nonparametric kernel estimation of flood frequencies a currently used approach to flood frequency analysis is based on the concept of parametric statistical inference in this analysis the assumption is made that the distribution function describing flood data is known for example a log pearson type iii distribution however such an assumption is not always justified and often leads to other difficulties it could also result in considerable variability in the estimation of design floods a new method is developed in this article based on the nonparametric procedure for estimating probability distribution function the results indicate that design floods computed from the different assumed distribution and from the nonparametric method provide comparable results however the nonparametric method is a viable alternative with the advantage of not requiring a distributional assumption and has the ability of estimating multimodal distributions

a geometrical method for removing edge effects from kernel type nonparametric regression estimators abstract we introduce a simple geometric method for removing edge effects from kernel type nonparametric regression estimators it involves reflecting the data set in two estimated points thereby generating a new data set with three times the range of the original data the usual kernel type estimator may be applied to the new enlarged data set without any danger of edge effects this technique is applicable generally to both regularly spaced and randomly spaced designs and admits a natural analog of leave one out cross validation the new cross validation algorithm may be extended to the very ends of the design interval unlike its more conventional counterpart which must be downweighted at the ends of the interval to avoid edge effects

transformations to reduce boundary bias in kernel density estimation we consider kernel estimation of a univariate density whose support is a compact interval if the density is non zero at either boundary then the usual kernel estimator can be seriously biased reflection at a boundary removes some bias but unless the first derivative of the density is 0 at the boundary the estimator with reflection can still be much more severely biased at the boundary than in the interior we propose to transform the data to a density that has its first derivative equal to 0 at both boundaries the density of the transformed data is estimated and an estimate of the density of the original data is obtained by a change of variables the transformation is selected from a parametric family which is allowed to be quite general in our theoretical study we propose algorithms where the transformation is either a quartic polynomial a b cumulative density function cdf or a linear combination of a polynomial and a b cdf the last two types of transformation are designed to accommodate possible poles at the boundaries the first two algorithms are tested on simulated data and compared with an adjusted kernel method of rice we find that our proposal performs similarly to rice s for densities with one sided derivatives at the boundaries unlike rice s method our proposal is guaranteed to produce non negative estimates this can be a distinct advantage when the density is 0 at either boundary our algorithm for densities with poles outperforms the rice adjustment when the density has a pole at a boundary

reliability of uncertain flexible laminated skewed plates under random compressions a geometrically nonlinear stochastic thin plate finite element is formulated to study the reliability of fiberreinforced laminated plates with structural uncertainties under random in plane loads the structural uncertainties considered include modulus of elasticity poisson s ratio thickness fiber orientation of individual lamina and geometric imperfection of the plate the deterministic formulation for a 48 degree of f reedom dof skewed quadrilateral laminated thin plate element is based on tensorial mathematics and classical laminate theory the stochastic element formulation is accomplished by including the effect of structural uncertainties and random in plane loads the stochastic solution procedure is developed base on the mean centered secondorder perturbation technique together with the newton raphson iterative method the hill tsai failure criterion for unidirectional lamina and a displacement criterion for the plate are used to set up the limit state functions first order reliability methods are adopted to derive the safety index to demonstrate the applicability of the present developments a series of fracture and postbuckling analyses of thin plates with structural uncertainties under random in plane loads are performed the results quantify the effects of these uncertain parameters on the reliability of the example laminated plates under in plane loads the results also show the capability of the current method in analyzing and designing the laminated structures with uncertain parameters subjected to random loads

smoothing splines regression derivatives and deconvolution abstract the statistical properties of a cubic smoothing spline and its derivative are analyzed it is shown that unless unnatural boundary conditions hold the integrated squared bias is dominated by local effects near the boundary similar effects are shown to occur in the regularized solution of a translation kernel integral equation these results are derived by developing a fourier representation for a smoothing spline author

