global attractor for some partial functional differential equations with finite delay abstract in this paper we study a class of partial functional differential equations with finite delay whose linear part is not necessarily densely defined but satisfies the hille yosida condition using the classical theory about global attractors in infinite dimensional dynamical systems we establish some sufficient conditions for guaranteeing the existence of a global attractor under small delays

a novel decomposition analysis of nonlinear distortion in ofdm transmitter systems in orthogonal frequency division multiplexing ofdm transmitter systems nonlinear distortion is a major impairment caused by power amplifier pa the distortion is constituted by numerous noise like inter modulation products imps although the overall behavior of nonlinear imp distortion has been well studied in large multi carrier contexts such as in ofdm the knowledge of individual imps and their quantitative interrelationships together with the derivation of behavioural knowledge and the predictability of consequences arising from such interrelationships is a fairly unexplored topic this is the subject of this paper the powers of the very numerous individual imps generated are analytically derived based on a bessel fourier pa behavioural model and it is proven that these powers have only a small number of distinct powers proven also is that the ratios of these power values are constants and that these constants are invariant with the particular pa s nonlinearity characteristics or operating point further it is proven that specific types of imps dominate nonlinear distortion effects finally it is shown that imp power spectra can be derived from a simple product of two polynomials which are quadrature functions of frequency and pa operating point respectively application possibilities for findings presented in this paper such as their potential to contribute efficiency improvements in ofdm system modulation fidelity calculations over 1100 times faster than conventional methods are also outlined in the conclusions

local existence and regularity of solutions for some partial functional integrodifferential equations with infinite delay in banach spaces abstract in this work we study the existence and regularity of solutions for some partial functional integrodifferential equations with infinite delay in banach spaces we suppose that the undelayed part admits a resolvent operator in the sense of grimmer r grimmer resolvent operators for integral equations in a banach space transactions of the american mathematical society 273 1982 333 349 the delayed part is assumed to be locally lipschitz firstly we show the existence of the mild solutions secondly we give sufficient conditions ensuring the existence of strict solutions

quantum cohomology of flag manifolds and toda lattices we discuss relations of vafa s quantum cohomology with floer s homology theory introduce equivariant quantum cohomology formulate some conjectures about its general properties and on the basis of these conjectures compute quantum cohomology algebras of the flag manifolds the answer turns out to coincide with the algebra of regular functions on an invariant lagrangian variety of a toda lattice

vortex partition functions wall crossing and equivariant gromov witten invariants in this paper we identify the problem of equivariant vortex counting in a 2 2 supersymmetric two dimensional quiver gauged linear sigma model with that of computing the equivariant gromov witten invariants of the git quotient target space determined by the quiver we provide new contour integral formulae for the mathcal i and mathcal j functions encoding the equivariant quantum cohomology of the target space its chamber structure is shown to be encoded in the analytical properties of the integrand this is explained both via general arguments and by checking several key cases we show how several results in equivariant gromov witten theory follow just by deforming the integration contour in particular we apply our formalism to compute gromov witten invariants of the mathbb c 3 mathbb z n orbifold of the uhlembeck partial compactification of the moduli space of instantons on mathbb c 2 and of an and dn singularities both in the orbifold and resolved phases moreover we analyse dualities of quantum cohomology rings of holomorphic vector bundles over grassmannians which are relevant to bps wilson loop algebrae

variation of constants formula and almost periodic solutions for some partial functional differential equations with infinite delay abstract in this work we give a variation of constants formula for partial functional differential equations with infinite delay we assume that the linear part is not necessarily densely defined and its resolvent operator satisfies the hille yosida condition we establish a reduction of the problem to a finite dimensional space which allows us to prove the existence of almost periodic solutions

resolvent positive operators resolvent positive operators on an ordered banach space with generating and normal positive cone are by definition linear possibly unbounded operators whose resolvent exists and is positive on a right half line even though these operators are defined by a simple purely algebraic condition analogues of the basic results of the theory of q semigroups can be proved for them in fact if a is resolvent positive and has a dense domain then the cauchy problem associated with a has a unique solution for every initial value in the domain of a and the solution is positive if the initial value is positive also the converse is true if we assume that a has a non empty resolvent set and d a n e is dense in moreover every positive resolvent is a laplace stieltjes transform of a so called integrated semigroup and conversely every such increasing non degenerate integrated semigroup defines a unique resolvent positive operator

