some common fixed point theorems for mappings and multi valued mappings using certain weak conditions of commutativity we prove some common fixed point theorems in complete metrically convex spaces which in turn generalize results due to assad and kirk itoh khan and several others

cauchy problems for fractional differential equations with riemann liouville fractional derivatives abstract in this paper we are concerned with cauchy problems of fractional differential equations with riemann liouville fractional derivatives in infinite dimensional banach spaces we introduce the notion of fractional resolvent obtain some its properties and present a generation theorem for exponentially bounded fractional resolvents moreover we prove that a homogeneous order cauchy problem is well posed if and only if its coefficient operator is the generator of an order fractional resolvent and we give sufficient conditions to guarantee the existence and uniqueness of weak solutions and strong solutions of an inhomogeneous order cauchy problem

common fixed points for multimaps in a metric space on etablit certaines proprietes des fonctions reelles et on les applique pour obtenir des ameliorations aux resultats de papageorgiou sur les points fixes des fonctions multiformes on etend au cas non borne

patterns in eigenvalues the 70th josiah willard gibbs lecture typical large unitary matrices show remarkable patterns in their eigenvalue distribution these same patterns appear in telephone encryption the zeros of riemann s zeta function a variety of physics problems and in the study of toeplitz operators this paper surveys these applications and what is currently known about the patterns

mizoguchi takahashi s fixed point theorem is a real generalization of nadler s abstract we give an example which says that mizoguchi takahashi s fixed point theorem for set valued mappings is a real generalization of nadler s we also give a very simple proof of mizoguchi takahashi s theorem

on the generalized navier stokes equations in this paper we present a general model of the classical navier stokes equations with the help of laplace fourier sine transforms finite fourier sine transforms and finite hankel transforms an exact solutions for three different special cases have been obtained

sticky spheres and related systems some properties of a system of hard core particles with attractive wells in the baxter sticky sphere limit and a related limit are considered as is the approach to these limits a demonstration of the result of stell and williams that sticky spheres of equal diameter in the baxter limit are not thermodynamically stable is given and the way in which size polydispersity can be expected to restore thermodynamic stability is discussed the implications of these results for the py sticky sphere approximation and recent sticky sphere computer simulations are then examined it is concluded that the baxter py sticky sphere approximation for a monodisperse system may well be a reasonable one for a slightly polydisperse system of sticky spheres and that existing simulation results may also be relevant to such a system how polydisperse a system must be in quantitative terms in order for the py approximation to be useful remains to be seen however the question of whether the py sticky sphere approximation may prove to be useful and appropriate in describing monodisperse systems with pair potentials for which the attractive wells arenot extremely narrow is also considered it is noted that firm evidence concerning this question also appears to be lacking implications for systems near but not in the limit of zero attractive well width are also considered especially in terms of the relative size of the well width and the degree of size polydispersity in the repulsive cores the possible pertinence of such considerations to colloidal systems is observed the importance of taking into consideration the extremely long equilibration times that can be expected for systems with very narrow attractive wells is also pointed out in connection both with real colloidal systems and in computer simulations it is further observed that in the baxter limit sticky spheres described quantum mechanically are indistinguishable from hard spheres so described near the zero well width limit the quantal behavior hinges on the number of bound states and thus the well depth as well as the relative size of the de broglie thermal wavelength and the well width related results and investigations relevant to the issues described above are cited

analysis of time fractional and space nonlocal stochastic incompressible navier stokes equation driven by white noise abstract in this paper we consider the stochastic time space fractional incompressible navier stokes equation driven by white noise we firstly derive the regularity of the nonlocal stochastic convolution then we prove the global existence and uniqueness of the mild solution finally the holder continuity for the stochastic time space fractional incompressible navier stokes equation driven by white noise is established the optimal holder continuity accords with the result of integer order time incompressible navier stokes equation

stochastic navier stokes equations with caputo derivative driven by fractional noises abstract in this paper we consider the extended stochastic navier stokes equations with caputo derivative driven by fractional brownian motion we firstly derive the pathwise spatial and temporal regularity of the generalized ornstein uhlenbeck process then we discuss the existence uniqueness and holder regularity of mild solutions to the given problem under certain sufficient conditions which depend on the fractional order and hurst parameter h the results obtained in this study improve some results in existing literature

