elliptic random walk equation for suspension and tracer transport in porous media abstract we propose a new approach to transport of the suspensions and tracers in porous media the approach is based on a modified version of the continuous time random walk ctrw theory in the framework of this theory we derive an elliptic transport equation the new equation contains the time and the mixed dispersion terms expressing the dispersion of the particle time steps the properties of the new equation are studied and the fundamental analytical solutions are obtained the solution of the pulse injection problem describing a common tracer injection experiment is studied in greater detail the new theory predicts delay of the maximum of the tracer compared to the velocity of the flow while its forward tail contains much more particles than in the solution of the classical parabolic advection dispersion equation this is in agreement with the experimental observations and predictions of the ctrw theory

invariant manifolds for impulsive equations and nonuniform polynomial dichotomies for impulsive differential equations in banach spaces we construct stable and unstable invariant manifolds for sufficiently small perturbations of a polynomial dichotomy we also consider the general case of nonuniform polynomial dichotomies moreover we introduce the notions of polynomial lyapunov exponent and of regularity coefficient for a linear impulsive differential equation and we show that when the lyapunov exponent never vanishes the linear equation admits a nonuniform polynomial dichotomy

exit problems associated with affine reflection groups we obtain a formula for the distribution of the first exit time of brownian motion from the alcove of an affine weyl group in most cases the formula is expressed compactly in terms of pfaffians expected exit times are derived in the type widetilde a case the results extend to other markov processes we also give formulas for the real eigenfunctions of the dirichlet and neumann laplacians on alcoves observing that the hot spots conjecture of j rauch is true for alcoves

schur subalgebras and an application to the symmetric group abstract let k be an infinite field of prime characteristic p and let d r be positive integers of the same parity satisfying a certain congruence condition we prove that the schur algebra s 2 d is isomorphic to a subalgebra of the form es 2 r e where e is a certain idempotent of s 2 r translating this result via ringel duality to the symmetric groups d and r we obtain lattice isomorphisms between specht modules between young modules and between permutation modules here modules labelled by the partitions r k k correspond to modules labelled by d k k this provides a representation theoretical interpretation for part of the fractal structures observed for the decomposition numbers of the symmetric groups corresponding to two part partitions

a solution to an open problem for wave equations with generalized wentzell boundary conditions in this paper we solve an open problem put forward by a favini g r goldstein j a goldstein and s romanelli concerning the mixed problem for wave equations with generalized wentzell boundary conditions as a consequence we also develop the previous wellposedness result regarding the mixed problem for heat equations with generalized wentzell boundary conditions

a stochastic theory for deep bed filtration accounting for dispersion and size distributions abstract we develop a stochastic theory for filtration of suspensions in porous media the theory takes into account particle and pore size distributions as well as the random character of the particle motion which is described in the framework of the theory of continuous time random walks ctrw in the limit of the infinitely many small walk steps we derive a system of governing equations for the evolution of the particle and pore size distributions we consider the case of concentrated suspensions where plugging the pores by particles may change porosity and other parameters of the porous medium a procedure for averaging of the derived system of equations is developed for polydisperse suspensions with several distinctive particle sizes a numerical method for solution of the flow equations is proposed sample calculations are applied to compare the roles of the particle size distribution and of the particle flight dispersion on the deposition profiles it is demonstrated that the temporal flight dispersion is the most likely mechanism forming the experimentally observed hyperexponential character of the deposition profiles

peclet dependent memory kernels for transport in heterogeneous media transport in heterogeneous media can be described by partial differential equations which exhibit convolutions with time and or space memory kernels in this work we characterize the full time spectrum of time memory kernels by applying a nonparametric inversion algorithm to macroscopic synthetic data for heterogeneous porous media our findings put into evidence the inherent nonuniqueness of the transport parameters for nonlocal transport models notably we find that the peclet number can be interpreted as an ancillary parameter of a family of probability distribution functions that characterizes the memory kernels of transport