global attractor for a class of functional differential inclusions with hille yosida operators abstract we study the dynamics for a class of functional differential inclusions whose linear part generates an integrated semigroup some techniques of measure of noncompactness are deployed to prove the global solvability and the existence of a compact global attractor for the m semiflow generated by our system the obtained results generalize recent ones in the same direction

existence of a periodic solution for some partial functional differential equations with infinite delay abstract this paper deals with the existence of periodic solutions for some partial functional differential equations with infinite delay we suppose that the linear part is nondensely defined and satisfies the hille yosida condition in the nonlinear case we give several criteria to ensure the existence of a periodic solution in the nonhomogeneous linear case we prove the existence of a periodic solution under the existence of a bounded solution

quantum cohomology of flag manifolds g b and quantum toda lattices let g be a connected semi simple complex lie group b its borel subgroup t a maximal complex torus contained in b and lie t its lie algebra this setup gives rise to two constructions the generalized nonperiodic toda lattice 28 29 and the flag manifold g b the toda lattice for g b t is the dynamical system on the cotangent bundle t lie t endowed with the canonical holomorphic symplectic form and the holomorphic hamiltonian function we consider in this paper

a class of linear partial neutral functional differential equations with nondense domain abstract we consider a system of linear partial neutral functional differential equations with nondense domain a natural generalized notion of solutions is provided by the integral solutions we derive a variation of constants formula which allows us to transform the integral solutions of the neutral equation to solutions of an abstract volterra integral equation the basic existence and uniqueness results are given and the solutions are shown to generate an integrated semigroup

existence and stability for some partial neutral functional differential equations with infinite delay abstract in this paper we study a class of partial neutral functional differential equations with infinite delay we suppose that the linear part is not necessarily densely defined but satisfies the resolvent estimates of the hille yosida theorem we give some sufficient conditions ensuring the existence uniqueness and regularity of solutions a principle of linearized stability is also established in the autonomous case to illustrate our abstract results we conclude this work by an example

a conjectural peterson isomorphism in k theory abstract we state a precise conjectural isomorphism between localizations of the equivariant quantum k theory ring of a flag variety and the equivariant k homology ring of the affine grassmannian in particular relating their schubert bases and structure constants this generalizes peterson s isomorphism in co homology we prove a formula for the pontryagin structure constants in the k homology ring and we use it to check our conjecture in few situations

ultimate boundedness and periodicity for some partial functional differential equations with infinite delay abstract in this work we study the existence of periodic solutions for some partial functional differential equation with infinite delay we assume that the linear part is not necessarily densely defined and satisfies the known hille yosida condition firstly we give some estimates of the solutions secondly we prove that the poincare map is condensing which allows us to prove the existence of periodic solutions when the solutions are ultimately bounded

kernel functions and backlund transformations for relativistic calogero moser and toda systems we obtain kernel functions associated with the quantum relativistic toda systems both for the periodic version and for the nonperiodic version with its dual this involves taking limits of previously known results concerning kernel functions for the elliptic and hyperbolic relativistic calogero moser systems we show that the special kernel functions at issue admit a limit that yields generating functions of backlund transformations for the classical relativistic calogero moser and toda systems we also obtain the nonrelativistic counterparts of our results which tie in with previous results in the literature

twisted k theoretic gromov witten invariants we introduce twisted k theoretic gromov witten gw invariants in the frameworks of both ordinary and permutation equivariant k theoretic gw theory defined recently by givental we focus on the case when the twisting is given by the euler class of an index bundle which allows one under a convexity assumption on the bundle to relate k theoretic gw invariants of hypersurfaces with those of the ambient space using the methods developed in givental and tonita math sci res inst publ 62 43 92 cambridge univ press cambridge 2014 we characterize the range of the j function of the twisted theory in terms of the untwisted theory as applications we use the mathcal d q module structure in the permutation equivariant case to generalize results of givental permutation equivariant quantum k theory i viii https math berkeley edu giventh perm perm html 2015 we prove a general quantum lefschetz type theorem for complete intersections given by zero sections of convex vector bundles and we relate points on the cones of the total space with those of the base of a toric fibration