a geometrical approach to computing free energy landscapes from short ranged potentials particles interacting with short ranged potentials have attracted increasing interest partly for their ability to model mesoscale systems such as colloids interacting via dna or depletion we consider the free energy landscape of such systems as the range of the potential goes to zero in this limit the landscape is entirely defined by geometrical manifolds plus a single control parameter these manifolds are fundamental objects that do not depend on the details of the interaction potential and provide the starting point from which any quantity characterizing the system equilibrium or nonequilibrium can be computed for arbitrary potentials to consider dynamical quantities we compute the asymptotic limit of the fokker planck equation and show that it becomes restricted to the low dimensional manifolds connected by sticky boundary conditions to illustrate our theory we compute the low dimensional manifolds for identical particles providing a complete description of the lowest energy parts of the landscape including floppy modes with up to 2 internal degrees of freedom the results can be directly tested on colloidal clusters this limit is a unique approach for understanding energy landscapes and our hope is that it can also provide insight into finite range potentials

langevin dynamics with constraints and computation of free energy differences in this paper we consider langevin processes with mechanical constraints the latter are a fundamental tool in molecular dynamics simulation for sampling purposes and for the computation of free energy differences the results of this paper can be divided into three parts i we propose a simple discretization of the constrained langevin process based on a standard splitting strategy we show how to correct the scheme so that it samples em exactly the canonical measure restricted on a submanifold using a metropolis rule in the spirit of the generalized hybrid monte carlo ghmc algorithm moreover we obtain in some limiting regime a consistent discretization of the overdamped langevin brownian dynamics on a submanifold also sampling exactly the correct canonical measure with constraints the corresponding numerical methods can be used to sample without any bias a probability measure supported by a submanifold ii for free energy computation using thermodynamic integration we rigorously prove that the longtime average of the lagrange multipliers of the constrained langevin dynamics yields the gradient of a rigid version of the free energy associated with the constraints a second order time discretization using the lagrange multipliers is proposed iii the jarzynski crooks fluctuation relation is proved for langevin processes with mechanical constraints evolving in time an original numerical discretization without time step error is proposed numerical illustrations are provided for ii and iii

packing measure of the sample paths of fractional brownian motion let x t t r be a fractional brownian motion of index in rd if 1 0 where s s 1 log log 1 s 1 2 and p x 0 t is the packing measure of x 0 t

on the time fractional navier stokes equations abstract this paper is concerned with the navier stokes equations with time fractional derivative of order 0 1 this type of equations can be used to simulate anomalous diffusion in fractal media we establish the existence and uniqueness of local and global mild solutions in h q meanwhile we also give local mild solutions in j q moreover we prove the existence and regularity of classical solutions for such equations in j q

fixed point theorems for generalized metrically inward maps we prove fixed point results for multimaps satisfying a generalized metric or an metric inwardness condition our results extend generalize or improve several known results

finding the optimal nets for self folding kirigami three dimensional shells can be synthesized from the spontaneous self folding of two dimensional templates of interconnected panels called nets however some nets are more likely to self fold into the desired shell under random movements the optimal nets are the ones that maximize the number of vertex connections i e vertices that have only two of its faces cut away from each other in the net previous methods for finding such nets are based on random search and thus they do not guarantee the optimal solution here we propose a deterministic procedure we map the connectivity of the shell into a shell graph where the nodes and links of the graph represent the vertices and edges of the shell respectively identifying the nets that maximize the number of vertex connections corresponds to finding the set of maximum leaf spanning trees of the shell graph this method allows us not only to design the self assembly of much larger shell structures but also to apply additional design criteria as a complete catalog of the maximum leaf spanning trees is obtained

mild solutions to the time fractional navier stokes equations in r n abstract this paper addresses the existence and uniqueness of mild solutions to the navier stokes equations with time fractional differential operator of order 0 1 several interesting properties about the solution are also highlighted like regularity and decay rate in lebesgue spaces which will depend on the fractional exponent moreover it is shown that the l p exponent range which the solution belongs to is different from the range for the solution of the classical problem with 1

