initial boundary value problem for the system of compressible adiabatic flow through porous media abstract we study the initial value problem for the system of compressible adiabatic flow through porous media in the one space dimension with fixed boundary condition under the restriction on the oscillations in the initial data we establish the global existence and large time behavior for the classical solutions via the combination of characteristic analysis and energy estimate methods the time asymptotic states for the solution are found and the exponential convergence to the asymptotic states is proved it is also shown that this problem can be approximated very well time asymptotically by an initial boundary problem for the related diffusion equations obtained from the original hyperbolic system by darcy s law provided that the initial total mass is the same the difference between these two solutions tends to zero exponentially fast as time goes to infinity in the sense of h 1 the diffusive phenomena caused by damping mechanism with boundary effects are thus observed

wkb approximation to the power wall we present a semiclassical analysis of the quantum propagator of a particle confined on one side by a steeply monotonically rising potential the models studied in detail have potentials proportional to x for x 0 the limit would reproduce a perfectly reflecting boundary but at present we concentrate on the cases 1 and 2 for which exact solutions in terms of well known functions are available for comparison we classify the classical paths in this system by their qualitative nature and calculate the contributions of the various classes to the leading order semiclassical approximation for each classical path we find the action s the amplitude function a and the laplacian of a the laplacian is of interest because it gives an estimate of the error in the approximation and is needed for computing higher order approximations the resulting semiclassical propagator can be used to rewrite the exact problem as a volterra integral equation whose formal solution by iteration neumann series is a semiclassical not perturbative expansion we thereby test in the context of a concrete problem the validity of the two technical hypotheses in a previous proof of the convergence of such a neumann series in the more abstract setting of an arbitrary smooth potential not surprisingly we find that the hypotheses are violated when caustics develop in the classical dynamics this opens up the interesting future project of extending the methods to momentum space

prime characters and primitivity a natural question in the character theory of finite groups is which quasi primitive characters are actually primitive a character is said to be quasi primitive if it is irreducible and its restriction to every normal subgroup is homogeneous if the group is solvable t berger 9 th 11 331 has shown that every quasi primitive character is actually primitive if the group is simple however every irreducible character is quasi primitive and may or may not be primitive the character of degree 5 of alt 5 for example is not primitive it follows that a generalization of berger s theorem to non solvable groups must include some extra hypotheses which become vacuous when the group is solvable in this paper we prove the following such theorem with hypotheses on the chief factors and the character degrees

gamow vectors and borel summability in a class of quantum systems we analyze the detailed time dependence of the wave function x t for one dimensional hamiltonians h partial x 2 v x where v for example modeling barriers or wells and x 0 are compactly supported

a characterization of the finite simple groups abstract in this paper we obtain a quantitative characterization of all finite simple groups let t g denote the set of indices of maximal subgroups of group g and let p g be the smallest number in t g we have the following theorems theorem 2 let n and g be finite simple groups if n divides g p n p g and t n t g then or and 2 11 or 2 and 3 theorem 3 let n be a finite simple and let g be a finite group if g n and t g t n then g n

convergence to nonlinear diffusion waves for solutions of a system of hyperbolic conservation laws with damping we consider a model of hyperbolic conservation laws with damping and show that the solutions tend to those of a nonlinear parabolic equation time asymptotically the hyperbolic model may be viewed as isentropic euler equations with friction term added to the momentum equation to model gas flow through a porous media in this case our result justifies darcy s law time asymptotically our model may also be viewed as an elastic model with damping

existence and asymptotic behavior of global smooth solution for p system with damping and boundary effect abstract in this paper we study the existence and asymptotic behavior of global smooth solution for p system with damping on the strip 0 1 0 v t u x 0 u t p v x u with the null dirichlet boundary condition u 0 t u 1 t 0 first we prove the existence of the global smooth solution under the assumption that only the c 0 norm of the first derivatives of the initial data is sufficiently small while the c 0 norm of the initial data is not necessarily small second when the initial data is in c 2 and the c 0 norm of the first derivatives of the initial data is large enough then the first derivatives of the corresponding c 2 smooth solution must blow up in finite time finally we consider the asymptotic behavior of the global smooth solution precisely we show that the solution of this problem tends to the corresponding nonlinear diffusive wave governed by the classical darcy s law exponentially fast as time goes to infinity in the sense of h 1 norm provided the initial total mass is the same and thus justifies the validity of darcy s law in large time

