a numerical method for an integro differential equation with memory in banach spaces qualitative properties a first order method is considered for the discretization in time of an integro differential equation which can be written as d alpha u t a u t f t 1 alpha 2 where a d a subset x to x is a sectorial operator in a banach space x qualitative properties of the numerical solution such as contractivity and positivity are studied a numerical illustration is provided

bohr neugebauer type theorem for some partial neutral functional differential equations in this work we study the existence of almost periodic solutions for some partial neutral functional dierential equations using the variation of constants formula and the spectral decomposition of the phase space developed in 6 we prove that the existence of an almost periodic solution is equivalent to the existence of a bounded solution on r

secant zeta functions abstract we study the series s z n 1 sec n z n s and prove that it converges under mild restrictions on z and s the function possesses a modular transformation property which allows us to evaluate s z explicitly at certain quadratic irrational values of z this supports our conjecture that k k j q whenever k and j are positive integers with k even we conclude with some speculations on the bernoulli numbers

weighted pseudo almost automorphic mild solutions to semilinear fractional differential equations this paper is concerned with the existence and uniqueness of a weighted pseudo almost automorphic mild solution to the semilinear fractional equation d t au t au t d t a 1f t u t t r 1 a 2 in complex banach spaces with s p weighted pseudo almost automorphic coefficients where a is a linear densely defined operator of sectorial type on a complex banach space x moreover we present an application to a fractional wave equation

existence of s asymptotically ω periodic solutions to abstract integro differential equations we study the existence of solutions for a class of abstract equations we construct an exponentially stable resolvent operator solutions s asymptotically periodic are obtained we obtained existence results with less restrictions on the constants we provide a concrete example for the abstract results the main aim of this work is to study the existence of s asymptotically periodic solutions for a class of abstract integro differential equations modeled in the following form d dt x t 0 t n t s x s ds ax t 0 t b t s x s ds f t x t t 0 x 0 x 0 x where a b t for t 0 are closed linear operators defined on a common domain d a which is dense in x n t for t 0 are bounded linear operators on x and f 0 i x x is an appropriate function the existence results are obtained by applying the theory of exponentially stable resolvent operators we also discuss an application of these results

a cauchy problem for some fractional abstract differential equation with non local conditions abstract we discuss in this paper the existence and uniqueness of solutions to the cauchy problem for the fractional differential equation with non local conditions d q x t f t x t t 0 t x 0 g x x 0 where 0 q 1 in a banach space we use classical tools from functional analysis to obtain the results

s asymptotically ω periodic and asymptotically ω periodic solutions to semi linear cauchy problems with non dense domain abstract in this work we study the existence and uniqueness of s asymptotically periodic and asymptotically periodic solutions to a first order differential equation with linear part dominated by a hille yosida operator with non dense domain applications to partial differential equations fractional integro differential and neutral differential equations are given

on stepanov almost periodic semigroups and cosine functions of operators abstract in this paper we consider stepanov asymptotically almost periodic sp a a p mild solutions of first and second order abstract differential equations specifically we prove that a c0 semigroup is sp a a p if and only if it is asymptotically almost periodic and that a c0 cosine function of operators is sp a a p if and only if it is almost periodic

regularized solutions for abstract volterra equations abstract we introduce a two kernel dependent family of strong continuous operators defined in a banach space which allows us to consider in an unified treatment the notions of among others c 0 semigroups of operators cosine families n times integrated semigroups resolvent families and k generalized solutions the results are applied to the study of existence and uniqueness of solutions for the volterra equation of convolution type u f a au in the case a is not necessarily densely defined examples for equations defined in l p spaces are also given

an example of a generalized brownian motion we present an example of a generalized brownian motion it is given by creation and annihilation operators on a twisted fock space ofl2 these operators fulfill for a fixed 1 1 the relationsc f c g c g c f f g 1 f g l2 we show that the distribution of these operators with respect to the vacuum expectation is a generalized gaussian distribution in the sense that all moments can be calculated from the second moments with the help of a combinatorial formula we also indicate that our brownian motion is one component of ann dimensional brownian motion which is invariant under the quantum groups u n of woronowicz with v2

