stochastic reaction diffusion equations on networks with dynamic time delayed boundary conditions abstract we consider a reaction diffusion equation on a network subjected to dynamic boundary conditions with time delayed behavior also allowing for multiplicative gaussian noise perturbations exploiting semigroup theory we rewrite the aforementioned stochastic problem as an abstract stochastic partial differential equation taking values in a suitable product hilbert space for which we prove the existence and uniqueness of a mild solution eventually a stochastic optimal control application is studied

on the admissibility of observation for perturbed c0 semigroups on banach spaces abstract this paper concerns linear infinite dimensional systems with unbounded observation operators we study the invariance of admissibility for observation operators under some unbounded perturbations of the generator we give also some relations between the extensions of such observation operators with respect to the original generator and the perturbed generator our results are applied to functional differential linear systems

fast generalized fourier transforms abstract let g be a f inite group then ls g the linear complexity of a suitable wedderburn transform corresponding to g is smaller than 2 g 2 we improve this trivial upper bound by showing that ls g is smaller than min s t l t g 7 q t g 3 2 where the minimum is taken over all towers t g n g n 1 g 0 1 of subgroups of g gn and where q t resp s t is the maximum resp sum of all indices gi 1 gi corresponding to t and l t n is the length of the tower a similar upper bound is valid for the linear complexity of the inverse of such a wedderburn transform for symmetric groups our technique yields the stronger estimate ls sn 0 sn log3 sn

fast fourier transforms for symmetric groups theory and implementation recently it has been proved that a fourier transform for the symmetric group s based on young s seminormal form can be evaluated in less than 0 5 n3 n2 n arithmetic operations we look at this algorithm in more detail and show that it allows an efficient software implementation using appropriate data structures we also describe a similarly efficient algorithm for the inverse fourier transform we compare the time and memory requirements of our program to those of other existing implementations

on invariance of p admissibility of control and observation operators to q type of perturbations of generator of c0 semigroup abstract in this paper it is proved in general setting that p admissibilities of control operators and observation operators are invariant to any q type of perturbations of generator of c 0 semigroups on banach space moreover some relations between the extensions of observation operators with respect to the original generator and the perturbed generator are also characterized so that the output can be expressed in the mild sense as an application the admissibility as well as the mild expressibility of output of a class of observation systems with time delay in state is deduced

fourier multipliers and periodic solutions of delay equations in banach spaces abstract in this paper we characterize the existence and uniqueness of periodic solutions of inhomogeneous abstract delay equations and establish maximal regularity results for strong solutions the conditions are obtained in terms of r boundedness of linear operators determined by the equations and l p fourier multipliers periodic mild solutions are also studied and characterized

efficient computation of the fourier transform on finite groups let g be a finite group f g c a function and p an ir reducible representation of g the fourier transform is defined as f p eseeg f s p s direct computation for all irreducible representations involves order igi operations we derive fast algorithms and develop them for the symmetric group sn there n 2 is reduced to nf nf al2 where a is the constant for matrix multiplication 2 38 as of this writing variations of the algorithm allow efficient computation for small representations a practical version of the algorithm is given on sn numerical evidence is presented to show a speedup by a factor of 100 for n 9 department of mathematics harvard university cambridge massachusetts 02138 department of mathematics columbia university new york new york 10027 this content downloaded from 157 55 39 153 on mon 19 sep 2016 04 53 00 utc all use subject to http about jstor org terms

on the smoothing property of linear delay partial differential equations abstract we consider linear partial differential equations with an additional delay term which under spatial discretization lead to ordinary differential equations with fixed delay of retarded type this means that the semi discrete solution gains smoothness over time for the concept of classical mild and weak solutions we analyse whether this effect also takes place in the original system we show that some systems behave in a neutral way only as a result the smoothness of the exact solution remains unchanged instead of gaining smoothness over time

