diffusion approximation and computation of the critical size this paper is devoted to the mathematical definition of the extrapolation length which appears in the diffusion approximation to obtain this result we describe the spectral properties of the transport equation and we show how the diffusion approximation is related to the computation of the critical size the paper also contains some simple numerical examples and some new results for the milne problem introduction the computation of the critical size and the diffusion approximation for the transport equation have been closely related and this is due to the following facts first the computation of the critical size is much easier for the diffusion approximation than for the original transport equation second for the critical size one can consider a host media x nxq with x0 given and 17 a positive number the problem of the critical size is then reduced to the computation of the parameter zj it turns out that when the transport operator is almost conservative the critical value of the parameter 17 is large and it is exactly for this range of value that the diffusion approximation is accurate on the other hand the physical boundary condition for the diffusion approxi mation is of the form

computing finite galois groups arising from automorphic forms abstract we study modulo p reduction of compatible systems of p adic representations of the absolute galois group of q arising from an algebraic automorphic representation in particular we prove that there is a field extension of q with the galois group g 2 p ramified at 5 and p only for a set of primes p of density one

even sectors of lie superalgebras as locally convex lie algebras let g be a finite dimensional lie superalgebra over a graded commutative local augmented arens michael ground algebra a lie group is associated with a number of pleasant properties to the even sector g0 viewed as an ordinary complete locally convex lie algebra which is in general infinite dimensional

fractional diffusion limit for collisional kinetic equations this paper is devoted to diffusion limits of linear boltzmann equations when the equilibrium distribution function is a maxwellian distribution it is well known that for an appropriate time scale the small mean free path limit gives rise to a diffusion equation in this paper we consider situations in which the equilibrium distribution function is a heavy tailed distribution with infinite variance we then show that for an appropriate time scale the small mean free path limit gives rise to a fractional diffusion equation

examples of braided groups and braided matrices matrix braided groups are developed as an analog of the coordinate functions on a group or supergroup the 1 in the super case is replaced by braid statistics there are braided group analogs of all the classical simple lie groups as well as braided matrix groups and braided matrices b r for every regular solution r of the quantum yang baxter equations a direct verification of b r is provided and some of the simplest examples are computed in detail

geometric families of 4 dimensional galois representations with generically large images we study compatible families of four dimensional galois representations constructed in the etale cohomology of a smooth projective variety we prove a theorem asserting that the images will be generically large if certain conditions are satisfied we only consider representations with coefficients in an imaginary quadratic field we apply our result to an example constructed by jasper scholten a non selfdual 4 dimensional galois representation www math uiuc edu algebraic number theory 0183 1999 obtaining a family of linear groups and one of unitary groups as galois groups over mathbb q

superspaces and supersymmetries a theory of graded banach modules over a banach grassmann algebra is developed and applied to differential geometry of super manifolds the explicit structure of superspaces carrying poincare supersymmetry and extended supersymmetry including central charges is described

computations of siegel modular forms of genus two we explain the basic notions and theorems for doing computations in the theory of siegel modular forms of degree two on the full modular group and of even weight this synopsis concludes with a handy and computationally realistic algorithm for tabulating the fourier coefficients of such forms and the euler factors of their spinor zeta functions in the second part of this paper we present and discuss some of the results of actual computations which we performed following this algorithm we point out two theoretically striking phenomena that are implied by the results of these computations

on the images of the galois representations attached to genus 2 siegel modular forms we address the problem of the determination of the images of the galois representations attached to genus 2 siegel cusp forms of level 1 having multiplicity one these representations are symplectic we prove that the images are as large as possible for almost every prime if the siegel cusp form is not a maass spezialform and verifies two easy to check conditions mathematics subject classification 11f80 11f46

an asymptotic preserving scheme for linear kinetic equation with fractional diffusion limit we present a new asymptotic preserving scheme for the linear boltzmann equation which under appropriate scaling leads to a fractional diffusion limit our scheme rests on novel micro macro decomposition to the distribution function which splits the original kinetic equation following a reshuffled hilbert expansion as opposed to classical diffusion limit a major difficulty comes from the fat tail in the equilibrium which makes the truncation in velocity space depending on the small parameter our idea is while solving the macro micro part in a truncated velocity domain truncation only depends on numerical accuracy to incorporate an integrated tail over the velocity space that is beyond the truncation and its major component can be precomputed once with any accuracy such an addition is essential to drive the solution to the correct asymptotic limit numerical experiments validate its efficiency in both kinetic and fractional diffusive regimes

a hybrid kinetic fluid model for solving the vlasov bgk equation our purpose is to derive a model for charged particles which combines a kinetic description of the fast particles with a fluid description of the slow ones in a previous paper a similar model was derived from a kinetic bgk equation that uses a constant relaxation time and does not include the effect of an electric field in this paper we consider a more general kinetic equation including an electric field and a varying relaxation time fast particles will be described through a collisional kinetic equation of vlasov bgk type while thermal particles will be modeled by a hydrodynamic model then we construct a numerical scheme for this model and validate the approach by presenting various numerical tests

potential automorphy and change of weight we prove an automorphy lifting theorem for l adic representations where we impose a new condition at l which we call potentential diagonalizability this result allows for change of weight and seems to be substantially more exible than previous theorems along the same lines we derive several applications for instance we show that any irreducible totally odd essentially self dual regular weakly compatible system of l adic representations of the absolute galois group of a totally real eld is potentially automorphic and hence is pure and its l function has meromorphic continuation to the whole complex plane and satises the expected functional equation

anomalous diffusion limit induced on a kinetic equation using a compactness argument based on the velocity averaging lemma of golse et al it is shown that the limiting behavior of a kinetic linearized bgk gas model confined between two plates with maxwell boundary conditions when the distance between the plates goes to zero under a suitable anomalous scaling is diffusive we do not require the use of central limit theorems as in the method of borgers et al

soul expansion of g superfunctions supersmooth or g superfunctions with coefficients in the banach grassmann rogers algebra b are described in terms of the soul expansion and the notion of pringsheim regular real function

how different are the supermanifolds of rogers and dewitt a dewitt supermanifold always has the structure of a vector bundle over an ordinary spacetime manifold whereas a rogers supermanifold is not so restricted corresponding to the vector space fibers of the dewitt supermanifold a rogers supermanifold has a foliation by submanifolds or leaves parametrized by soul coordinates only we show that the universal covering space of any leaf always admits a flat metric if the covering space is complete in this metric it must in fact be a vector space we combine this result with known theorems about foliations to give conditions under which a compact rogers supermanifold with a single even dimension is necessarily a quotient space of flat superspace we also show that a supermanifold defined by a polynomial equation in flat superspace is always of the dewitt type finally we exhibit new supermanifold structures forr2 and the 2 torus which show that the foliation of a rogers supermanifold can be quite exotic

superfiber bundle structure of gauge theories with faddeev popov fields in this work the mathematical structure of principal superfiber bundle ps is used to give a geometrical description of gauge theories the base space of ps is an s4 2 supermanifold xs four commuting and two anticommuting variables and the structure group an sn 0 supergroup gs where n is the dimension of the gauge group for the classical theory the body of ps is the usual principal fiber bundle p of gauge theories gauge and faddeev popov fields arise as superfields components of the connections in ps in a local coordinate system brs becchi rouet and stora and anti brs transformations are gauge transformations in ps of parameters the ghost and antighost superfields respectively in the case of soul flat connections which are connections in ps coming from connections in p the brs and anti brs transformations are finite translations along the anticommuting directions of xs and generate an s0 2 supergroup