtain the graded betti table of the veronese surface nu 6 p 2 subset of p 27 in characteristic 40 009 this allows us to formulate precise conjectures predicting what certain entries look like in the case of an arbitrary veronese surface nu d p 2

extreme continuous selectors of multivalued maps and their applications abstract a theorem on the existence of continuous selectors whose values are extreme points is proved for a class of multivalued maps the theorem is used to study existence and properties of solutions to differential inclusions in banach spaces

discrete approximations relaxation and optimization of one sided lipschitzian differential inclusions in hilbert spaces we study discrete approximations of nonconvex differential inclusions in hilbert spaces and dynamic optimization optimal control problems involving such differential inclusions and their discrete approximations the underlying feature of the problems under consideration is a modified one sided lipschitz condition imposed on the right hand side i e on the velocity sets of the differential inclusion which is a significant improvement of the conventional lipschitz continuity our main attention is paid to establishing efficient conditions that ensure the strong approximation in the w1 p norm as p 1 of feasible trajectories for the one sided lipschitzian differential inclusions under consideration by those for their discrete approximations and also the strong convergence of optimal solutions to the corresponding dynamic optimization problems under discrete approximations to proceed with the latter issue we derive a new extension of the bogolyubov type relaxation density theorem to the case of differential inclusions satisfying the modified one sided lipschitzian condition all the results obtained are new not only in the infinite dimensional hilbert space framework but also in finite dimensional spaces

on the vanishing of higher syzygies of curves ii we verify green s conjecture for a generic k gonal curve of genus g for g geq k k 1 2

toward a mathematical holographic principle in work started in 17 and continued in this paper our objective is to study selectors of multivalued functions which have interesting dynamical properties such as possessing absolutely continuous invariant measures we specify the graph of a multivalued function by means of lower and upper boundary maps tau 1 and tau 2 on these boundary maps we define a position dependent random map r p tau 1 tau 2 p 1 p which at each time step moves the point x to tau 1 x with probability p x and to tau 2 x with probability 1 p x under general conditions for each choice of p r p possesses an absolutely continuous invariant measure with invariant density f p let varvec tau be a selector which has invariant density function f one of our objectives is to study conditions under which p x exists such that r p has f as its invariant density function when this is the case the long term statistical dynamical behavior of a selector can be represented by the long term statistical behavior of a random map on the boundaries of g we refer to such a result as a mathematical holographic principle we present examples and study the relationship between the invariant densities attainable by classes of selectors and the random maps based on the boundaries and show that under certain conditions the extreme points of the invariant densities for selectors are achieved by bang bang random maps that is random maps for which p x in 0 1

absolutely continuous invariant measures for random maps with position dependent probabilities abstract a random map is discrete time dynamical system in which one of a number of transformations is randomly selected and applied at each iteration of the process usually the map k is chosen from a finite collection of maps with constant probability p k in this note we allow the p k s to be functions of position in this case the random map cannot be considered to be a skew product the main result provides a sufficient condition for the existence of an absolutely continuous invariant measure for position dependent random maps on 0 1 geometrical and topological properties of sets of absolutely continuous invariant measures attainable by means of position dependent random maps are studied theoretically and numerically

baire s category and the bang bang property for evolution differential inclusions of contractive type abstract the baire category method is employed in order to establish that the bang bang property holds for a class of evolution differential inclusions of contractive type in reflexive and separable real banach spaces

green s conjecture for curves on rational surfaces with an anticanonical pencil green s conjecture is proved for smooth curves c lying on a rational surface s with an anticanonical pencil under some mild hypotheses on the line bundle l mathcal o s c constancy of clifford dimension clifford index and gonality of curves in the linear system vert l vert is also obtained

birational morphisms of rational surfaces abstract a fairly complete characterization on anticanonical rational surfaces of the divisor classes whose sections define birational morphisms is given most results are proven over an algebraically closed field of arbitrary characteristic

attainable densities for random maps abstract we consider a random map t t where 1 2 k is a collection of maps of an interval and p 1 p 2 p k is a collection of the corresponding position dependent probabilities that is p k x 0 for k 1 2 k and k 1 k p k x 1 at each step the random map t moves the point x to k x with probability p k x for a fixed collection of maps t can have many different invariant probability density functions depending on the choice of the weighting probabilities most of the results in this paper concern random maps where is a family of piecewise linear semi markov maps we investigate properties of the set of invariant probability density functions of t that are attainable by allowing the probabilities in to vary in a certain class of functions we prove that the set of all attainable densities can be determined algorithmically we also study the duality between random maps generated by transformations and random maps constructed from a collection of their inverse branches such representation may be of greater interest in view of new methods of computing entropy w slomczynski j kwapien k yczkowski entropy computing via integration over fractal measures chaos 10 2000 180 188