strongly pseudoconvex cr structures over small balls part i an a priori estimate the purpose of the present series of papers is to develop the theory of harmonic integrals on strongly pseudoconvex cr structures over small balls along the line developed by d c spencer c b morrey j j kohn and l nirenberg 5 6 7 8 for strongly pseudoconvex complex manifolds we consider a strongly pseudoconvex cr structure on a manifold of real dimension 2n 1 in part i we establish the a priori estimate for the neumann boundary value problem on the complex associated with the structure in the case the structure is induced by an embedding in c and restricted to a small ball of special type provided i c q c n 3 where q is the degree of differential forms we consider in part ii we derive the regularity theorem of solutions of the neumann boundary value problem based on the a priori estimate of part i as an application we prove in part il that when n 5 the structure is realized on a neighborhood of a reference point by an embedding in cn we note here that l nirenberg gave an example of a strongly pseudoconvex cr structure which cannot be induced by such an embedding when n 2 9 l boutet de monvel proved that in the case of such structures over a compact manifold we can find such an embedding when n 3 1 there are two major differences between the cases of strongly pseudoconvex integrable almost complex structures and cr structures firstly the principal parts of the associated laplacians in cr structures are no longer elliptic secondly we have characteristic points on the boundary as a result when we follow over the predecessor s calculation in our case we end up with terms which may not be absorbed in the main non negative terms fortunately these leftover terms depend mostly on the levi form of the cr structure and the hessian form with respect to the cr structure of the equation of the boundary of our

generic formulas for the values at the singular points of some special monic classical hq ω orthogonal polynomials it is well known that the classical orthogonal polynomials of jacobi bessel laguerre and hermite are solutions of a sturm liouville problem of the type s x y n email protected x y n email protected ny n 0 where s and t are polynomials such that email protected 2 and email protected 1 and l n is a constant independent of x recently based on the hypergeometric character of the solutions of this differential equation w koepf and m masjed jamei a generic formula for the values at the boundary points of monic classical orthogonal polynomials j comput appl math 191 2006 98 105 found a generic formula only in terms of the coefficients of s and t for the values of the classical orthogonal polynomials at the singular points of the above differential hypergeometric equation in this paper we generalize the mentioned result giving the analogous formulas for both the classical q orthogonal polynomials of the q hahn tableau and the classical d w orthogonal polynomials both are special cases of the classical h q w orthogonal polynomials which are solutions of the hypergeometric type difference equation s x h q wh 1 q wy email protected x h q wy email protected ny n 0 where h q w is the difference operator introduced by hahn and s t and l n being as above our approach is algebraic and it does not require hypergeometric functions

classes of representable disjoint np pairs for a propositional proof system p we introduce the complexity class dnpp p of all disjoint np pairs for which the disjointness of the pair is efficiently provable in the proof system p we exhibit structural properties of proof systems which make canonical np pairs associated with these proof systems hard or complete for dnpp p moreover we demonstrate that non equivalent proof systems can have equivalent canonical pairs and that depending on the properties of the proof systems different scenarios for dnpp p and the reductions between the canonical pairs exist

fredholm property of a family of operators on the five dimensional heisenberg group abstract an expansion in euclidean spherical harmonics on the ball in the heisenberg group of dimension five decomposes the dirichlet problem for the laplacian in an infinite number of two dimensional problems fundamental solutions are obtained for each of the partial differential operators in these problems thus reducing them further via layer potentials to one dimensional integral equations the main result in this article states that the corresponding integral operators are fredholm in appropriate weighted l 2 spaces

a nonterminating 8 φ 7 summation for the root system c r using multiple q integrals and a determinant evaluation we establish a nonterminating 8 7 summation for the root system cr we also give some important specializations explicitly

infinite horizon backward stochastic differential equations and elliptic equations in hilbert spaces solutions of semilinear elliptic differential equations in infinite dimensional spaces are obtained by means of forward and backward infinite dimensional stochastic evolution equations the backward equation is considered on an infinite time horizon and a suitable growth condition replaces the final condition elliptic equations are intended in a mild sense suitable also for applications to optimal control we finally notice that due to the lack of smoothing properties the elliptic partial differential equation considered here could not be treated by analytic methods

