cubic curves and totally geodesic subvarieties of moduli space in this paper we present the rst example of a primitive totally geodesic subvariety f m g n with dim f 1 the variety we consider is a surfacef m 1 3 dened using the projective geometry of

finiteness of teichmuller curves in non arithmetic rank 1 orbit closures we show that in any non arithmetic rank 1 orbit closure of translation surfaces there are only finitely many teichm uller curves we also show that in any non arithmetic rank 1 orbit closure any completely parabolic surface is veech

the boundary of an affine invariant submanifold we study the boundary of an affine invariant submanifold of a stratum of translation surfaces in a partial compactification consisting of all finite area abelian differentials over nodal riemann surfaces modulo zero area components the main result is a formula for the tangent space to the boundary we also prove finiteness results concerning cylinders a partial converse to the cylinder deformation theorem and a result generalizing part of the veech dichotomy

local well posedness for the sixth order boussinesq equation abstract in this work we study the local well posedness of the initial value problem for the nonlinear sixth order boussinesq equation u t t u x x u x x x x u x x x x x x u 2 x x where 1 we prove the local well posedness with initial data in non homogeneous sobolev spaces h s r for negative indices of s r

a matching algorithm for generation of statistically dependent random variables with arbitrary marginals simulation has gained acceptance in the operations research community as a viable method for analyzing complex problems while random generation of variables with various marginal distributions has been studied at length developing ability to preserve a given degree of statistical dependence among them has been lagging behind this paper includes a short summary of the previous work and a description of the proposed algorithm for efficient re arranging of generated random variables such that a desired product moment correlation matrix is induced the proposed approach is different from similar algorithms that induce a desired rank order correlation among random variables the algorithm is demonstrated using three numerical examples one of which also includes a comparison with risk commercial package its main features are simplicity ease of implementation and the ability to handle either theoretical or empirical distribution functions

the limit behavior of solutions for the nonlinear schrodinger equation including nonlinear loss gain with variable coefficient abstract this paper is devoted to the limit behavior as e 0 for the solution of the cauchy problem of the nonlinear schrodinger equation including nonlinear loss gain with variable coefficient i u t u u u i e a t u p u 0 such an equation appears in the recent studies of bose einstein condensates and optical systems under some conditions we show that the solution will locally converge to the solution of the limiting equation i u t u u u 0 with the same initial data in l 0 l w 1 for all admissible pairs where l 0 t we also show that if the limiting solution u is global and has some decay property as t then u e is global if e is sufficiently small and u e converges to u in l 0 w 1 for all admissible pairs in particular our results hold for both subcritical and critical nonlinearities

global existence for 2d nonlinear schrodinger equations via high low frequency decomposition method abstract we study global existence of solutions for the cauchy problem of the nonlinear schrodinger equation i u t u u 2 m u in the 2 dimension case where m is a positive integer m 2 using the high low frequency decomposition method we prove that if 10 m 6 10 m 5 s 1 then for any initial value h s r 2 the cauchy problem has a global solution in c r h s r 2 and it can be split into u t e i t y t with y c r h 1 r 2 satisfying y t h 1 1 t 2 1 s 10 m 5 s 10 m 6 where is an arbitrary sufficiently small positive number

an improved local well posedness result for the one dimensional zakharov system abstract the 1d cauchy problem for the zakharov system is shown to be locally well posed for low regularity schrodinger data u 0 h k p and wave data n 0 n 1 h l p h l 1 p under certain assumptions on the parameters k l and 1 p 2 where u 0 h k p k u 0 l p generalizing the results for p 2 by ginibre tsutsumi and velo especially we are able to improve the results from the scaling point of view and also allow suitable k 0 l 1 2 i e data u 0 l 2 and n 0 n 1 h 1 2 h 3 2 which was excluded in the case p 2