the radiation condition at infinity for the high frequency helmholtz equation with source term a wave packet approach abstract we consider the high frequency helmholtz equation with a given source term and a small absorption parameter 0 the high frequency or semi classical parameter is 0 we let and go to zero simultaneously we assume that the zero energy is non trapping for the underlying classical flow we also assume that the classical trajectories starting from the origin satisfy a transversality condition a generic assumption under these assumptions we prove that the solution u radiates in the outgoing direction uniformly in in particular the function u when conveniently rescaled at the scale close to the origin is shown to converge towards the outgoing solution of the helmholtz equation with coefficients frozen at the origin this provides a uniform version in of the limiting absorption principle writing the resolvent of the helmholtz equation as the integral in time of the associated semi classical schrodinger propagator our analysis relies on the following tools i for very large times we prove and use a uniform version of the egorov theorem to estimate the time integral ii for moderate times we prove a uniform dispersive estimate that relies on a wave packet approach together with the above mentioned transversality condition iii for small times we prove that the semi classical schrodinger operator with variable coefficients has the same dispersive properties as in the constant coefficients case uniformly in

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

semi classical propagation of wavepackets for the phase space schrodinger equation interpretation in terms of the feichtinger algebra the nearby orbit method is a powerful tool for constructing semi classical solutions of schrodinger s equation when the initial datum is a coherent state in this paper we first extend this method to arbitrary squeezed states and thereafter apply our results to the schrodinger equation in phase space this adaptation requires the phase space weyl calculus developed in previous work of ours we also study the regularity of the semi classical solutions from the point of view of the feichtinger algebra familiar from the theory of modulation spaces

on the automorphism groups of quasiprimitive almost simple graphs let gamma be a graph and let g be a subgroup of automorphisms of gamma then g is said to be locally primitive on gamma if for each vertex upsilon the stabilizer g upsilon induces a primitive group of permutations on the set of vertices adjacent to upsilon this paper investigates pairs gamma g for which g is locally primitive on gamma g is an almost simple group that is l less than or equal to g less than or equal to aut l for some nonabelian simple group l and the simple socle l is transitive on vertices each such graph is a cover of a possibly smaller graph l gamma over tildeg on which g is also locally primitive and for which in addition aut l gamma over tildeg is quasiprimitive on vertices that is every nontrivial normal subgroup of aut l gamma over tildeg is vertex transitive it is proved that aut l gamma over tildeg is also an almost simple group tn the general case in which aut gamma is not quasiprimitive on vertices we show that either every intransitive minimal normal subgroup of aut gamma centralizes l or l is of lie type and aut gamma involves an explicitly known same characteristic module for l c 1999 academic press

on the mumford tate group of an abelian variety with complex multiplication let k be a primitive cm type with k o 2n for definitions and previous results see section 1 1 fix n and consider the collection s n rank where rank counts the number of independent translates of qi under the galois action and k ranges over all primitive types the smallest element of s n denoted by b n is referred to as the sharp lower bound for the rank in dimension n as was brought to the author s attention by ribet bounds on b n of the form p 1 for p a prime dividing n follow directly from the proof of ribet s nondegeneracy theorem 21 this is recorded as theorem 1 4 ribet s method also gives bounds of the form 2q for q a prime with q2 dividing n as is observed in theorem 1 12 when combined with the author s constructions of abelian varieties in s 91 we obtain the precise value of b n for many values of n corollaries 1 5 to 1 8 and 1 13 we recall that these constructions use the analytic method of weil and shimura together with new results on the reflex field from an investigation suggested to the author by shim ura the interest of the rank comes from the theory of complex multiplication if a is an abelian variety of cm type k then the kubota rank of a is rank and controls properties of the classfields constructed from a as in kubota 161 and ribet 20 this is connected with the fact that the rank of is also the dimension of the mumford tate group of a and with the relation of this group to the i adic representations of a as in serre 24 251 the main body of the paper contains results that provide information on s n the main result theorem 2 5 asserts that when n is odd there is a computable subset s n of s n that accounts for the ranks of many cm types on most cm fields more precisely let k be the maximal totally real subfield of k and kg be the galois closure of k we consider the per

