modules of the 0 hecke algebra and quasisymmetric schur functions abstract we begin by deriving an action of the 0 hecke algebra on standard reverse composition tableaux and use it to discover 0 hecke modules whose quasisymmetric characteristics are the natural refinements of schur functions known as quasisymmetric schur functions furthermore we classify combinatorially which of these 0 hecke modules are indecomposable from here we establish that the natural equivalence relation arising from our 0 hecke action has equivalence classes that are isomorphic to subintervals of the weak bruhat order on the symmetric group focussing on the equivalence classes containing a canonical tableau we discover a new basis for the hopf algebra of quasisymmetric functions and use the cardinality of these equivalence classes to establish new enumerative results on truncated shifted reverse tableau studied by panova and adin king roichman generalizing our 0 hecke action to one on skew standard reverse composition tableaux we derive 0 hecke modules whose quasisymmetric characteristics are the skew quasisymmetric schur functions of bessenrodt et al this enables us to prove a restriction rule that reflects the coproduct formula for quasisymmetric schur functions which in turn yields a quasisymmetric branching rule analogous to the classical branching rule for schur functions

nonlinear three point third order boundary value problems abstract in this paper we consider three point boundary value problems for third order differential equations we provide simple sufficient conditions in order to obtain a priori bounds on solutions we then rely on the topological transversality theorem of granas or on schaefer s theorem to prove existence of solutions

multiple well invasion percolation when the invasion percolation model is applied as a simplified model for the displacement of a viscous fluid by a less viscous one the distribution of displaced mass follows two distinct universality classes depending on the criteria used to stop the displacement here we study the distribution of mass for this process in the case where four extraction wells are placed around a single injection well in the middle of a square lattice our analysis considers the limit where the pressure of the extraction well p e is zero in other words an extraction well is capped as soon as less viscous fluid reaches that extraction well our results show that as expected the probability of stopping the production with small amounts of displaced mass is greatly reduced we also investigate whether or not creating extra extraction wells is an efficient strategy we show that the probability of increasing the amount of displaced fluid by adding an extra extraction well depends on the total recovered mass obtained before adding this well the results presented here could be relevant to determine efficient strategies in oil exploration

three point boundary value problems for ordinary differential equations by matching solutions motivational results for solution matching were proven first in the text by bailey et al l where they dealt with solutions of two point problems for y f x y y by matching solutions of initial value problems then in 1973 barr sherman 2 adapted the arguments of bailey et al to match solutions of two point boundary value problems for third order equations to obtain solutions of three point problems in the same paper they showed that this result could be generalized to equations of arbitrary order yielding solutions of l 2 barr miletta 3 matched solutions of k point problems for nth order linear equations and obtained solutions of n point conjugate type boundary value problems in 1978 moorti garner 4 extended the results of 2 to boundary value problems similar to l 3 except p y were restricted

scaling of the distribution of shortest paths in percolation we present a scaling hypothesis for the distribution function of the shortest paths connecting any two points on a percolating cluster which accounts for i the effect of the finite size of the system and ii the dependence of this distribution on the site occupancy probability p we test the hypothesis for the case of two dimensional percolation

random walk percolation based modeling of two phase flow in porous media breakthrough time and net to gross ratio estimation abstract fluid flow modeling in porous media has many applications in waste treatment hydrology and petroleum engineering in any geological model flow behavior is controlled by multiple properties these properties must be known in advance of common flow simulations when uncertainties are present deterministic modeling often produces poor results percolation and random walk rw methods have recently been used in flow modeling their stochastic basis is useful in dealing with uncertainty problems they are also useful in finding the relationship between porous media descriptions and flow behavior this paper employs a simple methodology based on random walk and percolation techniques the method is applied to a well defined model reservoir in which the breakthrough time distributions are estimated the results of this method and the conventional simulation are then compared the effect of the net to gross ratio on the breakthrough time distribution is studied in terms of shannon entropy use of the entropy plot allows one to assign the appropriate net to gross ratio to any porous medium