asymptotic smoothing and attractors for the generalized benjamin bona mahony equation on r 3 abstract we study the asymptotic behavior of the solutions of the benjamin bona mahony equation defined on r 3 we first provide a sufficient condition to verify the asymptotic compactness of an evolution equation defined in an unbounded domain which involves the littlewood paley projection operators we then prove the existence of an attractor for the benjamin bona mahony equation in the phase space h 1 r 3 by showing the solutions are point dissipative and asymptotic compact finally we establish the regularity of the attractor and show that the attractor is bounded in h 2 r 3

asymptotic smoothing effect for a weakly damped nonlinear schrodinger equation in t2 abstract we prove that the global attractor for a weakly damped two dimensional nonlinear schrodinger equation in the usual energy space is in fact included and compact in a more regular energy space the method relies on a suitable approximation when time goes to infinity of the high frequency modes of the solutions

correlations and copulas for decision and risk analysis the construction of a probabilistic model is a key step in most decision and risk analyses typically this is done by defining a joint distribution in terms of marginal and conditional distributions for the model s random variables we describe an alternative approach that uses a copula to construct joint distributions and pairwise correlations to incorporate dependence among the variables the approach is designed specifically to permit the use of an expert s subjective judgments of marginal distributions and correlations the copula that underlies the multivariate normal distribution provides the basis for modeling dependence but arbitrary marginals are allowed we discuss how correlations can be assessed using techniques that are familiar to decision analysts and we report the results of an empirical study of the accuracy of the assessment methods the approach is demonstrated in the context of a simple example including a study of the sensitivity of the results to the assessed correlations

on the cauchy problem for the nonlinear schrodinger equations with time dependent linear loss gain abstract this paper is devoted to the cauchy problem for the nonlinear schrodinger equation with time dependent loss gain which reads i u t u u u i a t u 0 this equation appears in the recent studies of bose einstein condensates and optical systems we obtain some global existence and blow up results which depend on the size of the loss gain coefficient in particular we prove the global existence for the energy critical nonlinearity by scaling and compactness arguments we also discuss asymptotic profiles and concentration properties of blow up solutions

an approximate method for sampling correlated random variables from partially specified distributions this paper presents an algorithm for generating correlated vectors of random numbers the user need not fully specify the joint distribution function instead the user partially specifies only the marginal distributions and the correlation matrix the algorithm may be applied to any set of continuous strictly increasing distribution functions the marginal distributions need not all be of the same functional form the correlation matrix is first checked for mathematical consistency positive semi and adjusted if necessary then the correlated random vectors are generated using a combination of cholesky decomposition and gauss newton iteration applications are made to cost analysis where correlations are often present between cost elements in a work breakdown structure

sharp local well posedness for the good boussinesq equation abstract in the present article we prove the sharp local well posedness and ill posedness results for the good boussinesq equation on 1d torus the initial value problem is locally well posed in h 1 2 t and ill posed in h s t for s 1 2 well posedness result is obtained from reduction of the problem into a quadratic nonlinear schrodinger equation and the contraction argument in suitably modified x s b spaces the proof of the crucial bilinear estimates in these spaces especially in the lowest regularity rely on some bilinear estimates for periodic functions in x s b spaces which are generalization of the bilinear refinement of the l 4 strichartz estimate on r our result improves the known local well posedness in h s t with s 3 8 given by oh stefanov 2012 similar ideas also establish the sharp local well posedness in h 1 2 r and ill posedness below h 1 2 for the nonperiodic case which improves the result of tsugawa and the author 2010 in h s r with s 1 2

well posedness for the cauchy problem associated to a periodic boussinesq equation abstract we consider the initial value problem associated to the nonlinear periodic sixth order boussinesq equation for given initial data in sobolev spaces h s t the local well posedness of this equation is established for s 1 2

low regularity solutions of non homogeneous boundary value problems of a higher order boussinesq equation in a quarter plane abstract in this article we study an initial boundary value problem of the sixth order boussinesq equation on a half line with nonhomogeneous boundary conditions u t t u x x u x x x x u x x x x x x u 2 x x 0 x 0 t 0 u x 0 x u t x 0 x x 0 u 0 t h 1 t u x x 0 t h 2 t u x x x x 0 t h 3 t t 0 where 1 it is shown that the problem is locally well posed in c r l o c h s r with initial condition h s r h s 1 r and boundary condition h 1 h 2 h 3 in the product space h s 1 3 r h s 1 3 r h s 3 3 r for 1 2 s 0

