a new super kp system and a characterization of the jacobians of arbitrary algebraic super curves a set of super commuting vector fields is defined on the super grassmannians a characterization of the jacobian varieties of super curves super schottky problem is established in the following manner every finite dimensional integral manifold of these vector fields has a canonical structure of the jacobian variety of an algebraic super curve and conversely the jacobian variety of an arbitrary algebraic super curve is obtained in this way the vector fields restricted on the super grassmannian of index 0 0 give a completely integrable system of partial super differential equations which gives a new supersymmetric generalization of the kp system thus every finite dimensional solution of this new system gives rise to a jacobian variety of an algebraic super curve the correspondence between this super grassmannian and the group of monic super pseudo differential operators of order zero the super sato correspondence is also established table of

exit problems associated with affine reflection groups we obtain a formula for the distribution of the first exit time of brownian motion from the alcove of an affine weyl group in most cases the formula is expressed compactly in terms of pfaffians expected exit times are derived in the type widetilde a case the results extend to other markov processes we also give formulas for the real eigenfunctions of the dirichlet and neumann laplacians on alcoves observing that the hot spots conjecture of j rauch is true for alcoves

a solution to an open problem for wave equations with generalized wentzell boundary conditions in this paper we solve an open problem put forward by a favini g r goldstein j a goldstein and s romanelli concerning the mixed problem for wave equations with generalized wentzell boundary conditions as a consequence we also develop the previous wellposedness result regarding the mixed problem for heat equations with generalized wentzell boundary conditions

hua operators poisson transform and relative discrete series on line bundles over bounded symmetric domains let d g k be a bounded symmetric domain and s k l be its shilov boundary we consider the action of g with weight nu in mathbb z on functions on d viewed as sections the line bundle and the corresponding eigenspace of g invariant di erential operators the poisson transform maps hyperfunctions on the s to the eigenspaces we characterize the image in terms of hua operators on the sections of the line bundle for some special parameter the poisson transform is of szego type mapping into the relative discrete series we compute the corresponding elements in the discrete series

shimura invariant differential operators and their eigenvalues let bar d be the covariant cauchy riemann operator and mathcal d the covariant holomorphic differential operator on a line bundle over a hermitian symmetric space g k we study the shimura invariant differential operators defined via bar d and mathcal d we find the eigenvalues of a family of the shimura operators and of the generators

classes of representable disjoint np pairs for a propositional proof system p we introduce the complexity class dnpp p of all disjoint np pairs for which the disjointness of the pair is efficiently provable in the proof system p we exhibit structural properties of proof systems which make canonical np pairs associated with these proof systems hard or complete for dnpp p moreover we demonstrate that non equivalent proof systems can have equivalent canonical pairs and that depending on the properties of the proof systems different scenarios for dnpp p and the reductions between the canonical pairs exist

koszul algebras of invariants the notion of a koszul algebra is recalled in section 1 the cases of o n so n and u n 2 are dealt with in s 91 for these groups a and its quadratic dual have an interesting interpretation in terms of the representation theory of spin n 1 and su n 1 moreover a appears in a natural way in differential geometry in the orthogonal resp unitary case a is the universal algebra of invariant differential operators acting on differential forms on a riemannian resp kahlerian manifold and was implicitly presented in 16 resp 17 this aspect is developed in 9 the last section is dedicated to the proof of the following fact suppose g is an arbitrary subgroup of gl n c and let a oka0 ak denote the grading of a xn end a c here and in the sequel jc end end and horn horn also let d a and d a a be respectively the absolute global dimension of a and the a relative global dimension of a in the sense of lo see sect 1