a chevalley theorem for difference equations by a theorem of chevalley the image of a morphism of varieties is a constructible set the algebraic version of this fact is usually stated as a result on extension of specializations or lifting of prime ideals we present a difference analog of this theorem the approach is based on the philosophy that occasionally one needs to pass to higher powers of where is the endomorphism defining the difference structure in other words we consider difference pseudo fields which are finite direct products of fields rather than difference fields we also prove a result on compatibility of pseudo fields and present some applications of the main theorem e g constrained extension and uniqueness of differential picard vessiot rings with a difference parameter

bootstrap confidence regions for the intensity of a poisson point process abstract bootstrap methods are developed for constructing confidence regions for the intensity function of a nonstationary poisson process several different resampling algorithms are suggested ranging from resampling a poisson process with intensity equal to that estimated nonparametrically from the data to resampling the data points themselves in the same manner that the bootstrap is used in problems involving independent and identically distributed observations for each different bootstrap method various percentile t ways of constructing confidence bands are described the effectiveness of these different approaches is demonstrated both theoretically and numerically for real and simulated data issues such as bias correction are addressed

f structures and integral points on semiabelian varieties over finite fields motivated by the problem of determining the structure of integral points on subvarieties of semiabelian varieties defined over finite fields we prove a quantifier elimination and stability result for finitely generated modules over certain finite simple extensions of the integers given together with predicates for cycles of the distinguished generator of the ring

on von neumann regular rings with an automorphism abstract we study the first order theory of bezout difference rings in particular we show that rings of sequences very rarely have decidable theories as difference rings or even decidable model completions

effective bounds for the number of transcendental points on subvarieties of semi abelian varieties let a be a semi abelian variety and x a subvariety of a both denned over a number field assume that x does not contain x x2 for any positive dimensional subvarieties x x2 of a let r be a subgroup of a c of finite rational rank we give doubly exponential bounds for the size of x n 0 x q among the ingredients is a uniform bound doubly exponential in the data on finite sets which are quantifier free definable in differentially closed fields we also give uniform bounds on x n v in the case where x contains no translate of any semi abelian subvariety of a and r is a subgroup of a c of finite rational rank which has trivial intersection with a q here a is assumed to be defined over a number field but x need not be algebraic torus c 2 and both a and x are defined over a number field the question asked by bombieri was to find uniform bounds for the number of generic points of x fl t namely those points which are not rational over the al gebraic closure of q buium obtained uniform bounds of an iterated exponential nature in the data deg x 9 rank t buium used differential algebraic methods the aim in the present paper is to improve the bounds to being doubly exponen tial in the relevant data as well as to treat the more general case of semi abelian varieties we are also able to slightly weaken the hypothesis on x the methods are also differential algebraic closely following buium but there are additional model theoretic ingredients coming from the theory of commutative groups of finite morley rank and there is also one more key observation regarding the differential algebraic set up which yields the doubly exponential bounds before stating the results let us discuss the nature of the data which for us will be quite naive we work for now over the complex numbers let a be a semi abelian variety of dimension n9 and x a subvariety of dimension ra both defined over q denote q by k assume a to be given as a locally closed

strongly semistable sheaves and the mordell lang conjecture over function fields we give a new proof of the mordell lang conjecture in positive characteristic in the situation where the variety under scrutiny is a smooth subvariety of an abelian variety our proof is based on the theory of semistable sheaves in positive characteristic in particular on langer s theorem that the harder narasimhan filtration of sheaves becomes strongly semistable after a finite number of iterations of frobenius pull backs the interest of this proof is that it provides simple effective bounds depending on the degree of the canonical line bundle for the degree of the isotrivial finite cover whose existence is predicted by the mordell lang conjecture we also present a conjecture on the harder narasimhan filtration of the cotangent bundle of a smooth projective variety of general type in positive characteristic and a conjectural refinement of the bombieri lang conjecture in positive characteristic

non integrability by discrete quadratures we give a necessary condition for integrability by discrete quadratures of systems of difference equations the discrete variational equations along algebraic solutions must have virtually solvable galois groups this necessary condition a la morales and ramis is used in order to prove that q analogues of painleve i and painleve iii equations are not integrable by discrete quadratures