availability analysis for software system with intrusion tolerance this paper is devoted to analyzing the instantaneous availability of a typical software system with intrusion tolerance by formulating the system with a couple of ordinary differential and partial differential equations this paper describes the system as a time delay partial differential equation based on the time delay model both steady state availability and instantaneous availability are investigated the optimal policy for preventive patch management to maximize the steady state availability of the software system is obtained and its related availability criterions are also presented employing the finite difference scheme and trotter kato theorem we converted the time delay partial equation into a time delay ordinary equation as a result the instantaneous availability of the system is derived some numerical results are given to show the effectiveness of the method presented in the paper

separation of variables and the computation of fourier transforms on finite groups ii we present a general diagrammatic approach to the construction of efficient algorithms for computing the fourier transform of a function on a finite group by extending work which connects bratteli diagrams to the construction of fast fourier transform algorithms we make explicit use of the path algebra connection to the construction of gel fand tsetlin bases and work in the setting of quivers we relate this framework to the construction of a configuration space derived from a bratteli diagram in this setting the complexity of an algorithm for computing a fourier transform reduces to the calculation of the dimension of the associated configuration space our methods give improved upper bounds for computing the fourier transform for the general linear groups over finite fields the classical weyl groups and homogeneous spaces of finite groups while also recovering the best known algorithms for the symmetric group

approximate controllability of a system of parabolic equations with delay abstract in this paper we give necessary and sufficient conditions for the approximate controllability of the following system of parabolic equations with delay z t x t d z l z t b u t x t 0 r z 0 x t 0 r z 0 x 0 x x z s x s x s 0 x where is a bounded domain in r n d is an n n nondiagonal matrix whose eigenvalues are semi simple with nonnegative real part the control u l 2 0 r u l 2 0 r l 2 r m and b l u z with u l 2 r m z l 2 r n the standard notation z t x defines a function from 0 to r n with x fixed by z t x s z t s x s 0 here 0 is the maximum delay which is supposed to be finite we assume that the operator l l 2 0 z z is linear and bounded and 0 z l 2 0 z to this end first we reformulate this system into a standard first order delay equation secondly the semigroup associated with the first order delay equation on an appropriate product space is expressed as a series of strongly continuous semigroups and orthogonal projections related with the eigenvalues of the laplacian operator a 2 this representation allows us to reduce the controllability of this partial differential equation with delay to a family of ordinary delay equations finally we use the well known result on the rank condition for the approximate controllability of delay system to derive our main result

integrated semigroups and linear partial differential equations with delay abstract we study existence and uniqueness of solutions for linear partial differential equations with delay in l p spaces using an approach of batkai and piazzera and a recent perturbation result for integrated semigroups we apply our result to an equation with delay in the highest order derivatives

a framework of rogers ramanujan identities and their arithmetic properties the two rogers ramanujan q series where 0 1 play many roles in mathematics and physics by the rogers ramanujan identities they are essentially modular functions their quotient the rogers ramanujan continued fraction has the special property that its singular values are algebraic integral units we find a framework which extends the rogers ramanujan identities to doubly infinite families of q series identities if a 1 2 and m n 1 then we have infinite product modular function where the p x x q are hall littlewood polynomials these q series are specialized characters of affine kac moody algebras generalizing the rogers ramanujan continued fraction we prove in the case of a that the relevant q series quotients are integral units

on feedback stabilizability of linear systems with state and input delays in banach spaces the feedback stabilizability of a general class of well posed linear systems with state and input delays in banach spaces is studied in this paper using the properties of infinite dimensional linear systems a necessary condition for the feedback stabilizability of delay systems is presented which extends the well known results for finite dimensional systems to infinite dimensional ones this condition becomes sufficient as well if the semigroup of the delay free system is immediately compact and the control space is finite dimensional moreover under the condition that the banach space is reflexive a rank condition in terms of eigenvectors and control operators is proposed when the delay free state space and control space are all finite dimensional a very compact rank condition is obtained finally the abstract results are illustrated with examples

