generalized tate curve and integral teichmuller modular forms in this paper we establish a higher genus version of the tate elliptic curve i e for a given degenerate curve we construct its universal deformation defined over the ring of formal power series of certain deformation parameters whose coefficients are in a finitely generated z algebra described by the dual graph of the degenerate curve further we study automorphic forms on the moduli space of algebraic curves which we call teichmuller modular forms by evaluating these forms on the generalized tate curve in particular we show that integral teichmuller modular forms of given degree make a finitely generated ring and we describe the structure of this ring in degree 2 and 3 cases introduction the aim of this paper is to construct a higher genus version of the tate elliptic curve over a nonlocal base ring and to study integral automor phic forms on the moduli space of algebraic curves of genus 2 by evaluating these forms on the generalized tate curve as will be stated below our results extend earlier results of the author in 10 11 12 14 and are obtained especially by using excellent works of mumford faltings and chai 22 21 3 4 the periods and 1 forms of the generalized tate curve were used in 13 to construct universal and p adic solutions of the kp kadomtsev petvyashvili hierarchy in 10 section 2 the author obtained universal power series for multiplica tive periods of curves of fixed genus g which combined with the results of 21 and 4 chapter iii allowed us to deduce the existence of a universal jacobian semi abelian scheme j univ of relative dimension g over the ring

on the jacobian ring of a complete intersection abstract let f 1 f r k x k is a field be homogeneous polynomials and put f i 1 r y i f i k x y the quotient j k x y i where i is the ideal generated by the f x i and f y j is the jacobian ring of f we describe j by computing the cohomology of a certain complex whose top cohomology group is j

impulsive boundary value problems with nonlinear boundary conditions abstract in this paper the upper and lower solution method and schauder s fixed point theorem are employed in the study of boundary value problems for a class of second order impulsive ordinary differential equations with nonlinear boundary conditions we prove the existence of solutions to the problem under the assumption that there exist lower and upper solutions associated with the problem

impulsive bvps with nonlinear boundary conditions for the second order differential equations without growth restrictions abstract the paper deals with the impulsive nonlinear boundary value problem u t f t u t u t g 1 u a u b 0 g 2 u a u b 0 u t j i j u t j j 1 p u t j m j u t j j 1 p where j a b f car j r 2 g 1 g 2 c r 2 i j m j c r we prove the existence of a solution to this problem under the assumption that there exist lower and upper functions associated with the problem our proofs are based on the schauder fixed point theorem and on the method of a priori estimates no growth restrictions are imposed on f g1 g2 ij mj

equiangular lines and spherical codes in euclidean space a family of lines through the origin in euclidean space is called equiangular if any pair of lines defines the same angle the problem of estimating the maximum cardinality of such a family in mathbb r n was extensively studied for the last 70 years motivated by a question of lemmens and seidel from 1973 in this paper we prove that for every fixed angle theta and sufficiently large n there are at most 2n 2 lines in mathbb r n with common angle theta moreover this bound is achieved if and only if theta arccos frac 1 3 indeed we show that for all theta ne arccos frac 1 3 and and sufficiently large n the number of equiangular lines is at most 1 93n we also show that for any set of k fixed angles one can find at most o n k lines in mathbb r n having these angles this bound conjectured by bukh substantially improves the estimate of delsarte goethals and seidel from 1975 various extensions of these results to the more general setting of spherical codes will be discussed as well

on the monodromy of the moduli space of calabi yau threefolds coming from eight planes in mathbb p 3 it is a fundamental problem in geometry to decide which moduli spaces of polarized algebraic varieties are embedded by their period maps as zariski open subsets of locally hermitian symmetric domains in the present work we prove that the moduli space of calabi yau threefolds coming from eight planes in mathbb p 3 does not have this property we show furthermore that the monodromy group of a good family is zariski dense in the corresponding symplectic group moreover we study a natural sublocus which we call hyperelliptic locus over which the variation of hodge structures is naturally isomorphic to wedge product of a variation of hodge structures of weight one it turns out the hyperelliptic locus does not extend to a shimura subvariety of type iii siegel space within the moduli space besides general hodge theory representation theory and computational commutative algebra one of the proofs depends on a new result on the tensor product decomposition of complex polarized variations of hodge structures