local andre oort conjecture for the universal abelian variety we prove a p adic version of the andre oort conjecture for subvarieties of the universal abelian varieties let g and n be integers with n 3 and p a prime number not dividing n let r be a finite extension of w mathbb f p alg the ring of witt vectors of the algebraic closure of the field of p elements the moduli space mathcal a mathcal a g 1 n of g dimensional principally polarized abelian varieties with full level n structure as well as the universal abelian variety pi mathcal x to mathcal a over mathcal a may be defined over r we call a point xi in mathcal x r r special if mathcal x pi xi is a canonical lift and is a torsion point of its fibre employing the model theory of difference fields and work of moonen on special subvarieties of mathcal a we show that an irreducible subvariety of mathcal x r containing a dense set of r special points must be a special subvariety in the sense of mixed shimura varieties

kernel density estimation via diffusion we present a new adaptive kernel density estimator based on linear diffusion processes the proposed estimator builds on existing ideas for adaptive smoothing by incorporating information from a pilot density estimate in addition we propose a new plug in bandwidth selection method that is free from the arbitrary normal reference rules used by existing methods we present simulation examples in which the proposed approach outperforms existing methods in terms of accuracy and reliability

invariant varieties for polynomial dynamical systems we study algebraic dynamical systems and more generally s varieties f a n c a n c given by coordinatewise univariate polynomials by refining an old theorem of ritt on compositional identities amongst polynomials more precisely we find a nearly canonical way to write a polynomial as a composition of clusters from which one may easily read off possible compositional identities our main result is an explicit description of the weakly skew invariant varieties that is for a fixed field automorphism s c c those algebraic varieties x a n c for which f x x s as a special case we show that if f x c x is a polynomial of degree at least two that is not conjugate to a monomial chebyshev polynomial or a negative chebyshev polynomial and x a 2 c is an irreducible curve that is invariant under the action of x y f x f y and projects dominantly in both directions then x must be the graph of a polynomial that commutes with f under composition as consequences we deduce a variant of a conjecture of zhang on the existence of rational points with zariski dense forward orbits and a strong form of the dynamical manin mumford conjecture for liftings of the frobenius we also show that in models of acfa 0 a disintegrated set defined by s x f x for a polynomial f has morley rank one and is usually strongly minimal that model theoretic algebraic closure is a locally finite closure operator on the nonalgebraic points of this set unless the skew conjugacy class of f is defined over a fixed field of a power of s and that nonorthogonality between two such sets is definable in families if the skew conjugacy class of f is defined over a fixed field of a power of s

a lindemann weierstrass theorem for semi abelian varieties over function fields we prove an analogue of the lindemann weierstrass theorem that the exponentials of a q linearly independent set of algebraic numbers are algebraically independent replacing q alg by c t alg and g n by a semiabelian variety over c t alg both the formulations of our results and the methods are dierential algebraic in nature

independence in computable algebra abstract we give a sufficient condition for an algebraic structure to have a computable presentation with a computable basis and a computable presentation with no computable basis we apply the condition to differentially closed real closed and difference closed fields with the relevant notions of independence to cover these classes of structures we introduce a new technique of safe extensions that was not necessary for the previously known results of this kind we will then apply our techniques to derive new corollaries on the number of computable presentations of these structures the condition also implies classical and new results on vector spaces algebraically closed fields torsion free abelian groups and archimedean ordered abelian groups

random field finite elements the probabilistic finite element method pfem is formulated for linear and non linear continua with inhomogeneous random fields analogous to the discretization of the displacement field in finite element methods the random field is also discretized the formulation is simplified by transforming the correlated variables to a set of uncorrelated variables through an eigenvalue orthogonalization furthermore it is shown that a reduced set of the uncorrelated variables is sufficient for the second moment analysis based on the linear formulation of the pfem the method is then extended to transient analysis in non linear continua the accuracy and efficiency of the method is demonstrated by application to a one dimensional elastic plastic wave propagation problem and a two dimensional plane stress beam bending problem the moments calculated compare favourably with those obtained by monte carlo simulation also the procedure is amenable to implementation in deterministic fem based computer programs