global properties of supermanifolds we construct new examples of supermanifolds and determine the vector bundle structure of the supermanifolds commonly used in physics we show that any supermanifold admits a foliation whose leaves are locally tangent to the soul directions in the coordinate charts and which is one of a nested sequence of foliations we point out that the existence of these foliations implies restrictions on the possible topologies of supermanifolds for example a compact supermanifold with a single even dimension must have vanishing euler characteristic we also show that a globally defined superfield on a nice compact supermanifold must be constant along the leaves of the foliations by this mechanism the global topology of a supermanifold can be used to impose physically interesting constraints on superfields as an example we exhibit a supermanifold which has the local geometry of flat superspace but is such that all globally defined superfields are chiral

super riemann surfaces uniformization and teichmuller theory teichmuller theory for super riemann surfaces is rigorously developed using the supermanifold theory of rogers in the case of trivial topology in the soul directions relevant for superstring applications the following results are proven the super teichmuller space is a complex super orbifold whose body is the ordinary teichmuller space of the associated riemann surfaces with spin structure for genusg 1 it has 3g 3 complex even and 2g 2 complex odd dimensions the super modular group which reduces super teichmuller space to super moduli space is the ordinary modular group there are no new discrete modular transformations in the odd directions the boundary of super teichmuller space contains not only super riemann surfaces with pinched bodies but rogers supermanifolds having nontrivial topology in the odd dimensions as well we also prove the uniformization theorem for super riemann surfaces and discuss their representation by discrete supergroups of fuchsian and schottky type and by beltrami differentials finally we present partial results for the more difficult problem of classifying super riemann surfaces of arbitrary topology

harmonic analysis for spinor fields in complex hyperbolic spaces abstract l2 harmonic analysis for dirac spinors on the complex hyperbolic space hn c is developed the spinor spherical functions are calculated in terms of jacobi functions the plancherel and paley wiener theorems for the spherical transform are obtained by reduction to jacobi analysis we demonstrate analytically the existence of harmonic l2 spinors in the case of n even the action of the invariant differential operators on the poisson transforms is given explicitly

a nonterminating 8 φ 7 summation for the root system c r using multiple q integrals and a determinant evaluation we establish a nonterminating 8 7 summation for the root system cr we also give some important specializations explicitly

infinite horizon backward stochastic differential equations and elliptic equations in hilbert spaces solutions of semilinear elliptic differential equations in infinite dimensional spaces are obtained by means of forward and backward infinite dimensional stochastic evolution equations the backward equation is considered on an infinite time horizon and a suitable growth condition replaces the final condition elliptic equations are intended in a mild sense suitable also for applications to optimal control we finally notice that due to the lack of smoothing properties the elliptic partial differential equation considered here could not be treated by analytic methods

characterization of jacobian varieties in terms of soliton equations pour dans le demi espace superieur de siegel h g soit x c g z g z g la variete abelienne principalement polarisee correspondante et soit z z m e z gexp 2 i t mz i t m m la fonction theta de riemann pour x les deux conditions a et b pour x sont equivalentes a 1 il existe des vecteurs a 1 a 2 a 3 c g a 1 0 et une forme quadratique q t i j 1 3 q ij t i t j q ij c tel que pour c g t t exp q t t 1 a 1 t 2 a 2 t 3 a 3 donne une solution a l equation de kadomtsev petviashvili sous la forme d hirota d 1 4 3d 2 2 4d 1 d 3 0 2 le diviseur de x est irreductible b x est isomorphe a la variete jacobienne d une courbe lisse complete de genre g sur c

double centralizing theorems for the alternating groups let v n be the n fold tensor product of a vector space v following i schur we consider the action of the symmetric group sn on v n by permuting coordinates in the super z2 graded case v v0 v1 a sign is added these actions give rise to the corresponding schur algebras s sn v here s sn v is compared with s an v the schur algebra corresponding to the alternating subgroup an sn while in the classical signless case these two schur algebras are the same for n large enough it is proved that in the super case where dim v0 dim v1 s an v is isomorphic to the cross product algebra s an v s sn v z2