linear theory of abstract functional differential equations of retarded type abstract the purpose of this paper is to provide an extension of the linear theory of functional differential equations of retarded type to abstract equations such equations include examples borrowed from population dynamics to which the theory applies an application will be given elsewhere our main effort in this work consists in providing a suitable extension of the formal adjoint equation and the formal duality the solutions of the linear autonomous retarded functional differential equation x t l x t 1 where l is a bounded linear operator mapping the space c r 0 e into the banach space e define a strongly continuous translation semigroup we show the existence of a direct sum decomposition of c r 0 e into two subspaces which are semigroup invariants the flow induced by the solutions of eq 1 can be interpreted as the flow induced by an ordinary differential equation in a finite dimensional space we explicitly characterize this decomposition by an orthogonality relation associated to a certain definition of formal duality the existence of an integral representation for the operator l leads to an equation formally adjoint to 1 characterizing the projection operator defined by the above decomposition of c r 0 e

necessary and sufficient conditions for the regularity and stability for some partial functional differential equations with infinite delay abstract in this work we give necessary and sufficient conditions for the regularity and stability of solutions for some partial functional differential equations with infinite delay we establish also a new characterization of the infinitesimal generator of the solution semigroup

approximate controllability of second order distributed implicit functional systems abstract in this paper we study the approximate controllability of control systems with states and controls in hilbert spaces and described by a second order semilinear abstract functional differential equation with infinite delay initially we establish a characterization for the approximate controllability of a second order abstract linear system and in the last section we compare the approximate controllability of a semilinear abstract functional system with the approximate controllability of the associated linear system

existence of nondensely defined evolution equations with nonlocal conditions abstract this paper is concerned with the existence for nondensely defined evolution equations with nonlocal conditions using the techniques of fixed point theory and approximate solutions existence results are obtained for integral solutions when the nonlocal item is lipschitz continuous or continuous respectively examples are also given to illustrate our results

solutions to non autonomous integrodifferential equations with infinite delay abstract the conclusions of da prato and sinestrari concerning the non autonomous evolution operator of hyperbolic type for the equation u t a t u t f t t 0 t u 0 z are applied to find the uniqueness and existence of solution to u t a t u t 0 t k t u d l t u t f t t 0 t u 0 where a maybe nondensely defined moreover some relative problems are concerned

nonsymmetric difference whittaker functions starting with nonsymmetric global difference spherical functions we define and calculate spinor nonsymmetric global q whittaker functions for arbitrary reduced root systems which are reproducing kernels of the daha fourier transforms of nil daha and solutions of the q toda dunkl eigenvalue problem we introduce the spinor q toda dunkl operators as limits of the difference dunkl operators in daha theory under the spinor variant of the ruijsenaars procedure their general algebraic theory any reduced root systems is the key part of this paper based on the new technique of w spinors and corresponding developments in combinatorics of affine root systems

integrated semigroups and integrated solutions to abstract cauchy problems abstract concepts which have been developed in the theory of weakly continuous semigroups on dual banach spaces are extended to integrated semigroups the relation to integrated solutions of homogeneous and inhomogeneous abstract cauchy problems is established the results are illustrated for the wave equation in l2 rm

stability of functional partial differential equations on etablit des conditions necessaires et suffisantes pour qu une classe d equations aux derivees partielles fonctionnelles soit asymptotiquement stable pour toutes les valeurs des retards

a practical analysis of performance optimization in ostbc based nonlinear mimo ofdm systems this paper presents a practical performance analysis of an orthogonal space time block code ostbc based multiple input multiple output mimo orthogonal frequency division multiplexing ofdm system in the presence of nonlinear power amplifiers pas the equivalent single input single output siso scalar model is introduced and this then is used to construct a model for the nonlinear mimo ofdm system based on an unique inter modulation product imp analysis it is shown how the receiver signal to noise ratio snr may be derived to a polynomial based function of the system operating point it is also shown that expressions for the asymptotical behavior of this snr when the linear and highly nonlinear pa operations are applied may also be derived based on these derivations it is further shown that the optimal system operating point which corresponds to the maximum receiver snr and sep lower bound can be identified and be derived to a polynomial based expression additionally a general expression for the different integral expressions of sep for the phase shift keying psk and quadrature amplitude modulation qam signals is found by means of these analytical results it was found possible to advance analytical explanations of observed behaviour in simulations and also to provide a practical analysis of performance optimization of nonlinear mimo ofdm systems