double centralizing theorems for the alternating groups let v n be the n fold tensor product of a vector space v following i schur we consider the action of the symmetric group sn on v n by permuting coordinates in the super z2 graded case v v0 v1 a sign is added these actions give rise to the corresponding schur algebras s sn v here s sn v is compared with s an v the schur algebra corresponding to the alternating subgroup an sn while in the classical signless case these two schur algebras are the same for n large enough it is proved that in the super case where dim v0 dim v1 s an v is isomorphic to the cross product algebra s an v s sn v z2

robust nonuniform dichotomies and parameter dependence abstract we establish the robustness of linear cocycles with an exponential dichotomy under sufficiently small lipschitz perturbations in the sense that the existence of an exponential dichotomy for a given cocycle persists under these perturbations we consider cocycles in banach spaces as well as the general case of nonuniform exponential dichotomies and also the general case of an exponential behavior e c n given by an arbitrary sequence n including the usual exponential behavior n n as a very special case moreover we show that the projections of the exponential dichotomies obtained from the perturbation vary continuously with the parameter and in fact that they are locally lipschitz on finite dimensional parameters

modular invariant of quantum tori the quantum modular invariant j qt of 2r is defined as a discontin uous pgl2 z invariant multi valued map using the distance to the nearest integer function k k for 2 q it is shown that j qt 1 and for quadratic irrationalities pari gp experiments suggest that j qt is a finite set in the case of the golden mean we produce explicit formulas involving weighted versions of the rogers ramanujan functions for the experimental supremum and infimum we then define a universal modular invariant j a mod c as a continuous and single valued map of ultrasolenoids such that 1 the classical modular invariant is a quotient of the re striction of j to a subsolenoid mod cl a mod fibering over the classical moduli space of elliptic curves and 2 the quantum modular invariant is a quotient of the restric tion of j to a subsolenoid mod qt a mod fibering over the moduli space of elliptic curves equipped with a kronecker foliation

coding the principal character formula for affine kac moody lie algebras in this paper an algorithm for computing the principal character for affine lie algebras is discussed and presented the principal characters discovered using this program are given and or proven results include level 2 and 3 character formulas in a2n 1 2 and the sole existence of the rogers ramanujan products in a1 1 a2 1 a2 2 c3 1 f4 1 g2 1 a7 2

zeros of jones polynomials for families of knots and links abstract we calculate jones polynomials v l t for several families of alternating knots and links by computing the tutte polynomials t g x y for the associated graphs g and then obtaining v l t as a special case of the tutte polynomial for each of these families we determine the zeros of the jones polynomial including the accumulation set in the limit of infinitely many crossings a discussion is also given of the calculation of jones polynomials for non alternating links

combining hook length formulas and bg ranks for partitions via the littlewood decomposition recently the first author has studied hook length formulas for partitions in a systematic manner in the present paper we show that most of those hook length formulas can be generalized and include more variables via the littlewood decomposition which maps each partition to its t core and t quotient in the case t 2 we ob tain new formulas by combining hook lengths and bg ranks introduced by berkovich and garvan as applications we list several multivari able generalizations of classical and new hook length formulas including the nekrasov okounkov the han carde loubert potechin sanborn the bessenrodt bacher manivel the okada panova and the stanley panova formulas summary

invariant measures and regularity properties of perturbed ornstein uhlenbeck semigroups abstract this paper deals with perturbations of the ornstein uhlenbeck operator on l 2 spaces with respect to a gaussian measure we perturb the generator of the ornstein uhlenbeck semigroup by a certain unbounded non linear drift and show various properties of the perturbed semigroup such as compactness and positivity strong feller property existence and uniqueness of an invariant measure are discussed as well

positive energy representations holomorphic discrete series and finite dimensional irreps let g be a semi simple non compact lie group with unitary lowest highest weight representations we consider explicitly the relation among three types of representations of g positive energy unitary lowest weight representations holomorphic discrete series representations and non unitary finite dimensional irreps we consider mainly the conformal groups soo n 2 treating in full detail the cases n 1 3 4

trace representation of some generalized cyclotomic sequences of length pq this paper contributes to trace representation of some generalized cyclotomic sequences of length pq p qprime which are defined by ding and helleseth from the relations between these sequences and the legendre sequence we firstly confirm the defining pairs of these sequences of arbitrary order then we obtain their trace representation from which we give their linear complexity using key s method it can be seen that bai et al s conclusion is a special case of our result when the order is two finally an example is given to illustrate the validity of our result