modular invariant of quantum tori the quantum modular invariant j qt of 2r is defined as a discontin uous pgl2 z invariant multi valued map using the distance to the nearest integer function k k for 2 q it is shown that j qt 1 and for quadratic irrationalities pari gp experiments suggest that j qt is a finite set in the case of the golden mean we produce explicit formulas involving weighted versions of the rogers ramanujan functions for the experimental supremum and infimum we then define a universal modular invariant j a mod c as a continuous and single valued map of ultrasolenoids such that 1 the classical modular invariant is a quotient of the re striction of j to a subsolenoid mod cl a mod fibering over the classical moduli space of elliptic curves and 2 the quantum modular invariant is a quotient of the restric tion of j to a subsolenoid mod qt a mod fibering over the moduli space of elliptic curves equipped with a kronecker foliation

shock fitted multidomain solution of supersonic flows abstract shock fitting is presented as a way to compute shocks with spectral methods with fitting spectral approximation is performed on smooth portions of the flow and a precise description of a discontinuous shock is possible coupled with spectral domain decomposition one has the ability to resolve efficiently and without stretching transformations boundary layers and other regions in the flow where increased local resolution is needed a supersonic blunt body problem is solved to provide an example of the use of the approach comparisons between computations and experimental measurements are made for body surface quantities shock shape and body normal direction profiles

coding the principal character formula for affine kac moody lie algebras in this paper an algorithm for computing the principal character for affine lie algebras is discussed and presented the principal characters discovered using this program are given and or proven results include level 2 and 3 character formulas in a2n 1 2 and the sole existence of the rogers ramanujan products in a1 1 a2 1 a2 2 c3 1 f4 1 g2 1 a7 2

asymptotic behavior of matrix coefficients of admissible representations introduction 869 1 generalities on reductive groups 873 2 the infinitesimal cartan decomposition 876 3 the t radial components 880 4 differential equations satisfied by sphereical functions 885 5 asymptotic behavior of spherical functions on a 888 6 asymptotic behavior of spherical functions along the walls of a 892 7 leading characters and growth estimates on the group 898 8 admissible representations and their matrix coefficients 906 appendix 917

branching problems in reproducing kernel spaces for a semisimple lie group g satisfying the equal rank condition the most basic family of unitary irreducible representations is the discrete series found by harish chandra in our work here we study some of the branching laws for discrete series when restricted to a subgroup h of the same type by combining classical results with recent work of kobayashi in particular we prove discrete decomposability under harish chandra s condition of cusp form on the reproducing kernel we show a relation between discrete decomposability and representing certain intertwining operators in terms of differential operators

invariant measures and regularity properties of perturbed ornstein uhlenbeck semigroups abstract this paper deals with perturbations of the ornstein uhlenbeck operator on l 2 spaces with respect to a gaussian measure we perturb the generator of the ornstein uhlenbeck semigroup by a certain unbounded non linear drift and show various properties of the perturbed semigroup such as compactness and positivity strong feller property existence and uniqueness of an invariant measure are discussed as well

wiener tauberian type theorems for radial sections of homogenous vector bundles on certain rank one riemannian symmetric spaces of noncompact type we will show that an uniform treatment yields wiener tauberian type results for various banach algebras and modules consisting of radial sections of some homogenous vector bundles on rank one riemannian symmetric spaces g k of noncompact type one example of such a vector bundle is the spinor bundle the algebras and modules we consider are natural generalizations of the commutative banach algebra of integrable radial functions on g k the first set of them are beurling algebras with analytic weights while the second set arises due to kunze stein phenomenon for noncompact semisimple lie groups

the plancherel formula for spherical functions with a one dimensional k type on a simply connected simple lie group of hermitian type abstract we generalize the harish chandra inversion formula for the spherical transform on a riemannian symmetric space to homogeneous line bundles on a hermitian symmetric space we determine the plancherel measure explicitly

super w 3 ward identities and differential equations of correlation functions on a supertorus using the operator formalism ward identities are derived for super w3 conformal field theories on a supertorus differential equations of correlation functions on the supertorus are also derived by using the ward identities and null vectors

