blocks of small defect abstract let g be a finite solvable group let p be a prime such that p 5 and o p g 1 and we denote g p p n then g contains a block of defect less than or equal to 3 n 5 let g be a finite solvable group and let p a be the largest power of p dividing 1 for an irreducible character of g we show that g f g p p 3 a for p 5

hyperbolic conservation laws with relaxation the effect of relaxation is important in many physical situations it is present in the kinetic theory of gases elasticity with memory gas flow with thermo non equilibrium water waves etc the governing equations often take the form of hyperbolic conservation laws with lower order terms in this article we present and analyze a simple model of hyperbolic conservation laws with relaxation effects dynamic subcharacteristics governing the propagation of disturbances over strong wave forms are identified stability criteria for diffusion waves expansion waves and traveling waves are found and justified nonlinearly time asymptotic expansion and the energy method are used in the analysis for dissipative waves the expansion is similar in spirit to the chapman enskog expansion in the kinetic theory for shock waves however a different approach is needed

simple classical groups of lie type are determined by their character degrees let g be a finite group denote by irr g the set of all irreducible complex characters of g let cd g be the set of all irreducible complex character degrees of g forgetting multiplicities that is cd g 1 irr g and let x1 g be the set of all irreducible complex character degrees of g counting multiplicities let h be a finite nonabelian simple classical group in this paper we will show that if g is a finite group and x1 g x1 h then g is isomorphic to h in particular this implies that the nonabelian simple classical groups of lie type are uniquely determined by the structure of their complex group algebras

brauer characters and normal sylow p subgroups abstract in this paper we study some variations of the well known ito michler theorem for p brauer characters using various inequalities involving the p brauer character degrees of finite groups several new criteria for the existence of a normal sylow p subgroup of finite groups are obtained using the p parts and p parts of the p brauer character degrees

asymptotic stability of rarefaction wave for the navier stokes equations for a compressible fluid in the half space this paper is concerned with the asymptotic stability towards a rarefaction wave of the solution to an outflow problem for the navier stokes equations in a compressible fluid in the eulerian coordinate in the half space this is the second one of our series of papers on this subject in this paper firstly we classify completely the time asymptotic states according to some parameters that is the spatial asymptotic states and boundary conditions for this initial boundary value problem and some pictures for the classification of time asymptotic states are drawn in the state space in order to prove the stability of the rarefaction wave we use the solution to burgers equation to construct a suitably smooth approximation of the rarefaction wave and establish some time decay estimates in lp norm for the smoothed rarefaction wave we then employ the l2 energy method to prove that the rarefaction wave is non linearly stable under a small perturbation as time goes to infinity

almost global existence of classical discontinuous solutions to genuinely nonlinear hyperbolic systems of conservation laws with small bv initial data abstract in the present paper the author investigates the initial problem for genuinely nonlinear quasilinear hyperbolic systems of conservation laws under small bv perturbations of the riemann initial data where the perturbations are in bv but they are assumed to be c 1 smooth with bounded and possibly large c 1 norms combining the techniques employed by li and kong with the modified glimm s functional the author obtains the almost global existence and lifespan of classical discontinuous solutions to the above problem this result is also applied to the system of one dimensional isentropic flow

the generalized nonlinear initial boundary riemann problem for linearly degenerate quasilinear hyperbolic systems of conservation laws abstract this work is a continuation of our previous work in the present paper we study the generalized nonlinear initial boundary riemann problem with small bv data for linearly degenerate quasilinear hyperbolic systems of conservation laws with nonlinear boundary conditions in a half space t x t 0 x 0 we prove the global existence and uniqueness of piecewise c 1 solution containing only contact discontinuities to a class of the generalized nonlinear initial boundary riemann problem which can be regarded as a small bv perturbation of the corresponding nonlinear initial boundary riemann problem for general n n linearly degenerate quasilinear hyperbolic system of conservation laws moreover this solution has a global structure similar to the one of the self similar solution u u x t to the corresponding nonlinear initial boundary riemann problem some applications to quasilinear hyperbolic systems of conservation laws arising in the string theory and high energy physics are also given