approximate controllability of fractional order semilinear systems with bounded delay abstract in this paper sufficient conditions are established for the approximate controllability of a class of semilinear delay control systems of fractional order the existence and uniqueness of mild solution of the system is also proved the results are obtained by using contraction principle and the schauder fixed point theorem some examples are given to illustrate the theory

well posedness of a linearized fractional derivative fluid model the one dimensional fractional derivative maxwell model e g palade et al rheol acta 35 1996 265 of importance in modeling the linear viscoelastic response in the glass transition region has been generalized in palade et al internat j engrg sci 37 1999 315 to objective three dimensional constitutive equations ces for both fluids and solids regarding the rest state stability of the fluid ce in heibig and palade j math phys 49 2008 043101 we gave a proof for the existence of weak solutions to the corresponding boundary value problem the aim of this work is to achieve the study of the existence and uniqueness of the aforementioned solutions and to present smoothness results

on some fractional evolution equations abstract in this paper the solutions of some evolution equations with fractional orders in a banach space are considered conditions are given which ensure the existence of a resolvent operator for an evolution equation in a banach space

hybrid monte carlo methods for sampling probability measures on submanifolds probability measures supported on submanifolds can be sampled by adding an extra momentum variable to the state of the system and discretizing the associated hamiltonian dynamics with some stochastic perturbation in the extra variable in order to avoid biases in the invariant probability measures sampled by discretizations of these stochastically perturbed hamiltonian dynamics a metropolis rejection procedure can be considered the so obtained scheme belongs to the class of generalized hybrid monte carlo ghmc algorithms we show here how to generalize to ghmc a procedure suggested by goodman holmes cerfon and zappa for metropolis random walks on submanifolds where a reverse projection check is performed to enforce the reversibility of the algorithm for any timesteps and hence avoid biases in the invariant measure we also provide a full mathematical analysis of such procedures as well as numerical experiments demonstrating the importance of the reverse projection check on simple toy examples

the packing measure of a general subordinator precise conditions are obtained for the packing measure of an arbitrary subordinator to be zero positive and finite or infinite it develops that the packing measure problem for a subordinatorx t is equivalent to the upper local growth problem fory t min y1 t y2 t wherey1 andy2 are independent copies ofx a finite and positive packing measure is possible for subordinators close to cauchy for such a subordinator there is non random concave upwards function that exactly describes the upper local growth ofy although as is well known there is no such function for the subordinatorx itself

the local and global existence of solutions for a time fractional complex ginzburg landau equation abstract we study the following time fractional complex nonlinear ginzburg landau equation e i 0 c d t u u e i u p 1 u x r n t 0 u 0 x u 0 x x r n where 0 1 r 2 2 p 1 u 0 l q r n q q c n p 1 2 and q 1 is a complex valued function and d t 0 c u t 0 i t 1 u t x u 0 x where i t 1 0 denotes a left riemann liouville fractional integral of order 1 by defining two operators and establishing some estimates of them we prove the well posedness of the mild solution for this problem in c 0 t l q r n and l 2 r q n r q 0 t l r r n where r satisfies 1 q 1 r 2 n moreover we also obtain the existence of global solutions when u 0 l q c r n is sufficiently small

approximate controllability of second order distributed implicit functional systems abstract in this paper we study the approximate controllability of control systems with states and controls in hilbert spaces and described by a second order semilinear abstract functional differential equation with infinite delay initially we establish a characterization for the approximate controllability of a second order abstract linear system and in the last section we compare the approximate controllability of a semilinear abstract functional system with the approximate controllability of the associated linear system

fixed points of generalized contractive multi valued mappings in a recent paper n mizoguchi and w takahashi gave a positive answer to the conjecture of s reich concerning the existence of fixed points of multi valued mappings that satisfy a certain contractive condition in this paper we provide an alternative and somewhat more straightforward proof for the theorem of mizoguchi and takahashi also the problems associated with fixed points of weakly contractive multi valued mappings are studied finally we make a few comments that improve other results from their paper j math anal appl 141 1989 177 188