dichotomies for impulsive differential systems abstract we obtain necessary and sufficient conditions for the bounded growth for differential systems with impulses we derive sufficient conditions for the existence of exponential dichotomy for the constant impulse systems a relation between the dichotomy and bounded growth is given dichotomies and boundedness are discussed in the last section

nonoscillation of first order impulse differential equations with delay abstract oscillation properties of impulse functional differential equations are studied for equations of the type x t i 1 m p i t x t i t 0 t a b x 0 a b x t j j x t j 0 j 1 k a t 1 t 2 t k b pthe proven test for oscillation generalizes the known ones and allows consideration of the solvability of boundary value problems for the corresponding nonhomogeneous impulse equations in particular for the scalar impulse equation x t p t x t t 0 t 0 x 0 for 0 x t j j x t j 0 j 0 j 1 2 denoteb t j dt j wheredt i ti t t t p t max p t 0 p roposition let 1 ln b t e r t t p s ds wherer t max t t 0 t 0 then the nontrivial solution of this equation has no zeros on 0

periodic boundary value problems for second order impulsive differential systems on etudie le probleme aux valeurs limites periodiques pour un systeme d equations differentielles d ordre 2 faiblement couplees avec impulsion

factorial property of a ring of automorphic forms a ring of automorphic forms is shown to be factorial under some conditions on the domain and on the picard group as an application we show that any divisor on the moduli space 2jf k of curves of genus g 3 is defined by a single element and that the satake compactification of u is is written as a projective spectrum of a factorial graded ring we find a single element which defines the closure of w4 in 5w4 where 3tf 4 is the moduli of curves of genus four whose canonical curves are exhibited as complete intersections of quadric cones and of cubics in p3 introduction let x be a normal quasi projective variety over c such that i x has a normal projective compactification x with codim a a 2 and ii x is a quotient space 2 t of a connected domain 2 with pic 0 by a discontinu ous group t of holomorphic automorphisms then the canonically determined homogeneous coordinate ring of x is factorial under some conditions on t or essentially on the picard group pic t in our notation theorem 1 when 2 is the siegel space and t is the modular group freitag 9 10 has shown that the homogeneous coordinate ring of x or more precisely the graded ring of siegel modular forms is factorial provided that the degree is greater than two our theorem is applicable to the case when x is the moduli space wlg of curves of genus g we need to know the first or second betti number of 3rg or of the teichmuller modular group tg which will almost determine the picard group in mumford 19 the first betti number ex 2rg of 3 would be one harer 12 proved it for g 5 and in this paper we show it for g 3 4 which seems more or less well known as for the case of 2 being a bounded symmetric domain the determination of the betti numbers is covered by the calculation of the stable real cohomology due to borel 2 for a fairly large class of 2 as an application of our method we show that the closure in 9ji4 of the moduli w4 of nonhyperelliptic curves of genus four exhibited as complete intersections of quadric cones and of cubics in ip3 is a subvariety defined by a principal ideal and gives the generator of the principal ideal this work was done while the author was staying at harvard university he

nonlinear second order equations with functional implicit impulses and nonlinear functional boundary conditions abstract in this paper we present existence results for solutions of nonlinear second order boundary value problems with impulses our impulses are applied at p points in the interval and given implicitly by nonlinear functions of the solution moreover we allow functional dependence on the solution our existence results follow from the existence of a pair of well ordered lower and upper solutions we generalize earlier results of cabada and tomec ek allowing more general compatible boundary conditions impulses and laplacian equations

a multiplicity result for second order impulsive differential equations via the leggett williams fixed point theorem using the leggett williams fixed point theorem we present in this paper criteria which guarantee the existence of three nonnegative solutions to second order impulsive equations

existence of solution for m point boundary value problems of second order differential systems with impulses with the help of the coincidence degree continuation theorem we get a general theorem concerning the existence of solution of the m point boundary value problems for second order differential systems with impulses we also give a definition of autonomous curvature bound set relative to this m point boundary value problems and by using this definition and the above existence theorem we obtain some simple existence conditions of solution for these boundary value problems in particular when the impulses are absent our results can be applied to study the usual m point boundary value problems at resonance

