on the structure of specht modules in the principal block of fσ3p abstract let f be a field of characteristic p at least 5 we study the loewy structures of specht modules in the principal block of f 3 p we show that a specht module in the block has loewy length at most 4 and composition length at most 14 furthermore we classify which specht modules have loewy length 1 2 3 or 4 produce a specht module having 14 composition factors describe the second radical layer and the socle of the reducible specht modules and prove that if a specht module corresponds to a partition that is p regular and p restricted then the head of the specht module does not extend the socle

corner singularities and boundary layers in a simple convection diffusion problem abstract a singularly perturbed convection diffusion problem posed on the unit square is considered its solution may have exponential and parabolic boundary layers and corner singularities may also be present pointwise bounds on the solution and its derivatives are derived the dependence of these bounds on the small diffusion coefficient on the regularity of the data and on the compatibility of the data at the corners of the domain are all made explicit the bounds are derived by decomposing the solution into a sum of solutions of elliptic boundary value problems posed on half planes then analyzing these simpler problems

boundary layer for a class of nonlinear pipe flow we establish the mathematical validity of the prandtl boundary layer theory for a family of nonlinear parallel pipe flow the convergence is verified under various sobolev norms including the physically important space time uniform norm as well as thel 1 h 1 norm higher order asymptotics is also studied

boundary layers associated with incompressible navier stokes equations the noncharacteristic boundary case abstract the goal of this article is to study the boundary layer of wall bounded flows in a channel at small viscosity when the boundaries are uniformly noncharacteristic i e there is injection and or suction everywhere at the boundary following earlier work on the boundary layer for linearized navier stokes equations in the case where the boundaries are characteristic no slip at the boundary and non permeable we consider here the case where the boundary is permeable and thus noncharacteristic the form of the boundary layer and convergence results are derived in two cases linearized equation and full nonlinear equations we prove that there exists a boundary layer at the outlet downwind of the form e uz e where u is the speed of injection suction at the boundary z is the distance to the outlet of the channel and e is the kinematic viscosity we improve an earlier result of s n alekseenko 1994 siberian math j 35 no 2 209 230 where the convergence in l 2 of the solutions of the navier stokes equations to that of the euler equations at vanishing viscosity was established in the two dimensional case we are able to derive the physically relevant uniform in space l norm estimates of the boundary layer the uniform in space estimate is derived by properly developing our previous idea of better control on the tangential derivative and the use of an anisotropic sobolev imbedding to the best of our knowledge this is the first rigorously proved result concerning boundary layers for the full nonlinear navier stokes equations for incompressible fluids

convergence in l2 norm of the sdfem on a shishkin triangular mesh for problems with characteristic layers in this paper we analyze a streamline diffusion finite element method sdfem on a shishkin triangular mesh which is applied to a model singularly perturbed convection diffusion problem the main result is to show the sdfem solution on the triangular mesh possesses the optimal convergence order in the l2 norm provided that the diffusion coefficient is sufficiently small compared with the mesh size numerical experiments illustrate the theoretical result

a singular reaction diffusion system modelling prey predator interactions invasion and co extinction waves abstract we consider a singular reaction diffusion system arising in modelling prey predator interactions in a fragile environment since the underlying odes system exhibits a complex dynamics including possible finite time quenching one first provides a suitable notion of global travelling wave weak solution then our study focusses on the existence of travelling waves solutions for predator invasion in such environments we devise a regularized problem to prove the existence of travelling wave solutions for predator invasion followed by a possible co extinction tail for both species under suitable assumptions on the diffusion coefficients and on species growth rates we show that travelling wave solutions are actually positive on a half line and identically zero elsewhere such a property arising for every admissible wave speeds