on shinbrot s conjecture for the navier stokes equations marvin shinbrot conjectured that the weak solution of the navier stokes equations possess fractional derivatives in time of any order less than textstyle frac 1 2 in this paper using the hardy littlewood maximal theorem we prove that the conjecture is true in the two dimensional case and it is true conditionally in the three dimensional case

harnack s inequality for a space time fractional diffusion equation and applications to an inverse source problem abstract in this paper we focus on a space time fractional diffusion equation with the generalized caputo s fractional derivative operator and a general space nonlocal operator with the fractional laplace operator as a special case a weak harnack s inequality has been established by using a special test function and some properties of the space nonlocal operator based on the weak harnack s inequality a strong maximum principle has been obtained which is an important characterization of fractional parabolic equations with these tools we establish a uniqueness result of an inverse source problem on the determination of the temporal component of the inhomogeneous term which seems to be the first theoretical result of the inverse problem for such a general fractional diffusion model

fixed point results for set valued contractions by altering distances in complete metric spaces nadler s contraction principle has led to fixed point theory of set valued contraction in non linear analysis inspired by the results of nadler the fixed point theory of set valued contraction has been further developed in different directions by many authors in particular by reich mizoguchi takahashi feng liu and many others in the present paper the concept of generalized contractions for set valued maps in metric spaces is introduced and the existence of fixed point for such a contraction are guaranteed by certain conditions our first result extends and generalizes the nadler feng liu and klim wardowski theorems and the second result is different from the reich and mizoguchi takahashi results as a consequence we derive some results related to fixed point of set valued maps satisfying certain conditions of integral type

hausdorff measure of trajectories of multiparameter fractional brownian motion consider 0 1 and the gaussian process y t on r n with covariance e y t y s t 2 s 2 t s 2 where t is the euclidean norm of t consider independent copies x 1 x d of y and the process x t x 1 t x d t valued in r d in the transient case n d we show that a s for each compact set l of r n with nonempty interior we have 0 x l where denotes the hausdorff measure associated with the function e e n log log 1 e this result extends work of a goldman in the case 1 2 the proofs are considerably simpler

analytical solution of a time fractional navier stokes equation by adomian decomposition method abstract the aim of the present analysis is to apply adomian decomposition method for the solution of a time fractional navier stokes equation in a tube by using an initial value the explicit solution of the equation has been presented in the closed form and then its numerical solution has been represented graphically the present method performs extremely well in terms of efficiency and simplicity

holder continuous solutions for fractional differential equations and maximal regularity abstract we characterize the existence and uniqueness of solutions of an abstract fractional differential equation with infinite delay in holder spaces

an exact algorithm for the maximum leaf spanning tree problem given an undirected graph with n vertices the maximum leaf spanning tree problem is to find a spanning tree with as many leaves as possible when parameterized in the number of leaves k this problem can be solved in time o 4kpoly n using a simple branching algorithm introduced by a subset of the authors kneis et al 2008 16 daligault et al 2010 6 improved the branching and obtained a running time of o 3 72kpoly n in this paper we study the problem from an exponential time viewpoint where it is equivalent to the connected dominating set problem here fomin grandoni and kratsch showed how to break the 2n barrier and proposed an o 1 9407n time algorithm fomin et al 2008 11 based on some useful properties of kneis et al 2008 16 and daligault et al 2010 6 we present a branching algorithm whose running time of o 1 8966n has been analyzed using the measure and conquer technique finally we provide a lower bound of 1 4422n for the worst case running time of our algorithm

center stable manifold for planar fractional damped equations in this paper we discuss the existence of a center stable manifold for planar fractional damped equations by constructing a suitable lyapunovperron operator via giving asymptotic behavior of mittagleffler function we obtain an interesting center stable manifold theorem finally an example is provided to illustrate the result

cauchy problem for fractional diffusion equations abstract we consider an evolution equation with the regularized fractional derivative of an order 0 1 with respect to the time variable and a uniformly elliptic operator with variable coefficients acting in the spatial variables such equations describe diffusion on inhomogeneous fractals a fundamental solution of the cauchy problem is constructed and investigated