determining simplicity and computing topological change in strongly normal partial tilings of r2 or r3 abstract a convex polygon in r2 or a convex polyhedron in r3 will be called a tile a connected set p of tiles is called a partial tiling if the intersection of any two of the tiles is either empty or is a vertex or edge in r3 or face of both p is called strongly normal sn if for any partial tiling p p and any tile p p the neighborhood n p p of p the union of the tiles of p that intersect p is simply connected let p be sn and let n p p be the excluded neighborhood of p in p i e the union of the tiles of p other than p itself that intersect p we call p simple in p if n p p and n p p are topologically equivalent this paper presents methods of determining for an sn partial tiling p whether a tile p p is simple and if not of counting the numbers of components and holes in r3 components tunnels and cavities in n p p

lattices on simplicial partitions which are not simply connected in this paper d 1 pencil lattices on simplicial partitions in r d which are not simply connected are studied it is shown how the fact that a partition is not simply connected can be used to increase the flexibility of a lattice a local modification algorithm is developed also to deal with slight partition topology changes that may appear afterwards a lattice has already been constructed

strongly normal sets of contractible tiles in n dimensions the second and third authors and others have studied collections of usually convex tiles a generalization of pixels or voxels in r 2 and r 3 that have a property called strong normality sn for any tile p only finitely many tiles intersect p and any nonempty intersection of those tiles also intersects p this paper extends basic results about strong normality to collections of contractible polyhedra in r n whose nonempty intersections are contractible we also give sufficient and trivially necessary conditions on a locally finite collection of contractible polyhedra in r 2 or r 3 for their nonempty intersections to be contractible

generation of localization in a discrete chain with periodic boundary conditions numerical and analytical results we study the generation of localization in a discrete chain composed of n subsystems and periodic boundary conditions strongly localized motions are studied that is time periodic motions where nearly all of the energy is spatially confined to a single subsystem for varying n numerical results indicate that the strongly localized solutions are generated through a bifurcation from an in phase spatially extended solution however in the limit as n rightarrow infty the bifurcation point tends to infinity and a smooth transition from localization to nonlocalization occurs we then present an analytic technique to complement the numerical results it is based on the matching local asymptotic expansions of a solution branch using pade approximants this leads to global analytic representations of the considered solutions valid over the entire range of the control parameter

the exceptional lie algebra e7 25 multiplets and invariant differential operators in the present paper we continue the project of systematic construction of invariant differential operators on the example of the non compact exceptional algebra e7 25 our choice of this particular algebra is motivated by the fact that it belongs to a narrow class of algebras which we call conformal lie algebras which have very similar properties to the conformal algebras of n dimensional minkowski spacetime this class of algebras is identified and summarized in a table another motivation is related to the ads cft correspondence we give the multiplets of indecomposable elementary representations including the necessary data for all relevant invariant differential operators

the complexity of weighted boolean csp with mixed signs we give a complexity dichotomy for the problem of computing the partition function of a weighted boolean constraint satisfaction problem such a problem is parameterized by a set c of rational valued functions which generalize constraints each function assigns a weight to every assignment to a set of boolean variables our dichotomy extends previous work in which the weight functions were restricted to being non negative we represent a weight function as a product of the form 1 sg where the polynomial s determines the sign of the weight and the non negative function g determines its magnitude we show that the problem of computing the partition function the sum of the weights of all possible variable assignments is in polynomial time if either every function in c can be defined by a pure affine magnitude with a quadratic sign polynomial or every function can be defined by a magnitude of product type with a linear sign polynomial in all other cases computing the partition function is fp p complete

new combinatorial interpretations of ramanujan s partition congruences mod 5 7 and 11 soit p n le nombre de partitions non restreintes de n on donne de nouvelles interpretations combinatoires des congruences p 5n 4 p 7n 5 et p 11n 6 0 mod 5 7 et 11 respectivement