realizability of a model in infinite statistics following greenberg and others we study a space with a collection of operatorsa k satisfying the q mutator relations a l a k a l k l corresponding forq 1 to classical bose and fermi statistics we show that then n matrixa n q representing the scalar products ofn particle states is positive definite for alln ifq lies between 1 and 1 so that the commutator relations have a hilbert space representation in this case this has also been proved by fivel and by bozejko and speicher we also give an explicit factorization ofa n q as a product of matrices of the form 1 q jt 1 with 1 j n andt a permutation matrix in particular a n q is singular if and only ifq m 1 for some integerm of the formk 2 k 2 k n

a q deformed poisson distribution based on orthogonal polynomials we introduce certain q deformations of the binomial distribution and the poisson distribution by virtue of q deformed sequences of orthogonal polynomials they correspond to the case of free independence for q 0 and are reduced to the usual commutative case when q 1 furthermore we determine the probability measure for a q deformed poisson distribution by using the formulae for the al salam chihara polynomials of askey and ismail

stochastic integration with respect to q brownian motion we develop a stochastic integration with respect to a q brownian motion for i e a non commutative process where the operator at and its adjoint fulfill the q commutation relation under the vacuum state expectation we show that this process enjoys a predictable representation type property

minimal sets of almost periodic motions les conditions de nemytskii stepanov et deysach sell pour un mouvement x sont equivalentes a la presque periodicite asymptotique de x r la presque periodicite asymptotique de x r n est pas necessaire afin que x soit un ensemble minimal de mouvements presque periodiques

asymptotically periodic solutions of abstract differential equations abstract in this paper we introduce the concept of s asymptotically periodicity in the stepanov sense we study some properties of the space consisting of s asymptotically periodic functions and we use this notion to establish the existence of s asymptotically periodic solutions to linear and semi linear first order abstract differential equations in particular we characterize the strongly continuous semigroups of bounded linear operators defined on reflexive spaces which are s asymptotically periodic as those semigroups which are the direct sum of an periodic and a strongly stable semigroup

asymptotic almost periodicity and motions of semigroups of operators abstract in this survey we present an overview of recent work in resolving certain questions that arise in a qualitative study of solutions to the abstract cauchy problem focusing on motions of c 0 semigroups of operators and their asymptotic behavior we address 1 the characterization of asymptotically almost periodic motions and 2 the characterization of those asymptotically almost periodic functions for which this property carries over to their integral moreover we take up the problem raised by nemytskii and stepanov as to when the limit set of a motion of a dynamical system is a minimal set of almost periodic motions

weighted pseudo almost periodic functions and applications to evolution equations with delay in this paper we introduce a new class of vector valued weighted pseudo almost periodic functions and present some basic properties about these new functions moreover we obtain an new existence theorem of vector valued weighted pseudo almost periodic solution to the evolution equations x t ax t f t x t with delay in a banach space x

a real space renormalization approach to the kubo greenwood formula in mirror fibonacci systems an exact real space renormalization method is developed to address the electronic transport in mirror fibonacci chains at a macroscopic scale by means of the kubo greenwood formula the results show that the mirror symmetry induces a large number of transparent states in the dc conductivity spectra contrary to the simple fibonacci case a length scaling analysis over ten orders of magnitude reveals the existence of critically localized states and their ac conduction spectra show a highly oscillating behaviour for multidimensional quasiperiodic systems a novel renormalization plus convolution method is proposed this combined renormalization convolution method has shown an extremely elevated computing efficiency being able to calculate electrical conductance of a three dimensional non crystalline solid with 10 30 atoms finally the dc and ac conductances of mirror fibonacci nanowires are also investigated where a quantized dc conductance variation with the fermi energy is found as observed in gold nanowires

existence of periodic solutions of partial neutral functional differential equations with unbounded delay abstract in this article we establish a result of existence of periodic solutions for the class of quasi linear partial neutral functional differential equations with unbounded delay that can be described as the abstract functional differential equation d dt x t f t x t ax t g t x t where a is the infinitesimal generator of a strongly continuous semigroup of linear operators on a banach space and f and g are appropriate functions defined on a phase space

q gaussian processes non commutative and classical aspects we examine for 1 q 1 q gaussian processes i e families of operators non commutative random variables where the a t fulfill the q commutation relations for some covariance function equipped with the vacuum expectation state we show that there is a q analogue of the gaussian functor of second quantization behind these processes and that this structure can be used to translate questions on q gaussian processes into corresponding and much simpler questions in the underlying hilbert space in particular we use this idea to show that a large class of q gaussian processes possesses a non commutative kind of markov property which ensures that there exist classical versions of these non commutative processes this answers an old question of frisch and bourret fb