approximate controllability of a delayed semilinear control system with growing nonlinear term abstract this paper deals with the approximate controllability of a semilinear control system with delay where the nonlinear term satisfies the linear growth condition sufficient conditions for the approximate controllability of a semilinear control system have been established by assuming that the corresponding linear control system with delay is approximately controllable to prove our results the schauder fixed point theorem is applied and instead of a co semigroup associated with the mild solution of the system we use the so called fundamental solution

fixed point theorems for generalized contractive multi valued maps in n mizoguchi w takahashi fixed point theorems for multi valued mappings on complete metric spaces j math anal appl 141 1989 177 188 the authors gave a positive answer to the conjecture of s reich concerning the existence of fixed points of multi valued mappings that satisfy certain contractive conditions in this paper we establish some results for multi valued mappings that satisfy a generalized contractive condition in a way that it contains mizoguchi s result as one of its special cases in addition our results not only improve the results of kiran and kamran q kiran t kamran nadler s type principle with high order of convergence nonlinear anal tma 69 2008 4106 4120 and some results of agarwal et al r p agarwal jewgeni dshalalow donal o regan fixed point and homotopy results for generalized contractive maps of reich type appl anal 82 4 2003 329 350 but also provide the high order of convergence of the iterative scheme and error bounds as an application of our results we obtain an existence result for a class of integral inclusions

a galerkin finite element method for time fractional stochastic heat equation abstract in this study a galerkin finite element method is presented for time fractional stochastic heat equation driven by multiplicative noise which arises from the consideration of heat transport in porous media with thermal memory with random effects the spatial and temporal regularity properties of mild solution to the given problem under certain sufficient conditions are obtained numerical techniques are developed by the standard galerkin finite element method in spatial direction and gorenflo mainardi moretti paradisi scheme is applied in temporal direction the convergence error estimates for both semi discrete and fully discrete schemes are established finally numerical example is provided to verify the theoretical results

on fractional duhamelʼs principle and its applications abstract the classical duhamel principle established nearly 200 years ago by jean marie constant duhamel reduces the cauchy problem for an inhomogeneous partial differential equation to the cauchy problem for the corresponding homogeneous equation in this paper we generalize this famous principle to a wide class of fractional order differential operator equations

fixed point theorems for multivalued mappings on complete metric spaces on obtient une version multivaluee du theoreme de point fixe de caristi qui est equivalent au principe e variationnel du a ekeland on utilise ce resultat pour obtenir un theoreme qui deduit le theoreme de nadler et un theoreme de point fixe commun pour une application a 1 valeur et une application multivaluee

notes on the two dimensional fractional brownian motion we study the two dimensional fractional brownian motion with hurst parameter h 1 2 in particular we show using stochastic calculus that this process admits a skew product decomposition and deduce from this representation some asymptotic properties of the motion

abstract fractional cauchy problems with almost sectorial operators abstract of concern are the cauchy problems for linear and semilinear time fractional evolution equations involving in the linear part a linear operator a whose resolvent satisfies the estimate of growth 1 0 in a sector of the complex plane which occurs when one considers for instance the partial differential operators in the limit domain of dumb bell with a thin handle or in the space of holder continuous functions by constructing a pair of families of operators in terms of the generalized mittag leffler type functions and the resolvent operators associated with a for the first time and a deep analysis on the properties for these families we obtain the existence and uniqueness of mild solutions and classical solutions to the cauchy problems moreover we present three examples to illustrate the feasibility of our results

global existence and blow up of solutions of the cauchy problem for a time fractional diffusion system abstract we prove sharp blow up and global existence results for the cauchy problem of a time fractional diffusion system when initial values u 0 0 and v 0 0 the critical exponent of this problem is determined

time space fractional stochastic ginzburg landau equation driven by fractional brownian motion abstract the current paper is devoted to the time space fractional ginzburg landau equation driven by fractional brownian motion the spatial temporal regularity of the nonlocal stochastic convolution is firstly established and then the existence and uniqueness of the global mild solution are obtained by the banach fixed point theorem and mittag leffler functions finally the numerical simulations for the time fractional stochastic ginzburg landau equation are provided to verify the mathematical analysis results