l2 regularity for parabolic partial integrodifferential equations with delay in the highest order derivatives abstract a partial integrodifferential equation is studied in which the derivatives of highest order also contain a discrete and a distributed delay by means of abstract regularity results global existence and uniqueness of a strict solution are obtained moreover a characterization of the infinitesimal generator of the solution operator is given

fast fourier transforms for finite inverse semigroups abstract we extend the theory of fast fourier transforms on finite groups to finite inverse semigroups we use a general method for constructing the irreducible representations of a finite inverse semigroup to reduce the problem of computing its fourier transform to the problems of computing fourier transforms on its maximal subgroups and a fast zeta transform on its poset structure we then exhibit explicit fast algorithms for particular inverse semigroups of interest specifically for the rook monoid and its wreath products by arbitrary finite groups

robust stability ofc0 semigroups and an application to stability of delay equations abstract let a be a closed linear operator on a complex banach space x and let a be a fixed element of the resolvent set of a let u and y be banach spaces and let d l u x and e l x y be bounded linear operators we define r a d e by formula and prove that formula we give two applications of this result the first is an exact formula for the so called stability radius of the generator of a c 0 semigroup of linear operators on a hilbert space it is derived from a precise result about robustness under perturbations of uniform boundedness in the right half plane of the resolvent of an arbitrary semigroup generator the second application gives sufficient conditions on the norm of the operators b j l x such that the classical solutions of the delay equation formula are exponentially stable in l p h 0 x

differentiability and growth bounds of solutions of delay equations abstract we consider the question of eventual differentiability of the delay semigroups associated with the retarded equation u t a u t u t t 0 where u t is the history function a generates an immediately norm continuous semigroup and is bounded we show that this is determined by the rate of decay of the resolvent of a along vertical lines

optimal control of linear retarded systems in banach spaces this paper deals with standard optimal control problems namely the fixed time integral convex cost problem and the time optimal control problem for linear retarded systems in banach spaces for the basis of optimal control theory the fundamental solution is constructed and a variation of constant formula of mild solutions is established after the controlled system description and the formulation of optimal control problems are given the retarded adjoint system is introduced for the integral convex cost problem two existence theorems of optimal controls and necessary conditions of optimality are given these conditions are precisely characterized by the solution of retarded adjoint system the pointwise maximum principle for time varying control domain is derived from the optimality conditions the bang bang principle is also established for the terminal value cost problem under some regularity condition of the adjoint system for the time optimal control problem to a target set an existence theorem is shown in the case where the target set has interior the maximum principle and the bang bang principle are established for the time optimal control finally a convergence theorem of time optimal controls to a point target set is given this paper also contains illustrative examples which give technologically important control problems

the efficient computation of fourier transforms on the symmetric group this paper introduces new techniques for the efficient computation of fourier transforms on symmetric groups and their homogeneous spaces we replace the matrix multiplications in clausen s algorithm with sums indexed by combinatorial objects that generalize young tableaux and write the result in a form similar to horner s rule the algorithm we obtain computes the fourier transform of a function on s n in no more than 3 4n n 1 s n multiplications and the same number of additions analysis of our algorithm leads to several combinatorial problems that generalize path counting we prove corresponding results for inverse transforms and transforms on homogeneous spaces

eventual norm continuity for neutral semigroups on banach spaces in this paper we prove under suitable hypotheses eventually norm continuity and compactness of the solution semigroups of certain neutral differential equations in banach spaces our approach is based on a general perturbation theorem obtained from closed loop systems of infinite dimensional control systems with unbounded control and observation operators in fact the solution semigroup can be viewed as the semigroup of an appropriate closed loop system in product state spaces

global well posedness and exponential stability for heterogeneous anisotropic maxwell s equations under a nonlinear boundary feedback with delay abstract we consider an initial boundary value problem for the maxwell s system in a bounded domain with a linear nonhomogeneous anisotropic instantaneous material law subject to a nonlinear silver muller type boundary feedback mechanism incorporating both an instantaneous damping and a time localized delay effect by proving the maximal monotonicity property of the underlying nonlinear generator we establish the global well posedness in an appropriate hilbert space further under suitable assumptions and geometric conditions we show the system is exponentially stable