quantum k theory of grassmannians we show that equivariant k theoretic 3 point gromov witten invariants of genus zero on a grassmann variety are equal to triple intersec tions computed in the equivariant k theory of a two step flag manifold thus generalizing an earlier result of buch kresch and tamvakis in the process we show that the gromov witten variety of curves passing through 3 general points is irreducible and rational our applications include pieri and giambelli formulas for the quantum k theory ring of a grassmannian which determine the multiplication in this ring we also compute the dual schubert basis for this ring and show that its structure constants satisfy s3 symmetry our for mula for gromov witten invariants can be partially generalized to cominuscule homogeneous spaces by using a construction of chaput manivel and perrin

existence and controllability results for nondensely defined impulsive semilinear functional differential inclusions abstract in this paper we shall establish sufficient conditions for the existence of integral solutions and extremal integral solutions for some nondensely defined impulsive semilinear functional differential inclusions in separable banach spaces we shall rely on a fixed point theorem for the sum of completely continuous and contraction operators the question of controllability of these equations and the topological structure of the solutions set are considered too

on q deformed mathfrak gl _ ell 1 whittaker function ii a representation of a specialization of a q deformed class one lattice mathfrak gl ell 1 whittaker function in terms of cohomology groups of line bundles on the space mathcal qm d mathbb p ell of quasi maps mathbb p 1 to mathbb p ell of degree d is proposed for l 1 this provides an interpretation of the non specialized q deformed mathfrak gl 2 whittaker function in terms of mathcal qm d mathbb p 1 in particular the q version of the mellin barnes representation of the mathfrak gl 2 whittaker function is realized as a semi infinite period map the explicit form of the period map manifests an important role of q version of function as a topological genus in semi infinite geometry a relation with the givental lee universal solution j function of q deformed mathfrak gl 2 toda chain is also discussed

stabilization of linear distributed control systems with unbounded delay in this paper we study the asymptotic stabilization of linear distributed parameter control systems with unbounded delay assuming that the semigroup of operators associated with the uncontrolled and nondelayed equation is compact and that the phase space is a uniform fading memory space we characterize those systems that can be stabilized using a feedback control as consequence we conclude that every system of this type is stabilizable with an appropriated finite dimensional control

existence of some neutral partial differential equations with infinite delay this study intends to investigate a class of quasi linear partial neutral functional differential equations with infinite delay we assume that the linear part generates an analytic compact semigroup and the nonlinear part satisfies certain conditions a sufficient condition is given to ensure the existence of mild and classical solutions finally an example is given to illustrate our abstract results

stability and asymptotic behavior of solutions for some linear partial functional differential equations in critical cases abstract in this work we study the stability of the solution semigroup for some linear partial functional differential equations with infinite delay in a banach space when the exponential stability fails we use the so called characteristic equation to compute the order of each pole of the resolvent operator associated with the infinitesimal generator of the solution semigroup this result allows us to give sufficient conditions for having stability of the solution semigroup

a path model for whittaker vectors in this paper we construct weighted path models to compute whittaker vectors in the completion of verma modules as well as whittaker functions of fundamental type for all finite dimensional simple lie algebras affine lie algebras and the quantum algebra u q mathfrak sl r 1 this leads to series expressions for the whittaker functions we show how this construction leads directly to the quantum toda equations satisfied by these functions and to the q difference equations in the quantum case we investigate the critical limit of affine whittaker functions computed in this way

wellposedness and wave propagation for a class of integrodifferential equations in banach space in recent years there has been an increasing interest in the mathematical treatment of problems which originate in the theory of viscoelastic materials in such problems the constitutive relations for these materials incorporate the history of the strain or the strain rate and in the linear theory lead to linear volterra integrodifferential equations with infinite memory in a banach space x the purpose of this paper is to examine the problems of wellposedness and wave propagation for one such equation in particular we are concerned with equations of the form x t 4 x r j f t s x s ds al