on lattice sums and wigner limits abstract wigner limits are given formally as the difference between a lattice sum associated to a positive definite quadratic form and a corresponding multiple integral to define these limits which arose in work of wigner on the energy of static electron lattices in a mathematically rigorous way one commonly truncates the lattice sum and the corresponding integral and takes the limit along expanding hypercubes or other regular geometric shapes we generalize the known mathematically rigorous two and three dimensional results regarding wigner limits as laid down in 3 to integer lattices of arbitrary dimension in doing so we also resolve a problem posed in 6 chapter 7 for the sake of clarity we begin by considering the simpler case of cubic lattice sums first before treating the case of arbitrary quadratic forms we also consider limits taken along expanding hyperballs with respect to general norms and connect with classical topics such as gauss s circle problem appendix a is included to recall certain properties of epstein zeta functions that are either used in the paper or serve to provide perspective

existence and uniqueness of pseudo almost periodic solutions to some abstract partial neutral functional differential equations and applications the paper considers the existence and uniqueness of pseudo almost periodic mild solutions to some classes of first order partial neutral functional differential equations upon making some suitable assumptions existence and uniqueness results are obtained applications include both a partial integro differential equation arising in control systems and the scalar reaction diffusion equation with delay

exponential sums and lattice points iii the gauss circle problem and the dirichlet divisor problem are special cases of the problem of counting the points of the integer lattice in a planar domain bounded by a piecewise smooth curve in the bombieri iwaniec mozzochi exponential sums method we must count the number of pairs of arcs of the boundary curve which can be brought into coincidence by an automorphism of the integer lattice these coincidences are parametrised by integer points close to certain plane curves the resonance curves this paper sets up an iteration step from a strong hypothesis about integer points close to curves to a bound for the discrepancy the number of integer points minus the area as in the latest work on single exponential sums the bombieri iwaniec mozzochi method itself gives bounds for the number of integer points close to a curve in part of the required range and it can in principle be used iteratively we use a bound obtained by swinnerton dyer s approximation determinant method in the discrepancy estimate o r k log r lambda in terms of the maximum radius of curvature r we reduce k from 2 3 classical and 46 73 paper ii in this series to 131 208 the corresponding exponent in the dirichlet divisor problem becomes k 2 131 416

fourth moment theorem and q brownian chaos in 2005 nualart and peccati ann probab 33 1 177 193 2005 proved the so called fourth moment theorem asserting that for a sequence of normalized multiple wiener ito integrals to converge to the standard gaussian law it is necessary and sufficient that its fourth moment tends to 3 a few years later kemp et al ann probab 40 4 1577 1635 2011 extended this theorem to a sequence of normalized multiple wigner integrals in the context of the free brownian motion the q brownian motion q in 1 1 introduced by the physicists frisch and bourret j math phys 11 364 390 1970 in 1970 and mathematically studied by bozejko and speicher commun math phys 137 519 531 1991 interpolates between the classical brownian motion q 1 and the free brownian motion q 0 and is one of the nicest examples of non commutative processes the question we shall solve in this paper is the following what does the fourth moment theorem become when dealing with a q brownian motion

weighted pseudo almost automorphic mild solutions to semilinear fractional differential equations abstract this paper is concerned with the existence and uniqueness of weighted pseudo almost automorphic mild solution to the semilinear fractional equation d t u t au t d t 1 f t u t bu t t r 1 2 where a is a linear densely defined operator of sectorial type on a complex banach space x and b is a bounded linear operator defined on x under the assumption of uniformly continuity on f we establish a composition of weighted pseudo almost automorphic in a general banach space and obtain existence results by means of banach contraction mapping the results obtained are utilized to study the existence and uniqueness of a weighted pseudo almost automorphic solution to fractional diffusion wave equation with dirichlet conditions

cauchy problem for fractional diffusion equations abstract we consider an evolution equation with the regularized fractional derivative of an order 0 1 with respect to the time variable and a uniformly elliptic operator with variable coefficients acting in the spatial variables such equations describe diffusion on inhomogeneous fractals a fundamental solution of the cauchy problem is constructed and investigated