new criteria for the solvability of finite groups see 6 or 7 p 291 it has been conjectured that a group is solvable if and only if it has a hall 2 subgroup and a hall 3 subgroup see 11 we verify this conjecture for groups whose composition factors are known simple groups along the way we also verify for groups whose composition factors are known simple groups a conjecture of hall s that if a group has a hall

finite groups with certain subgroups of sylow subgroups complemented abstract let g be a finite group and h a subgroup of g we say that h is complemented in g if there exists a subgroup k of g such that g h k and h k 1 for each prime p dividing the order of g let p be a sylow p subgroup of g we fix in each p a subgroup d such that 1 d p and study the structure of g under the assumption that each subgroup h of p with h d and h p d is complemented in g

hall subgroups and π separable groups abstract let g be a finite group and a set of primes in this paper some new criteria for separable groups and solvable groups in terms of hall subgroups are proved the main results are the following theorem g is a separable group if and only if 1 g satisfies e and e 2 g satisfies e q and e p for all p q theorem g is a separable group if and only if 1 g satisfies e and e 2 g satisfies e p q for all p and q

exceptional polynomials of affine type abstract let k be a finite field of characteristic p a polynomial f with coefficients in k is said to be exceptional if it induces a permutation on infinitely many finite extensions of k let t be a transcendental and k be an algebraic closure of k the exceptional polynomials known to date are constructed from certain twists of polynomials g such that the splitting field of g x t over k is rational on the other hand we know that except for p 2 or 3 either the degree of an exceptional polynomial f is a power of the characteristic p or f is a dickson polynomial the case deg f p has been settled completely we give a new series of exceptional polynomials of degree p m with m even which does not follow the above mentioned construction principle we show under certain additional hypotheses that the associated monodromy groups of exceptional polynomials will be severely restricted in particular we determine precisely what the geometric monodromy groups of exceptional polynomials of degree p 2 will be

convergence to strong nonlinear diffusion waves for solutions to p system with damping on quadrant in this paper we consider the so called p system with linear damping on quadrant we show that for a certain class of given large initial data v0 x u0 x the corresponding initial boundary value problem admits a unique global smooth solution v x t u x t and such a solution tends time asymptotically at the lp 2 p optimal decay rates to the corresponding nonlinear diffusion wave v x t u x t which satisfies 1 9 provided the corresponding prescribed initial error function v0 x u0 x lies in h3 r l1 r h2 r l1 r

primitive permutation groups of odd degree and an application to finite projective planes one of the most beautiful and important results concerning finite projective planes is the ostrom wagner theorem 26 such a plane admitting a 2 transitive collineation group must be desarguesian it has long been conjectured that the same conclusion must hold if it is only assumed that there is a collineation group transitive on incident point line pairs ll pp 208 214 171 the starting point for this paper was a proof of this conjecture modulo a degenerate situation

quasiprimitive groups containing a transitive alternating group abstract this paper classifies quasiprimitive permutation groups with a transitive subgroup which is isomorphic to a n for some n 5

exponentially accurate semiclassical asymptotics of low lying eigenvalues for 2 2 matrix schrodinger operators abstract we consider a simple molecular type quantum system in which the nuclei have one degree of freedom and the electrons have two levels the hamiltonian has the form h 4 2 2 y 2 h y where h y is a 2 2 real symmetric matrix near a local minimum of an electron level e y that is not at a level crossing we construct quasimodes that are exponentially accurate in the square of the born oppenheimer parameter by optimal truncation of the rayleigh schrodinger series that is we construct e and such that o 1 and h e exp 2 where 0

symplectic structure for gaussian diffusions using information exclusively about classical hamiltonian boundary value problems with quadratic time dependent potentials we construct probability measures providing a symplectic structure associated with some inhomogeneous gaussian diffusion processes introduced earlier t kolsrod and j c zambrini j math phys 33 1301 1992