existence of positive solutions for singular higher order differential equations abstract in this paper we consider the existence of positive solutions for the following singular higher order eigenvalue problem hep 1 n u 2 n t a t f t u t u t u 2 n 1 t 0 t 1 i u 2 i 0 i u 2 i 1 0 0 i u 2 i 1 i u 2 i 1 1 0 0 i n 1 where 0 is a parameter a t may have singularity at t 0 and or 1 furthermore f t v 1 v 2 v n may also be singular at v i 0 i 1 2 n without making any monotone type assumptions we establish various lemmas and theorems for the existence of positive solutions of the hep when is in an explicit interval in addition the associated green function for the above problem is derived

piecewise complementary lidstone interpolation and error inequalities the purpose of this paper is to develop piecewise complementary lidstone interpolation in one and two variables and establish explicit error bounds for the derivatives in l and l 2 norms

irreducible projective modules of the hecke algebras of a finite coxeter group in this paper we classify the irreducible projective modules or equivalently see e g 6 the irreducible principal indecomposable modules of a non semisimple hecke algebra h w e of a finite coxeter group w let w 3 be a finite coxeter system 2 and t an indeterminate q t we denote by h w q the generic hecke iwaho algebra 9 2 lo this means that h w q is the c t algebra with the basis t w we w and the multiplication defined by

triple positive solutions and dependence on higher order derivatives abstract in this paper we consider the lidstone boundary value problem y 2 m t f y t y 2 j t y 2 m 1 t 0 t 1 y 2 i 0 0 y 2 i 1 0 i m 1 where 1 m f 0 growth conditions are imposed on f and inequalities involving an associated green s function are employed which enable us to apply the leggett williams fixed point theorem to cones in ordered banach spaces this in turn yields the existence of at least three positive symmetric concave solutions the emphasis here is that f depends on higher order derivatives

multiplicity results for a three point boundary value problem at resonance this paper deals with second order three point boundary value problem u t f t u t t 0 1 u 0 0 u 1 u where f 0 1 r r is continuous 0 and 0 1 are given constants such that 1 we develop the methods of lower and upper solutions by the connectivity properties of the solution set of parameterized families of compact vector fields as applications of these methods we get several multiplicity results for the problems under consideration

existence uniqueness and iterative methods for third order boundary value problems abstract in this paper we shall provide necessary and sufficient conditions for the existence and uniqueness of solutions of third order nonlinear differential equations satisfying three point boundary conditions for the linear case we propose a constructive method which is a variation of the method of chasing for the nonlinear problems sufficient conditions are provided to ensure the convergence of a general class of iterative methods several examples are also included

a subalgebra of 0 hecke algebra let w i be a finite coxeter group in the case where w is a weyl group berenstein and kazhdan in a berenstein d kazhdan geometric and unipotent crystals ii from unipotent bicrystals to crystal bases in quantum groups in contemp math vol 433 amer math soc providence ri 2007 pp 13 88 constructed a monoid structure on the set of all subsets of i using unipotent linear bicrystals in this paper we will generalize this result to all types of finite coxeter groups including non crystallographic types our approach is more elementary based on some combinatorics of coxeter groups moreover we will calculate this monoid structure explicitly for each type

dependency of percolation critical exponents on the exponent of power law size distribution abstract the standard percolation theory uses objects of the same size moreover it has long been observed that the percolation properties of the systems with a finite distribution of sizes are controlled by an effective size and consequently the universality of the percolation theory is still valid in this study the effect of power law size distribution on the critical exponents of the percolation theory of the two dimensional models is investigated two different object shapes i e stick shaped and square are considered these two shapes are the representative of the fractures in fracture reservoirs and the sandbodies in clastic reservoirs the finite size scaling arguments are used for the connectivity to determine the dependency of the critical exponents on the power law exponent in particular the deviations of percolation exponents from their universal values as well as the connectivity behavior of such systems are investigated numerically as a result this extends the applicability of the conventional percolation approach to study the connectivity of systems with a very broad size distribution

confluence and koszulity abstract a lattice theoretic approach to koszulity is well known this paper gives a lattice theoretic approach to polynomiality i e existence of a p b w basis in priddy s sense this provides a straightforward proof for priddy s theorem polynomiality is interpreted in terms of confluence in noncommutative computational algebra the basic notion of a reduction operator is investigated in some detail the reduction algebras are introduced to study the confluence of two reduction operators in terms of representation theory the meet and the join of two reduction operators are constructed in an algorithmic way a geometric characterization of the confluence is obtained