lattices on simplicial partitions which are not simply connected in this paper d 1 pencil lattices on simplicial partitions in r d which are not simply connected are studied it is shown how the fact that a partition is not simply connected can be used to increase the flexibility of a lattice a local modification algorithm is developed also to deal with slight partition topology changes that may appear afterwards a lattice has already been constructed

cohomological structure in soliton equations and jacobian varieties on etudie la structure des orbites du systeme dynamique definie par la hierarchie kp totale on montre que chaque orbite est localement isomorphe a un certain groupe de cohomologie associe a une algebre commutative le systeme dynamique kp restreint a chaque orbite determine un systeme dynamique de mouvements lineaires sur lui par rapport a la structure lineaire du groupe de cohomologie

n 2 superprojective transformations and the nilpotent invariant the nilpotent quantity that is invariant under the n 2 superprojective transformations is constructed also commented on is the parametrization of such transformations

nearly holomorphic sections on compact hermitian symmetric spaces abstract let x be a kahler manifold and e be a hermitian vector bundle on x we investigate the space n x e of nearly holomorphic sections in e which generalizes the notion of nearly holomorphic functions introduced by shimura if x u k is a compact hermitian symmetric space and e is u homogeneous it turns out that n x e coincides with the space of u finite vectors in c x e and we obtain new results on the u type decomposition of the hilbert space of square integrable sections as an application we determine this decomposition for the holomorphic tangent bundle of x

subconvex bounds for hecke maass forms on compact arithmetic quotients of semisimple lie groups let h be a semisimple algebraic group k a maximal compact subgroup of g h mathbb r and gamma subset h mathbb q a congruence arithmetic subgroup in this paper we generalize existing subconvex bounds for hecke maass forms on the locally symmetric space gamma backslash g k to corresponding bounds on the arithmetic quotient gamma backslash g for cocompact lattices using the spectral function of an elliptic operator the bounds obtained extend known subconvex bounds for automorphic forms to non trivial k types yielding such bounds for new classes of automorphic representations they constitute subconvex bounds for eigenfunctions on compact manifolds with both positive and negative sectional curvature we also obtain new subconvex bounds for holomorphic modular forms in the weight aspect

odd supersymmetric kronecker elliptic function and yang baxter equations we introduce an odd supersymmetric version of the kronecker elliptic function it satisfies the genus one fay identity and supersymmetric version of the heat equation as an application we construct odd supersymmetric extensions of the elliptic r matrices which satisfy the classical and the associative yang baxter equations

invariant syzygies and semisimple groups the purpose of this paper is to explore some intriguing connections between lie theory relative homological algebra invariant theory and representations of finite dimensional algebras in the process some results of hilbert 20 cartan and eilenberg 7 hochschild 21 gelfand 171 and others are generalized and a question of zl is partly answered in theorem 1 5 duflo seems to have stronger unpublished results on this problem sections 1 to 3 take place in a fairly general setting whereas section 4 focuses on semisimple lie groups the problem considered here goes back in some sense to hilbert 20 this paper was published 102 years ago to explain this let me start by singling out two out of many fundamental contributions of the great mathematician the first one is invariant theory namely the study of the algebra sv n consisting of those polynomial functions on a finite dimensional vector space v which are invariant under the action of a group h of linear transformations the second one is the so called syzygy theorem which asserts in today s language that the global dimension of the full symmetric algebra sv is dim v this prompts the question is there an algebra d attached to v as naturally as sv is on which h acts by automorphisms such that the global dimension of the algebra b dh of invariants is dim v the most natural candidate is