a reconstruction theorem in quantum cohomology and quantum k theory a reconstruction theorem for genus 0 gravitational quantum cohomology and quantum k theory is proved a new linear equivalence in the picard group of the moduli space of genus 0 stable maps relating the pull backs of line bundles from the target via different markings is used for the reconstruction result examples of calculations in quantum cohomology and quantum k theory are given

local existence for nonlinear volterra integrodifferential equations with infinite delay abstract in this paper we investigate the local existence and uniqueness of solutions to integrodifferential equations with infinite delay which are more general than those in previous studies we assume that the linear part of the equation is nondensely defined and satisfies a hille yosida condition moreover the continuity of solutions with respect to initial conditions is also studied in order to illustrate our abstract results we conclude this work with an example

extremal part of the pbw filtration and nonsymmetric macdonald polynomials abstract given a reduced irreducible root system the corresponding nil daha is used to calculate the extremal coefficients of nonsymmetric macdonald polynomials in the limit t and for antidominant weights which is an important ingredient of the new theory of nonsymmetric q whittaker function these coefficients are pure q powers and their degrees are expected to coincide in the untwisted setting with the extremal degrees of the so called pbw filtration in the corresponding finite dimensional irreducible representations of the simple lie algebras for any root systems this is a particular case of a general conjecture in terms of the level one demazure modules we prove this coincidence for all lie algebras of classical type and for g 2 and also establish the relations of our extremal degrees to minimal q degrees of the extremal terms of the kostant q partition function they coincide with the latter only for some root systems

necessary and sufficient conditions for the regularity and stability of solutions for some partial neutral functional differential equations with infinite delay abstract in this paper we give necessary and sufficient conditions for the regularity and stability of solutions for some partial neutral functional differential equations with infinite delay we establish also a generalization and extension of the characterization of the infinitesimal generator of the solution semigroup to illustrate our abstract results we study the stability of the neutral lotka volterra model with diffusion

quantum k theory on flag manifolds finite difference toda lattices and quantum groups let x y be homogeneous coordinates on cp a degree d holomorphic map cp 1 cp is uniquely determined up to a constant scalar factor by n 1 relatively prime degree d binary forms f0 x y fn x y omitting the condition that the forms are relatively prime we compactify the space of degree d holomorphic maps cp 1 cp to a complex projective space of dimension n 1 d 1 1 we denote this compactification of the space of maps by cp d this construction defines the compactification d r i 1cp ni 1 di of the space of degree d d1 dr maps from cp 1 to composing degree d holomorphic maps from cp 1 to the flag manifold x with the plucker embedding we embed the space of such maps into d the closure qmd of this space in d is often referred to as the drinfeld s compactification of the space of degree d maps from cp 1 to x and will be called the space of quasimaps following 14 it is a generally speaking singular irreducible projective variety of complex dimension dimx 2d1 2dr the flag manifold is a homogeneous space of the group slr 1 c and of its maximal compact subgroup sur 1 the action of these groups on x lifts naturally to the spaces d and qmd in addition to this action the spaces d and the subspaces qmd carry the circle action induced by the rotation of cp 1 defined by x y 7 x ey thus the product group g s sur 1 and its complex version gc c slr 1 c act on the quasimap spaces we will see later that qmd have g equivariant desingularizations qmd

stability of dichotomies in difference equations with infinite delay abstract for delay difference equations with infinite delay we consider the notion of nonuniform exponential dichotomy this includes the notion of uniform exponential dichotomy as a very special case our main aim is to establish a stable manifold theorem under sufficiently small nonlinear perturbations we also establish the robustness of nonuniform exponential dichotomies under sufficiently small linear perturbations finally we characterize the nonuniform exponential dichotomies in terms of strict lyapunov sequences in particular we construct explicitly a strict lyapunov sequence for each exponential dichotomy

elliptic stable envelopes we construct stable envelopes in equivariant elliptic cohomology of nakajima quiver varieties in particular this gives an elliptic generalization of the results of arxiv 1211 1287 we apply them to the computation of the monodromy of q difference equations arising the enumerative k theory of rational curves in nakajima varieties including the quantum knizhnik zamolodchikov equations