nonexistence of periodic solutions and s asymptotically periodic solutions in fractional difference equations nonexistence of periodic solution is proved for periodic right hand side existence of s asymptotically periodic solutions is discussed existence and uniqueness results are obtained for s asymptotically periodic solution nontrivial estimations of a ratio of gamma functions are used in this paper it is shown that a fractional difference equation with a periodic right hand side can not possess a periodic solution but it can have an s asymptotically periodic solution sufficient conditions are proved for the existence of a unique s asymptotically periodic solution an example is also given illustrating the obtained results

on s asymptotically ω periodic functions and applications abstract let x be a banach space and r a bounded function u c 0 x is called s asymptotically periodic if lim t u t u t 0 in this paper we establish conditions under which an s asymptotically periodic function is asymptotically periodic and we discuss the existence of s asymptotically periodic and asymptotically periodic solutions for an abstract integral equation some applications to partial differential equations and partial integro differential equations are considered

existence of s asymptotically ω periodic solutions for fractional order functional integro differential equations with infinite delay abstract we study s asymptotically periodic solutions of the abstract fractional equation u 1 a u f t u t 1 2 where a is a linear operator of sectorial type 0

free monotone transport by solving a free analog of the monge ampere equation we prove a non commutative analog of brenier s monotone transport theorem if an n tuple of self adjoint non commutative random variables z 1 z n satisfies a regularity condition its conjugate variables 1 n should be analytic in z 1 z n and j should be close to z j in a certain analytic norm then there exist invertible non commutative functions f j of an n tuple of semicircular variables s 1 s n so that z j f j s 1 s n moreover f j can be chosen to be monotone in the sense that and g is a non commutative function with a positive definite hessian in particular we can deduce that c z 1 z n c s 1 s n and w z 1 dots z n cong l mathbb f n thus our condition is a useful way to recognize when an n tuple of operators generate a free group factor we obtain as a consequence that the q deformed free group factors vargamma q mathbb r n are isomorphic for sufficiently small q with bound depending on n to free group factors we also partially prove a conjecture of voiculescu by showing that free gibbs states which are small perturbations of a semicircle law generate free group factors lastly we show that entrywise monotone transport maps for certain gibbs measure on matrices are well approximated by the matricial transport maps given by free monotone transport

hypercontractivity in non commutative holomorphic spaces we prove an analog of janson s strong hypercontractivity inequality in a class of non commutative holomorphic algebras our setting is the q gaussian algebras q associated to the q fock spaces of bozejko kummerer and speicher for q 1 1 we construct subalgebras open image in new window a q segal bargmann transform and prove janson s strong hypercontractivity open image in new window for r an even integer

generalized lambert series and arithmetic nature of odd zeta values it is pointed out that the generalized lambert series sum nolimits n 1 infty n n 2h e n nx 1 studied by kanemitsu tanigawa and yoshimoto can be found on page 332 of ramanujan s lost notebook in a slightly more general form we extend an important transformation of this series obtained by kanemitsu tanigawa and yoshimoto by removing restrictions on the parameters n and h that they impose from our extension we deduce a beautiful new generalization of ramanujan s famous formula for odd zeta values which for n odd and m 0 gives a relation between 2 m 1 and 2 nm 1 a result complementary to the aforementioned generalization is obtained for any even n and m it generalizes a transformation of wigert and can be regarded as a formula for 2 m 1 1 n applications of these transformations include a generalization of the transformation for the logarithm of dedekind eta function z zudilin and rivoal type results on transcendence of certain values and a transcendence criterion for euler s constant

s asymptotically ω positive periodic solutions for a class of neutral fractional differential equations in this paper we investigate the existence of the s asymptotically positive periodic solutions to a class of semilinear neutral caputo fractional differential equations with infinite delay given by d t x t f t x t a x t g t x t t 0 x 0 b the function is considered in a banach space x for 0 1 here a denotes the infinitesimal generator of an analytic semigroup t t t 0

statistical properties of one dimensional parametrically kicked hamilton systems we study the one dimensional hamiltonian systems and their statistical behavior assuming the initial microcanonical distribution and describing its change under a parametric kick which by definition means a discontinuous jump of a control parameter of the system following a previous work by papamikos and robnik j phys a math theor 44 315102 2011 we specifically analyze the change of the adiabatic invariant the action of the system under a parametric kick a conjecture has been put forward that the change of the action at the mean energy always increases which means for the given statistical ensemble that the gibbs entropy in the mean increases by means of a detailed analysis of a great number of case studies we show that the conjecture largely is satisfied except if either the potential is not smooth enough or if the energy is too close to a stationary point of the potential separatrix in the phase space very fast changes in a time dependent system quite generally can be well described by such a picture and by the approximation of a parametric kick if the change of the parameter is sufficiently fast and takes place on the time scale of less than one oscillation period we discuss our work in the context of the statistical mechanics in the sense of gibbs