the isotrivial case in the mordell lang theorem we determine the structure of the intersection of a finitely generated subgroup of a semiabelian variety g defined over a finite field with a closed subvariety x c g we also study a related question in the context of a power of the additive group scheme

equivalence of smoothing parameter selectors in density and intensity estimation abstract kernel smoothing is an attractive method for the nonparametric estimation of either a probability density function or the intensity function of a nonstationary poisson process in each case the amount of smoothing controlled by the bandwidth that is smoothing parameter is crucial to the performance of the estimator bandwidth selection by cross validation has been widely studied in the context of density estimation a bandwidth selector in the intensity estimation case has been proposed that minimizes an estimate of the mean squared error under the assumption that the data are generated by a stationary cox process this article shows that these two methods each select the same bandwidth even though they are motivated in much different ways in addition to providing further justification of each method this equivalence of smoothing parameter selectors yields new insights for both density and intensity estimation a benefit for intensity estimation is that this equivalence makes it clear how

smooth optimum kernel estimators near endpoints summary kernel estimators for smooth curves like density spectral density or regression functions require modifications when estimating near endpoints of the support both for practical and asymptotic reasons the construction of such boundary kernels as solutions of a variational problem is addressed and representations in orthogonal polynomials are given including explicit solutions for the most important cases based on explicit formulae for certain functionals of the kernels it is shown that local bandwidth variation might be indicated near boundaries various bandwidth variation schemes are discussed and

a skolem mahler lech theorem in positive characteristic and finite automata lech proved in 1953 that the set of zeroes of a linear recurrence sequence in a field of characteristic 0 is the union of a finite set and finitely many infinite arithmetic progressions this result is known as the skolem mahler lech theorem lech gave a counterexample to a similar statement in positive characteristic we will present some more pathological examples we will state and prove a correct analog of the skolem mahler lech theorem in positive characteristic the zeroes of a recurrence sequence in positive characteristic can be described using finite automata

geometric axioms for differentially closed fields with several commuting derivations abstract a geometric first order axiomatization of differentially closed fields of characteristic zero with several commuting derivations in the spirit of pierce and pillay 1998 13 is formulated in terms of a relative notion of prolongation for kolchin closed sets

bivariate frequency analysis of floods using a diffusion based kernel density estimator recent focus of flood frequency analysis ffa studies has been on development of methods to model joint distributions of variables such as peak flow volume and duration that characterize a flood event as comprehensive knowledge of flood event is often necessary in hydrological applications diffusion process based adaptive kernel d kernel is suggested in this paper for this purpose it is data driven flexible and unlike most kernel density estimators always yields a bona fide probability density function it overcomes shortcomings associated with the use of conventional kernel density estimators in ffa such as boundary leakage problem and normal reference rule the potential of the d kernel is demonstrated by application to synthetic samples of various sizes drawn from known unimodal and bimodal populations and five typical peak flow records from different parts of the world it is shown to be effective when compared to conventional gaussian kernel and the best of seven commonly used copulas gumbel hougaard frank clayton joe normal plackett and student s t in estimating joint distribution of peak flow characteristics and extrapolating beyond historical maxima selection of optimum number of bins is found to be critical in modeling with d kernel

differential arcs and regular types in differential fields we introduce differential arc spaces in analogy to the algebraic arc spaces and show that a differential variety is determined by its arcs at a point using differential arcs we show that if k 1 n is a differentially closed field of characteristic zero with n commuting derivations and p s k is a regular type over k then either p is locally modular or there is a definable subgroup g k of the additive group having a regular generic type that is nonorthogonal to p

on algebraic sigma groups we introduce the categories of algebraic varieties and groups over a difference field k under a linearly closed assumption on k a we prove an isotriviality theorem for groups this theorem immediately yields the key lemma in a proof of the manin mumford conjecture the present paper crucially uses ideas of pilay and ziegler 2003 but in a model theory free manner the applications to manin mumford are inspired by hrushovski s work 2001 and are also closely related to papers of pink and roessler 2002 and 2004

