the principle of linearized stability for a class of degenerate diffusion equations here u0 is a given bounded nonnegative function the functions b s and f s defined for s 2 0 are smooth for s 0 f 0 0 i o 0 y o co i s 0 for s o and fib is lipschitz continuous for s 30 the precise hypotheses on the data can be found in section 2 since p o co the diffusion is degenerate near points where u 0 in this paper we study the stability of steady state solutions of problem i by linearizing 1 1 near an equilibrium v so let 0 e c d satisfy

quantum galois theory for compact lie groups abstract we establish a quantum galois correspondence for compact lie groups of automorphisms acting on a simple vertex operator algebra

on the structure of unbounded positive solutions to the quasilinear logistic equation abstract for the quasilinear logistic equation p u m x u u in u 0 on with p 1 m x l q we obtain the existence of the maximal unbounded positive solutions their asymptotic behavior and global bifurcation from the trivial solution

monstrous moonshine from orbifolds we consider the monster module of frenkel lepowsky and meurman as az2 orbifold of a bosonic string compactified by the leech lattice we show that the main conway and norton monstrous moonshine properties stating that the thompson series for each monster group conjugacy class has a modular invariance group of genus zero follow from an orbifold construction based on an orbifold group composed of monster group elements it is shown that a conjectured vacuum structure for the orbifold twisted sectors is sufficient to specify the modular group and the genus zero property for each thompson series it is also shown that the power map formula of conway and norton follows from the same vacuum structure finally we demonstrate the validity of the vacuum conjectures for sectors twisted by leech lattice automorphisms in many cases

modular categories and orbifold models in this paper we try to answer the following question given a modular tensor category with an action of a compact group g is it possible to describe in a suitable sense the quotient category g we give a full answer in the case when is the category of vector spaces in this case g turns out to be the category of representation of drinfeld s double d g this should be considered as the category theory analog of the topological identity pt g bg this implies a conjecture of dijkgraaf vafa e verlinde and h verlinde regarding so called orbifold conformal field theories if is a vertex operator algebra which has a unique irreducible module itself and g is a compact group of automorphisms of and some not too restrictive technical conditions are satisfied then g is finite and the category of representations of the algebra of invariants g is equivalent as a tensor category to the category of representations of drinfeld s double d g we also get some partial results in the non holomorphic case i e when has more than one simple module

beauty and the beast superconformal symmetry in a monster module frenkel lepowsky and meurman have constructed a representation of the largest sporadic simple finite group the fischer griess monster as the automorphism group of the operator product algebra of a conformal field theory with central chargec 24 in string terminology their construction corresponds to compactification on az2 asymmetric orbifold constructed from the torusr24 where is the leech lattice in this note we point out that their construction naturally embodies as well a larger algebraic structure namely a super virasoro algebra with central charge 16 with the supersymmetry generator constructed in terms of bosonic twist fields

on the symbiotic lotka volterra model with diffusion and transport effects abstract in this work we analyze the existence stability and multiplicity of coexistence states for a symbiotic lotka volterra model with general diffusivities and transport effects global bifurcation theory blowing up arguments for a priori bounds singular perturbation results singularity theory and fixed point index in cones are among the techniques used to get our results and to explain the drastic change of behavior exhibited by the dynamics of the model between the cases of weak and strong mutualism between the species our methodology works out to treat much more general classes of symbiotic models

lower upper implicit schemes with multiple grids for the euler equations on montre qu une methode de surrelaxation successive pour la resolution du schema implicite non factorise est equivalente a une forme modifiee du schema implicite inferieur superieur

two constructions of affine lie algebra representations and boson fermion correspondence in quantum field theory we establish an isomorphism between the vertex and spinor representations of affine lie algebras for types dl 1 and dl 1 2 we also study decomposition of spinor representations using the infinite family of casimir operators and prove that they are either irreducible or have two irreducible components we show that the vertex and spinor constructions of the representations can be reformulated in the language of two dimensional quantum field theory in this physical context the two constructions yield the generalized sine gordon and thirring models respectively already in renormalized form the isomorphism of representations implies an equivalence of these two models which is known in quantum field theory as the boson fermion correspondence