elliptic equation for random walks application to transport in microporous media abstract we consider a process of random walks with arbitrary residence time distribution we show that in many cases this process may not be described by the classical fick parabolic diffusion equation but an elliptic equation an additional term proportional to the second time derivative takes into account the distribution of the residence times of molecules in pores the new elliptic diffusion equation is strictly derived by the operator approach a criterion showing where the new equation should be applied instead of the standard diffusion equation is obtained boundary conditions are studied and a principle for selection of a unique bounded solution is formulated fundamental solutions are obtained and compared with the results of direct simulation of the random walks

nonexistence of homotopy formula for 0 1 forms on hypersurfaces in mathbb c 3 soit g une 0 1 forme definie sur une hypersurface strictement convexe dans c 3 et on suppose que b g 0 mais b g est petit on considere la resolution locale approchee de l equation b u g

a de giorgi nash type theorem for time fractional diffusion equations we study the regularity of weak solutions to linear time fractional diffusion equations in divergence form of arbitrary time order alpha in 0 1 the coefficients are merely assumed to be bounded and measurable and they satisfy a uniform parabolicity condition our main result is a de giorgi nash type theorem which gives an interior holder estimate for bounded weak solutions in terms of the data and the l infty bound of the solution the proof relies on new a priori estimates for time fractional problems and uses de giorgi s technique and the method of non local growth lemmas which has been introduced recently in the context of nonlocal elliptic equations involving operators like the fractional laplacian

some inequalities for the q beta and the q gamma functions via some q integral inequalities some new inequalities for the q gamma the q beta and the q analogue of the psi functions are established via some q integral inequalities

quantitative characterization of pore scale disorder effects on transport in homogeneous granular media breakthrough curves btc of a passive tracer in macroscopically homogeneous granular materials well sorted unconsolidated sands or glass beads were measured in a series of column experiments the early and late arrival times are observed to differ systematically from theoretical predictions based on solution of the advective dispersion equation for uniform porous media we propose that subtle and residual pore scale disorder effects in the porous media can account for these observations we determine an ensemble averaged distribution of particle transfer rates based on a master equation for the local flux averaged concentration which incorporates these effects and utilize it to calculate btc that are in excellent agreement with the entire series of observations theoretical prediction of the dependence of the effective macroscopic parameters on measurable quantities is also in excellent agreement with the observations

the asymptotic bounds of solutions of linear delay systems abstract our aim is to obtain conditions under which every solutionyof the vector functional differential equation formula can be estimated in terms of a solution of a scalar functional equation formula wherea x is a suitable real positive function andbis a suitable real negative constant moreover ifb x is diagonal matrix we derive more precise estimates ofyin terms of a solution of a vector functional equation formula where the elements ofa x are formed by the absolute values of the corresponding elements ofa x these asymptotic results enable us to obtain sharp estimates of solutions of certain linear delay systems

the x ray transform and its inversion for the series expansion basis functions in three dimensional tomography a formula for the three dimensional x ray transform and an expression for its inversion have been derived the spherical harmonics and the rotation matrices in terms of euler angles are used in the generalized fourier series expansion some properties of the transformed fourier components are discussed

strictly pseudoconvex domains in c n the theory which we have developed so far will be expanded in two ways 1 in this chapter we shall use the cauchy fantappie calculus to transform the bochner martinelli kernel into a kernel adapted to strictly pseudoconvex domains in n and prove a number of finiteness and vanishing theorems for these domains 2 in the next chapter we shall pass from n to arbitrary hermitian manifolds and establish the analogue of the bmk formula in that context obtaining along the way the hodge decomposition theorem on compact manifolds both lines of thought will merge in the subsequent chapters and lead to a solution of the levi problem and finiteness theorems for strictly pseudoconvex manifolds as well as to a solution of the overline partial neumann problem to be formulated later

local and global topology preservation in locally finite sets of tiles abstract this paper deals with sets p of tiles compact convex sets in r 2 or r 3 tiles are a generalization of pixels or voxels they can have arbitrary shapes are allowed to have overlapping interiors and need not cover the space the union of all the tiles of p is denoted by u p the neighborhood n p p of a tile p is the union of the tiles of p that intersect p p is called simple if deletion of p from p does not change the topology in the homotopy sense of u p we show in this paper that if p satisfies a property called strong normality sn and deletion of p preserves the topology of n p p then p is simple this may not be true if p is not sn and even if p is sn p may be simple even if deletion of p does not preserve the topology of n p p