recognizing direct products from their conjugate type vectors see 5 for results of a similar nature there is astrong relation between information about character degrees and sizes ofconjugacy classes if the multiplication constants for the conjugacy classesare known then the character table can be reconstructed and similarly inreverse however if one knows only the sizes then there is less completeinformation and it is not possible to obtain a complete translation toillustrate this point if the conjugacy classes have sizes 1 4

characters of relative p degree over normal subgroups let z be a normal subgroup of a finite group g let irr z be an irreducible complex character of z and let p be a prime number if p does not divide the integers 1 1 for all irr g lying over then we prove that the sylow p subgroups of g z are abelian this theorem which generalizes the gluck wolf theorem to arbitrary finite groups is one of the principal obstacles to proving the celebrated brauer height zero conjecture

defect zero p blocks for finite simple groups we classify those finite simple groups whose brauer graph or decomposition matrix has a p block with defect 0 completing an investigation of many authors the only finite simple groups whose defect zero p blocks remained unclassified were the alternating groups an here we show that these all have a p block with defect 0 for every prime p 5 this follows from proving the same result for every symmetric group sn which in turn follows as a consequence of the t core partition conjecture that every non negative integer possesses at least one t core partition for any t 4 for t 17 we reduce this problem to lagrange s theorem that every non negative integer can be written as the sum of four squares the only case with t 17 that was not covered in previous work was the case t 13 this we prove with a very different argument by interpreting the generating function for t core partitions in terms of modular forms and then controlling the size of the coefficients using deligne s theorem nee the weil conjectures we also consider congruences for the number of p blocks of sn proving a conjecture of garvan that establishes certain multiplicative congruences when 5 p 23 by using a result of serre concerning the divisibility of coefficients of modular forms we show that for any given prime p and positive integer m the number of p blocks with defect 0 in sn is a multiple of m for almost all n we also establish that any given prime p divides the number of p modularly irreducible representations of sn for almost all n 1996 american mathematical society

asymptotic stability of the stationary solution to the compressible navier stokes equations in the half space we investigate the existence and the asymptotic stability of a stationary solution to the initial boundary value problem for the compressible navier stokes equation in a half space the main concern is to analyze the phenomena that happens when the fluid blows out through the boundary thus it is natural to consider the problem in the eulerian coordinate we have obtained the two results for this problem the first result is concerning the existence of the stationary solution we present the necessary and sufficient condition which ensures the existence of the stationary solution then it is shown that the stationary solution is time asymptotically stable if an initial perturbation is small in the suitable sobolev space the second result is proved by using an l 2 energy method with the aid of the poincare type inequality

nonlinear stability of rarefaction waves for compressible navier stokes equations it is shown that expansion waves for the compressible navier stokes equations are nonlinearly stable the expansion waves are constructed for the compressible euler equations based on the inviscid burgers equation our result shows that navier stokes equations and euler equations are time asymptotically equivalent on the level of expansion waves the result is proved using the energy method making essential use of the expansion of the underlining nonlinear waves and the specific form of the constitutive eqution for a polytropic gas

stability of rarefaction waves of the navier stokes poisson system abstract in the paper we are concerned with the large time behavior of solutions to the one dimensional navier stokes poisson system in the case when the potential function of the self consistent electric field may take distinct constant states at x precisely it is shown that if initial data are close to a constant state with asymptotic values at far fields chosen such that the riemann problem on the corresponding quasineutral euler system admits a rarefaction wave whose strength is not necessarily small then the solution exists for all time and tends to the rarefaction wave as t the construction of the nontrivial large time profile of the potential basing on the quasineutral assumption plays a key role in the stability analysis the proof is based on the energy method by taking into account the effect of the self consistent electric field on the viscous compressible fluid