on a class of retarded integro differential equations with nonlocal initial conditions of concern is the following cauchy problem for fractional integro differential equations with time delay and nonlocal initial condition u t email protected 0 t t s m email protected m 1 au s ds f t u t u k t t 0 u t h t u email protected t email protected email protected 0 where 1 0 a d a x x is a generator of a solution operator on a complex banach space x the convolution integral in the equation is known as the riemann liouville fractional integral k t 0 email protected representing the delay property is a function and h t is an operator defined from email protected 0 xc email protected 0 x into x for some t 0 which constitutes a nonlocal condition the local existence and uniqueness of mild solutions for the cauchy problem under various criteria are proved moreover we present an existence result of the global solution also an example is given to illustrate the applications of the abstract results

on a secant dirichlet series and eichler integrals of eisenstein series we consider the secant dirichlet series psi s tau sum n 1 infty frac sec pi n tau n s recently introduced and studied by lalin rodrigue and rogers in particular we show as conjectured and partially proven by lalin rodrigue and rogers that the values psi 2 m sqrt r with r 0 rational are rational multiples of pi 2 m we then put the properties of the secant dirichlet series into context by showing that for even s they are eichler integrals of odd weight eisenstein series of level 4 this leads us to consider eichler integrals of general eisenstein series and to determine their period polynomials in the level 1 case these polynomials were recently shown by murty smyth and wang to have most of their roots on the unit circle we provide evidence that this phenomenon extends to the higher level case this observation complements recent results by conrey farmer and imamoglu as well as el guindy and raji on zeros of period polynomials of hecke eigenforms in the level 1 case finally we briefly revisit results of a similar type in the works of ramanujan

some remarks on triple l functions we extend the garrett s result i 4 concerning triple l function in two aspects one concerns triple l functions of different weights and the other concerns special values of triple l functions of same weights at inner points of their critical strips let mk fn and sk fn be spaces of siegel modular forms and cuspforms of weight k and of degree n respectively for siegel modular forms f l fro of various degree and a field k we denote by k ft fro the field generated by all the fourier coefficients of f l fro over k we write fourier expansion of f sk f1

local coefficients as artin factors for real groups introduction the purpose of this paper is to prove the equality of certain local coefficients of arithmetic significance which were attached to representations of quasi split real reductive algebraic groups in 27 with their corresponding artin factors attached by local class field theory 21 as a consequence we establish an identity satisfied by certain normalized intertwining operators it seems to be useful in applications of the trace formula 1 29 more precisely let g be the group of real points of a quasi split reductive algebraic group over r let a be the set of simple roots defined by a fixed minimal parabolic subgroup po m0a0u of g fix 6 c a and let p p9 be the corresponding standard parabolic subgroup of g and write p man for its langlands decomposition fix a nondegenerate character x f u i a h o be an irreducible admissible x gic banach in particular x generic unitary representation of m cf section 1 given v g a the complex dual of the lie algebra of a let i v o 0 be the continuously quasi unitarily if o is unitary induced representation indp ga e v 9 and let v v o 0 be its space section 0 then f a vfoo o now let w be the weyl group of ao in g choose w g w such that w 0 c a let n be the unipotent group opposite to n define n u c wn w where w is a representative of w in g for g f a 00 define

regularity of mild solutions for a class of fractional order differential equations in this article we show sufficient conditions ensuring the existence and uniqueness of a mild solution to the equation d au t au t d a 1f t u t 1 a 2 email protected r in the same space where f belongs here a is a sectorial operator defined in a banach space x d a is the fractional derivative in the riemann liouville sense and f x email protected x for each email protected x where w x is a vector valued subspace of the space of continuous and bounded functions the subspaces w x that we will consider in this article are the space of periodic almost periodic almost automorphic and compact almost automorphic vector valued functions among others in particular we extend and unify recent results established for the equation in the papers agarwal et al 2010 cuevas et al 2010 and cuevas and lizama 2008