quantum integrability and generalised quantum schubert calculus abstract we introduce and study a new mathematical structure in the generalised quantum cohomology theory for grassmannians namely we relate the schubert calculus to a quantum integrable system known in the physics literature as the asymmetric six vertex model our approach offers a new perspective on already established and well studied special cases for example equivariant k theory and in addition allows us to formulate a conjecture on the so far unknown case of quantum equivariant k theory

behavior near hyperbolic stationary solutions for partial functional differential equations with infinite delay abstract the aim of this work is to investigate the asymptotic behavior of solutions near hyperbolic stationary solutions for partial functional differential equations with infinite delay we suppose that the linear part satisfies the hille yosida condition on a banach space and it is not necessarily densely defined firstly we establish a new variation of constants formula for the nonhomogeneous linear equations secondly we use this formula and the spectral decomposition of the phase space to show the existence of stable and unstable manifolds the estimations of solutions on these manifolds are obtained for illustration we propose to study the stability of stationary solutions for the lotka volterra model with diffusion

weyl modules and q whittaker functions let g be a semi simple simply connected group over mathbb c following gerasimov et al comm math phys 294 97 119 2010 we use the q toda integrable system obtained by quantum group version of the kostant whittaker reduction cf etingof in am math soc trans ser 2 9 25 1999 sevostyanov in commun math phys 204 1 16 1999 to define the notion of q whittaker functions varpsi check lambda q z this is a family of invariant polynomials on the maximal torus t subset g here z in t depending on a dominant weight check lambda of g whose coefficients are rational functions in a variable q in mathbb c for a conjecturally the same but a priori different definition of the q toda system these functions were studied by ion duke math j 116 1 16 2003 and by cherednik int math res notices 20 3793 3842 2009 we shall denote the q whittaker functions from cherednik int math res notices 20 3793 3842 2009 by varpsi check lambda q z for g sl n these functions were extensively studied in gerasimov et al comm math phys 294 97 119 2010 comm math phys 294 121 143 2010 lett math phys 97 1 24 2011 we show that when g is simply laced the function hat varpsi check lambda q z varpsi check lambda q z cdot prod nolimits i in i prod nolimits r 1 langle alpha i check uplambda rangle 1 q r here i denotes the set of vertices of the dynkin diagram of g is equal to the character of a certain finite dimensional g mathsf t rtimes mathbb c module d check lambda the demazure module when g is not simply laced a twisted version of the above statement holds this result is known for varpsi check lambda replaced by varpsi check lambda cf sanderson in j algebraic combin 11 269 275 2000 and ion in duke math j 116 1 16 2003 however our proofs are algebro geometric and rely on our previous work braverman finkelberg in semi infinite schubert varieties and quantum k theory of flag manifolds arxiv 1111 2266 2011 and thus they are completely different from sanderson j algebraic combin 11 269 275 2000 and ion duke math j 116 1 16 2003 in particular we give an apparently new algebro geometric interpretation of the modules d check lambda

dynamic range and other fundamentals of the complex bessel function series approximation model for memoryless nonlinear devices an explanation is given of the application of the complex bessel function series approximation model of the memoryless amplitude and phase characteristics of nonlinear devices confusion had arisen because of the choice of a value of a parameter in the approximating expression the practice had been to choose this simply as though it was just an arbitrary constant which scales the input or as an optimizing parameter in the effort to get a best fit of the approximation to the measured data by examining the derivation of the particular approximation a determining and important link between this parameter and the desired operating dynamic range of the nonlinear characteristic being approximated is shown how values for this parameter are calculated in terms of input overdrive relative to device saturation is also shown in examining the origin of the approximating expressions an alternative and simpler derivation to that given by j c fuenzalida et al 1973 is presented that is based on the work of m j eric et al 1972

non autonomous nonlinear integro differential equations with infinite delay abstract in this paper we consider a non autonomous abstract nonlinear volterra integro differential equation with infinite delay in a banach space we establish the existence and uniqueness of a strict solution under a certain local lipschitz condition on the nonlinear map and an integrability condition on the kernel