a generalization of the banach contraction principle with high order of convergence of successive approximations in this paper we present the following generalization of the banach contraction principle let t d x xt d x x be a continuous operator on a complete metric space x d x d satisfying d tx t2x d x tx for all x d tx d with d x tx j where j r j r is an interval containing 0 j j j j is a gauge function of order r 1r 1 on jj in the sense that 0 0 t tr 0 0 t tr is nondecreasing on j 0 j 0 and t t t t on j 0 j 0 suppose that x0 dx0 d is an initial point such that d x0 tx0 jd x0 tx0 j and all of the iterates xn 1 txn n 0 1 belong to dd then the iterative sequence xn 1 txnxn 1 txn converges to a fixed point of tt with error estimates d xn sn r 1 rnd x0 tx0 andd xn d xn xn 1 1 d xn xn 1 where sn r 1 r rn 1 d x0 tx0 sn r 1 r rn 1 d x0 tx0 and is a nonnegative and nondecreasing function on jj such that t t t this fixed point theorem includes as special cases some results of mysovskih i p mysovskih on the convergence of l v kantorovic s method of solution of functional equations and its applications dokl acad nauk sssr 70 1950 565 568 in russian rheinboldt w c rheinboldt a unified convergence theory for a class of iterative processes siam j numer anal 5 1968 42 63 gel man a gel man a certain fixed point principle dokl akad nauk sssr 198 1971 506 508 in russian soviet math dokl 12 1971 813 816 engl transl huang z d huang on newton s method under holder continuous derivative j math anal appl 270 2002 332 339 and others

on a nonclassical fractional boundary value problem for the laplace operator abstract in this paper we consider a boundary value problem for the poisson equation with a boundary condition comprising the fractional derivative in time and the right hand sides dependent on time we prove the one valued solvability of this problem and provide the coercive estimates of the solution

a note on property of the mittag leffler function abstract recently the authors have found in some publications that the following property 0 1 of mittag leffler function is taken for granted and used to derive other properties 0 1 e a t s e a t e a s t s 0 where a is a real constant and 0 in this note it is proved that the above property is unavailable unless 1 or a 0 moreover a new equality on e a t is developed whose limit state as 1 is just the property 0 1

algorithmic design of self folding polyhedra self assembly has emerged as a paradigm for highly parallel fabrication of complex three dimensional structures however there are few principles that guide a priori design yield and defect tolerance of self assembling structures we examine with experiment and theory the geometric principles that underlie self folding of submillimeter scale higher polyhedra from two dimensional nets in particular we computationally search for nets within a large set of possibilities and then test these nets experimentally our main findings are that i compactness is a simple and effective design principle for maximizing the yield of self folding polyhedra and ii shortest paths from 2d nets to 3d polyhedra in the configuration space are important for rationalizing experimentally observed folding pathways our work provides a model problem amenable to experimental and theoretical analysis of design principles and pathways in self assembly

structure of finite sphere packings via exact enumeration implications for colloidal crystal nucleation we analyze the geometric structure and mechanical stability of a complete set of isostatic and hyperstatic sphere packings obtained via exact enumeration the number of nonisomorphic isostatic packings grows exponentially with the number of spheres n and their diversity of structure and symmetry increases with increasing n and decreases with increasing hyperstaticity h n c n iso where n c is the number of pair contacts and n iso 3n 6 maximally contacting packings are in general neither the densest nor the most symmetric analyses of local structure show that the fraction f of nuclei with order compatible with the bulk rhcp crystal decreases sharply with increasing n due to a high propensity for stacking faults five and near fivefold symmetric structures and other motifs that preclude rhcp order while f increases with increasing h a significant fraction of hyperstatic nuclei for n as small as 11 retain non rhcp structure classical theories of nucleation that consider only spherical nuclei or only nuclei with the same ordering as the bulk crystal cannot capture such effects our results provide an explanation for the failure of classical nucleation theory for hard sphere systems of n 10 particles we argue that in this size regime it is essential to consider nuclei of unconstrained geometry our results are also applicable to understanding kinetic arrest and jamming in systems that interact via hard core like repulsive and short ranged attractive interactions