vertex operator algebras generalized doubles and dual pairs let v be a simple vertex operator algebra and g a finite automorphism group then there is a natural right g action on the set of all inequivalent irreducible v modules let cal s be a finite set of inequivalent irreducible v modules which is closed under the action of g there is a finite dimensional semisimple associative algebra a alpha g cal s for a suitable 2 cocycle alpha naturally determined by the g action on cal s such that a alpha g cal s and the vertex operator algebra v g form a dual pair on the sum of v modules in cal s in the sense of howe in particular every irreducible v module is completely reducible v g module

parallel processing scheme for the navier stokes equations part 1 scheme development using a lower and upper decomposition procedure an implicit parallel processing scheme for the compressible navier stokes equations is developed in this scheme the solution for a multidimensional problem is obtained by the superposition of two independent solution cycles because of the independence of these two solutions they can be performed on separate processors simultaneously to confirm the analytical developments numerical results are obtained using the proposed scheme and compared with other available solutions and experimental data a study of other characteristics of the proposed scheme such as stability symmetry preserving and effects of domain decomposition on convergence and stability is also conducted

g elliptic systems and the genus zero problem for m_ 24 toward the end of the 1970s j h conway and s p norton wrote a quite unique and influential paper 3 in which they produced incontrovertible evidence based partly on ideas of j mckay and j g thompson 13 that the fischer griess monster simple group m was intimately related to the modular function j x familiar from the theory of modular forms thus was so called moonshine brought into the world among other things it was conjectured that there is a natural infinite dimensional complex vector space v which carries a z grading into finite dimensional subspaces f v x e vx 0 v2 0 such that each vi is a cmmodule moreover the graded character chvt q j2n dimf tf of f should be the fourier expansion of j r namely q 196884 21 493 760 if the indeterminate q is interpreted as e for r in the upper half plane h there should in addition be an analogous interpretation for

calculus of twisted vertex operators starting from an arbitrary isometry of an arbitrary even lattice twisted and shifted vertex operators are introduced under commutators these operators provide realizations of twisted affine lie algebras this construction generalizing a number of known ones is based on a self contained calculus

a primitive variable method for the solution of three dimensional incompressible viscous flows abstract in this paper we present a new primitive variable method for the solution of the three dimensional incompressible reynolds averaged navier stokes equations in generalized curvilinear coordinates the governing equations are discretized on a non staggered grid and the discrete continuity equation is replaced by a discrete pressure poisson equation the discrete pressure equation is designed in such a way that i the compatibility condition for the poisson neumann problem is automatically satisfied and ii the discrete incompresibility constraint is satisfied to at least truncation error accuracy while the computed pressure is smooth the momentum equations are integrated in time using the four stage runge kutta algorithm while the pressure equation is solved using the point successive relaxation technique the method is applied to calculate the turbulent flow field over a ship model the computed results are in very good agreement with the experimental data

parallel processing scheme for the navier stokes equations part 2 parallel implementation parallel performance of two implicit schemes for solving the compressible navier stokes equations on two parallel computational platforms using the standard portable message passing interface is studied these two schemes are a lower upper cycle independent scheme developed by the authors and the symmetric successive overrelaxation scheme representative of cycle dependent schemes the parallel computational platforms used here are the lewis advanced cluster environment which is an example of a network of workstations and the ohio supercomputer cray t3d massive parallel computing environment two versions of the lower upper cycleindependent scheme are studied version i where one processor per block is used and version ii where two processors per block are used however only version i is possible with the symmetric successive overrelaxation scheme thecompetitivenessoftheworkstationclustertothecrayt3disdemonstrated moreover parallelperformance results indicate that version i of the lower upper cycle independent scheme is superior to version ii in the range of a moderate number of processors however in the future as the number of processors increases and the communication cost decreases this scheme will provide a means for using larger computational power relative to version i that would otherwise be idle

nonabelian orbifolds and the boson fermion correspondence for a positive integerl divisible by 8 there is a bosonic holomorphic vertex operator algebra voa v gamma l associated to the spin lattice l for a broad class of finite groupsg of automorphisms of v gamma l we prove the existence and uniqueness of irreducibleg twisted v gamma l modules and establish the modular invariance of the partition functionsz g h for commuting elements ing in particular for any finite group there are infinitely many holomorphic voas admittingg for which these properties hold the proof is facilitated by a boson fermion correspondence which gives a voa isomorphism between v gamma l and a certain fermionic construction and which extends work of frenkel and others