a proof of the mullineux conjecture a partition of a positive integer n is a sequence 1 2 m 0 of integers such that i n for a positive integer p a partition 1 2 m or its young diagram is called p regular if it does not have p or more equal parts i e if there does not exist t m p 1 with t t 1 t p 1 let f be a field of characteristic p 0 it is well known that irreducible representations of the symmetric group sn over f are naturally parametrized by pregular partitions of n cf for example 9 12 if is such a partition we denote the corresponding irreducible module by d let sgnn be the one dimensional sign representation of sn over f i e sgnn f as a vector space and g f sgn g f for any g sn f f here sgn g is just the sign of the permutation g it is clear that for any irreducible d the tensor product d sgnn is also irreducible the problem usually called the problem of mullineux is to find the p regular partition such that d sgnn d put d sgnn dn in this way a bijection bn on the set pn of p regular partitions of n is defined for each positive integer n and the problem is

boundedness of singular radon transforms on l p spaces under a finite type condition in this paper a new method is presented for proving boundedness of singular radon transforms on l p for 1 p two closely related results generalizing the corresponding theorem of christ nagel stein and wainger are proven 1 introduction in this paper a new method is presented for proving boundedness of singular radon transforms on l p for 1 p two closely related results generalizing the corresponding theorem of christ nagel stein and wainger in 3 are proved singular radon transforms are a type of singular integral operator a prototype for which is the hilbert transform along curves let 1 1 r n be a curve with 0 0 and let f be a schwarz function on r n 1

symmetric group blocks of small defect has a specht module s and a p modular irreducible module d the decomposition number s d is de ned to be the composition multiplicity of d in s the following facts areknown about blocks of weight w a if w 0 or 1 then all the decomposition numbers of the block are 0 or 1 b if w 2 and p 2 then all the decomposition numbers of the block are 0 or 1 s2 c if w 4 then some decomposition numbers of a block can be greater than 1 even if p w moreover if w 0 1 or 2 then there is a known method for determining the decompositionnumbers r the situation for the case w 3 is still not properly understood in particular thedecomposition number s 2p 2 2p 2 p 1 1 d 3p 3 2p 1 is yet to be determined for p 5 this is just one of a collection of decomposition numbers forweight 3 which we are unable to evaluate our investigation of blocks of weight 3 grew out of an attempt to improve upon the earlier resultsof martin and russell mr by explicitly calculating the decomposition numbers this led us todiscover various errors and omissions in mr which place in doubt the claim made there that whenp w all the decomposition numbers are 0 or 1 note incidentally that if the decompositionnumbers for a given block are known to be 0 or 1 then the decomposition numbers can in principle be determined by applying schaper s theorem sch jm1 2 basic resultsby using a result of brundan and kleshchev we are able to improve upon the presentation ofseveral of the basic techniques used in s1 s2 mr for estimating decomposition numbers in orderto state these results recall that the diagram of a partition is the set of nodes i j 1 j

classes of singular integrals along curves and surfaces this paper is concerned with singular convolution operators in rd d 2 with convolution kernels supported on radial surfaces yd r ly l we show that if r s log s then lp boundedness holds if and only if p 2 this statement can be reduced to a similar statement about the multiplier m r 71 lrl i 7 in r2 we also construct smooth r for which the corresponding operators are bounded for po p 2 but unbounded for p po for given po e 1 2 finally we discuss some examples of singular integrals along convex curves in the plane with odd extensions

continuous discontinuous finite element method for convection diffusion problems with characteristic layers we study convergence properties of a numerical method for convection diffusion problems with characteristic layers on a layer adapted mesh the method couples standard galerkin with an h version of the nonsymmetric discontinuous galerkin finite element method with bilinear elements in an associated norm we derive the error estimate as well as the supercloseness result that are uniform in the perturbation parameter applying a post processing operator for the discontinuous galerkin method we construct a new numerical solution with enhanced convergence properties

boundary layers for the 3d primitive equations in a cube the supercritical modes abstract in this article we study the boundary layers for the viscous linearized primitive equations lpes when the viscosity is small the lpes are considered here in a cube besides the usual boundary layers that we analyze here too corner layers due to the interaction between the different boundary layers are also studied