finite groups whose prime graphs are regular abstract let g be a finite group and let irr g be the set of all irreducible complex characters of g let cd g be the set of all character degrees of g and denote by g the set of primes which divide some character degrees of g the prime graph g associated to g is a graph whose vertex set is g and there is an edge between two distinct primes p and q if and only if the product pq divides some character degree of g in this paper we show that the prime graph g of a finite group g is 3 regular if and only if it is a complete graph with four vertices

asymptotic stability of nonlinear wave for the compressible navier stokes equations in the half space in the present paper we investigate the large time behavior of the solution to an initial boundary value problem for the isentropic compressible navier stokes equations in the eulerian coordinate in the half space this is one of the series of papers by the authors on the stability of nonlinear waves for the outflow problem of the compressible navier stokes equations some suitable assumptions are made to guarantee that the time asymptotic state is a nonlinear wave which is the superposition of a stationary solution and a rarefaction wave employing the l2 energy method and making use of the techniques from the paper s kawashima y nikkuni stability of rarefaction waves for the discrete boltzmann equations adv math sci appl 12 1 2002 327 353 we prove that this nonlinear wave is nonlinearly stable under a small perturbation the complexity of nonlinear wave leads to many complicated terms in the course of establishing the a priori estimates however those terms are of two basic types and the terms of each type are good and can be evaluated suitably by using the decay in both time and space variables estimates of each component of nonlinear wave

stability of boundary layer and rarefaction wave to an outflow problem for compressible navier stokes equations under large perturbation abstract in this paper we investigate the large time behavior of solutions to an outflow problem for compressible navier stokes equations in 2003 kawashima nishibata and zhu s kawashima s nishibata p zhu asymptotic stability of the stationary solution to the compressible navier stokes equations in the half space comm math phys 240 2003 483 500 showed there exists a boundary layer i e stationary solution to the outflow problem and the boundary layer is nonlinearly stable under small initial perturbation in the present paper we show that not only the boundary layer above but also the superposition of a boundary layer and a rarefaction wave are stable under large initial perturbation the proofs are given by an elementary energy method

finite group elements where no irreducible character vanishes in this paper we consider elements x of a finite group g with the property that x 0 for all irreducible characters of g if g is solvable and x has odd order we show that x must lie in the fitting subgroup f g

finite groups with graphs containing no triangles abstract let g be a non abelian finite group g the attached graph related to its conjugacy classes the aim of this paper is to prove that the symmetric group s 3 the dihedral group d 5 the three pairwise non isomorphic non abelian groups of order 12 and the non abelian group t 21 of order 21 is the complete list of all g such that g contains no triangles

finite solvable groups whose character graphs are trees abstract the aim of this paper is to classify all the finite solvable groups g whose character graphs g have no triangles they are exactly the finite groups with at most two non linear irreducible characters and the symmetric group s 4

vanishing viscosity limit for a coupled navier stokes allen cahn system abstract in this paper we study the vanishing viscosity limit for a coupled navier stokes allen cahn system in a bounded domain we first show the local existence of smooth solutions of the euler allen cahn equations by modified galerkin method then using the boundary layer function to deal with the mismatch of the boundary conditions between navier stokes and euler equations and assuming that the energy dissipation for navier stokes equation in the boundary layer goes to zero as the viscosity tends to zero we prove that the solutions of the navier stokes allen cahn system converge to that of the euler allen cahn system in a proper small time interval in addition for strong solutions of the navier stokes allen cahn system in 2d the convergence rate is c 1 2

p parts of brauer character degrees abstract let g be a finite group and let p be an odd prime under certain conditions on the p parts of the degrees of its irreducible p brauer characters we prove the solvability of g as a consequence we answer a question proposed by b huppert in 1991 if g has exactly two distinct irreducible p brauer character degrees then is g solvable we also determine the structure of non solvable groups with exactly two irreducible 2 brauer character degrees