strongly minimal expansions of ℂ definable in o minimal fields we characterize those functions f definable in o minimal expansions of the reals for which the structure f is strongly minimal such functions must be complex constructible possibly after conjugating by a real matrix in particular we prove a special case of the zilber dichotomy an algebraically closed field is definable in certain strongly minimal structures which are definable in an o minimal field

on function field mordell lang the semiabelian case and the socle theorem in this paper we complete our second generation model theoretic account of the function field mordell lang conjecture where we avoid appeal to dichotomy theorems for generalized zariski geometries in the current paper we reduce the semiabelian case to the abelian case using model theoretic tools we also use our results from 2 to prove modularity of the manin kernels over f p t sep in positive characterstic and over c t alg in characteristic 0

the dip test of unimodality the dip test measures multimodality in a sample by the maximum difference over all sample points between the empirical distribution function and the unimodal distribution function that minimizes that maximum difference the uniform distribution is the asymptotically least favorable unimodal distribution and the distribution of the test statistic is determined asymptotically and empirically when sampling from the uniform

cross validation of multivariate densities abstract in recent years the focus of study in smoothing parameter selection for kernel density estimation has been on the univariate case while multivariate kernel density estimation has been largely neglected in part this may be due to the perception that calibrating multivariate densities is substantially more difficult in this article we explicitly derive and compare multivariate versions of the bootstrap method of taylor the least squares cross validation method developed by bowman and rudemo and a biased cross validation method similar to that of scott and terrell for multivariate kernel estimation using the product kernel estimator the theoretical behavior of these cross validation algorithms is shown to improve surprisingly as the dimension increases approaching the best rate of o n 1 2 simulation studies suggest that the new biased cross validation method performs quite well and with reasonable variability as compared to the other two methods bivariate examples with heart disease

generalized basic hypergeometric equations this paper deals with regular singular generalized q hypergeometric equations with either large or small galois groups in particular we consider the fundamental problem of finding appropriate galoisian substitutes for the usual notion of local monodromy

on the uniform boundedness conjecture for drinfeld modules in analogy with the famous theorems of mazur and merel on the torsion subgroups of elliptic curves one can formulate similar conjectures for the torsion points of drinfeld modules we prove some partial results for rank 2 drinfeld q t modules for example the uniform boundedness of the primary torsion

kernels for nonparametric curve estimation summary the choice of kernels for the nonparametric estimation of regression functions and of their derivatives is investigated explicit expressions are obtained for kernels minimizing the asymptotic variance or the asymptotic integrated mean square error imse the present proof of the optimality of the latter kernels is restricted up to order k 5 these kernels are also of interest for the nonparametric estimation of probability densities and spectral densities a finite sample study indicates that higher order kernels asymptotically improving the rate of convergence may become attractive for realistic finite sample size suitably modified kernels are considered for estimating at the extremities of the data in a way which allows to retain the order of the bias found for interior points

the mordell lang conjecture for function fields we give a proof of the geometric mordell lang conjecture in any characteristic our method involves a model theoretic analysis of the kernel of manin s homomorphism and of a certain analog in characteristic p department of mathematics massachusetts institute of technology 2 277 cambridge massachusetts 02139 current address department of mathematics hebrew university jerusalem israel e mail address ehud math mit edu

primitive permutation groups of bounded orbital diameter we give a description of infinite families of finite primitive permutation groups for which there is a uniform finite upper bound on the diameter of all orbital graphs this is equivalent to describing families of finite permutation groups such that every ultraproduct of the family is primitive a key result is that in the almost simple case with socle of fixed lie rank apart from very specific cases there is such a diameter bound this is proved using recent results on the model theory of pseudofinite fields and difference fields

groups definable in separably closed fields we consider the groups which are infinitely definable in separably closed fields of finite degree of imperfection we prove in particular that no new definable groups arise in this way we show that any group definable in such a field l is definably isomorphic to the group of l rational points of an algebraic group defined over l

krull dimension of solvable groups in this paper we prove that free solvable groups have finite krull dimension in fact this is true for much wider class of solvable groups termed rigid groups along the way we study the algebraic structure of the limit solvable groups fully residually free solvable groups