singular integrals associated to hypersurfaces l2 theory abstract we consider singular integrals associated to a classical calderon zygmund kernel k and a hypersurface given by the graph of t where is an arbitrary c 1 function and is a smooth convex function of finite type we give a characterization of those calderon zygmund kernels k and convex functions so that the associated singular integral operator is bounded on l 2 for all c 1 functions

finite element approximation of convection diffusion problems using an exponentially graded mesh we present the analysis of an h version finite element method for the approximation of the solution to convection diffusion problems the method uses piece wise polynomials of degree p 1 defined on an exponentially graded mesh optimally constructed for the approximation of exponential layers we consider a model convection diffusion problem posed on the unit square and establish robust optimal convergence rates in the energy and in the maximum norm we also present the results of some numerical computations that illustrate our theoretical findings and compare the proposed method with others found in the literature

boundary layer analysis of nonlinear reaction diffusion equations in a polygonal domain abstract we propose a boundary layer analysis which fits a domain with corners in particular we consider nonlinear reaction diffusion problems posed in a polygonal domain having a small diffusive coefficient e 0 we present the full analysis of the singular behaviours at any orders with respect to the parameter e where we use a systematic nonlinear treatment initiated in jung et al 2016 the boundary layers are formed near the polygonal boundaries and two adjacent ones overlap at a corner p and the overlapping produces additional layers the so called corner layers it is noteworthy that the boundary layers are also degenerate due to the singularities of the solutions involving a negative power of the radial distance to the corner p which are present in the laplace operator on a sector sector corresponding to the part of the polygon near the corner the corner layers are then designed to absorb both the singularities and the interaction of the two boundary layers at p

singular reaction diffusion equations of porous medium type abstract a class of reaction diffusions equations with nonlinear boundary conditions and porous medium type of diffusion is investigated by the method of upper and lower solutions the diffusion term in the equation includes the so called slow diffusion m 1 fast diffusion 0 m 1 and super diffusion m 0 and the reaction term may involve a singular function the aim of this paper is to show the existence of a global time dependent solution the existence of positive minimal and maximal steady state solutions including the uniqueness of the positive solution and the asymptotic behavior of the time dependent solution in relation to the positive steady state solutions of particular concern is the convergence of the time dependent solution to a unique positive steady state solution and the global attraction property of the reaction diffusion problem applications are given to several specific problems which are of considerable interest in the current literature

asymptotic analysis and shishkin type decomposition for an elliptic convection diffusion problem abstract we consider a singularly perturbed elliptic convection diffusion problem on the unit square a new asymptotic expansion of its solution is constructed giving precise conditions under which the solution can be decomposed in a particularly opportune way into a sum of smooth and layer functions

some inequalities for singular convolution operators in spaces suppose that a bounded function m satisfies a localized multiplier condition supt o ii0m tp imp 0 the purpose of this paper is to find easily verified conditions that 1 implies me mp the condition llmll 0 then we ask under which conditions supt 0 qm tp 1mp oc implies m c mp throughout this paper x will always be chosen as in the following definition x c co rn satisfies a tauber condition with respect to the dilations tp if for every x 0 there is a tx such that q tpx 0 sometimes we need special bump functions of the following kind let p e c rn be a p homogeneous distance function this means that p tpx tp x received by the editors august 21 1986 1980 mathermatics subject lassijication 1985 revision primary 42b15 42b20 42b25

boundary layers for the subcritical modes of the 3d primitive equations in a cube abstract in this article we study the boundary layers for the subcritical modes of the viscous linearized primitive equations lpes in a cube at small viscosity the boundary layers include the parabolic boundary layers ordinary boundary layers and their interaction corner layers the boundary layer correctors are determined by a phenomenological study reminiscent of the prandtl corrector approach and then a rigorous convergence result is proved which a posteriori justifies the phenomenological study

