on l1 invariant sequence spaces abstract we introduce and investigate a new sectional property for topological sequence spaces which we call the kb property it turns out that multipliers into l and multiplication by l 1 play a very similar role for kb as multipliers into bs and multiplication by bv 0 do for the well known sectional property ab however we also encounter significant differences one of these differences motivates the study of l 1 invariant sequence spaces that is sequence spaces e with l 1 e e

gromov witten classes quantum cohomology and enumerative geometry the paper is devoted to the mathematical aspects of topological quantum field theory and its applications to enumerative problems of algebraic geometry in particular it contains an axiomatic treatment of gromov witten classes and a discussion of their properties for fano varieties cohomological field theories are defined and it is proved that tree level theories are determined by their correlation functions application to counting rational curves on del pezzo surfaces and projective spaces are given

symmetries of lagrangian fibrations abstract we construct fiber preserving anti symplectic involutions for a large class of symplectic manifolds with lagrangian torus fibrations in particular we treat the k3 surface and the six dimensional examples constructed by castano bernard and matessi 2009 8 which include a six dimensional symplectic manifold homeomorphic to the quintic threefold we interpret our results as corroboration of the view that in homological mirror symmetry an anti symplectic involution is the mirror of duality in the same setting we construct fiber preserving symplectomorphisms that can be interpreted as the mirror to twisting by a holomorphic line bundle

real gromov witten theory in all genera and real enumerative geometry construction the first part of this work constructs positive genus real gromov witten invariants of realorientable symplectic manifolds of odd complex dimensions the second part studies the orientations on the moduli spaces of real maps used in constructing these invariants the present paper applies the results of the latter to obtain quantitative and qualitative conclusions about the invariants defined in the former after describing large collections of real orientable symplectic manifolds we show that the genus 1 real gromov witten invariants of sufficiently positive almost kahler threefolds are signed counts of real genus 1 curves only and thus provide direct lower bounds for the counts of these curves in such targets we specify real orientations on the real orientable complete intersections in projective spaces the real gromov witten invariants they determine are in a sense canonically determined by the complete intersection itself at least in most cases we also obtain equivariant localization data that computes the real invariants of projective spaces and determines the contributions from many torus fixed loci for other complete intersections our results confirm walcher s predictions for the vanishing of these invariants in certain cases and for the localization data in other cases

floor diagrams relative to a conic and gw w invariants of del pezzo surfaces abstract we enumerate via floor diagrams complex and real curves in c p 2 blown up in n points on a conic as an application we deduce gromov witten and welschinger invariants of del pezzo surfaces these results are mainly obtained using li s degeneration formula and its real counterpart

open gromov witten invariants in dimension six let l be a closed orientable lagrangian submanifold of a closed symplectic six manifold x omega we assume that the first homology group h 1 l a with coefficients in a commutative ring a injects into the group h 1 x a and that x contains no maslov zero pseudo holomorphic disc with boundary on l then we prove that for every generic choice of a tame almost complex structure j on x every relative homology class d in h 2 x l mathbb z and adequate number of incidence conditions in l or x the weighted number of j holomorphic discs with boundary on l homologous to d and either irreducible or reducible disconnected which satisfy the conditions does not depend on the generic choice of j provided that at least one incidence condition lies in l these numbers thus define open gromov witten invariants in dimension six taking values in the ring a

some new sequence spaces derived by the domain of generalized difference matrix let l denote any one of the classical spaces c c 0 and p of bounded convergent null and absolutely p summable sequences respectively and l also be the domain of the generalized difference matrix b r s in the sequence space l where 1 p the present paper is devoted to studying on the sequence space l furthermore the b and c duals of the space l are determined and the schauder bases for the spaces c c 0 and p are given and some topological properties of the spaces c 0 1 and p are examined finally the classes l 1 l 2 and l 1 l 2 of infinite matrices are characterized where l 1 c c 0 p 1 and l 2 c c 0 1

tropical real hurwitz numbers in this paper we define tropical analogues of real hurwitz numbers i e numbers of covers of surfaces with compatible involutions satisfying prescribed ramification properties we prove a correspondence theorem stating the equality of the tropical numbers with their real counterparts we apply this theorem to the case of double hurwitz numbers which generalizes our result from guay paquet et al 2014

enumeration of real curves in mathbb c mathbb p 2n 1 and a witten dijkgraaf verlinde verlinde relation for real gromov witten invariants