indices in classical mechanics the authors discuss the linearization of the equations of motion around a periodic orbit in a conservative two degree of freedom hamiltonian system with an emphasis on computationally useful formulae indices are defined using singularities in projections conjugate points self conjugate points and the possibility of assigning a symbolic code are discussed

on fully ramified brauer characters let z be a normal subgroup of a finite group let p 5 be a prime and let ibr z be an irreducible g invariant p brauer character of z suppose that g e for some ibr g then g z is solvable in other words a twisted group algebra over an algebraically closed field of characteristic not 5 with a unique class of simple modules comes from a solvable group

existence of global smooth solutions for euler equations with symmetry ii eventhough existence of global smooth solutions for one dimensional quasilinear hyperbolic systems has been well established much less is known about the corresponding results for higher dimensional cases in this paper we study the existence of global smooth solutions for the initial boundary value problem of euler equtions satisfying gamma law with damping and axisymmetry or spherical symmetry when the damping is strong enough we give some sufficient conditions for existence of global smooth solutions as 1 gamma 5 3 and 5 3 gamma 3 the proof is based on technical estimation of the c 1 norm of the solutions

the trivial intersection problem for characters of principal indecomposable modules abstract for a prime p and a finite group g let p g denote the complex character associated to the projective indecomposable module in characteristic p with trivial head let irr p g denote the set of irreducible characters occurring as constituents in p g we characterize all finite simple groups which satisfy irr p g irr q g 1 g for all primes p q

the van vleck formula maslov theory and phase space geometry the van vleck formula is an approximate semiclassical expression for the quantum propagator it is the starting point for the derivation of the gutzwiller trace formula and through this a variety of other expansions representing eigenvalues wave functions and matrix elements in terms of classical periodic orbits these are currently among the best and most promising theoretical tools for understanding the asymptotic behavior of quantum systems whose classical analogs are chaotic nevertheless there are currently several questions remaining about the meaning and validity of the van vleck formula such as those involving its behavior for long times this article surveys an important aspect of the van vleck formula namely the relationship between it and phase space geometry as revealed by maslov s theory of wave asymptotics the geometrical constructions involved are developed with a minimum of mathematical formalism

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

semiclassical dynamics with exponentially small error estimates we construct approximate solutions to the time dependent schrodinger equation for small values of if v satisfies appropriate analyticity and growth hypotheses and these solutions agree with exact solutions up to errors whose norms are bounded by for some c and 0 under more restrictive hypotheses we prove that for sufficiently small t implies the norms of the errors are bounded by for some c 0 and 0

complex wkb evolution of markovian open systems we derive a consistent complex wkb expression for the characteristic function that is the fourier transform of the wigner function of a markovian open system defined by a generic lindblad equation the hamiltonian can be a general function of positions and momenta so the only restriction is that linear coupling to the environment is assumed the propagation is shown to correspond to a classical evolution of the liouville type in a complex double phase space the imaginary part of the double hamiltonian being responsible for decoherence whereas dissipation is included in the real part the theory exact in the quadratic case is designed to describe the decoherent and dissipative evolution of localized states such as the interference terms of a schrodinger cat state as well as the evolution of extended states which were the exclusive subjects of our previous real wkb approximation the present rederivation allows us to interpret the real formalism as a first order classical perturbation of the complex theory and to discuss its validity this is also clarified by a simple cubic hamiltonian that illustrates various levels of approximation derived from the complex wkb theory

finitely generated groups p adic analytic groups and poincare series this is equivalent to the coefficients apn g satisfing a linear recurrence relation with constant coefficients for sufficiently large n these poincare series were first studied in the case when g is a finitely generated torsion free nilpotent group in a paper by grunewald segal and smith gssm there the authors established that for such a group g p s is a rational function in p8s in that setting the functions g p s are the local factors associated with the dirichlet series

large time behavior for the system of compressible adiabatic flow through porous media in r3 abstract the cauchy problem of the system of compressible adiabatic flow through porous media in r 3 is considered we obtain the global existence and large time behavior of the solution when the initial data is close to its equilibrium in h 3 norm this is a continuing work of 31 where due to non dissipative property of the entropy s an additional assumption that the initial data is bounded in l 1 norm plays a key role in closing the a priori energy estimates and hence establishing the global existence of the solution in this paper to remove this assumption we first decompose the solution u into high frequency part u h and low frequency part u l then by constructing delicate energy functionals for u h and optimal decay rates for u l we can get the desired energy estimates to close the a priori assumption furthermore we get the optimal l 2 l 2 decay rate of the solution and show that the velocity decays faster than the density