super beltrami differentials superconformal structures on a given 2 2 dim supermanifold give rise to the notion of super riemann surfaces srs s we investigate super beltrami coefficients which parametrize almost superconformal structures on the supermanifold the integrability condition of the structure reduces to a simple relation among the coefficients taking this into account we can write the super beltrami equations in a transparent form then an analysis of these equations enables us to prove the possibility of the special gauge choice of the wess zumino type for the super beltrami differentials this gauge choice simplifies the description of the deformations of srs s considerably and its existence will afford a better understanding of the structure of the super teichmuller space

generation of localization in a discrete chain with periodic boundary conditions numerical and analytical results we study the generation of localization in a discrete chain composed of n subsystems and periodic boundary conditions strongly localized motions are studied that is time periodic motions where nearly all of the energy is spatially confined to a single subsystem for varying n numerical results indicate that the strongly localized solutions are generated through a bifurcation from an in phase spatially extended solution however in the limit as n rightarrow infty the bifurcation point tends to infinity and a smooth transition from localization to nonlocalization occurs we then present an analytic technique to complement the numerical results it is based on the matching local asymptotic expansions of a solution branch using pade approximants this leads to global analytic representations of the considered solutions valid over the entire range of the control parameter

a multivariate version of the disk convolution abstract we present an explicit product formula for the spherical functions of the compact gelfand pairs g k 1 su p q su p su q with p 2 q which can be considered as the elementary spherical functions of one dimensional k type for the hermitian symmetric spaces g k with k s u p u q due to results of heckman they can be expressed in terms of heckman opdam jacobi polynomials of type bc q with specific half integer multiplicities by analytic continuation with respect to the multiplicity parameters we obtain positive product formulas for the extensions of these spherical functions as well as associated compact and commutative hypergroup structures parametrized by real p 2 q 1 we also obtain explicit product formulas for the involved continuous two parameter family of heckman opdam jacobi polynomials with regular but not necessarily positive multiplicities the results of this paper extend well known results for the disk convolutions for q 1 to higher rank

matrix elements of irreducible representations of su n 1 x su n 1 and multivariable matrix valued orthogonal polynomials abstract in part 1 we study the spherical functions on compact symmetric pairs of arbitrary rank under a suitable multiplicity freeness assumption and additional conditions on the branching rules the spherical functions are taking values in the spaces of linear operators of a finite dimensional representation of the subgroup so the spherical functions are matrix valued under these assumptions these functions can be described in terms of matrix valued orthogonal polynomials in several variables where the number of variables is the rank of the compact symmetric pair moreover these polynomials are uniquely determined as simultaneous eigenfunctions of a commutative algebra of differential operators in part 2 we verify that the group case su n 1 meets all the conditions that we impose in part 1 for any k n 0 we obtain families of orthogonal polynomials in n variables with values in the n n matrices where n n k k the case k 0 leads to the classical heckman opdam polynomials of type a n with geometric parameter for k 1 we obtain the most complete results in this case we give an explicit expression of the matrix weight which we show to be irreducible whenever n 2 we also give explicit expressions of the spherical functions that determine the matrix weight for k 1 these expressions are used to calculate the spherical functions that determine the matrix weight for general k up to invertible upper triangular matrices this generalizes and gives a new proof of a formula originally obtained by koornwinder for the case n 1 the commuting family of differential operators that have the matrix valued polynomials as simultaneous eigenfunctions contains an element of order one we give explicit formulas for differential operators of order one and two for n k equal to 2 1 and 3 1

n extended superelliptic integrable systems a supersymmetric extension for an arbitrary number of odd parameters of the stationary kdv equation is studied we call this an n extended super kdv it is shown that it is related to superelliptic curves and thereafter the complete ring of superdifferential operators commuting with the associated schrodinger operator is constructed

supertori are algebraic curves super riemann surfaces of genus 1 with arbitrary spin structures are shown to be the sets of zeroes of certain polynomial equations in projective superspace we conjecture that the same is true for arbitrary genus properties of superelliptic functions and super theta functions are discussed the boundary of the genus 1 super moduli space is determined