connected components of the moduli spaces of abelian differentials with prescribed singularities consider the moduli space of pairs c where c is a smooth compact complex curve of a given genus and is a holomorphic 1 form on c with a given list of multiplicities of zeroes we describe connected components of this space this classification is important in the study of dynamics of interval exchange transformations and billiards in rational polygons and in the study of geometry of translation surfaces

dynamics of sl2 ℝ over moduli space in genus two this paper classifies orbit closures and invariant measures for the natural action of sl2 r on um2 the bundle of holomorphic 1 forms over the moduli space of riemann surfaces of genus two

well posedness for a quadratic derivative nonlinear schrodinger system at the critical regularity abstract we consider the cauchy problem for a quadratic derivative nonlinear schrodinger system in sobolev space h s in this paper under the null condition and the mass resonance relation we prove large data local well posedness if the space dimension d 3 and s s c d 2 and s s c or d 1 and s 0 where s c is the scaling critical regularity moreover under the same assumptions we also prove small data global well posedness and scattering in h s if d 3 and s s c our proof is based on a contraction argument using the u p and v p type function spaces

a copulas based approach to modeling dependence in decision trees this paper presents a general framework based on copulas for modeling dependent multivariate uncertainties through the use of a decision tree the proposed dependent decision tree model allows multiple dependent uncertainties with arbitrary marginal distributions to be represented in a decision tree with a sequence of conditional probability distributions this general framework could be naturally applied in decision analysis and real options valuations as well as in more general applications of dependent probability trees while this approach to modeling dependencies can be based on several popular copula families as we illustrate we focus on the use of the normal copula and present an efficient computational method for multivariate decision and risk analysis that can be standardized for convenient application

regularity of the global attractor and finite dimensional behavior for the second grade fluid equations abstract this paper is devoted to the large time behavior and especially to the regularity of the global attractor of the second grade fluid equations in the two dimensional torus we first recall that for any size of the material coefficient 0 these equations are globally well posed and admit a compact global attractor a in h 3 t 2 2 we prove that for any 0 there exists 0 such that a belongs to h 3 t 2 2 if the forcing term is in h 1 t 2 2 we also show that this attractor is contained in any sobolev space h 3 m t 2 2 provided that is small enough and the forcing term is regular enough these arguments lead also to a new proof of the existence of the compact global attractor a furthermore we prove that on a the second grade fluid system can be reduced to a finite dimensional system of ordinary differential equations with an infinite delay moreover the existence of a finite number of determining modes for the equations of the second grade fluid is established

on the existence of a maximizer for the strichartz inequality it is shown that a maximizing function u l 2 does exist for the strichartz inequality e it x 2 u l 6 t l 6 x s u l 2 with s 0 being the sharp constant

bilinear estimates and applications to 2d nls the three bilinearities uv uv uv for functions u v r2 0 t 7 c are sharply estimated in function spaces xs b associated to the schrodinger operator i t these bilinear estimates imply local wellposedness results for schrodinger equations with quadratic nonlinearity improved bounds on the growth of spatial sobolev norms of finite energy global in time and blow up solutions of the cubic nonlinear schrodinger equation and certain generalizations are also obtained

low regularity global well posedness for the zakharov and klein gordon schrodinger systems we prove low regularity global well posedness for the id zakharov system and the 3d klein gordon schrodinger system which are systems in two variables u r d x x r t c and n r d x x r t r the zakharov system is known to be locally well posed in u n l 2 x h and the klein gordon schrodinger system is known to be locally well posed in u n l 2 x l 2 here we show that the zakharov and klein gordon schrodinger systems are globally well posed in these spaces respectively by using an available conservation law for the l 2 norm of u and controlling the growth of n via the estimates in the local theory