a priori estimates for operational differential inclusions we prove a set valued gronwall lemma and a relaxation theorem for the semilinear differential inclusion x ax f t x x 0 x0 where a is the infinitesimal generator of a c0 semigroup on a separable banach space x and f 0 t x x is a set valued map this allows us to investigate infinitesimal generators of reachable sets and variational inclusions the results are applied to a semilinear optimal control problem with end point constraints

optimal existence theorems for nonhomogeneous differential inclusions abstract in this paper we address the question of solvability of the differential inclusions 1 1 our approach to these problems is based on the idea of constructing a sequence of approximate solutions which converges strongly and makes use of gromov s idea following earlier work of nash and kuiper to control convergence of the gradients by appropriate selection of the elements of the sequence in this paper we identify an optimal setting of this method in particular we show that the existence result holds for general upper semicontinuous functions h without extra requirements like quasiconvexity of h with respect to du which was assumed in previous works where the idea to apply the baire category lemma to the sets of approximate solutions was developed we also apply our result to identify the minimal sets where the function h should vanish to guarantee solvability of the inclusions

flow of a viscoelastic fluid with the fractional maxwell model between two side walls perpendicular to a plate the unsteady flow of a viscoelastic fluid with the fractional maxwell model between two side walls perpendicular to a plate is investigated exact solutions for the velocity field are established by means of the fourier and laplace transforms the similar solutions for maxwell and newtonian fluids can be obtained as limiting cases of our results in the absence of side walls all solutions that have been determined reduce to those corresponding to the motion over an infinite plate

invariant densities for random maps of the interval on etudie des applications aleatoires de 0 1 qui representent des systemes dynamiques sur le carre 0 1 0 1 on donne des conditions suffisantes pour qu une application aleatoire ait une mesure invariante absolument continue

periodic solutions for nonlinear differential inclusions with multivalued perturbations abstract in this paper the periodic solutions for nonlinear differential inclusion governed by convex subdifferential and different perturbations are studied it is firstly proved that the differential inclusion has unique periodic solution if the perturbation function is a single valued function then by schauder s fixed point theorem and kakutani s fixed point theorem we prove that the differential inclusion has at least a periodic solution when the perturbation function is an upper semicontinuous or lower semicontinuous multifunction moreover the existence of the extremal solution for the differential inclusion is also studied finally based on one sided lipschitz osl assumption we prove the related relaxation theorem

multivalued mappings in generalized chaos synchronization the onset of generalized synchronization of chaos in directionally coupled systems corresponds to the formation of a continuous mapping that enables one to persistently define the state of the response system from the trajectory of the drive system a recently developed theory of generalized synchronization of chaos deals only with the case where this synchronization mapping is a single valued function in this paper we explore generalized synchronization in a regime where the synchronization mapping can become a multivalued function specifically we study the properties of the multivalued mapping that occurs between the drive and response systems when the systems are synchronized with a frequency ratio other than one to one and address the issues of the existence and continuity of such mappings the basic theoretical framework underlying the considered synchronization regimes is then developed

unsteady flow and heat transfer of a generalized maxwell fluid due to a hyperbolic sine accelerating plate this paper deals with the unsteady flow and heat transfer of a generalized maxwell fluid over a moving flat plate with variable temperature and hyperbolic sine velocity exact solutions are established for the velocity and temperature fields in terms of discrete fourier sine transform coupled with laplace transform for the fractional calculus graphs are sketched for values of parameters and associated dynamic characteristics are analyzed

compact difference scheme for distributed order time fractional diffusion wave equation on bounded domains in this paper we derive and analyse a compact difference scheme for a distributed order time fractional diffusion wave equation this equation is approximated by a multi term fractional diffusion wave equation which is then solved by a compact difference scheme the unique solvability of the difference solution is discussed using the discrete energy method we prove the compact difference scheme is unconditionally stable and convergent finally numerical results are presented to support our theoretical analysis