plancherel formula for berezin deformation of l 2 on riemannian symmetric space consider natural representations of the pseudounitary group u p q in the space of holomorphic functions on the cartan domain hermitian symmetric space u p q u p u q berezin representations of o p q are the restrictions of such representations to the subgroup o p q we obtain the explicit plancherel formula for the berezin representations the support of the plancherel measure is a union of many series of representations the density of the plancherel measure on each piece of the support is an explicit product of functions we also show that the berezin representations give an interpolation between l2 on noncompact symmetric space o p q o p o q and l2 on compact symmetric space o p q o p o q

on the semigroup nature of superconformal symmetry a semigroup of n 1 superconformal transformations is introduced and analyzed noninvertible ones can describe transitions from body to soul and form a proper ideal containing a set of nilpotent transformations the projective superspace is also considered transformations twisting the parity of a tangent space are brought in they can be a nonsuperconformal square root of noninvertible superconformal transformations and the analogs of the poincare metric and conformal invariance are suggested for them

new combinatorial interpretations of ramanujan s partition congruences mod 5 7 and 11 soit p n le nombre de partitions non restreintes de n on donne de nouvelles interpretations combinatoires des congruences p 5n 4 p 7n 5 et p 11n 6 0 mod 5 7 et 11 respectivement

standardized pseudospectral formulation of the inviscid supsersonic blunt body problem a highly accurate pseudospectral numerical approximation to the generalized coordinate nonconservative form of the euler equations is implemented for supersonic flow over an axisymmetric blunt body geometry shock fitting is employed to maintain global accuracy and minimize the corrupting influence of numerical viscosity the variables in the euler equations as well as the physical grid coordinates are collocated via lagrange interpolating polynomials and the problem is then cast in the standard form of a large system of ordinary differential equations dx d q x which can be solved using standard solution techniques that do not require an explicit criteria for the minimum time step code verification is performed by demonstrating through a series of grid refinement tests that the error in the approximation to a taylor maccoll solution converges to 10 12 grid refinement tests for flow over a blunt body show convergence of the numerical error also to 10 12 the code is validated for supersonic flow over a blunt body by comparison with the modified newtonian approximation for the surface pressure distribution and empirical predictions for the shock shape the ability of the method to capture unsteady flow phenomena is demonstrated on the problem of a planar acoustic wave interacting with an attached shock

eigenforms of the laplacian on real and complex hyperbolic spaces on decrit l espace total des solutions de l equation c ou est une p forme sur un espace x hyperbolique reel ou complexe a n dimensions et c une constante complexe

boundary value problems for various boundaries of hermitian symmetric spaces abstract the image of the poisson transform on a principal series representations on a boundary component of a hermitian symmetric space is considered we prove that the image is characterized by a covariant differential operator on a homogeneous line bundle on the symmetric space

a de giorgi nash type theorem for time fractional diffusion equations we study the regularity of weak solutions to linear time fractional diffusion equations in divergence form of arbitrary time order alpha in 0 1 the coefficients are merely assumed to be bounded and measurable and they satisfy a uniform parabolicity condition our main result is a de giorgi nash type theorem which gives an interior holder estimate for bounded weak solutions in terms of the data and the l infty bound of the solution the proof relies on new a priori estimates for time fractional problems and uses de giorgi s technique and the method of non local growth lemmas which has been introduced recently in the context of nonlocal elliptic equations involving operators like the fractional laplacian