existence of closed geodesics through a regular point on translation surfaces we show that on any translation surface if a regular point is contained in some simple closed geodesic then it is contained in infinitely many simple closed geodesics whose directions are dense in mathbb rp 1 moreover the set of points that are not contained in any simple closed geodesic is finite we also construct explicit examples showing that such points exist on some translation surfaces for a surface in any hyperelliptic component we show that this finite exceptional set is actually empty the proofs of our results use apisa s classifications of periodic points and of text gl 2 mathbb r orbit closures in hyperelliptic components as well as a recent result of eskin filip wright

periodic points on veech surfaces and the mordell weil group over a teichmuller curve periodic points are points on veech surfaces whose orbit under the group of affine diffeomorphisms is finite we characterize those points as being torsion points if the veech surfaces is suitably mapped to its jacobian or an appropriate factor thereof for a primitive veech surface in genus two we show that the only periodic points are the weierstras points and the singularities

isolation equidistribution and orbit closures for the sl 2 r action on moduli space we prove results about orbit closures and equidistribution for the sl 2 r action on the moduli space of compact riemann surfaces which are analogous to the theory of unipotent ows the proofs of the main theorems rely on the measure classication theorem of the rst two authors and a certain isolation property of closed sl 2 r invariant manifolds developed in this paper

polynomial chaos representation of spatio temporal random fields from experimental measurements two numerical techniques are proposed to construct a polynomial chaos pc representation of an arbitrary second order random vector in the first approach a pc representation is constructed by matching a target joint probability density function pdf based on sequential conditioning a sequence of conditional probability relations in conjunction with the rosenblatt transformation in the second approach the pc representation is obtained by having recourse to the rosenblatt transformation and simultaneously matching a set of target marginal pdfs and target spearman s rank correlation coefficient srcc matrix both techniques are applied to model an experimental spatio temporal data set exhibiting strong non stationary and non gaussian features the data consists of a set of oceanographic temperature records obtained from a shallow water acoustics transmission experiment 1 the measurement data observed over a finite denumerable subset of the indexing set of the random process is treated as a collection of observed samples of a second order random vector that can be treated as a finite dimensional approximation of the original random field a set of properly ordered conditional pdfs that uniquely characterizes the target joint pdf in the first approach and a set of target marginal pdfs and a target srcc matrix in the second approach are estimated from available experimental data digital realizations sampled from the constructed pc representations based on both schemes capture the observed statistical characteristics of the experimental data with sufficient accuracy the relative advantages and disadvantages of the two proposed techniques are also highlighted

braid groups and hodge theory this paper gives an account of the unitary representations of the braid group that arise via the hodge theory of cyclic branched coverings of mathbb p 1 highlighting their connections with ergodic theory complex reflection groups moduli spaces of 1 forms and open problems in surface topology

splitting mixed hodge structures over affine invariant manifolds we prove that affine invariant manifolds in strata of flat surfaces are algebraic varieties the result is deduced from a generalization of a theorem of moller namely we prove that the image of a certain twisted abel jacobi map lands in the torsion of a factor of the jacobians this statement can be viewed as a splitting of certain mixed hodge structures

semisimplicity and rigidity of the kontsevich zorich cocycle we prove that invariant subbundles of the kontsevich zorich cocycle respect the hodge structure in particular we establish a version of deligne semisimplicity in this context this implies that invariant subbundles must vary polynomially on affine manifolds all results apply to tensor powers of the cocycle and this implies that the measurable and real analytic algebraic hulls coincide we also prove that affine manifolds typically parametrize jacobians with non trivial endomorphisms if the field of affine definition is larger than mathbb q then a factor has real multiplication the tools involve curvature properties of the hodge bundles and estimates from random walks in the appendix we explain how methods from ergodic theory imply some of the global consequences of schmid s work on variations of hodge structures we also derive the kontsevich forni formula using differential geometry

closed trajectories for quadratic differentials with an application to billiards on considere les orbites periodiques pour le systeme dynamique d une table polygonale avec des angles multiples rationnels de le billard rationnel