generalization of the sequence space l p derived by weighted mean abstract the sequence space l p was introduced and studied by maddox i j maddox spaces of strongly summable sequences quart j math oxford 2 18 1967 345 355 in the present paper the sequence spaces l u v p of non absolute type which is derived by the generalized weighted mean is defined and proved that the spaces l u v p and l p are linearly isomorphic besides this the and duals of the space l u v p are computed and the basis of that space is constructed further it is established that the sequence space l p u v has ad property and given f dual of the space l p u v finally the matrix mappings from the sequence spaces l u v p to the sequence space and from the sequence space to the sequence space l u v p are characterized

certain topological properties and duals of the domain of a triangle matrix in a sequence space the matrix domain of the particular limitation methods cesaro riesz difference summation and euler were studied by several authors in the present paper certain topological properties and and duals of the domain of a triangle matrix in a sequence space have been examined as an application of the characterization of the related matrix classes

lower bounds for enumerative counts of positive genus real curves abstract we transform the positive genus real gromov witten invariants of many real orientable symplectic threefolds into signed counts of curves these integer invariants provide lower bounds for counts of real curves of a given genus that pass through conjugate pairs of constraints we conclude with some implications and related conjectures for hodge integrals

on the b difference sequence space derived by generalized weighted mean and compact operators abstract in the present paper by using generalized weighted mean and difference matrix b we introduce the paranormed sequence space l u v p b which consist of all sequences whose generalized weighted b difference means are in the linear space l p introduced by i j maddox also we give the basis of this space and compute its and duals further we characterize the classes of matrix mappings from l u v p b to l c and c 0 finally we apply the hausdorff measure of noncompactness to characterize some classes of compact operators given by matrices on the space l p u v b 1 p

some new paranormed sequence spaces maddox defined the sequence spaces l p c p and c0 p in proc camb philos soc 64 1968 335 quart j math oxford 2 18 1967 345 in the present paper the sequence spaces a0r u p and acr u p of non absolute type have been introduced and proved that the spaces a0r u p and a0r u p are linearly isomorphic to the spaces c0 p and c p respectively besides this the and duals of the spaces a0r u p and acr u p have been computed and their basis have been constructed finally a basic theorem has been given and later some matrix mappings from a0r u p to the some sequence spaces of maddox and to some new sequence spaces have been characterized

automorphismes reels d un fibre et operateurs de cauchy riemann soit n c n un fibre vectoriel complexe muni d une structure reelle au dessus d une courbe reelle sigma g c sigma de genre g in mathbb n nous etudions le signe de l action des automorphismes de n c n relevant l identite de sigma g sur les orientations du fibre determinant au dessus de l espace des operateurs de cauchy riemann reels de n c n ce signe s obtient comme le produit de deux termes le premier calcule la signature des permutations induite par les automorphismes sur les structures pin pm de la partie reelle de n c n le second provient de l action des automorphismes du fibre sur les classes de bordisme de structures spin reelles de sigma g c sigma

on the euler sequence spaces which include the spaces lp and l ii abstract by e p r we mean the space of all sequences whose euler transforms of order r are in the sequence spaces l p and l see b altay f basar m mursaleen on the euler sequence spaces which include the spaces l p and l i inform sci 2005 in press where 1 p in the present paper we essentially characterize the classes e p r l e 1 r l p and e p r f of infinite matrices for 1 p and give the characterizations of some other matrix mappings from the space e p r to the euler riesz difference etc sequence spaces by means of a given basic lemma we devote the final section of the paper to examining some geometric properties of the space e p r

spinor states of real rational curves in real algebraic convex 3 manifolds and enumerative invariants let x be a real algebraic convex 3 manifold whose real part is equipped with a pin i structure we show that every irreducible real rational curve with non empty real part has a canonical spinor state belonging to f 1g the main result is then that the algebraic count of the number of real irreducible rational curves in a given numerical equivalence class passing through the appropriate number of points does not depend on the choice of the real conflguration of points provided that these curves are counted with respect to their spinor states these invariants provide lower bounds for the total number of such real rational curves independantly of the choice of the real conflguration of points

matrix transformations between sequence spaces of generalized weighted means the main object of this paper is to introduce and study some sequence spaces which arise from concept of weighted means determine their b duals and characterize matrix transformations between them

on some new generalized sequence spaces abstract in this paper we define the sequence sets l u 2 p c u 2 p and c0 u 2 p and give and duals of these sets further we investigate matrix transformations in the spaces and give a characterization of the class l u 2 p l

open gromov witten disk invariants in the presence of an anti symplectic involution abstract for a symplectic manifold with an anti symplectic involution having non empty fixed locus we construct a model of the moduli space of real sphere maps out of moduli spaces of decorated disk maps and give an explicit expression for its first stiefel whitney class as a corollary we obtain a large number of examples which include all odd dimensional projective spaces and many complete intersections for which many types of real moduli spaces are orientable for these manifolds we define open gromov witten invariants with no restriction on the dimension of the manifolds or the type of the constraints if there are no boundary marked points a wdvv type recursion obtained in a sequel computes these invariants for many real symplectic manifolds if there are boundary marked points we define the invariants under some restrictions on the allowed boundary constraints even though the moduli spaces are not orientable in these cases