an improved sectional anosov closing lemma we prove that all nonwandering points of a sectional anosov flow on a compact 3 manifold can be approximated by periodic points or by points for which the omega limit set is a singularity this improves the closing lemma in morales mich math j 56 1 29 53 2008 we also describe a sectional anosov flow for which the recurrent points are not dense in the nonwandering set

n point pade approximants to real valued stieltjes series with nonzero radii of convergence abstract by employing special continued fractions to two stieltjes series with nonzero radii of convergence we extend the inequalities for one point pade approximants reported by baker 1975 corollory 17 1 to the case of two point pade approximants we prove that some convergents of the continued fractions form a monotone sequences of upper and lower bounds converging uniformly to stieltjes function x1 x on compact subsets of r where r is a radius of convergence of an expansion of x f1 x at x 0 for an illustration of theoretical results we provide nontrivial numerical examples as an application to real physical problems second order pade approximants bounds on the effective conductivity of a square array of cylinders are evaluated

strongly pseudoconvex cr structures over small balls part ii a regularity theorem the purpose of the present paper is to prove the regularity theorem for the solution of the generalized neumann boundary value problem for a strongly pseudoconvex cr structure say t over a small ball this will be based on the a priori estimate established in i namely we take an admissible distance function t to a reference point cf 2 12 in i and consider a sufficiently small ball ur t r denote by d the differential operator in the complex associated with 0t and consider the metric given by a levi form set b dt which is a function of u we consider the hilbert space of l2 norm with weight factor b2a 11 11 a and a denoting its norm and inner product respectively let ad be the adjoint of d set qa u v du dv a ad u ad v a for 0t q forms u v the generalized neumann boundary value problem is to solve the following equation for a given 0t q form a and an unknown 0t q form u withuldt 0

central limit theorem for products of random matrices using the semigroup product formula of p chernoff a central limit theorem is derived for products of random matrices applications are presented for representations of solutions to linear systems of stochastic differential equations and to the corresponding partial differential evolution equations included is a discussion of stochastic semigroups and a stochastic version of the lie trotter product formula

on the q analogues of some transformations of nearly poised hypergeometric series a number of transformation formulas for very well poised basic hypergeometric series have been obtained which in the limit q 1 approach the known transformation formulas for nearly poised ordinary hypergeometric series

on modular homology in the boolean algebra iii abstract let be a set ra ring of characteristicp 0 and denote bymkther module withk element subsets of as basis theset inclusion map mk mk 1is the homomorphism which associates to ak element subset the sum 1 2 kof all its k 1 element subsets i in this paper we study the chain formula arising from we introduce the notion ofp exactness for a sequence if is infinite we show that isp exact for all prime characteristicsp 0 this result can be extended to various submodules and quotient modules and we give general constructions arising from permutation groups with a finitary section two particular applications are the following the orbit module sequence of such a permutation group on isp exact for every primep and we give a formula for thep rank of the orbit inclusion matrix if the group has finitely many orbits onk element subsets

exponents of nonnegative matrix pairs the notions of primitivity and exponent of a square nonnegative matrix a are classical a is primitive provided there is a nonnegative integer k such that a k is entrywise positive and in the case a is primitive the exponent of a is the smallest such k fornasini and valcher have extended the notion of primitivity to pairs a b of square nonnegative matrices of the same order the pair a b is primitive provided there exist nonnegative integers h and k such that the sum of all products formed by words consisting of ha s and kb s is entrywise positive this paper defines the exponent of a nonnegative matrix pair to be the smallest value of h k over all such h and k it is then shown that the largest exponent of a primitive pair of n by n nonnegative matrices lies in the interval n 3 5n 2 2 3n 3 2n 2 2n 2 in addition the exponent of a pair of nonnegative matrices is related to properties of an associated twodimensional dynamical system 2001 elsevier science inc all rights reserved