lidstone polynomials and boundary value problems abstract we define lidstone polynomials provide their explicit representations give their relations with bernoulli polynomials obtain best possible error estimates in lidstone interpolation and establish several best possible sharp inequalities which compare favourably with the known results next we use these results to study even order differential equations together with lidstone boundary conditions

explicit polynomial expansions of regular real functions by means of even order bernoulli polynomials and boundary values for a function f c2n 1 a b an explicit polynomial interpolant in a and in the even derivatives up to the order 2n 1 at the end points of the interval is derived explicit cauchy and peano representations and bounds for the error are given and the analysis of the remainder term allows to find sufficient conditions on f so that the polynomial approximant converges to f these results are applied to derive a new summation formula with application to rectangular quadrature rule the polynomial interpolant is related to a fairly interesting boundary value problem for odes we will exhibit solutions for this problem in some special situations

upper and lower solution methods for fully nonlinear boundary value problems abstract sufficient conditions are given for the existence of a solution of a fourth order nonlinear boundary value problem with nonlinear boundary conditions the conditions assume the existence of a strong upper solution lower solution pair a concept that is defined in the paper the differential equation has nonlinear dependence on all lower order derivatives of the unknown in particular appropriate nagumo conditions are obtained and employed

hecke algebras difference operators and quasi symmetric functions abstract we define a new action of the symmetric group and its hecke algebra on polynomial rings whose invariants are exactly the quasi symmetric polynomials we interpret this construction in terms of a demazure character formula for the irreducible polynomial modules of a degenerate quantum group we use the action of the generic hecke algebras to define quasi symmetric and noncommutative analogues of hall littlewood functions we show that these generalized functions share many combinatorial properties with the classical ones nous introduisons de nouvelles actions du groupe symetrique et de son algebre de hecke sur les polynomes pour lesquelles les invariants sont les polynomes quasi symetriques nous interpretons cette construction en termes de caracteres de demazure d un groupe quantique degenere nous utilisons l action de l algebre de hecke generique pour definir des analogues quasi symetriques et non commutatifs des fonctions de hall littlewood nous montrons que ces fonctions generalisees ont un certain nombre de proprietes communes avec les fonctions classiques

on three point boundary value problems associated with third order differential equations introduction in this paper we shall be concerned with the existence and uniqueness of solutions to three point boundary value problems associated with the differential equation y f x y y s y 1 1 where f x y z w is assumed to be continuous on a subset of r4 initial value problems associated with 1 1 exist and are unique in the interval x1 x a monotonicity restriction on f x y z w ensures that the following boundary value problems y j x y y y y xj y y xj y y x m i 1 2 12i y j x y y y y x y y x m2 2 2 9 y x y i 421 le3i

conductivity exponent and backbone dimension in 2 d percolation abstract we present high statistics simulations for 2 d percolation clusters in the bus bar geometry at the critical point for site and for bond percolation we measured their backbone sizes and electrical conductivities for all sets of measurements we find large corrections to scaling most of which do not seem to be described by single powers using single power terms for the corrections to scaling of the backbone masses we would obtain fractal dimensions which are different for site and bond percolation while the correct result is d b 1 6432 0 0008 for both for the conductivity the corrections to scaling are strongly non monotonic for bond percolation the exponent t t is measured as 0 9826 0 0008 in disagreement with the alexander orbach and other conjectures

existence and uniqueness of solutions for nth order nonlinear two point boundary value problems in this paper we present some general results of existence and uniqueness of solutions for nth order nonlinear two point boundary value problems by using shooting method together with maximum principle and kneser hukahara continuum theorem as applications we give certain concrete sufficient conditions for the existence and uniqueness of solutions of nonlinear two point boundary value problems of nth order lipschitz equations

using percolation theory to predict oil field performance in this paper we apply scaling laws from percolation theory to the problem of estimating the time for a fluid injected into an oil field to breakthrough into a production well the main contribution is to show that when these previously published results are used on realistic data they are in good agreement with results calculated in a more conventional way but they can be obtained significantly more quickly as a result they may be used in practical engineering circumstances and aid decision making for real field problems