convergence to strong nonlinear diffusion waves for solutions of p system with damping this paper is concerned with the p system with frictional damping and our main purpose is two fold first we show that for a certain class of given large initial data nu 0 x u 0 x the cauchy problem 1 1 1 2 admits a unique global smooth solution nu t x u t x and such a solution tends time asymptotically at the optimal l p 2 less than or equal to p less than or equal to infinity decay rates to the corresponding nonlinear diffusion wave over bar t x u over bar t x governed by the classical darcy s law provided that the corresponding prescribed initial error function v 0 x u 0 x ties in h 3 x h 2 r boolean and l 1 x l 1 r compared with former results in this direction obtained by l hsiao and t p liu 1992 comm math phys 143 599 605 k nishihara 1996 j differential equations 131 171 188 and k nishihara w k wang and t yang 2000 j differential equations 161 191 218 our main novelty lies in the facts that the nonlinear diffusion wave over bar t x u over bar t x need not to be weak and v 0 x u 0 x can be chosen arbitrarily large secondly we show that the nonlinear diffusion waves over bar t x u over bar t x are nonlinear stable provided that the strength or the nonlinear diffusion waves is weak and that the initial disturbance v 0 x u 0 x satisfies the assumption that parallel tov 0xx x parallel to l infinity parallel tou 0x x parallel to l infinity is sufficiently small we also show that the smallness assumption imposed oil the strength of the diffusion waves is a necessary condition to guarantee the nonlinear stability result and compared with the corresponding results obtained by l hsiao and t p liu 1992 comm math phys 143 599 605 the smallness conditions we imposed on the initial disturbance are much more weaker c 2001 academic press

features of moyal trajectories we study the moyal evolution of the canonical position and momentum variables we compare it with the classical evolution and show that contrary to what is commonly found in the literature the two dynamics do not coincide we prove that this divergence is quite general by studying hamiltonians of the form p2 2m v q several alternative formulations of moyal dynamics are then suggested we introduce the concept of star function and use it to reformulate the moyal equations in terms of a system of ordinary differential equations on the noncommutative moyal plane we then use this formulation to study the semiclassical expansion of moyal trajectories which is cast in terms of a order by order in recursive hierarchy of i first order partial differential equations as well as ii systems of first order ordinary differential equations the latter formulation is derived independently for analytic hamiltonians as well as for the more general case of locally integrable ones we present various examples i

accuracy of the semiclassical approximation for the time dependent propagator for chaotic systems the semiclassical approximation to the time dependent propagator consists of a large number of terms some of which may involve classical trajectories near focal points caustics despite this the approximation has been found to remain accurate for relatively long times in this article that accuracy and potential reasons for its breakdown are studied the principal tool is the jacobi morse equation the eigenvalue equation associated with the second variational derivative of the classical action our explanation for the accuracy lies partly in the following considerations 1 verification of the efficacy of phase space smearing 2 given an explicit form of the near caustic propagator it is seen that the arguments concerning loops in phase space may be less relevant than the determination of the amount of separation in path space 3 and finally the caustics in the chaotic examples studied may not be placed for maximum mischief

asymptotic behavior of the solutions to the damped compressible euler equations with vacuum abstract the asymptotic behavior of solutions of the damped compressible euler equations is conjectured to obey to the famous porous media equations pmes the previous works on this topic concern the case away from vacuum where the system is strictly hyperbolic in present paper we prove that the l entropy weak solution with vacuum obtained by the compensated compactness theory converges strongly in l loc p 1 p space to the unique similarity solution of the related pme as time goes to infinity

semiclassical limit for multistate klein gordon systems almost invariant subspaces and scattering theory by using the method of helffer and sjostrand to construct moyal projections we extend the almost invariant subspace theory to the semiclassical context applications to the semiclassical limit for two component klein gordon hamiltonian are given more precisely under the conditions that the potential is analytic and its eigenvalues never cross we prove that the scattering matrix is block diagonal up to exponentially small errors also we show how the existence of almost invariant subspaces leads to the existence of quasimodes with exponentially long lifetimes