local existence for retarded volterra integrodifferential equations with hille yosida operators abstract this paper is devoted to finding some existence and uniqueness theorems for classical solutions of the integrodifferential equations with infinite delay we give some sufficient conditions ensuring the existence and uniqueness of solutions we assume the linear part is not necessary to be densely defined and satisfies a hille yosida condition so that it is the generator of a nondegenerated locally lipschitz continuous integrated semigroup by using matrix operators and fixed point theorems we obtain new results for the retarded integrodifferential equations

projectors on the generalized eigenspaces for functional differential equations using integrated semigroups the aim of this article is to derive explicit formulas for the projectors on the generalized eigenspaces associated to some eigenvalues for linear functional differential equations fde by using integrated semigroup theory the idea is to formulate the fde as a non densely defined cauchy problem and obtain an explicit formula for the integrated solutions of the non densely defined cauchy problem from which we then derive explicit formulas for the projectors on the generalized eigenspaces associated to some eigenvalues the results are useful in studying bifurcations in some semi linear problems

normal forms for semilinear equations with non dense domain with applications to age structured models normal form theory is very important and useful in simplifying the forms of equations restricted on the center manifolds in studying nonlinear dynamical problems in this paper using the center manifold theorem associated with the integrated semigroup theory we develop a normal form theory for semilinear cauchy problems in which the linear operator is not densely defined and is not a hille yosida operator and present procedures to compute the taylor expansion and normal form of the reduced system restricted on the center manifold we then apply the main results and computation procedures to determine the direction of the hopf bifurcation and stability of the bifurcating periodic solutions in a structured evolutionary epidemiological model of influenza a drift and an age structured population model

local existence and stability for some partial functional differential equations with infinite delay we study the existence regularity and stability of solutions for some partial functional dierential equations with infinite delay we assume that the linear part is not necessarily densely defined and satisfies the hille yosida condition on a banach space x the nonlinear term takes its values in space larger than x namely the extrapolated favard class of the extrapolated semigroup corresponding to the linear part our approach is based on the theory of the extrapolation spaces

variation of constants formula and reduction principle for a class of partial functional differential equations with infinite delay abstract in this work the dynamic behavior of solutions is investigated for a class of partial functional differential equations with infinite delay we suppose that the undelayed homogeneous part generates an analytic semigroup and the delayed part is continuous with respect to fractional powers of the generator firstly a variation of constants formula is obtained in the corresponding norm space which is mainly used to establish a reduction principle of complexity of the considered equation the reduction principle proves that the dynamics of the considered equation is governed by an ordinary differential equation in finite dimensional space as an application we investigate the existence of periodic almost periodic and almost automorphic solutions for the original equation

generalized weyl modules and nonsymmetric q whittaker functions abstract we introduce generalized global weyl modules and relate their graded characters to nonsymmetric macdonald polynomials and nonsymmetric q whittaker functions in particular we show that the series part of the nonsymmetric q whittaker function is a generating function for the graded characters of generalized global weyl modules

baxter q operator from quantum k theory abstract we define and study the quantum equivariant k theory of cotangent bundles over grassmannians for every tautological bundle in the k theory we define its one parametric deformation referred to as quantum tautological bundle we prove that the spectrum of operators of quantum multiplication by these quantum classes is governed by the bethe ansatz equations for the inhomogeneous xxz spin chain in addition we prove that each such operator corresponds to the universal elements of quantum group u sl 2 in particular we identify the baxter operator for the xxz spin chain with the operator of quantum multiplication by the exterior algebra tautological bundle the explicit universal combinatorial formula for this operator is found the relation between quantum line bundles and quantum dynamical weyl group is shown

existence results for partial neutral functional differential equations with unbounded delay abstract we prove the existence of mild solutions for a partial neutral functional integrodifferential equation with unbounded delay using the leray schauder alternative

center manifolds for infinite delay we obtain a c1 center manifold theorem for perturbations of delay difference equations in banach spaces with infinite delay our results extend in several directions the existing center manifold theorems besides considering infinite delay equations we consider perturbations of nonuniform exponential trichotomies and generalized trichotomies that may exhibit stable unstable and central behaviors with respect to arbitrary asymptotic rates ec n for some diverging sequence n this includes as a very special case the usual exponential behavior with n n