existence result for impulsive third order periodic boundary value problems this paper is devoted to the study of periodic boundary value problems for nonlinear third order differential equations subjected to impulsive effects we provide sufficient conditions on the nonlinearity and the impulse functions that guarantee the existence of at least one periodic solution our approach is based on a priori estimates the method of upper and lower solutions combined with an iterative technique which need not be monotone

existence results for impulsive second order periodic problems abstract this paper provides existence results for the nonlinear impulsive periodic boundary value problem u f t u u u t i j i u t i u t i m i u t i i 1 2 m u 0 u t u 0 u t where f car 0 t r 2 and j i m i c r the basic assumption is the existence of lower upper functions 1 2 associated with the problem here we generalize and extend the existence results of our previous papers

periodic boundary value problem for first order impulsive delay differential equations in this paper by means of the method of upper and lower solutions and the monotone iterative technique the existence of maximal and minimal solutions of the periodic boundary value problem for first order impulsive delay differential equations is considered

half canonical series on algebraic curves preprint enviat per a la seva publicacio en una revista cientifica transactions of the american mathematical society vol 302 no 1 1987 pp 99 115 https www jstor org stable 2000899

multiple positive solutions of singular two point boundary value problems for second order impulsive differential equations we study the existence behavior of positive solutions to a singular two point boundary value problem of second order impulsive equation with fixed moments proofs are based on combining a method of upper and lower solutions with fixed point index theorems on a cone

existence of solutions and nonnegative solutions for weighted p r laplacian impulsive system multi point boundary value problems abstract this paper investigates the existence of solutions for weighted p r laplacian impulsive system multi point boundary value problems our analysis is based on gaines and mawhin s coincidence degree theory several criteria for the existence of solutions are given in particular we obtain the existence of nonnegative solutions

existence results for boundary value problems of second order impulsive differential equations abstract with the help of lower and upper solutions the extremal solutions of a second order impulsive differential equation are obtained as limits of monotone iterates several existence results for the second order impulsive differential equation subject to nonlinear boundary conditions which include the usual periodic and linear separated boundary conditions are also established

the modular variety of hyperelliptic curves of genus three the modular variety of nonsingular and complete hyperelliptic curves with level two structure of genus 3 is a 5 dimensional quasi projective variety which admits several standard compactifications the first one realizes this variety as a subvariety of the siegel modular variety of level two and genus three it has 36 irreducible isomorphic components one of the purposes of this paper will be to describe the equations of one of these components two further models use the fact that hyperelliptic curves of genus three can be obtained as coverings of a projective line with 8 branch points there are two important compactifications of this configuration space the first one y uses the semistable degenerated point configurations in p 1 8 this variety also can be identified with a baily borel compactified ball quotient y b 1 i we will describe these results in some detail and obtain new proofs including some finer results for them the other compactification uses the fact that families of marked projective lines can degenerate to stable marked curves of genus 0 we use the standard notation m 0 8 for this compactification we have a diagram the horizontal arrow is only birational but not everywhere regular in this paper we find another realization of this triangle which uses the fact that there are graded algebras closely related to algebras of modular forms a b such that x proj a y proj b

periodic solutions to impulsive differential inclusions with constraints abstract the existence of a periodic solution to an impulsive differential inclusion being invariant with respect to a non convex set of state constraints is established by the use a lefschetz type fixed point theorem for set valued maps

boundary value problems for higher order linear impulsive differential equations in this paper higher order linear impulsive differential equations with fixed moments of impulses subject to linear boundary conditions are studied green s formula is defined for piecewise differentiable functions properties of green s functions for higher order impulsive boundary value problems are introduced an appropriate example of the green s function for a boundary value problem is provided furthermore eigenvalue problems and basic properties of eigensolutions are considered

extremal solutions for nonlinear functional ϕ laplacian impulsive equations abstract in this paper we deal with some nonlinear laplacian second order boundary value problems with impulses subject to a general type of boundary value conditions which cover dirichlet and periodic boundary data as particular cases our approach is that of upper and lower solutions together with growth restrictions of nagumo s type the impulsive functions depend implicitly on the different considered variables and the boundary value conditions are nonlinear in both cases functional dependence on the solution is allowed

on the distribution of the maximum eigenvalue of graphs abstract given a graph g let g denote the largest eigenvalue of the adjacency matrix of g we prove that for any 2 5 2 058 there exists a sequence of graphs g1 g2 such that limk gk thus answering a question posed by hoffman