formation of singularities in three dimensional compressible fluids presented are several results on the formation of singularities in solutions to the three dimensional euler equations for a polytropic ideal fluid under various assumptions on the initial data in particular it is shown that a localized fluid which is initially compressed and outgoing on average will develop singularities regardless of the size of the initial disturbance

a small scale density of states formula let m g be a c compact riemann manifold with classical hamiltonian h c t m assume that the corresponding quantization p1 op h is quantum completely integrable we establish an microlocal weyl law on short spectral intervals of size 2 e e 0 for various families of operators p1u u i containing p1 both in the mean and pointwise a e for u i the microlocalization refers to a small tubular neighbourhood of a non degenerate stable periodic bicharacteristic t m 0

convergence rate for compressible euler equations with damping and vacuum we study the asymptotic behavior of l weak entropy solutions to the compressible euler equations with damping and vacuum previous works on this topic are mainly concerned with the case away from the vacuum and small initial data in the present paper we prove that the entropy weak solution strongly converges to the similarity solution of the porous media equations in lp r 2 p with decay rates the initial data can contain vacuum and can be arbitrary large a new approach is introduced to control the singularity near vacuum for the desired estimates

darcy s law as long time limit of adiabatic porous media flow abstract it is conjectured that darcy s law governs the motion of compressible porous media flow in large time this has been justified for one dimensional isentropic flows in this work we show the conjecture is true for one dimensional adiabatic flows with generic small smooth initial data

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

asymptotic behavior of solutions of quasilinear hyperbolic equations with linear damping we consider the asymptotic behavior of the solution of quasilinear hyperbolic equation with linear dampingvtt a vx x vt 0 x t r 0 subsequent to k nishihara j differential equations131 1996 171 188 in that article the system with dampingvt ux 0 ut p v x u p v 0 was treated and the convergence rates to the diffusion wave by l hsiao and t p liu comm math phys 143 1992 599 605 and l hsiao and t p liu chinese ann math ser b14 1993 465 480 were improved for initial data v0 u0 x satisfying v0 u0 v0 0 and v0 x v0 dx 0 this system is reduced to the quasilinear hyperbolic equation with linear dampingvtt p v0 vx p v0 x vt 0 and the decay rates v t l o t 1 2 vx t l o t 1 vt t l o t 3 2 were obtained provided that v vt t 0 h3 h2 is small and inl1 l1 from these decay rates vis expected to behave as a solution to the parabolic equation the aims of this paper are to seek the asymptotic profile x t satisfying t l o t 1 2 x t l o t 1 t t l o t 3 2 and to show that the solution of satisfies v t l o t 1 v x t l o t 3 2 v t t l o t 2 the proof is based on the elementary energy method and the green function method for the parabolic equation

asymptotic behavior of solutions for p system with relaxation in this paper we consider the asymptotic behavior of solutions for the cauchy problem for p system with relaxationvt ux 0 ut p v x 1e f v u e with initial data v u x 0 v 0 x u 0 x v u v 0 asx i we are interested to show the solutions of e i tend also to the equilibrium rarefaction waves and the traveling waves even if the limits v u of the initial data at x do not satisfy the equilibrium equation i e u f v when the limits of the initial data at infinity satisfy equilibrium states liu 9 studied the stability of rarefaction waves and traveling waves for the general 2 2 hyperbolic conservation laws with relaxation

the probabilistic zeta function of finite simple groups abstract let g be a finite group there exists a uniquely determined dirichlet polynomial p g s such that if t n then p g t gives the probability of generating g with t randomly chosen elements we show that it may be recognized from the knowledge of p g s whether g frat g is a simple group

two results related to the solvability of m groups abstract the results of this paper are as follows for a finite group g if all primitive irreducible characters are linear or if all nonmonomial irreducible characters have the same degree then g is solvable