a novel characteristic of solution operator for the fractional abstract cauchy problem abstract motivated by an equality of the mittag leffler function proved recently by the authors this paper develops an operator theory for the fractional abstract cauchy problem facp with order 0 1 the notion of fractional semigroup is introduced it is proved that a family of bounded linear operator is a solution operator for facp if and only if it is a fractional semigroup moreover the well posedness of the problem facp is also discussed it is shown that the problem facp is well posed if and only if its coefficient operator generates a fractional semigroup

exploring delayed mittag leffler type matrix functions to study finite time stability of fractional delay differential equations abstract in this paper we introduce a concept of delayed two parameters mittag leffler type matrix function which is an extension of the classical mittag leffler matrix function with the help of the delayed two parameters mittag leffler type matrix function we give an explicit formula of solutions to linear nonhomogeneous fractional delay differential equations via the variation of constants method in addition we prove the existence and uniqueness of solutions to nonlinear fractional delay differential equations thereafter we present finite time stability results of nonlinear fractional delay differential equations under mild conditions on nonlinear term finally an example is presented to illustrate the validity of the main theorems

how to compute the volume in high dimension in some areas of theoretical computer science we feel that randomized algorithms are better and in some others we can prove that they are more efficient than the deterministic ones

time discretization of fractional subdiffusion equations via fractional resolvent operators abstract in this work we study time discretization of subdiffusion equations that is fractional differential equations of order 0 1 assuming that a is the generator of a fractional resolvent family s t t 0 which allows to write the solution to the subdiffusion equation t u t a u t f t as a variation of constants formula we find an interesting connection between s t t 0 and a discrete resolvent family s n n n and then by using the properties of s t t 0 we study the existence of solutions to the discrete subdiffusion equation c u n a u n f n n n where based on the backward euler method for a 0 given c u n is an approximation of t u t at time t n n we study simultaneously the fractional derivative in the caputo and riemann liouville sense we also provide error estimates and some experiments to illustrate the results

stochastic burgers equation with fractional derivative driven by multiplicative noise abstract this article is devoted to the study of the existence and uniqueness of mild solution to time and space fractional stochastic burgers equation perturbed by multiplicative white noise the required results are obtained by stochastic analysis techniques fractional calculus and semigroup theory moreover we prove the regularity properties of mild solution to this generalized burgers equation in the framework of bochner spaces

free energy of singular sticky sphere clusters networks of particles connected by springs model many condensed matter systems from colloids interacting with a short range potential and complex fluids near jamming to self assembled lattices and various metamaterials under small thermal fluctuations the vibrational entropy of a ground state is given by the harmonic approximation if it has no zero frequency vibrational modes yet such singular modes are at the epicenter of many interesting behaviors in the systems above we consider a system of n spherical particles and directly account for the singularities that arise in the sticky limit where the pairwise interaction is strong and short ranged although the contribution to the partition function from singular clusters diverges in the limit its asymptotic value can be calculated and depends on only two parameters characterizing the depth and range of the potential the result holds for systems that are second order rigid a geometric characterization that describes all known ground state rigid sticky clusters to illustrate the applications of our theory we address the question of emergence how does crystalline order arise in large systems when it is strongly disfavored in small ones we calculate the partition functions of all known rigid clusters up to n 21 and show the cluster landscape is dominated by hyperstatic clusters those with more than 3n 6 contacts singular and isostatic clusters are far less frequent despite their extra vibrational and configurational entropies since the most hyperstatic clusters are close to fragments of a close packed lattice this underlies the emergence of order in sticky sphere systems even those as small as n 10

weak solutions of the time fractional navier stokes equations and optimal control abstract in this paper we deal with the navier stokes equations with the time fractional derivative of order 0 1 which can be used to simulate anomalous diffusion in fractal media we firstly give the concept of the weak solutions and establish the existence criterion of weak solutions by means of galerkin approximations in the case that the dimension n 4 moreover a complete proof of the uniqueness is given when n 2 at last we give a sufficient condition of optimal control pairs