a quasilinearization method for second order four point boundary value problems abstract in this paper we obtain the existence and uniqueness results for general second order four point boundary value problems by applying the method of upper and lower solutions together with leray schauder degree also we obtain monotone iteration schemes which converge quadratically to the unique solution of some specific second order four point boundary value problems by using the method of quasilinearization

eigenvalue intervals for higher order problems with singular nonlinearities abstract we study eigenvalue intervals for higher order problems with multipoint boundary conditions we consider the case when the nonlinearity may be singular at t 0 or t 1 our approach is based on topological methods and cover both sublinear and superlinear cases we also study the continuous dependence of solutions on functional parameters

on eigenvalue intervals and twin eigenfunctions of higher order boundary value problems abstract in this paper we shall consider the boundary value problem y n q t y y 1 y n 2 p t y y 1 y n 2 n 2 t 1 1 y i 0 0 0 i n 3 y n 2 0 y n 1 0 0 yy n 2 1 y n 1 1 0 where 0 and are constants satisfying 0 0 0 and 0 intervals of are determined to ensure the existence of a positive solution of the boundary value problem for 1 we shall also offer criteria for the existence of two positive solutions of the boundary value problem in addition upper and lower bounds for these positive solutions are obtained for special cases several examples are included to dwell upon the importance of the results obtained

characters of an 1 hecke algebras at roots of unity a frobenius formula is presented for the characters phi sigma p q of the irreducible representations pi sigma of the an 1 hecke algebras hn q labelled by m k standard partitions sigma where q is a primitive pth root of unity with p m k using this result the characters phi sigma p q may be expressed as linear combinations of the characters chi lambda p q of representations which are irreducible when q is not a root of unity the appropriate linear combinations are found by using fusion modification rules for 1 or n or 5 all the remaining characters of irreducible representations of hn q are then found allowing a complete tabulation to be made for 2 or p or 5 along with the corresponding decomposition matrices

eigenvalues of a general class of boundary value problem with derivative dependent nonlinearity we consider a general class of boundary value problem bvp comprising the differential equation y m t f t y t y t y t y q t t 0 1 where 1 q m 1 and 0 together with multi point boundary conditions y 0 y 0 y 0 y q 1 0 0 a i y q t j y q 1 t j y m 1 t j 0 j r 0 1 i m q where 0 t 0 t 1 t r 1 particular cases of this general bvp include the well known abel gontscharoff focal m p sturm liouville and complementary lidstone bvps it is noted that bvps with derivative dependent nonlinear terms are less investigated in the literature due to technical difficulty in this paper a new technique is developed to characterize the eigenvalues so that the bvp has a positive solution explicit eigenvalue intervals are also established we include several well known examples in the literature to illustrate the results obtained

centralizers of iwahori hecke algebras to date integral bases for the centre of the iwahori hecke algebra of a finite coxeter group have relied on character theoretical results and the isomorphism between the iwahori hecke algebra when semisimple and the group algebra of the finite coxeter group in this paper we generalize the minimal basis approach of f1 to provide a way of describing and calculating elements of the minimal basis for the centre of an iwahori hecke algebra which is entirely combinatorial in nature and independent of both the above mentioned theories this opens the door to further generalization of the minimal basis approach to other cases in particular we show that generalizing it to centralizers of parabolic subalgebras requires only certain properties in the coxeter group we show here that these properties hold for groups of type a and b giving us the minimal basis theory for centralizers of any parabolic subalgebra in these types of iwahori hecke algebra

unbounded upper and lower solutions method for sturm liouville boundary value problem on infinite intervals abstract unbounded upper and lower solutions theories are established for the sturm liouville boundary value problem of a second order ordinary differential equation on infinite intervals by using such techniques and the schauder fixed point theorem the existence of solutions as well as the positive ones is obtained nagumo conditions play an important role in the nonlinear term involved in the first order derivatives