on the length of the conjugacy classes of finite groups abstract let g be a finite group the question of how certain arithmetical conditions on the degrees of the irreducible characters of g influence the group structure was studied by several authors our purpose here is to impose analogous conditions on the lengths of the conjugacy classes of g and to describe the group structure under these conditions

contact discontinuity with general perturbations for gas motions the contact discontinuity is one of the basic wave patterns in gas motions the stability of contact discontinuities with general perturbations for the navier stokes equations and the boltzmann equation is a long standing open problem general perturbations of a contact discontinuity may generate diffusion waves which evolve and interact with the contact wave to cause analytic difficulties in this paper we succeed in obtaining the large time asymptotic stability of a contact wave pattern with a convergence rate for the navier stokes equations and the boltzmann equation in a uniform way one of the key observations is that even though the energy norm of the deviation of the solution from the contact wave may grow at the rate it can be compensated by the decay in the energy norm of the derivatives of the deviation which is of the order of thus this reciprocal order of decay rates for the time evolution of the perturbation is essential to close the a priori estimate containing the uniform bounds of the l8 norm on the lower order estimate and then it gives the decay of the solution to the contact wave pattern

an answer to a question of isaacs on character degree graphs abstract let n be a normal subgroup of a finite group g we consider the graph g n whose vertices are the prime divisors of the degrees of the irreducible characters of g whose kernel does not contain n and two vertices are joined by an edge if the product of the two primes divides the degree of some of the characters of g whose kernel does not contain n we prove that if g n is disconnected then g n is solvable this proves a strong form of a conjecture of isaacs

large time behaviors of solutions to an inflow problem in the half space for a one dimensional system of compressible viscous gas the inflow problem for a one dimensional compressible barotropic flow on the half line r 0 is investigated not only classical waves but also the new wave which is called the boundary layer solution arise large time behaviors of the solutions to be expected have been classified in terms of the boundary values by a matsumura inflow and outflow problems in the half space for a one dimensional isentropic model system of compressible viscous gas to appear in proceedings of ims conference on differential equations from mechanics hong kong 1999 in this paper we give the rigorous proofs of the stability theorems on both the boundary layer solution and a superposition of the boundary layer solution and the rarefaction wave

asymptotic stability of planar rarefaction wave to 3d micropolar equations abstract we are concerned with the large time behavior of the cauchy problem to the 3d micropolar fluids in an infinite long flat nozzle domain r t 2 in one dimensional case this system tends time asymptotically to the navier stokes equations that is to say the basic wave patterns to the compressible micropolar fluids model are stable hence in this paper we consider the nonlinear stability of planar rarefaction wave to the corresponding three dimensional model some cancellations on the flux terms and viscous terms are crucial moreover a proper combining of damping term and rotation terms can provide an extra regularity of w

a local conjecture on brauer character degrees of finite groups recently a new conjecture on the degrees of the irreducible brauer characters of a finite group was presented by w willems in this paper we propose a local version of this conjecture for blocks b of finite groups giving a lower bound for 1 2 where the sum runs through the set of irreducible brauer characters of b in terms of invariants of b a slight reformulation leads to interesting open questions about traces of cartan matrices of blocks we show that the local conjecture is true for blocks with one simple module blocks of p solvable groups and blocks with cyclic defect groups it also holds for many further examples of blocks of sporadic groups symmetric groups or groups of lie type finally we prove that the conjecture is true for blocks of tame representation type