upper and lower bounds of temporal and spatial decays for the navier stokes equations we obtain the lower bounds of the temporal spatial decays for weak solutions of the navier stokes equations c0 1 t 5 2i4 1 2 i 2u t l2 c1 1 t 5 2i4 for i 1 2 the upper bound parts are estimated in several papers for example bae and jin submitted and he and xin proc roy soc edinburg section a 131 3 2001 597 by the interpolation arguments we also have c0 1 t 54 2 1 x 2 2u t l2 c1 1 t 54 2 for 0 2

nadler s type principle with high order of convergence abstract recently proinov p d proinov a generalization of the banach contraction principle with high order of convergence of successive approximations nonlinear analysis 2006 doi 10 1016 j na 2006 09 008 generalized banach contraction principle with high order of convergence we extend some results of proinov to the case of multi valued maps from a complete metric space x into the space of all nonempty proximinal closed subsets of x our results not only generalize nadler s fixed point theorem in the case when t is a mapping from a complete metric space x into the space of all nonempty proximinal closed subsets of x but also gives high order of convergence as an application we obtain an existence theorem for first order initial value problem

projection of diffusions on submanifolds application to mean force computation we consider the problem of sampling a boltzmann gibbs probability distribution when this distribution is restricted in some suitable sense on a manifold of r n implicitly defined by n constraints q1 x qn x 0 this problem arises for example in systems subject to hard constraints or in the context of free energy calculations we prove that the constrained stochastic di erential equations i e di usions proposed in w e and e vanden eijnden in multiscale modelling and simulation eds s attinger and p koumoutsakos lncse 39 springer 2004 and g ciccotti r kapral and e vanden eijnden chemphyschem 6 1809 2005 are ergodic with respect to this restricted distribution we also construct numerical schemes for the integration of the constrained di usions finally we show how these schemes can be used to compute the gradient of the free energy associated with the constraints

controllability of semilinear control systems dominated by the linear part while various equivalent conditions for controllability have been obtained in the case of linear control systems controllability problems of semilinear control systems usually require some complicated and limited assumptions in this paper we show the approximate controllability of an abstract semilinear control system under the assumption which has a simple form and can be easily checked in many examples

on fractional calculus and fractional multipoles in electromagnetism using the concept and tools of fractional calculus we introduce a definition for fractional order multipoles of electric charge densities and we show that as far as their scalar potential distributions are concerned such fractional order multipoles effectively behave as intermediate sources bridging the gap between the cases of integer order point multipoles such as point monopoles point dipoles point quadrupoles etc this technique which involves fractional differentiation or integration of the dirac delta function provides a tool for formulating an electric source distribution whose potential functions can be obtained by using fractional differentiation or integration of potentials of integer order point multipoles of lower or higher orders as illustrative examples the cases of three dimensional point source and two dimensional line source problems in electrostatics are treated in detail and an extension to the time harmonic case is also addressed in the three dimensional electrostatic example we suggest an electric charge distribution which can be regarded as an intermediate case between cases of the electric point monopole point charge and the electric point dipole point dipole and we present its electrostatic potential which behaves as r sup 1 spl alpha p sub spl alpha cos spl theta where 0 spl alpha 1 and p sub spl alpha spl middot is the legendre function of noninteger degree spl alpha thus denoting this charge distribution as a fractional 2 sup spl alpha pole at the two limiting cases of spl alpha 0 and spl alpha 1 this fractional 2 sup spl alpha pole becomes the standard point monopole and point dipole respectively a corresponding intermediate fractional order multipole is also given for the two dimensional electrostatic case potential applications of this treatment to the image method in electrostatic problems are briefly mentioned physical insights and interpretation for such fractional order 2 sup spl alpha poles are also given

on the solution of fractional evolution equations this paper is devoted to the solution of the bi fractional differential equation for real 0 0 and 0 with the initial conditions here cd tu t x is the partial derivative coinciding with the caputo fractional derivative for 0 0 the laplace and fourier transforms are applied to solve the above problem in closed form the fundamental solution of these problems is established and its moments are calculated the special case 1 2 and 1 is presented and its application is given to obtain the dirac type decomposition for the ordinary diffusion equation