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

spectral methods for the euler equations the blunt body problem revisited we solve the blunt body problem using shock fitting and a chehyshev spectral collocation method careful attention is paid to the boundary and shock acceleration equations

a karhunen loeve least squares technique for optimization of geometry of a blunt body in supersonic flow a novel karhunen loeve kl least squares model for the supersonic flow of an inviscid calorically perfect ideal gas about an axisymmetric blunt body employing shock fitting is developed the kl least squares model is used to accurately select an optimal configuration which minimizes drag accuracy and efficiency of the kl method is compared to a pseudospectral method employing global lagrange interpolating polynomials kl modes are derived from pseudospectral solutions at mach 3 5 from a uniform sampling of the design space and subsequently employed as the trial functions for a least squares method of weighted residuals results are presented showing the high accuracy of the method with less than 10 kl modes close agreement is found between the optimal geometry found using the kl model to that found from the pseudospectral solver not including the cost of sampling the design space and building the kl model the kl least squares method requires less than half the central processing unit time as the pseudospectral method to achieve the same level of accuracy a decrease in computational cost of several orders of magnitude as reported in the literature when comparing the kl method against discrete solvers is shown not to hold for the current problem the efficiency is lost because the nature of the nonlinearity renders a priori evaluation of certain necessary integrals impossible requiring as a consequence many costly reevaluations of the integrals

morita equivalence of noncommutative supertori in this paper we study the extension of morita equivalence of noncommutative tori to the supersymmetric case the structure of the symmetry group yielding morita equivalence appears to be intact but its parameter field becomes supersymmetrized having both body and soul parts our result is mainly in the two dimensional case in which noncommutative supertori have been constructed recently the group so 2 2 vz0 where vz0 denotes grassmann even number whose body part belongs to z yields morita equivalent noncommutative supertori in two dimensions

some inequalities for the q beta and the q gamma functions via some q integral inequalities some new inequalities for the q gamma the q beta and the q analogue of the psi functions are established via some q integral inequalities

the x ray transform and its inversion for the series expansion basis functions in three dimensional tomography a formula for the three dimensional x ray transform and an expression for its inversion have been derived the spherical harmonics and the rotation matrices in terms of euler angles are used in the generalized fourier series expansion some properties of the transformed fourier components are discussed

n 2 supertori and their representation as algebraic curves n 2 supertori n 2 super riemann surfaces of genus 1 are classified according to their superconformal equivalence classes a detailed description of the corresponding supermoduli space is based on this classification superelliptic functions are constructed and used for representing the supertori as algebraic varieties in projective superspace the boundary of n 2 genus 1 supermoduli space is discussed

the geometry of the super kp flows a supersymmetric generalization of the krichever map is used to construct algebro geometric solutions to the various super kadomtsev petviashvili skp hierarchies the geometric data required consist of a suitable algebraic supercurve of genusg generallynot a super riemann surface with a distinguished point and local coordinates z there and a generic line bundle of degreeg 1 with a local trivialization near the point the resulting solutions to the manin radul skp system describe coupled deformations of the line bundle and the supercurve itself in contrast to the ordinary kp system which deforms line bundles but not curves two new skp systems are introduced an integrable jacobian system whose solutions describe genuine jacobian flows deforming the bundle but not the curve and a nonintegrable maximal system describing independent deformations of bundle and curve the kac van de leur skp system describes the same deformations as the maximal system but in a different parametrization

l2 concrete spectral analysis of the invariant laplacianδαβin the unit complex ballbn for every fixed real number related to the continuous spectrum of the invariant laplacians 4 1 z 2 i j 1n ij zizj 2 zj zj j 1nzj zj j 1nzj zj inbn we characterize the eigenfunctions of that are poisson integrals ofl2 functions on the boundary ofbn these eigenfunctions occurred in the weighted plancherel formula of the unit complex ball see zhang studia math 102 2 1992 for the weighted plancherel formula in the ball the obtained characterization generalizes our announced result in boussejra and intissar c r acad sci 315 1992 1353 1357 for the bergman laplacian 00of the unit complex ball to the laplacians for arbitrary inr

an improved sectional anosov closing lemma we prove that all nonwandering points of a sectional anosov flow on a compact 3 manifold can be approximated by periodic points or by points for which the omega limit set is a singularity this improves the closing lemma in morales mich math j 56 1 29 53 2008 we also describe a sectional anosov flow for which the recurrent points are not dense in the nonwandering set