finite groups with generalized ore supplement conditions for primary subgroups abstract we associate with every group g a set g of subgroups of g with 1 g if h g then we say that h is a subgroup of g if g g for each epimorphism g g then we say that is a subgroup functor we say also that a subgroup functor is hereditary provided h e whenever h e g and h g regular provided for any group g whenever h g is a p group and n is a minimal normal subgroup of g then g n g h n is a power of p regular respectively quasiregular provided for any primitive group g whenever h g is a p group and n is a respectively abelian minimal normal subgroup of g then g n g h n is a power of p let k h be subgroups of g and a subgroup functor then we say that the pair k h satisfies the f supplement condition in g if g has a subgroup t such that h t g and h t k z f t h is f supplemented in g if for some subgroup s of g contained in h the pair s h satisfies the f supplement condition in g where g g h g and h h h g in this paper we study the structure of a group g under the condition that some primary subgroups of g are f supplemented in g in particular we prove the following result theorem a let f be a saturated formation containing the class u of all supersoluble groups e a normal subgroup of g with g e f x e or x f e and a regular or hereditary regular subgroup functor suppose that every subgroup of g contained in x is subnormally embedded in g if every maximal subgroup of every non cyclic sylow subgroup of x is u supplemented in g then g f moreover in the case when is regular then every chief factor of g below e is cyclic the results in this paper not only cover and unify a long list of some known results but also cause a wide series of new results

on thompson s theorem let p be a prime divisor of the order of a finite group g thompson 1970 j algebra14 129 134 has proved the following remarkable result a finite group g is p nilpotent if the degrees of all its nonlinear irreducible characters are divisible by p in fact in that case g is solvable in this note we prove that a group g having only one nonlinear irreducible character of p degree is a cyclic extension of thompson s group this result is a consequence of the following theorem a nonabelian simple group possesses two nonlinear irreducible characters 1 and 2 of distinct degrees such that p does not divide 1 1 2 1 here p is arbitrary but fixed our proof depends on the classification of finite simple groups some properties of solvable groups possessing exactly two nonlinear irreducible characters of p degree are proved some open questions are posed

group classes and mutually permutable products abstract let g a b be the mutually permutable product of the nontrivial subgroups a and b of the group g then a or b contains a nontrivial normal subgroup of g it is also established that s g a s a where s u is the solvable radical of u these facts lead to some generalized results about mutually permutable products of sc groups it is also shown that if g is a pts group then a and b are pst groups

weak solutions of a two phase navier stokes model with a general slip law abstract this work is devoted to a study of a gas liquid navier stokes model with a general slip law that allows the two phases to flow with unequal fluid velocity the slip law is general enough to describe counter current flow i e a situation where gas and liquid move in opposite direction motivated by applications in the context of wellbore flow systems we assume that there is a free interface which separates the gas liquid mixture region from a strongly gas dominated region which holds a specified positive pressure p the slip law is incorporated in the mass and momentum equations resulting in a model where flow is described in terms of the gas velocity however the mixture momentum equation contains a generalized pressure law composed of the standard pressure function combined with three new terms that depend on parameters characterizing the difference between gas and liquid velocity these new terms make the analysis challenging by carefully exploiting the positive external pressure p we are able to obtain uniform lower and upper bounds on a pressure related quantity this in turn allows for various higher order regularity estimates which imply that global existence and uniqueness of weak solutions can be shown

on the orders of zeros of irreducible characters abstract let g be a finite group and p a prime number we say that an element g in g is a vanishing element of g if there exists an irreducible character of g such that g 0 the main result of this paper shows that if g does not have any vanishing element of p power order then g has a normal sylow p subgroup also we prove that this result is a generalization of some classical theorems in character theory of finite groups

stability of a composite wave of two viscous shock waves for the full compressible navier stokes equation in this paper we investigate the asymptotic stability of a composite wave consisting of two viscous shock waves for the full compressible navier stokes equation by introducing a new linear diffusion wave special to this case we successfully prove that if the strengths of the viscous shock waves are suitably small with same order and also the initial perturbations which are not necessarily of zero integral are suitably small the unique global solution in time to the full compressible navier stokes equation exists and asymptotically tends toward the corresponding composite wave whose shifts in space of two viscous shock waves are uniquely determined by the initial perturbations we then apply the idea to study a half space problem for the full compressible navier stokes equation and obtain a similar result

structure of finite groups under certain arithmetical conditions on class sizes abstract let g be a finite solvable group we assume that the set of conjugacy class sizes of g is 1 m n m k with m and n coprime positive integers greater than 1 and k a divisor of n then we obtain several properties on the structure of g