rational points of varieties with ample cotangent bundle over function fields let k be the function field of a smooth curve over an algebraically closed field k let x be a scheme which is smooth and projective over k suppose that the cotangent bundle omega x k is ample let r mathrm zar x k cap x be the zariski closure of the set of all k rational points of x endowed with its reduced induced structure we prove that for each irreducible component mathfrak r of r there is a projective variety mathfrak r 0 over k and a finite and surjective k mathrm sep morphism mathfrak r 0 k mathrm sep rightarrow mathfrak r k mathrm sep which is birational when mathrm char k 0 this improves on results of noguchi and martin deschamps in characteristic 0 in positive characteristic our result can be used to give the first examples of varieties which are not embeddable in abelian varieties and satisfy an analog of the bombieri lang conjecture

a brief survey of bandwidth selection for density estimation abstract there has been major progress in recent years in data based bandwidth selection for kernel density estimation some second generation methods including plug in and smoothed bootstrap techniques have been developed that are far superior to well known first generation methods such as rules of thumb least squares cross validation and biased cross validation we recommend a solve the equation plug in bandwidth selector as being most reliable in terms of overall performance this article is intended to provide easy accessibility to the main ideas for nonexperts

on vanishing coefficients of algebraic power series over fields of positive characteristic let k be a field of characteristic p 0 and let f t1 td be a power series in d variables with coefficients in k that is algebraic over the field of multivariate rational functions k t1 td we prove a generalization of both derksen s recent analogue of the skolem mahler lech theorem in positive characteristic and a classical theorem of christol by showing that the set of indices n1 nd d for which the coefficient of t 1 n 1 cdots t d n d in f t1 td is zero is a p automatic set applying this result to multivariate rational functions leads to interesting effective results concerning some diophantine equations related to s unit equations and more generally to the mordell lang theorem over fields of positive characteristic

quantifier elimination for algebraic d groups we prove that if g is an algebraic d group in the sense of buium over a differentially closed field k of characteristic 0 then the first order structure consisting of g together with the algebraic d subvarieties of g g x g has quantifier elimination in other words the projection on g of a d constructible subset of g n 1 is d constructible among the consequences is that any finite dimensional differential algebraic group is interpretable in an algebraically closed field

definable sets in algebraically closed valued fields elimination of imaginaries it is shown that if k is an algebraically closed valued field with valuation ring r then th k has elimination of imaginaries if sorts are added whose elements are certain cosets in k n of certain definable r submodules of k n for all n 1 the proof involves the development of a theory of independence for unary types which play the role of 1 types followed by an analysis of germs of definable functions from unary sets to the sorts contents

groups and fields interpretable in separably closed fields we prove that any infinite group interpretable in a separably closed field f of finite ersov invariant is definably isomorphic to an f algebraic group using this result we show that any infinite field k interpretable in a separably closed field f is itself separably closed in particular in the finite invariant case k is definably isomorphic to a finite extension of f this paper answers a question raised by d marker whose help and guidance made this work possible i would like to thank a pillay for helpful discussions and e hrushovski for pointing out mistakes in the first version of this paper

on pseudodata methods for removing boundary effects in kernel density estimation we suggest a method for boundary correcting kernel density estimators based on generating pseudodata beyond the extremities of the density s support the estimator produced in this way enjoys optimal orders of bias and variance right up to the ends of the support and it may be used with kernels of arbitrary order our method is considerably more adaptive than the common data reflection approach which is not really appropriate for kernels of order 2 or more since it does not adequately correct boundary bias in a simulation study for densities on 0 1 with positive slope at x 0 our method was found to have lower mean squared error at x 0 than the boundary kernel method especially for small sample sizes our technique may be used in conjunction with plug in or least squares cross validation methods of bandwidth selection and has an analogue in the context of estimating a point process intensity