n point pade approximants to real valued stieltjes series with nonzero radii of convergence abstract by employing special continued fractions to two stieltjes series with nonzero radii of convergence we extend the inequalities for one point pade approximants reported by baker 1975 corollory 17 1 to the case of two point pade approximants we prove that some convergents of the continued fractions form a monotone sequences of upper and lower bounds converging uniformly to stieltjes function x1 x on compact subsets of r where r is a radius of convergence of an expansion of x f1 x at x 0 for an illustration of theoretical results we provide nontrivial numerical examples as an application to real physical problems second order pade approximants bounds on the effective conductivity of a square array of cylinders are evaluated

graded manifolds supermanifolds and infinite dimensional grassmann algebras a new approach to superdifferentiable functions of grassmann variables is developed which avoids ambiguities in odd derivatives this is used to give an improved definition of supermanifold over a finite dimensional grassmann algebra a natural embedding of super manifolds over grassmann algebras with increasing number l of generators is developed and thus a limit asl tends to infinity is possible a correspondence between graded manifolds and supermanifolds is constructed extending results of 5 and 8

spectral methods for the euler equations ii chebyshev methods and shock fitting on exprime chaque composante de la vitesse dans les equations d euler par une somme de polynomes de tchebycheff qui constitue une fonction d interpolation on utilise les expressions spectrales ainsi obtenues pour calculer plusieurs ecoulements gazeux bidimensionnels par la methode d ajustement d ondes de choc selon cette methode les conditions initiales correspondent a une onde de choc plane normale a un ecoulement supersonique et on determine la forme veritable de l onde a l aide des formules de rankine hugoniot qui expriment les conditions aux limites

spectral methods for hyperbolic problems we review the current state of fourier and chebyshev collocation methods for the solution of hyperbolic problems with an eye to basic questions of accuracy and stability of the numerical approximations throughout the discussion we emphasize recent developments in the area such as spectral penalty methods the use of filters the resolution of the gibbs phenomenon and issues related to the solution of nonlinear conservations laws such as conservation and convergence we also include a brief discussion on the formulation of multi domain methods for hyperbolic problems and conclude with a few examples of the application of pseudospectral collocation methods for solving nontrivial systems of conservation laws

on modular homology in the boolean algebra iii abstract let be a set ra ring of characteristicp 0 and denote bymkther module withk element subsets of as basis theset inclusion map mk mk 1is the homomorphism which associates to ak element subset the sum 1 2 kof all its k 1 element subsets i in this paper we study the chain formula arising from we introduce the notion ofp exactness for a sequence if is infinite we show that isp exact for all prime characteristicsp 0 this result can be extended to various submodules and quotient modules and we give general constructions arising from permutation groups with a finitary section two particular applications are the following the orbit module sequence of such a permutation group on isp exact for every primep and we give a formula for thep rank of the orbit inclusion matrix if the group has finitely many orbits onk element subsets

on accuracy of adaptive grid methods for captured shocks the accuracy of two grid adaptation strategies grid redistribution and local grid refinement is examined by solving the 2 d euler equations for the supersonic steady flow around a cylinder second and fourth order linear finite difference shock capturing schemes based on the lax friedrichs flux splitting are used to discretize the governing equations the grid refinement study shows that for the second order scheme neither grid adaptation strategy improves the numerical solution accuracy compared to that calculated on a uniform grid with the same number of grid points for the fourth order scheme the dominant first order error component is reduced by the grid adaptation while the design order error component drastically increases because of the grid nonuniformity as a result both grid adaptation techniques improve the numerical solution accuracy only on the coarsest mesh or on very fine grids that are seldom found in practical applications because of the computational cost involved similar error behavior has been obtained for the pressure integral across the shock a simple analysis shows that both grid adaptation strategies are not without penalties in the numerical solution accuracy based on these results a new grid adaptation criterion for captured shocks is proposed