defect 3 blocks of symmetric group algebras abstract in this paper we study if the following properties are present in defect 3 blocks of symmetric group algebras k g n where k has characteristic p 5 the ext quiver is bipartite the p i m s have a common loewy length 7 we obtain a criteria for a defect 3 block b of k g n to inherit these properties from a defect 3 block b of k g n 1 with which it forms a 3 1 pair we also verify that the principal blocks of k g n 3 p n 4 p 1 have these properties

greenʼs function estimates for a singularly perturbed convection diffusion problem we consider a singularly perturbed convection diusion problem posed in the unit square with a horizontal convective direction its solutions exhibit parabolic and exponential boundary layers sharp estimates of the green s function and its first and second order derivatives are derived in the l1 norm the dependence of these estimates on the small diusion parameter is shown explicitly the obtained estimates will be used in a forthcoming numerical analysis of the considered problem

cartan matrices and morita equivalence for blocks of the symmetric groups theorem 1 the blocks of the symmetric groups with a given weight w 0 over a field of characteristic p can be collected into families according to the shapes of their cores each family consists of morita equivalent blocks the number of such families is at most flf 1 i l w 1 11 and each family contains a block of some g where n is less than or equal to p2 p 1 2 w 1 2 4 wp

asymptotic analysis for singularly perturbed convection diffusion equations with a turning point turning points occur in many circumstances in fluid mechanics when the viscosity is small very complex phenomena can occur near turning points which are not yet well understood a model problem corresponding to a linear convection diffusion equation e g suitable linearization of the navier stokes or benard convection equations is considered our analysis shows the diversity and complexity of behaviors and boundary or interior layers which already appear for our equations simpler than the navier stokes or benard convection equations of course the diversity and complexity of these structures will have to be taken into consideration for the study of the nonlinear problems in our case at this stage the full theoretical asymptotic analysis is provided this study is totally new to the best of our knowledge numerical treatment and more complex problems will be considered elsewhere

optimal convergence of basic schemes for elliptic boundary value problems with strong parabolic layers we consider a convection diffusion problem with strong parabolic boundary layers and its discretization using upwind finite differences or bilinear finite elements on a layer adapted mesh based on a new decomposition of the solution we are able to prove optimal uniform convergence results

singularly perturbed linear two point boundary value problems finding asymptotic solutions to two point boundary value problems for linear singularly perturbed second order ordinary differential equations is now quite well understood troublesome exceptions involving turning points known as problems of boundary layer resonance have been studied by many experts since the initial work of ackerberg and o malley stud appl math 49 1970 pp 277 295 this significant work is surveyed here closely related literature involves the canard phenomena new generally more geometric approaches including gevrey asymptotics and blowup promise improved understanding of such sensitive asymptotics and their generalizations

on the numerical approximations of stiff convection diffusion equations in a circle our aim in this article is to study the numerical solutions of singularly perturbed convection diffusion problems in a circular domain and provide as well approximation schemes error estimates and numerical simulations to resolve the oscillations of classical numerical solutions due to the stiffness of our problem we construct via boundary layer analysis the so called boundary layer elements which absorb the boundary layer singularities using a p 1 p 1 classical finite element space enriched with the boundary layer elements we obtain an accurate numerical scheme in a quasi uniform mesh

equating decomposition numbers for different primes abstract this paper shows that certain decomposition numbers for the iwahori hecke algebras of the symmetric groups and the q schur algebras at different roots of unity in characteristic zero are equal to prove our results we first establish the corresponding theorem for the canonical basis of the level one fock space and then apply deep results of ariki and varagnolo vasserot

boundary layer analysis for the stochastic nonlinear reaction diffusion equations abstract singularly perturbed stochastic and deterministic nonlinear reaction diffusion equations are considered we first study the governing problem posed in the channel domain with lateral periodicity and extend the results to general smooth domains introducing corrector functions which correct the boundary values discrepancies we are able to develop the convergence analysis for the analysis we make use of the maximum principle to estimate the corrector functions the stochastic problems also rely on the deterministic corrector functions which lead to simpler computations than those of the stochastic version of the correctors