finite nonsolvable groups whose character graphs have no triangles in this paper we show that the alternating group a5 is the only nonsolvable group whose character graph has no triangles

asymptotic stability of rarefaction waves for 2 2 viscous hyperbolic conservation laws this paper concerns the asymptotic behavior toward rarefaction waves of the solution of a genera 2 x 2 hyperbolic conservation laws with positive viscosity we prove that if the initial data is close to a constant state and its values at a3 lie on the kth rarefaction curve for the corresponding hyperbolic conservation laws then the solution tends as i co to the rarefaction wave determined by these states

groups whose prime graphs have no triangles abstract let g be a finite group and let cd g be the set of all complex irreducible character degrees of g let g be the set of all primes which divide some character degree of g the prime graph g attached to g is a graph whose vertex set is g and there is an edge between two distinct primes u and v if and only if the product uv divides some character degree of g in this paper we show that if g is a finite group whose prime graph g has no triangles then g has at most 5 vertices we also obtain a classification of all finite graphs with 5 vertices and having no triangles which can occur as prime graphs of some finite groups finally we show that the prime graph of a finite group can never be a cycle nor a tree with at least 5 vertices

strong solutions of the navier stokes equations for a compressible fluid of allen cahn type in this work we study the navier stokes allen cahn system a combination of the compressible navier stokes equations with an allen cahn phase field description this model describes two phase patterns in a flowing liquid including phase transformations our purpose is to show the existence and uniqueness of local strong solutions for arbitrary initial data part of the proof is based on methods used in a companion paper which investigated the compressible navier stokes equations

square free class sizes in products of groups abstract we obtain some structural properties of a factorised group g a b given that the conjugacy class sizes of certain elements in a b are not divisible by p 2 for some prime p the case when g a b is a mutually permutable product is especially considered

variations on a theorem by alan camina on conjugacy class sizes let g be a finite group we extend alan camina s theorem on conjugacy class sizes which asserts that if the conjugacy class sizes of g are exactly 1 p a q b p a q b for two primes p and q t heng is nilpotent if we assume that g is solvable we show that when the set of conjugacy class sizes of g is 1 m n mn with m and n arbitrary positive integers such that m n 1 then g is nilpotent and m p a and n q b for two primes p and q

asymptotic stability of superposition of stationary solutions and rarefaction waves for 1d navier stokes allen cahn system abstract in this paper we investigate the large time behavior of the solutions to the inflow problem for the one dimensional navier stokes allen cahn system in the half space first we assume that the space asymptotic states u and the boundary data b u b b satisfy some conditions so that the time asymptotic state of solutions for the inflow problem is a nonlinear wave which is the superposition of a stationary solution and a rarefaction wave then we show the existence of the stationary solution by the center manifold theorem finally we prove that the nonlinear wave is asymptotically stable when the initial data is a small perturbation of the nonlinear wave the proof is mainly based on the energy method by taking into account the effect of the concentration and the complexity of nonlinear wave

convergence rate of solutions toward stationary solutions to the compressible navier stokes equation in a half line abstract we study a large time behavior of a solution to the initial boundary value problem for an isentropic and compressible viscous fluid in a one dimensional half space the unique existence and the asymptotic stability of a stationary solution are proved by s kawashima s nishibata and p zhu for an outflow problem where the fluid blows out through the boundary the main concern of the present paper is to investigate a convergence rate of a solution toward the stationary solution for the supersonic flow at spatial infinity we obtain an algebraic or an exponential decay rate precisely if an initial perturbation decays with the algebraic or the exponential rate in the spatial asymptotic point the solution converges to the corresponding stationary solution with the same rate in time as time tends to infinity an algebraic convergence rate is also obtained for the transonic flow these results are proved by the weighted energy method