multivariate hydrological frequency analysis using copulas 1 this article presents the modeling of multivariate extreme values using copulas our approach allows us to model the dependence structure independently of the marginal distributions which is not possible with standard classical methods the methodology has been applied on two different problems in hydrology the first application is concerned with the combined risk in the framework of frequency analysis four copulas have been tested on peak flows from the watershed of peribonka in quebec canada the second application relates to the joint modeling of peak flows and volumes three copulas have been applied to the watershed of the rimouski river in quebec canada this approach using copulas is promising since it allows us to take into account a wide range of correlation which can happen in hydrology

difference galois theory of linear differential equations abstract we develop a galois theory for linear differential equations equipped with the action of an endomorphism this theory is aimed at studying the difference algebraic relations among the solutions of a linear differential equation the galois groups here are linear difference algebraic groups i e matrix groups defined by algebraic difference equations

the brauer manin obstruction for subvarieties of abelian varieties over function fields we prove that for a large class of subvarieties of abelian varieties over global function fields the brauer manin condition on adelic points cuts out exactly the rational points this result is obtained from more general results concerning the intersection of the adelic points of a subvariety with the adelic closure of the group of rational points of the abelian variety

counting special points logic diophantine geometry and transcendence theory we expose a theorem of pila and wilkie on counting rational points in sets definable in o minimal structures and some applications of this theorem to problems in diophantine geometry due to masser peterzil pila starchenko and

a geometrically non linear tensorial formulation of a skewed quadrilateral thin shell finite element a 48 degree of freedom d o f skewed quadrilateral thin shell finite element including the effect of geometrical non linearity is formulated and appropriate numerical procedures are adopted for the development of an efficient approach for the static and dynamic analysis of general thin shell structures the element surface is described by a variable order polynomial in curvilinear co ordinates the displacement functions are described by bicubic hermitian polynomials in curvilinear co ordinates the directions of the curvilinear co ordinates at each nodal point are uniquely defined to coincide with the directions of the boundaries of the element in the present case of a skewed quadrilateral with non orthogonal curvilinear coordinates the coupling terms of the metric tensor and curvature tensor of the surface no longer vanish such as in the case of orthogonal co ordinates the tensor form is used in the setup of the shape functions geometric derivatives stiffness matrix and computer code this allows for the treatment of shells with irregular shapes and variable curvatures to evaluate the efficiency and accuracy of this formulation a systematic list of examples is chosen i linear and non linear static analysis of square and rhombic plates cylindrical and spherical shells ii linear vibrations of trapezoidal flat and curved plates iii large amplitude vibrations of a rhombic plate for the square plate and cylindrical and spherical shell shewed element meshes with various distortion angles are used to study the effect of the distortion angles on the accuracy of the results and to demonstrate the versatility of the present element all results are compared with alternative available solutions including those obtained using regular rectangular meshes pinched thin cylindrical and spherical shells are studied using different skewed meshes and various gauss integration meshes and no membrane locking phenomenon is observed

externally definable sets and dependent pairs ii 2015 american mathematical society we continue investigating the structure of externally definable sets in nip theories and preservation of nip after expanding by new predicates most importantly types over finite sets are uniformly definable over a model a family of non forking instances of a formula with parameters ranging over a type definable set can be covered with finitely many invariant types we give some criteria for the boundedness of an expansion by a new predicate in a distal theory naming an arbitrary small indiscernible sequence preserves nip while naming a large one doesn t there are models of nip theories over which all 1 types are definable but not all n types

reliability of uncertain laminated shells due to buckling and supersonic flutter a stochastic 48 dof quadrilateral laminated thin shell element with probabilistic modulus of elasticity mass density thickness fiber orientation geometric imperfection middle surface load and mass density of the air has been formulated the solution procedure was based on the mean centered second moment perturbation technique the effects of these uncertain parameters have been studied

imaginaries and invariant types in existentially closed valued differential fields we answer two open questions about the model theory of valued differential fields introduced by scanlon we show that they eliminate imaginaries in the geometric language introduced by haskell hrushovski and macpherson and that they have the invariant extension property these two result follow from an abstract criterion for the density of definable types in enrichments of algebraically closed valued fields finally we show that this theory is metastable