fock space associated to coxeter groups of type b abstract in this article we construct a generalized gaussian process coming from coxeter groups of type b it is given by creation and annihilation operators on an q fock space which satisfy the commutation relation b q x b q y q b q y b q x x y i x y q 2 n where x y are elements of a complex hilbert space with a self adjoint involution x x and n is the number operator with respect to the grading on the q fock space we give an estimate of the norms of creation operators we show that the distribution of the operators b q x b q x with respect to the vacuum expectation becomes a generalized gaussian distribution in the sense that all mixed moments can be calculated from the second moments with the help of a combinatorial formula related with set partitions our generalized gaussian distribution is associated to the orthogonal polynomials called the q meixner pollaczek polynomials yielding the q hermite polynomials when 0 and free meixner polynomials when q 0

on s asymptotically ω periodic functions on banach spaces and applications abstract this paper is devoted to the study of the class of continuous and bounded functions f 0 x for which exists 0 such that lim t f t f t 0 in the sequel called s asymptotically periodic functions we discuss qualitative properties and establish some relationships between this type of functions and the class of asymptotically periodic functions we also study the existence of s asymptotically periodic mild solutions of the first order abstract cauchy problem in banach spaces

pseudo s asymptotically periodic solutions of second order abstract cauchy problems in this work we discuss the existence of pseudo s asymptotically periodic mild solutions for a second order abstract cauchy problem in particular we show that pseudo s asymptotically periodic cosine functions of operators are periodic the paper is completed with an application to the nonautonomous wave equation

asymptotic periodicity for some evolution equations in banach spaces abstract this work deals with the existence and uniqueness of pseudo almost periodic and asymptotically periodic mild solutions to some evolution equations in banach spaces

asymptotic periodicity for hyperbolic evolution equations and applications we study the existence and uniqueness of pseudo s asymptotically periodic mild solutions for hyperbolic evolution equations we show concrete applications of our methods

weighted sp pseudo s asymptotic periodicity and applications to volterra integral equations abstract this paper is related to the function space formed by weighted sp pseudo s asymptotic periodicity and their applications initially the translation invariance and completeness of the function space are investigated additionally the composition theorem and convolution operator generated by lebesgue integrable functions are presented finally existence and uniqueness of solutions with weighted sp pseudo s asymptotic periodicity for two classes of volterra equations are proved by using the results obtained above and some concrete examples are given the methods mainly include minkowski s inequality convolution inequality contraction mapping principle and especially the generalized minkowski s inequality our results extend some known results on asymptotic periodicity

modular forms and period polynomials we study the space of period polynomials associated with modular forms of integral weight for finite index subgroups of the modular group for the modular group this space is en dowed with a pairing corresponding to the petersson inner product on modular forms via a formula of haberland and with an action of hecke operators defined algebraically by zagier we generalize haberland s formula to not necessarily cuspidal modular forms for finite index subgroups and we show that it conceals two stronger formulas we extend the action of hecke operators to period polynomials of modular forms we show that the pairing on period polynomials appearing in haber land s formula is nondegenerate and we determine the adjoints of hecke operators with respect to it we give a few applications for 1 n an extension of the eichler shimura isomorphism to the entire space of modular forms the determination of the relations satisfied by the even and odd parts of period polynomials associated with cusp forms which are independent of the period rela tions and an explicit formula for fourier coefficients of hecke eigenforms in terms of their period polynomials generalizing the coefficients theorem of manin

asymptotically periodic solutions of fractional differential equations abstract we study the existence of pseudo s asymptotically periodic mild solutions for a class of abstract fractional differential equation

type b gaussian statistics as noncommutative central limits abstract we show that the noncommutative central limit theorem of speicher can be adapted to produce the gaussian statistics associated to coxeter groups of type b in the sense of bozejko ejsmont and hasebe viewed through the lens of central limits the passage from q gaussian statistics associated with symmetric groups to the gaussian statistics associated with coxeter groups of type b is precisely the passage from a sequence of independent elements that pairwise commute or anticommute to a coupled pair of such sequences the results pave the way for the transfer of known results from the bosonic fermionic settings to such broader contexts

s asymptotically ω periodic solutions to some classes of partial evolution equations abstract in this paper we give some sufficient conditions for the existence and uniqueness of s asymptotically periodic mild solutions to some classes of partial evolution equations in banach spaces the main result is obtained by means of the banach fixed point principle