on p parts of character degrees and conjugacy class sizes of finite groups abstract let g be a finite group and irr g the set of irreducible complex characters of g let e p g be the largest integer such that p e p g divides 1 for some irr g we show that g f g p p k e p g for a constant k this settles a conjecture of a moreto 13 conjecture 4 we also study the related problems of the p parts of conjugacy class sizes of finite groups

irreducible character degree sets of solvable groups in this paper we examine the following general question given a set x of positive integers that includes 1 is there a finite group g whose 4 character degree set cd g s x 1 x g irr g equals x technically we should call cd g the set of irreducible character degrees but these are the only character degrees that we will look at in this paper thus when we say the character degrees of g we mean the irreducible character degrees while this is a very interesting question in order to answer it one must restrict the focus of the question we restrict p to be a prime and m and n to be coprime integers that are greater than 1 and are not divisible 4 by p we look at sets x that have the form x s 1 j p j m j n where 4 4 p is a set of powers of p m m mp with m g 1 and n n np with n g 1 we would like to know under what conditions x s cd g for some solvable group g in this paper we are able to give the following partial answer

a remark on the casimir elements of lie superalgebras and quantized lie superalgebras it is shown that the second order casimir operators c and cq of the lie superalgebra osp 1 2 and the quantized lie superalgebra ospq 1 2 respectively possess natural square roots

revisiting the askey wilson algebra with the universal r matrix of uq su 2 a description of the embedding of a centrally extended askey wilson algebra aw 3 in uq sl2 3 is given in terms of the universal r matrix of uq sl2 the generators of the centralizer of uq sl2 in its three fold tensor product are naturally expressed through conjugations of casimir elements with r they are seen as the images of the generators of aw 3 under the embedding map by showing that they obey the aw 3 relations this is achieved by introducing a natural coaction also constructed with the help of the r matrix

global structure stability of riemann solutions of quasilinear hyperbolic systems of conservation laws shocks and contact discontinuities abstract in this paper the author proves the global structure stability of the lax s riemann solution u u x t containing only shocks and contact discontinuities of general n n quasilinear hyperbolic system of conservation laws more precisely the author proves the global existence and uniqueness of the piecewise c1 solution u u t x of a class of generalized riemann problem which can be regarded as a perturbation of the corresponding riemann problem for the quasilinear hyperbolic system of conservation laws moreover this solution has a global structure similar to that of the solution u u x t combining the results in kong global structure instability of riemann solutions of quasilinear hyperbolic systems of conservation laws rarefaction waves to appear the author proves that the lax s riemann solution of general n n quasilinear hyperbolic system of conservation laws is globally structurally stable if and only if it contains only non degenerate shocks and contact discontinuities but no rarefaction waves and other weak discontinuities

the largest character degree and the sylow subgroups of finite groups let p be a sylow p subgroup and b g the largest irreducible character degree of a finite group g it is shown that p op g b g in general and p op g b g in case p is abelian

lie type like groups abstract a finite simple group of lie type in defining characteristic p has exactly two p blocks the principal block and a block of defect zero consisting of the steinberg character whose degree is the p part of the order of the group in this paper we characterize finite groups g which have exactly the principal p block and a p block of defect zero consisting of an irreducible character of degree g p

temperley lieb brauer and racah algebras and other centralizers of mathfrak su 2 in the spirit of the schur weyl duality we study the connections between the racah algebra and the centralizers of tensor products of three possibly different irreducible representations of su 2 as a first step we show that the racah algebra always surjects onto the centralizer we then offer a conjecture regarding the description of the kernel of the map which depends on the irreducible representations if true this conjecture would provide a presentation of the centralizer as a quotient of the racah algebra we prove this conjecture in several cases in particular while doing so we explicitly obtain the temperley lieb algebra the brauer algebra and the one boundary temperley lieb algebra as quotients of the racah algebra

centralizers of the superalgebra mathfrak osp 1 2 o s p 1 2 the brauer algebra as a quotient of the bannai ito algebra