a bohr neugebauer property for abstract almost periodic evolution equations in banach spaces application to a size structured population model abstract this work continues the investigations done in the literature about the so called bohr neugebauer property for almost periodic differential equations in hilbert spaces we give a new sufficient condition to ensure that an almost periodic linear evolution equation in a banach space has the bohr neugebauer property more specifically we investigate when all the bounded solutions on r are almost periodic this new sufficient condition involves the essential growth bound of the c 0 semigroup generated by the autonomous part of the equation this enables us to investigate the bohr neugebauer property for partial differential equations with solutions living in purely banach spaces an application to a size structured population model will be studied using the theory of positive c 0 semigroups

the modulus semigroup for linear delay equations iii abstract in this paper we describe the modulus semigroup of the c 0 semigroup associated with the linear differential equation with delay u t au t lu t t 0 u 0 x x u 0 f l p h 0 x in the banach lattice x l p h 0 x where x is a banach lattice with order continuous norm the progress with respect to previous papers is that a may be an unbounded generator of a c 0 semigroup possessing a modulus semigroup

universal estimate of the gradient for parabolic equations we suggest a modification of the estimate for weighted sobolev norms of solutions of parabolic equations such that the matrix of the higher order coefficients is included into the weight for the gradient more precisely we found the upper limit estimate that can be achieved by variations of the zero order coefficient as an example of applications an asymptotic estimate was obtained for the gradient at initial time the constant in the estimates is the same for all possible choices of the dimension domain time horizon and the coefficients of the parabolic equation as an another example of application existence and regularity results are obtained for parabolic equations with time delay for the gradient

on perturbations preserving the immediate norm continuity of semigroups we show that the desch schappacher perturbation and the miyadera voigt perturbation of an immediately norm continuous semigroup are immediately norm continuous we also show that a perturbation theorem of c batty c kaiser and l weis based on a generation theorem of a m gomilko d x feng and d h shi also preserves the immediate norm continuity of semigroups the novelty of these results is that contrary to the numerous related results we obtain the immediate norm continuity of the perturbed semigroup without additional assumptions

well posedness of linear partial differential equations with unbounded delay operators in this paper we show the well posedness of the following constant delay equation u t au t bu t r t 0 u 0 x u f r 0 where a d a generates a strongly continuous semigroup t t t 0 on a banach space x and b d b is an unbounded and closed linear operator on x our approach is to transform the delay equation into an abstract cauchy problem in a special phase space and apply semigroup theory furthermore we show that the solution semigroup corresponding to the above delay equation is uniformly exponentially bounded finally we give an example to explain the well posedness of delay equations

necessary conditions for partial differential equations with delay to generate c0 semigroups on etudie l existence des solutions ou le caractere bien pose d equations aux derivees partielles a retard du type du t dt f u t ou f est un operateur d un espace de fonction 7b f r 0 y dans l espace de banach y dans lequel l equation evolue

on sieved orthogonal polynomials iii orthogonality on several intervals on introduit deux generalisations des polynomes de chelryshev dont le spectre continu est x 2 c 1 c t k x 2 c 1 c ou c est un parametre positif on definit les fonctions poids on obtient les fonctions generatrices et les formules explicites

fourier theoretic probabilistic inference over permutations permutations are ubiquitous in many real world problems such as voting ranking and data association representing uncertainty over permutations is challenging since there are n possibilities and typical compact and factorized probability distribution representations such as graphical models cannot capture the mutual exclusivity constraints associated with permutations in this paper we use the low frequency terms of a fourier decomposition to represent distributions over permutations compactly we present kronecker conditioning a novel approach for maintaining and updating these distributions directly in the fourier domain allowing for polynomial time bandlimited approximations low order fourier based approximations however may lead to functions that do not correspond to valid distributions to address this problem we present a quadratic program defined directly in the fourier domain for projecting the approximation onto a relaxation of the polytope of legal marginal distributions we demonstrate the effectiveness of our approach on a real camera based multi person tracking scenario