almost convergence and generalized difference matrix let f denotes the space of almost convergent sequences introduced by lorentz g g lorentz a contribution to the theory of divergent sequences acta math 80 1948 167 190 and f also be the domain of the generalized difference matrix b r s in the sequence space f in this paper the b and c duals of the spaces f fs and f are determined furthermore two basic results on the space f are proved and the classes f m and m f of infinite matrices are characterized and the characterizations of some other classes are also given as an application of those main results where m is any given sequence space

bounds for the lq spectra of a self similar multifractal not satisfying the open set condition abstract by now the l q spectra of self similar measures satisfying the so called open set condition is well understood however if the open set condition is not satisfied then almost nothing is known in this paper we provide non trivial bounds for the l q spectra of an arbitrary self similar measure we emphasize that we are considering arbitrary self similar measures and sets which are not assumed to satisfy the open set condition or similar separation conditions

some new difference sequence spaces the difference sequence spaces d c d and c 0 d were studied by kizmaz canad math bull 24 2 1981 169 the sequence spaces a 0 r and a c r have been recently defined and examined by aydin and basar in hokkaido math j in press the main purpose of the present paper is to introduce the spaces a r 0 d and a r c d of difference sequences moreover it is proved that the spaces a r 0 d and a r c d are the bk spaces including the spaces c 0 and c and some inclusion relations have been given it is also proved that the sequence space a 0 r has ad property while the space a 0 r d has not furthermore the basis and the a b and c duals of the spaces a r 0 d and a r c d have been determined the last section of the paper has been devoted to theorems on the characterizations of the matrix classes a r c d p and a r c d c and the characterizations of some other matrix classes have been obtained by means of a given basic lemma where 1

the mixed lq spectra of self conformal measures satisfying the weak separation condition abstract by now the l q spectra of self conformal measures satisfying the so called open set condition are well understood however if the open set condition is not satisfied then almost nothing is known in this paper we compute the mixed l q spectra for self conformal measures which have bound distortion property and satisfy the weak separation condition

open gromov witten theory on symplectic manifolds and symplectic cutting abstract let x be a symplectic manifold and l be a lagrangian submanifold diffeomorphic to s n r p n or a lens space of a certain type using the symplectic cut and symplectic sum constructions we express the open gromov witten invariants of x l in terms of open gromov witten invariants of a pair x l determined by l and the standard gromov witten invariants of a symplectic manifold x determined by x l we also describe other applications of this approach

bounds for the lq spectra of self similar measures without any separation conditions abstract in this paper we obtain non trivial bounds for the l q spectra of self similar measures without any separation conditions for q 1 as an application we obtain non trivial upper bounds for the multifractal spectra of arbitrary self similar measure without any separation conditions some examples illustrating our results are also discussed

on the euler sequence spaces which include the spaces l p and l i in the present paper we introduce the euler sequence space e p r consisting of all sequences whose euler transforms of order r are in the space p of non absolute type which is the bk space including the space p and prove that the spaces e p r and p are linearly isomorphic for 1

multifractal measures and a weak separation condition abstract we define a new separation property on the family of contractive similitudes that allows certain overlappings this property is weaker than the open set condition of hutchinson it includes the well known class of infinite bernoulli convolutions associated with the p v numbers and the solutions of the two scale dilation equations our main purpose in this paper is to prove the multifractal formalism under such condition

generalized spaces of difference sequences abstract let l c and c 0 be the banach spaces of bounded convergent and null sequences x x k 1 respectively write x x k x k 1 1 and 2 x x k x k 1 1 in canad math bull 24 1981 169 176 h kizmaz has introduced and studied the sequence spaces e x x e where e c 0 c l recently doga mat 17 1993 18 24 mikail et defined the sets e 2 x 2 x e he obtained duals of these sets and characterized the matrix class e f 2 where e f c 0 c l in this paper we generalize these sets and define e u 2 x u 2 x e where u u k is another sequence such that u k 0 k 1 2 we obtain and duals of these sets and further we characterize the matrix classes e u 2 f and e f u 2