a scaling theory of bifurcations in the symmetric weak noise escape problem we consider two dimensional overdamped double well systems perturbed by white noise in the weak noise limit the most probable fluctuational path leading from either point attractor to the separatrix the most probable escape path or mpep must terminate on the saddle between the two wells however as the parameters of a symmetric double well system are varied a unique mpep may bifurcate into two equally likely mpeps at the bifurcation point in parameter space the activation kinetics of the system become non arrhenius we quantify the non arrhenius behavior of a system at the bifurcation point by using the maslov wkb method to construct an approximation to the quasistationary probability distribution of the system that is valid in a boundary layer near the separatrix the approximation is a formal asymptotic solution of the smoluchowski equation our construction relies on a new scaling theory which yields critical exponents describing weak noise behavior at the bifurcation point near the saddle

on finite factorizable groups in this paper we use freely the recent classification theorem for finite simple groups from the early stages of finite group theory finite factorizable groups satisfying h were studied by many authors in 1904 burnside 6 proved the solvability of groups factorizable by two prime power subgroups many years later wielandt 29 proved the solvability of finite groups factorizable by two nilpotent subgroups of relatively prime orders kegel extended wielandt s result in the case that both subgroups a and b are nilpotent without restrictions the second author in 121 classified finite factorizable groups of type h where a and b are solvable subgroups results on groups satisfying h can be found in 3 4 10 12 19 20 291 and in other papers on finite factorizable groups theorem 1 1 and corollary 1 2 of this paper state the final solution to the problem of classifying groups of type h we prove the following

existence of global smooth solution to the initial boundary value problem for p system with damping abstract this paper is concerned with the initial boundary value problem for the p system with damping we prove the existence of the global smooth solution under the assumption that only the c 0 norm of the derivative of the initial data is sufficiently small while the c 0 norm of the initial data is not necessarily small the proof is based on several key a priori estimates the maximum principle and the characteristic method

restrictions on the structure of subgroup lattices of finite alternating and symmetric groups let g be a finite alternating or symmetric group we describe an infinite class of finite lattices none of which is isomorphic to any interval h g in the subgroup lattice of g

exponentially accurate error estimates of quasiclassical eigenvalues we study the behaviour of truncated rayleigh schrodinger series for the low lying eigenvalues of the one dimensional time independent schrodinger equation in the semiclassical limit 0 under certain hypotheses on the potential v x we prove that for any given small 0 there is an optimal truncation of the series for the approximate eigenvalues such that the difference between an approximate and exact eigenvalue is smaller than exp c for some positive constant c we also prove the analogous results concerning the eigenfunctions

a time dependent born oppenheimer approximation with exponentially small error estimates we present the construction of an exponentially accurate time dependent born oppenheimer approximation for molecular quantum mechanics

a classification of the maximal subgroups of the finite alternating and symmetric groups following the classification of finite simple groups one of the major problems in finite group theory today is the determination of the maximal subgroups of the almost simple groups that is of groups x such that x0 u x aut x for some finite non abelian simple group x0 the problem has been solved for most sporadic groups and groups of lie type of low rank see 19 sects 3 43 for discussion and references this paper is a contribution to the case where x0 is an alternating group a so that for n 6 x is a or s the maximal subgroups of a and s are known for several classes of degrees n

on a class of non solvable groups abstract in this paper we use the properties of subgroups with given order to study the structure of finite groups the main result is as follows let g be a group and p be a sylow p subgroup of g suppose that 1 d p if every subgroup h of p with h d is m supplemented in g then every non abelian pd g chief factor a b satisfies one of the following conditions 1 a b p s l 2 7 and p 7 a b p s l 2 11 and p 11 2 a b p s l 2 2 t and p 2 t 1 3 is a fermat prime 3 a b p s l n q n 3 is a prime n q 1 1 and p q n 1 q 1 4 a b m 11 and p 11 a b m 23 and p 23 5 a b a p and p 5

on primitive overgroups of quasiprimitive permutation groups a permutation group is said to be quasiprimitive if all its non trivial normal subgroups are transitive we investigate pairs g h of permutation groups of degree n such that g h sn with g quasiprimitive and h primitive an explicit classification of such pairs is obtained except in the cases where the primitive group h is either almost simple or the blow up of an almost simple group the theory in these remaining cases is investigated in separate papers the results depend on the finite simple group classification