expansions of one density via polynomials orthogonal with respect to the other abstract we expand the chebyshev polynomials and some of its linear combination in linear combinations of the q hermite the rogers q utraspherical and the al salam chihara polynomials and vice versa we use these expansions to obtain expansions of some densities including q normal and some related to it in infinite series constructed of the products of the other density times polynomials orthogonal to it allowing deeper analysis and discovering new properties on the way we find an easy proof of expansion of the poisson mehler kernel as well as its reciprocal we also formulate simple rule relating one set of orthogonal polynomials to the other given the properties of the ratio of the respective densities of measures orthogonalizing these polynomials sets

lipschitzian semigroups and abstract functional differential equations abstract the paper is devoted to studying an abstract functional differential equation by a nonlinear semigroup approach we first prove in details the equivalence of the well posedness of an abstract functional differential equation and an associated abstract cauchy problem in the sense of strong solutions secondly a sufficient condition is derived for well posedness of the abstract functional differential equation thirdly we present principles of linearized stability for the abstract functional differential equation finally the results obtained are applied to a reaction diffusion equation with delays

fast fourier transforms for the rook monoid we define the notion of the fourier transform for the rook monoid also called the symmetric inverse semigroup and provide two efficient divide and conquer algorithms fast fourier transforms or ffts for computing it this paper marks the first extension of group ffts to nongroup semigroups

eventual differentiability of functional differential equations in banach spaces abstract this paper concerns the regularity of a functional differential equation in the form u t au t b 1 u t r r 0 a s b 2 u t s d s t 0 where a is the generator of an analytic semigroup on a banach space x and b 1 b 2 are a bounded linear operator for 0 1 by spectral analysis it is shown that the associated solution semigroup of this equation is eventually differentiable

tribasic integrals and identities of rogers ramanujan type some integrals involving three bases are evaluated as infinite products using complex analysis many special cases of these integrals may be evaluated in another way to find infinite sum representations for these infinite products the resulting identities are identities of rogers ramanujan type some integer partition interpretations of these identities are given generalizations of the rogers ramanujan type identities involving polynomials are given again as corollaries of integral evaluations

semigroups and linear partial differential equations with delay abstract we prove the equivalence of the well posedness of a partial differential equation with delay and an associated abstract cauchy problem this is used to derive sufficient conditions for well posedness exponential stability and norm continuity of the solutions applications to a reaction diffusion equation with delay are given

the non analytic growth bound of a c0 semigroup and inhomogeneous cauchy problems abstract the non analytic growth bound t of a c0 semigroup t measures the extent to which t can be approximated by a holomorphic function and it is related to spectral properties of the generator a in regions of c far from the real axis we show that t can be characterised by means of fourier multiplier properties of the resolvent of a far from the real axis and also by existence and uniqueness of mild solutions of inhomogeneous cauchy problems of the form u t au t f t on r where the carleman spectra of f and u are far from the origin the corresponding results for the exponential growth bound 0 t have been established earlier by other authors

on the structure and probabilistic interpretation of askey wilson densities and polynomials with complex parameters abstract we give equivalent forms of the askey wilson polynomials expressing them with the help of the al salam chihara polynomials after restricting parameters of the askey wilson polynomials to complex conjugate pairs we expand the askey wilson weight function in the series similar to the poisson mehler expansion formula and give its probabilistic interpretation in particular this result can be used to calculate explicit forms of q hermite moments of the askey wilson density hence enabling calculation of all moments of the askey wilson density on the way by setting certain parameter q to 0 we get some formulae useful in the rapidly developing so called free probability

on identities of the rogers ramanujan type abstract an elementary approach to a number of identities of the rogers ramanujan type is given it is shown that analytic formulas like e g the rogers ramanujan the rogers selberg and the gollnitz gordon identities can be obtained essentially as consequences of the q binomial theorem and the q vandermonde formula