infinitesimal variation of hodge structures and the weak global torelli theorem for complete intersections in this paper we will study the weak global torelli theorem for complete intersections of hypersurfaces in a projective space let x be a non singular projective variety of dimension r with an ample line bundle l over the complex number field c then the primitive part hrm x z of the cohomology of x has a polarized hodge structure if the moduli space x of x exists we can define the global period map ho d r from the moduli space x to the classifying space d r of hodge structures attaching the point p in x to the hodge structure of the primitive part hrim xp z of the cohomology group of xp p e 4

existence of simple jacobian varieties of genus g with rank at least 4g 5 we prove the existence of infinitely many curves of genus g over the rational number field which have absolutely simple jacobian varieties with mordell weil rank at least 4 g 5

the monodromy groups of dolgachev s cy moduli spaces are zariski dense abstract let m n 2 n 2 be the coarse moduli space of cy manifolds arising from a crepant resolution of double covers of p n branched along 2 n 2 hyperplanes in general position we show that the monodromy group of a good family for m n 2 n 2 is zariski dense in the corresponding symplectic or orthogonal group if n 3 in particular the period map does not give a uniformization of any partial compactification of the coarse moduli space as a shimura variety whenever n 3 this disproves a conjecture of dolgachev as a consequence the fundamental group of the coarse moduli space of m ordered points in p n is shown to be large once it is not a point similar zariski density result is obtained for moduli spaces of cy manifolds arising from cyclic covers of p n branched along m hyperplanes in general position a classification towards the geometric realization problem of b gross for type a bounded symmetric domains is given

characteristic polynomials of distance matrices of one dimensional sets abstract properties of the eigenvalues of the distance matrix of a one dimensional point set are derived from identities involving the characteristic polynomial and some related polynomials called the ant sym din and sof polynomials of the point set let a b denote the concatenation of the lists a and b and m s i j m m 1 i n 1 j the spin of the m by n matrix m the ant and sym polynomials come from a factorization of the characteristic polynomial of the distance matrix of the set a s a obtained by reflecting a about the origin the roots of ant are the eigenvalues with antisymmetric eigenvectors and the roots of sym are the eigenvalues with symmetric eigenvectors given a square matrix m and a vector a we say that v 0 is an eigenvector of m relative to a iff mv v ka and a v 0 some basic properties of relative eigenvectors are developed the roots of din are the eigenvalues of the distance matrix of a relative to the vector of 1 s and the roots of sof are the eigenvalues relative to a itself some simple recursions for these polynomials obtained using expansion by minors are elaborated into an extensive series of identities relating polynomials of lists to polynomials of concatenations of the lists these identities are then used to derive a linear time algorithm for computing the polynomials and proving some results about location distinctness and interlacing of eigenvalues

study of singular boundary value problems for second order impulsive differential equations this paper studies the existence of extremal solutions for a class of singular boundary value problems of second order impulsive differential equations by using the method of upper and lower solutions and the monotone iterative technique criteria of the existence of extremal solutions are established

nonlinear second order equations with functional implicit impulses and nonlinear functional boundary conditions in this paper we deal with nonlinear second order boundary value problems with impulses the impulsive functions depend implicitly on the different considered variables and the boundary value conditions are nonlinear in both cases functional dependence on the solution is allowed the existence results follow from the existence of a pair of well ordered lower and upper solutions

on the stability of invariant sets of systems with impulse effect abstract a system of differential equations with impulse effect is considered it is assumed that this system has an invariant set m by means of the direct lyapunov method the necessary and sufficient conditions of its uniform asymptotic stability are obtained the conditions on the perturbations of right hand sides of differential equations and impulse effects under which the uniform asymptotic stability of the invariant set m of the nonperturbed system implies the uniform asymptotic stability of the invariant set of the perturbed system are obtained the stability properties of invariant sets of periodic systems are also studied

monotone iterative techniques of v lakshmikantham for a boundary value problem for systems of impulsive differential difference equations by means of the monotone iterative techniques of v lakshmikantham a couple of minimal and maximal quasisolutions of a two point boundary value problem for a system of impulsive differential difference equations are constructed