quasilinear parabolic and elliptic equations with nonlinear boundary conditions abstract this paper is concerned with a class of quasilinear parabolic and elliptic equations in a bounded domain with both dirichlet and nonlinear neumann boundary conditions the equation under consideration may be degenerate or singular depending on the property of the diffusion coefficient the consideration of the class of equations is motivated by some heat transfer problems where the heat capacity and thermal conductivity are both temperature dependent the aim of the paper is to show the existence and uniqueness of a global time dependent solution of the parabolic problem existence of maximal and minimal steady state solutions of the elliptic problem including conditions for the uniqueness of a solution and the asymptotic behavior of the time dependent solution in relation to the steady state solutions applications are given to some heat transfer problems and an extended logistic reaction diffusion equation

an orbifold theory of genus zero associated to the sporadic groupm24 let v gamma l be the self dual or holomorphic bosonic conformal field theory associated with the spin lattice l of rankl divisible by 24 in earlier work of the authors we showed how it is possible to establish the existence and uniqueness of irreducibleg twisted sectors for v gamma l for certain automorphismsg of v gamma l and to establish the modular invariance of the space of partition functionsz g h corresponding to commuting pairsg h of elements in certain groupsg of automorphisms of v gamma l in the present work we show that if we takel 24 andg the sporadic simple groupm24 then the corresponding orbifold has thegenus zero property that is eachz g h is either identically zero or ahauptmodul i e it generates the field of functions on the subgroup ofsl2 which fixesz g h which then necessarily has genus zero

positivity versus localization in degenerate diffusion equations on considere le probleme de cauchy u t u m f u 0 dans s r n o u x o u 0 x x r n ou m 1 n 1 et les fonctions f et u 0 satisfont les hypotheses 1 f c 1 o f o 0 2 u 0 est une fonction continue non negative definie sur r n a support borne

existence of positive solutions for elliptic systems degenerate and nondegenerate ecological models with homogeneous dirichlet conditions w o on dd the function s satisfies the conditions rl e c o oo q o and s o for s o problems of this nature are of interest in reaction diffusion processes in biology and chemistry for example the case for u urn m 1 or m e 0 1 for single parabolic equations i e u du f x u has been studied recently for porous medium analysis and population dynamics cf 2 7 15 18 191 as t cc these solutions tend to a solution of the corresponding elliptic scalar equation studies have also been carried out in these and other papers e g 3 4 16 171 with urn replaced by u satisfying the conditions described above in this article however the hypotheses on f are quite different from those in the papers mentioned above for example f is not necessarily lipschitz in u and may depend discontinuously on x thus even for the scalar case the results here are not covered by the other papers although there are some overlaps moreover our emphasis here is on degenerate systems section 3 and their applications section 4 these results are quite different and generalize the papers mentioned above to practical interesting cases other relevant results for the nondegenerate cases can be found in s 9 111 in section 2 we discuss some existence and uniqueness theorems for

study of the optimal harvesting control and the optimality system for an elliptic problem an optimal harvesting problem with a concave nonquadratic cost functional and a diffusive degenerate elliptic logistic state equation type is investigated under certain assumptions we prove the existence and uniqueness of an optimal control a characterization of the optimal control via the optimality system is also derived which leads to approximating the optimal control

shifted vertex operator algebras and g elliptic systems shifted vertex operator algebras and superalgebras are defined both in bosonic and in fermionic pictures their isomorphism boson fermion correspondence is shown partition functions of bosonic shifted vertex operator algebras are realized analytically and are interpreted as string path integrals over elliptic curves their modular properties follow and elliptic systems are constructed based on fermionic shifted vertex operator algebras

on quantum galois theory the goals of the present paper are to initiate a program to systematically study and rigorously establish what a physicist might refer to as the operator content of orbifold models to explain what this might mean and to clarify the title of the paper we will assume that the reader is familiar with the algebraic formulation of 2 dimensional cft in the guise of vertex operator algebras voa see b flm and dm for more information on this point in the paper dvvv several ideas are proposed concerning the structure of a holomorphic orbifold in other words if v is a holomorphic voa and if g is a finite group of automorphisms of v then the sub voa v g of g invariants is itself a voa and the subject of dvvv is very much concerned with speculation on the nature of the v modules it turns out to be more useful at least for purpose of inductive proofs to take v to be a simple voa we will then see that v g is also simple whenever g is a finite group of automorphisms of v one consequence of our main results is the following