compact almost automorphic solutions to semilinear cauchy problems with non dense domain in this work we study the existence and uniqueness of compact almost automorphic solutions to a first order differential equation with a linear part dominated by a hille yosida type operator with non dense domain

statistical properties of the energy in time dependent homogeneous power law potentials we study classical 1d hamilton systems with a homogeneous power law potential and their statistical behavior assuming a microcanonical distribution of the initial conditions and describing its change under a monotonically increasing time dependent function a t the prefactor of the potential using the nonlinear wentzel kramers brillouin like method of papamikos and robnik 2012 j phys a math theor 44 315102 and following a previous work by papamikos and robnik 2011 j phys a math theor 45 015206 we specifically analyze the mean energy the variance and the adiabatic invariant action of the systems for large time and we show that the mean energy and variance increase as powers of a t while the action oscillates and finally remains constant by means of a number of detailed case studies we show that the theoretical prediction is excellent which demonstrates the usefulness of the method in such applications

compact almost automorphic solutions to integral equations with infinite delay abstract given a l 1 r and the generator a of an l 1 integrable resolvent family of linear bounded operators defined on a banach space x we prove the existence of compact almost automorphic solutions of the semilinear integral equation u t t a t s a u s f s u s d s for each f r x x compact almost automorphic in t for each x x and satisfying lipschitz and holder type conditions in the scalar linear case we prove that a l 1 r positive nonincreasing and log convex is sufficient to obtain the existence of compact almost automorphic solutions

energy of static electron lattices a new approach to evaluating the static lattice energy of any given wigner lattice is proposed the method is much simpler than the traditional one and the results are much faster to evaluate the new approach is applied to two dimensional triangular lattices where it is shown that the triangular lattice is more stable than the square lattice three dimensional hexagonal lattices are also investigated in addition the authors place many of their considerations on a rigorous mathematical footing

asymptotically almost periodic solutions of abstract differential equations abstract in this paper we are concerned with the problem of existence and uniqueness of asymptotically almost periodic mild solutions of nonhomogeneous first order abstract differential equations essentially we obtain existence of asymptotically almost periodic solutions when the semigroup is asymptotically almost periodic or when the forcing term is an asymptotically stepanov almost periodic function

characterizations of almost periodic strongly continuous cosine operator functions abstract we characterize in terms of the infinitesimal generator those cosine operator functions which are almost periodic or uniformly almost periodic

existence of mild solutions for fractional integrodifferential equations of sobolev type with nonlocal conditions abstract this paper is concerned with the fractional integrodifferential equations of sobolev type with nonlocal condition in a separable banach space with the help of the theory of propagation family as well as the theory of the measures of noncompactness and the condensing maps we obtain the existence result of mild solutions for above equations two examples are given to illustrate the existence theorem

almost periodic and pseudo almost periodic solutions to fractional differential and integro differential equations abstract we study the existence of almost periodic resp pseudo almost periodic mild solutions for fractional differential and integro differential equations in the case when the forcing term belongs to the class of stepanov almost resp stepanov like pseudo almost periodic functions

optimal hypercontractivity for fermi fields and related non commutative integration inequalities optimal hypercontractivity bounds for the fermion oscillator semigroup are obtained these are the fermion analogs of the optimal hypercontractivity bounds for the boson oscillator semigroup obtained by nelson in the process several results of independent interest in the theory of non commutative integration are established

existence results for fractional neutral integro differential equations with state dependent delay in this paper we study the existence of mild solutions for a class of abstract fractional neutral integro differential equations with state dependent delay the results are obtained by using the leray schauder alternative fixed point theorem an example is provided to illustrate the main results

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

global stability and asymptotically periodic solution for nonautonomous cooperative lotka volterra diffusion system two asymptotically cooperative lotka volterra populations in the two patch system with diffusion were considered in this paper each population could diffuse independently and discretely between its intrapatch and interpatch by means of constructing a suitable liapunov function we obtained that the systems had a unique asymptotically periodic solution which was globally asymptotically stable

on quasi periodic properties of fractional sums and fractional differences of periodic functions this article is devoted to the study of discrete fractional calculus our goal is to investigate quasi periodic properties of fractional order sums and differences of periodic functions using riemann liouville and caputo type definitions we study concepts close to the well known idea of periodic function such as asymptotically periodicity or s asymptotically periodicity we use basic tools of discrete fractional calculus boundedness of sums and differences of fractional order of a given periodic function is also investigated