periodic boundary value problem for first order differential equations with impulses at variable times in this paper we show the validity of the method of upper and lower solutions to obtain an existence result for a periodic boundary value problem of first order impulsive differential equations at variable times

periodic solutions of nonlinear boundary value problems one of the well known techniques in the theory of nonlinear boundary value problems bvp is the method of differential inequalities or the method of upper and lower solutions the method of alternative problems a global variant of the lyapunov schmidt method has been used in the study of problems at resonance the investigation of periodic bvp s forms an important subclass of problems at resonance our aim is to combine the two approaches to discuss nonlinear problems at resonance we restrict ourselves in this paper to the discussion of periodic boundary value problems in section 1 we shall indicate the method of upper and lower solutions the results for systems are given in a general way so as to include known results and also offer new directions section 2 deals with the abstract existence results at resonance in the desired framework in section 3 we consider the scalar periodic bvp s by combining the two techniques namely alternative methods and the method of differential inequalities

boundary value problems for nonlinear impulsive integrodifferential equations we consider boundary value problems for nonlinear impulsive integrodifferential equations in which impulses occur at fixed times by suitably modifying the notions of upper and lower solutions we establish existence results in a sector then develop the monotone method and prove the existence of extremal solutions of the impulsive integrodifferential equations as an application we derive some existence results for a boundary value problem for a third order impulsive differential equation

existence of solution for discontinuous third order boundary value problems abstract in this paper we obtain existence results for the problem u q u f t u with boundary conditions u a a u b b u a c and u a u b u a u b u a c we assume f a caratheodory function q l r 0 such that 1 q l loc r 0 and suppose the existence of lower and upper solutions the existence of solution for the first considered conditions is obtained as a consequence of the fixed points theorems we obtain the solution of the second problem as a limit of solutions of the first case for the first problem the monotone method is developed

classroom note some eigenvalue properties of persymmetric matrices a matrix is called persymmetric golub and van loan matrix computations the johns hopkins university press 1989 if it is symmetric across its lower left to upper right diagonal with similar definitions for per antisymmetric and per hermitian matrices this note shows some useful eigenvalue and eigenvector properties of matrices with two symmetries such as matrices which are symmetric and persymmetric

existence of periodic solutions of nonlinear systems of differential equations with impulse effect abstract sufficient conditions for the existence of periodic solutions of nonlinear systems of differential equations with impulses in a canonic domain have been found in the paper

existence and stability of periodic solution of a lotka volterra predator prey model with state dependent impulsive effects according to biological and chemical control strategy for pest we investigate the dynamic behavior of a lotka volterra predator prey state dependent impulsive system by releasing natural enemies and spraying pesticide at different thresholds by using poincare map and the properties of the lambert w function we prove that the sufficient conditions for the existence and stability of semi trivial solution and positive periodic solution numerical simulations are carried out to illustrate the feasibility of our main results

graph representations two distance sets and equiangular lines abstract using the new concepts of graph representations and heights it is shown among other results that all sufficiently large sets of equiangular lines with mutual angle arccos 1 5 are known

variational torelli implies generic torelli david cox 1 ron donagi 2 and loring tu 3 1 department of mathematics amherst college amherst ma 01002 usa z department of mathematics northeastern university boston ma 02115 usa 3 department of mathematics tufts university medford ma 02155 usa introduction the methods of infinitesimal variation of hodge structure cf 3 provide a powerful tool for proving generic torelli theorems see 6 for the case of projective hypersurfaces however the success of this method depends on the implication variational torelli generic torelli in the literature various forms of this implication have appeared sometimes with proof cf 2 3 5 7 9 14 and 17 all previous precise formulations have required several auxiliary hypotheses including the existence of a coarse moduli space for the varieties in question the existence of a regular value for the period map i e a

qualitative analysis and applications of a kind of state dependent impulsive differential equations this paper analyzes a certain type of impulsive differential equations ides several useful theorems for its periodic solutions and their stabilities are given the key idea is that a periodically time dependent ide can be transformed into the state dependent ide as applications of our theory the optimization problems in population dynamics are studied that is the maximum sustainable yields of single population models with periodically impulsive constant harvesting are discussed furthermore we apply these results to the studies of the order 1 periodic solutions and their stability of a single population model with stage structure in which the mature is impulsively proportionally harvested while the immature is impulsively added with the constant