quantum quasi symmetric functions and hecke algebras the algebra of quasi symmetric functions is known to describe the characters of the hecke algebra of type at v 0 we present a quantization of this algebra defined in terms of filtrations of induced representations of the 0 hecke algebra we show that this q deformed algebra admits a simple realization in terms of quantum polynomials for generic values of q the algebra of quantum quasi symmetric functions is isomorphic to the one of noncommutative symmetric functions this gives rise to a one parameter family of hilbert space structures on the algebra of noncommutative symmetric functions as well as to new interesting bases

traveling time and traveling length in critical percolation clusters we study traveling time and traveling length for tracer dispersion in two dimensional bond percolation modeling flow by tracer particles driven by a pressure difference between two points separated by euclidean distance r we find that the minimal traveling time t min scales as t min approximately r 1 33 which is different from the scaling of the most probable traveling time t approximately r 1 64 we also calculate the length of the path corresponding to the minimal traveling time and find l min approximately r 1 13 and that the most probable traveling length scales as l approximately r 1 21 we present the relevant distribution functions and scaling relations

positive solutions for nonlinear m point eigenvalue problems in this paper we are concerned with determining values of lambda for which there exist positive solutions of the nonlinear eigenvalue problem graphics where a b c d is an element of 0 infinity xi i is an element of 0 1 alpha i beta i is an element of 0 infinity for i is an element of 1 m 2 are given constants p q is an element of c 0 1 0 infinity h is an element of c 0 1 0 infinity and f is an element of c 0 infinity 0 infinity satisfying some suitable conditions our proofs are based on guo krasnoselskii fixed point theorem c 2004 elsevier inc all rights reserved

bvp s with odd differences of gaps in boundary conditions for nth order ode s by matching solutions matching of solutions of boundary value problems plays an important role in interface problems we are concerned with the existence and uniqueness of solutions to boundary value problems on an interval a c for the nth order ordinary differential equation y n f x y y y n 1 for n 3 by matching solutions on a b with solutions on b c in this paper we consider a general case where the gap in boundary conditions at b is odd different monotonicity conditions on f are imposed for distinct cases that arise

existence of positive solutions of lidstone boundary value problems abstract we show that there exists at least one positive solution for lidstone boundary value problem 1 n u 2 n t f t u t u t u 2 n 1 t 0 t 1 u 2 i 0 u 2 i 1 0 i 0 1 n 1 under some suitable conditions our proof is based upon global bifurcation techniques

existence and uniqueness of solutions for a fourth order boundary value problem abstract in this paper we study the fourth order two point boundary value problem x t f t x t x t x t x t 0 t 0 1 x 0 x 1 0 a x 0 b x 0 0 c x 1 d x 1 0 by means of lower and upper solution method growth conditions on the nonlinear term f which guarantee the existence of solutions for the above boundary value problem are given in particular we obtain the uniqueness of the solution by imposing a monotone condition of the term f

distribution of shortest paths at percolation threshold application to oil recovery with multiple wells abstract in this work we investigate the distribution of shortest paths in percolation systems at the percolation threshhold in two dimensions 2d we study paths from one given point to multiple other points in oil recovery terminology the given single point can be mapped to an injection well injector and the multiple other points to production wells producers in the previously studied standard case of one injection well and one production well separated by euclidean distance r the distribution of shortest paths l p l r shows a power law behavior with exponent g l 2 14 in 2d here we analyze the situation of one injector and an array a of producers symmetric arrays of producers lead to one peak in the distribution p l a the probability that the shortest path between the injector and any of the producers is l while the asymmetric configurations lead to several peaks in the distribution we analyze configurations in which the injector is outside and inside the set of producers the peak in p l a for the symmetric arrays decays faster than for the standard case for very long paths all the studied arrays exhibit a power law behavior with exponent g g l

a new modification of the adomian decomposition method for solving boundary value problems for higher order nonlinear differential equations abstract in this paper we propose a new modified recursion scheme for the resolution of multi order and multi point boundary value problems for nonlinear ordinary and partial differential equations by the adomian decomposition method adm our new approach including duan s convergence parameter provides a significant computational advantage by allowing for the acceleration of convergence and expansion of the interval of convergence during calculations of the solution components for nonlinear boundary value problems in particular for such cases when one of the boundary points lies outside the interval of convergence of the usual decomposition series we utilize the boundary conditions to derive an integral equation before establishing the recursion scheme for the solution components thus we can derive a modified recursion scheme without any undetermined coefficients when computing successive solution components whereas several prior recursion schemes have done so this modification also avoids solving a sequence of nonlinear algebraic equations for the undetermined coefficients fraught with multiple roots which is required to complete calculation of the solution by several prior modified recursion schemes using the adm