on the number of conjugacy classes in a finite group in the following g will denote a finite group and we will use the standard notation of the theory of groups we say that g is a d group if g contains a unique conjugacy class of maximal rc subgroups in addition a d group g is said to be a lx group if all epimorphic images of subgroups of g are d groups for example if g is n separable then g is a lx group in particular all rr solvable groups are l groups in this work we get new results relative to the conjugacy classes of a finite group g let n be a normal subgroup of g rt a set of prime numbers r g resp r g the number of conjugacy classes of elements resp n elements of g rc g the set of all different primes dividing igil g the set of all n elements of g and g g n in this paper we analyze the number r g of conjugacy classes of n elements of g through the local analysis of the number r gn of conjugacy classes of n elements of g which intersect the coset gn our aims are threefold to obtain upper and lower bounds of the number r g of conjugacy classes of rc elements of g in terms of the numbers r g n r n and g l where g denotes the derived subgroup of g to get the residue class of r g modulo the best number given in terms of the primes dividing gi and finally to analyze the conjugacy vector d ic g l ic g l of g assuming that g is the disjoint union of the classes cl g i 1 r r g and lcg g1 3 3 ic g l the results obtained are useful both for the calculation of the conjugacy vector of a finite group and for the classification of finite groups according to the number of conjugacy classes see examples 11 13 in section 4 moreover they enable us to obtain the following inequalities

the z 2 n dirac dunkl operator and a higher rank bannai ito algebra abstract the kernel of the z 2 n dirac dunkl operator is examined the symmetry algebra a n of the associated dirac dunkl equation on s n 1 is determined and is seen to correspond to a higher rank generalization of the bannai ito algebra a basis for the polynomial null solutions of the dirac dunkl operator is constructed the basis elements are joint eigenfunctions of a maximal commutative subalgebra of a n and are given explicitly in terms of jacobi polynomials the symmetry algebra is shown to act irreducibly on this basis via raising lowering operators a scalar realization of a n is proposed

global stability of the rarefaction wave of a one dimensional model system for compressible viscous gas this paper is concerned with the asymptotic behavior toward the rarefaction wave of the solution of a one dimensional barotropic model system for compressible viscous gas we assume that the initial data tend to constant states atx respectively and the riemann problem for the corresponding hyperbolic system admits a weak continuous rarefaction wave if the adiabatic constant satisfies 1 2 then the solution is proved to tend to the rarefaction wave ast under no smallness conditions of both the difference of asymptotic values atx and the initial data the proof is given by an elementaryl 2 energy method

dunkl shift operators and bannai ito polynomials abstract we consider the most general dunkl shift operator l with the following properties i l is of first order in the shift operator and involves reflections ii l preserves the space of polynomials of a given degree iii l is potentially self adjoint we show that under these conditions the operator l has eigenfunctions which coincide with the bannai ito polynomials we construct a polynomial basis which is lower triangular and two diagonal with respect to the action of the operator l this allows to express the bi polynomials explicitly we also present an anti commutator aw 3 algebra corresponding to this operator from the representations of this algebra we derive the structure and recurrence relations of the bi polynomials we introduce new orthogonal polynomials referred to as the complementary bi polynomials as an alternative q 1 limit of the askey wilson polynomials these complementary bi polynomials lead to a new explicit expression for the bi polynomials in terms of the ordinary wilson polynomials

asymptotic stability of combination of viscous contact wave with rarefaction waves for one dimensional compressible navier stokes system we are concerned with the large time behavior of solutions of the cauchy problem to the one dimensional compressible navier stokes system for ideal polytropic fluids where the far field states are prescribed when the corresponding riemann problem for the compressible euler system admits the solution consisting of contact discontinuity and rarefaction waves it is proved that for the one dimensional compressible navier stokes system the combination wave of a viscous contact wave which corresponds to the contact discontinuity with rarefaction waves is asymptotically stable provided the strength of the combination wave is suitably small this result is proved by using elementary energy methods