derived eigenvalues of symmetric matrices with applications to distance geometry abstract the concept of derived eigenvalues of a symmetric matrix is introduced and applied to give a new characterization for the embeddability of a finite metric space into euclidean space the particular case of two distance sets is discussed in more detail

algebraic correspondences between genus three curves and certain calabi yau varieties in this paper we construct certain algebraic correspondences between genus three curves and certain type of calabi yau threefolds which are double coverings of three dimensional projective spaces via this correspondence the first cohomology groups of the curves can be embedded into the third cohomology groups of the calabi yau three folds moreover we prove that the cokernel of this inclusion of variations of hodge structures cannot be a factor of any variations of hodge structures comming from polarized abelian schemes

the superstring cosmological constant and the schottky form in genus 5 combining certain identities for modular forms due to igusa with schottky jung relations we study the cosmological constant for the recently proposed ansatz for the chiral superstring measure in genus 5 the vanishing of this cosmological constant turns out to be equivalent to the long conjectured vanishing of a certain explicit modular form of genus 5 on the moduli of curves m5 and we disprove this conjecture thus showing that the cosmological constant for the proposed ansatz does not vanish identically we exhibit an easy modification of the genus 5 ansatz satisfying factorization constraints and yielding a vanishing cosmological constant we also give an expression for the cosmological constant for the proposed ansatz that should hold for any genus if certain generalized schottky jung identities hold

some nonlinear degenerate wave equations on etudie la resolubilite locale du probleme aux valeurs limites et initiales suivant 2 u t 2 m gradu x t 2 dx u 0 dans 0 u 0 sur w 0 u 0 0 u t 0 dans ou m r est une fonction c 1 non negative sur 0 un domaine borne de r n a frontiere lisse w

existence of solutions for weighted p r laplacian impulsive system periodic like boundary value problems abstract this paper investigates the existence of solutions for weighted p r laplacian impulsive system periodic like boundary value problems our method is based on gaines and mawhin s coincidence degree theory we give the sufficient conditions of the existence of solutions

on graphs whose smallest eigenvalue is at least 1 2 abstract the main result is that if the smallest eigenvalue of a graph h exceeds a fixed number larger than the smallest root 2 4812 of the polynomial x3 2x2 2x 2 and if every vertex of h has sufficiently large valency then the smallest eigenvalue of h is at least 1 2 and the structure of h is completely characterized through a new generalization of line graphs

asymptotic behavior of linear impulsive integro differential equations asymptotic equilibria of linear integro differential equations and asymptotic relations between solutions of linear homogeneous impulsive differential equations and those of linear integro differential equations are established a new gronwall bellman type lemma for integro differential inequalities is proved an example is given to demonstrate the validity of one of the results

relative eigenvalues of hermitian matrices abstract motivated by the interest in a more thorough understanding of the relationship between the eigenvalues of a hermitian matrix m and those of a matrix of the form a ma we study the relative eigenvalues of a hermitian matrix with respect to a subspace a geometrically meaningful result and some of its useful corollaries are established as a consequence some inertia theorems given in earlier work are also strengthened

singular dirichlet problem for ordinary differential equation with impulses abstract the paper deals with the impulsive dirichlet problem u t f t u t u t u 0 a u t b u t j i j u t j u t j m j u t j j 1 p where f car 0 t r 2 f has time singularities at t 0 and t t i j m j c 0 r a b r we prove the existence of a solution to this problem under the assumption that there exist lower and upper functions associated with the problem our proofs are based on the schauder fixed point theorem and on the method of a priori estimates

periodic boundary value problems for the first order impulsive functional differential equations this paper is concerned with the existence of extreme solutions of the periodic boundary value problems for a class of first order functional differential equations we introduce new concept of lower and upper solutions and present that the method of lower and upper solutions coupled with monotone iterative technique is still valid meanwhile we extend previous results

boundary value problems for nonlinear impulsive hamiltonian systems we study two point boundary value problems for nonlinear impulsive hamiltonian systems spectral analysis of the corresponding linear impulsive hamiltonian system and a fixed point theorem are employed to obtain an existence and uniqueness result for solutions of the nonlinear problem two examples are given in which the main condition is made explicit