wavelet like bases for thin wire integral equations in electromagnetics in this paper wavelets are used in solving by the method of moments a modified version of the thin wire electric field integral equation in frequency domain the time domain electromagnetic quantities are obtained by using the inverse discrete fast fourier transform the retarded scalar electric and vector magnetic potentials are employed in order to obtain the integral formulation the discretized model generated by applying the direct method of moments via point matching procedure results in a linear system with a dense matrix which have to be solved for each frequency of the fourier spectrum of the time domain impressed source therefore orthogonal wavelet like basis transform is used to sparsify the moment matrix in particular dyadic and m band wavelet transforms have been adopted so generating different sparse matrix structures this leads to an efficient solution in solving the resulting sparse matrix equation moreover a wavelet preconditioner is used to accelerate the convergence rate of the iterative solver employed these numerical features are used in analyzing the transient behavior of a lightning protection system in particular the transient performance of the earth termination system of a lightning protection system or of the earth electrode of an electric power substation during its operation is focused the numerical results obtained by running a complex structure are discussed and the features of the used method are underlined

flow between two sites on a percolation cluster we study the flow of fluid in porous media in dimensions d52 and 3 the medium is modeled by bond percolation on a lattice of l d sites while the flow front is modeled by tracer particles driven by a pressure difference between two fixed sites wells separated by euclidean distance r we investigate the distribution function of the shortest path connecting the two sites and propose a scaling ansatz that accounts for the dependence of this distribution i on the size of the system l and ii on the bond occupancy probability p w e confirm by extensive simulations that the ansatz holds for d52 and 3 further we study two dynamical quantities i the minimal traveling time of a tracer particle between the wells when the total flux is constant and ii the minimal traveling time when the pressure difference is constant a scaling ansatz for these dynamical quantities also includes the effect of finite system size l and off critical bond occupation probability p we find that the scaling form for the distribution functions for these dynamical quantities for d5 2a nd 3i s similar to that for the shortest path but with different critical exponents our results include estimates for all parameters that characterize the scaling form for the shortest path and the minimal traveling time in two and three dimensions these parameters are the fractal dimension the power law exponent and the constants and exponents that characterize the exponential cutoff functions

lower and upper solutions for a fully nonlinear beam equation abstract in this paper the two point fourth order boundary value problem is considered u i v f t u u u u 0 t 1 u 0 u 1 u 0 u 1 0 where f 0 1 r 4 r is a continuous function satisfying a nagumo type condition we prove the existence of a solution lying between lower and upper solutions using an a priori estimation lower and upper solutions method and degree theory the same arguments can be used with adequate modifications for any type of two point boundary value problem including all derivatives until order three with the second and the third derivatives given in different end points an application to the extended fisher kolmogorov problem will be obtained

the minimal basis for the centre of an iwahori hecke algebra abstract this paper arose out of an attempt to generalize the q q q 1 basis for the centre of an iwahori hecke algebra h q found by jones to z q q 1 and to other types considering the iwahori hecke algebra h over a subring z of z q1 2 q 1 2 where q1 2 q 1 2 we use a new and natural definition of positivity on h to describe the minimal z basis for z h in terms of a partial order on the positive part of h the main result is to show that this minimal basis is the set of primitive minimal elements of the positive part of the centre for any weyl group in addition the primitive minimal positive central elements can be characterized as exactly those positive central elements which specialize on setting 0 the equivalent of setting q 1 in z q1 2 q 1 2 to the sum of elements in a conjugacy class and which apart from the shortest elements from that conjugacy class sum contain no other terms corresponding to shortest elements of any conjugacy class a constructive algorithm is provided for obtaining the minimal basis we use the results of jones to achieve the result in type an without the need for character theory and give the result for all weyl groups using the character theoretical results of geck and rouquier finally we discuss the non crystallographic cases and give some explicit examples