the effects of coefficient correlation structure in two dimensional knapsack problems on solution procedure performance this paper presents the results of an empirical study of the effects of coefficient correlation structure and constraint slackness settings on the performance of solution procedures on synthetic two dimensional knapsack problems 2kp the population correlation structure among 2kp coefficients the level of constraint slackness and the type of correlation product moment or rank are varied in this study representative branch and bound and heuristic solution procedures are used to investigate the influence of these problem parameters on solution procedure performance population correlation structure and in particular the interconstraint component of the correlation structure is found to be a significant factor influencing the performance of both the algorithm and the heuristic in addition the interaction between constraint slackness and population correlation structure is found to influence solution procedure performance

an energy equation for the weakly damped driven nonlinear schro dinger equations and its application to their attractors abstract in this note we present an energy equation concerning the h 2 norm of a forced one dimensional nonlinear schrodinger equation as an application we are able to corroborate recent results on attractors of weakly damped forced nonlinear schrodinger equation by proving that the attractor is an attractor in the strong topology of h 2 and its hausdorff and fractal dimensions are finite in h 2 the energy equation for the h 1 norm can be derived in the same fashion and it implies corresponding results for the attractor in h 1

variations of hodge structures of a teichmuller curve teichmuller curves are geodesic discs in teichmuller space that project to an algebraic curve in the moduli space mg we show that for all g 2 teichmuller curves map to the locus of real multiplication in the moduli space of abelian varieties observe that mcmullen has shown that precisely for g 2 the locus of real multiplication is stable under the sl2 r action on the tautological bundle mg we also show that teichmuller curves are defined over number fields and we provide a completely algebraic description of teichmuller curves in terms of higgs bundles as a consequence we show that the absolute galois group acts on the set of teichmuller curves

quadratic dispersive generalized benjamin ono equation abstract this paper is concerned with quadratic dispersive generalized benjamin ono equation 1 1 1 2 we prove sharp local well posedness in h s s 1 4 with a solution map that is analytic from h s r to c 0 t h s r and the ill posed result in h s r as soon as s s in the sense that the flow map u 0 u t cannot be continuous

chessboard distributions and random vectors with specified marginals and covariance matrix there is a growing need for the ability to specify and generate correlated random variables as primitive inputs to stochastic models moti vated by this need several authors have explored the generation of random vectors with specified marginals together with a specified covariance matrix through the use of a transformation of a multivariate normal random vector the norta method a covariance matrix is said to be feasible for a given set of marginal distributions if a random vector exists with these characteristics we develop a computational approach for establishing whether a given covariance matrix is feasible for a given set of marginals the approach is used to rigorously establish that there are sets of marginals with feasible covariance matrix that the norta method cannot match in such cases we show how to modify the initialization phase of norta so that it will exactly match the marginals and approximately match the desired covariance matrix an important feature of our analysis is that we show that for almost any covariance matrix in a certain precise sense our computational procedure either explicitly provides a construction of a random vector with the required properties or establishes that no such random vector exists

teichmuller curves in moduli space eisenstein series and an application to triangular billiards there exists a teichmuller disc n containing the riemann surface ofy2 x n 1 in the genus n 1 2 teichmuller space such that the stabilizer of n in the mapping class group has a fundamental domain of finite poincare volume in n application is given to an asymptotic formula for the length spectrum of the billiard in isosceles triangles with angles n n n 2 n and to the uniform distribution of infinite billiard trajectories in the same triangles

quadratic forms for the 1 d semilinear schrodinger equation this paper is concerned with 1 d quadratic semilinear schr6dinger equations we study local well posedness in classical sobolev space hs of the associated initial value problem and periodic boundary value problem our main interest is to obtain the lowest value of s which guarantees the desired local well posedness result we prove that at least for the quadratic cases these values are negative and depend on the structure of the nonlinearity considered

billiards and teichmuller curves on hilbert modular surfaces this paper exhibits an infinite collection of algebraic curves isometrically embedded in the moduli space of riemann surfaces of genus two these teichmuller curves lie on hilbert modular surfaces parameterizing abelian varieties with real multiplication explicit examples constructed from l shaped polygons give billiard tables with optimal dynamical properties