some generalizations of the space b vp of p bounded variation sequences the spaces bvp and bv of sequences of p bounded variation have recently been introduced by basar and altay f basar b altay on the space of sequences of p bounded variation and related matrix mappings ukrainian math j 55 1 2003 136 147 where 1 p in the present paper the sequence spaces bv u p and bv u p of non absolute type have been defined and it has been proved that the spaces bv u p and bv u p are linearly isomorphic to the spaces l p and l p of maddox respectively besides this the and duals of the spaces bv u p and bv u p have been computed and the basis of the space bv u p has been constructed the classes bv u p l and bv u p c of infinite matrices have been characterized and the characterizations of some other classes have also been derived by means of a given basic lemma the final section of the paper has been devoted to some consequences about the rotundity of the space bv u p

matrix transformations on some sequence spaces related to strong cesaro summability and boundedness the spaces a 0 r d a c r d and a r d introduced by aydin and basar c aydin f basar some new difference sequence spaces appl math comput 157 3 2004 677 693 can be considered as the matrix domains of a triangle in the sets of all sequences that are summable to zero summable and bounded by the cesaro method of order 1 here we define the sets of sequences which are the matrix domains of that triangle in the sets of all sequences that are summable summable to zero or bounded by the strong cesaro method of order 1 with index p 1 we determine the b duals of the new spaces and characterize matrix transformations on them into the sets of bounded convergent and null sequences

mixed generalized dimensions of self similar measures abstract classical multifractal analysis studies the local scaling behaviour of a single measure however recently mixed multifractal has generated interest mixed multifractal analysis studies the simultaneous scaling behaviour of finitely many measures and provides the basis for a significantly better understanding of the local geometry of fractal measures the purpose of this paper is twofold firstly we define and develop a general and unifying mixed multifractal theory of mixed renyi dimensions also sometimes called the generalized dimensions mixed l q dimensions and mixed coarse multifractal spectra for arbitrary doubling measures secondly as an application of the general theory developed in this paper we provide a complete description of the mixed multifractal theory of finitely many self similar measures

the matrix domain and the spectra of a generalized difference operator abstract in this paper some results of the generalized difference operator b v m are studied the euler difference sequence spaces e 0 t b v m and e c t b v m are introduced furthermore some functional properties and duals of these sequence spaces are examined finally the sets of the spectrum the point spectrum the residual spectrum and the continuous spectrum of the operator b v m on the space l 1 are given

invariants of real symplectic 4 manifolds and lower bounds in real enumerative geometry we first build the moduli spaces of real rational pseudo holomorphic curves in a given real symplectic 4 manifold then following the approach of gromov and witten 3 19 11 we define invariants under deformation of real symplectic 4 manifolds these invariants provide lower bounds for the number of real rational j holomorphic curves which realize a given homology class and pass through a given real configuration of points

some paranormed sequence spaces of non absolute type derived by weighted mean abstract the sequence spaces l p c p and c 0 p were introduced and studied by maddox i j maddox paranormed sequence spaces generated by infinite matrices proc cambridge philos soc 64 1968 335 340 in the present paper the sequence spaces u v p of non absolute type which are derived by the generalized weighted mean are defined and proved that the spaces u v p and p are linearly isomorphic where denotes the one of the sequence spaces l c or c 0 besides this the and duals of the spaces u v p are computed and the basis of the spaces c 0 u v p and c u v p is constructed additionally it is established that the sequence space c 0 u v has ad property and given the f dual of the space c 0 u v p finally the matrix mappings from the sequence spaces u v p to the sequence space and from the sequence space to the sequence spaces u v p are characterized

opening mirror symmetry on the quintic aided by mirror symmetry we determine the number of holomorphic disks ending on the real lagrangian in the quintic threefold we hypothesize that the tension of the domainwall between the two vacua on the brane which is the generating function for the open gromov witten invariants satisfies a certain extension of the picard fuchs differential equation governing periods of the mirror quintic we verify consistency of the monodromies under analytic continuation of the superpotential over the entire moduli space we further check the conjecture by reproducing the first few instanton numbers by a localization computation directly in the a model and verifying ooguri vafa integrality this is the first exact result on open string mirror symmetry for a compact calabi yau manifold

some new sequence spaces derived by the domain of the triple band matrix let l denote any of the classical spaces c c 0 and p of bounded convergent null and absolutely p summable sequences respectively and let l b also be the domain of the triple band matrix b r s t in the sequence space l where 1

lower bounds and asymptotics of real double hurwitz numbers we study the real counterpart of double hurwitz numbers called real double hurwitz numbers here we establish a lower bound for these numbers with respect to their dependence on the distribution of branch points we use it to prove under certain conditions existence of real hurwitz covers as well as logarithmic equivalence of real and classical hurwitz numbers the lower bound is based on the tropical computation of real hurwitz numbers in markwig and rau math z 281 1 2 501 522 2015