a rational spectral collocation method for solving a class of parameterized singular perturbation problems a new kind of numerical method based on rational spectral collocation with the sinh transformation is presented for solving parameterized singularly perturbed two point boundary value problems with one boundary layer by means of the sinh transformation the original chebyshev points are mapped onto the transformed ones clustered near the singular points of the problem the results from asymptotic analysis as regards the singularity of the solution are employed to determine the parameters in the transformation numerical experiments including several nonlinear cases illustrate the high accuracy and efficiency of our method

sensitivity analysis for certain permutation inferences in matched observational studies summary in observational studies treatments are not randomly assigned to experimental units so that randomization tests and their associated interval estimates are not generally applicable in an effort to compensate for the lack of randomization treated and control units are often matched on the basis of observed covariates however the possibility remains of bias due to residual imbalances in unobserved covariates a general though simple method is proposed for displaying the sensitivity of permutation inferences to a range of assumptions about unobserved covariates in matched observational studies the sensitivity analysis is applicable to wilcoxon s signed rank test to the mcnemar cox test for paired binary responses and to some matching problems with a variable number of controls

a second order difference scheme for a parameterized singular perturbation problem in this paper we consider a singularly perturbed quasilinear boundary value problem depending on a parameter the problem is discretized using a hybrid difference scheme on shishkin type meshes we show that the scheme is second order convergent in the discrete maximum norm independent of singular perturbation parameter numerical experiments support these theoretical results

the finite deformation theory for beam plate and shell part v the shell element with drilling degree of freedom based on biot strain due to the facts that the spatial moment force is non conservative and the three components of the finite rotation pseudo vector are not independent the ordinary variational principle based on a functional achieving its stationary value is not suitable for the problem subject to non conservative loading the finite element method proposed in this paper is based on the virtual work principle rigid normal assumption polar decomposition and total lagrangian formulation

randomization inference and sensitivity analysis for composite null hypotheses with binary outcomes in matched observational studies abstractwe present methods for conducting hypothesis testing and sensitivity analyses for composite null hypotheses in matched observational studies when outcomes are binary causal estimands discussed include the causal risk difference causal risk ratio and the effect ratio we show that inference under the assumption of no unmeasured confounding can be performed by solving an integer linear program while inference allowing for unmeasured confounding of a given strength requires solving an integer quadratic program through simulation studies and data examples we demonstrate that our formulation allows these problems to be solved in an expedient manner even for large datasets and for large strata we further exhibit that through our formulation one can assess the impact of various assumptions about the potential outcomes on the performed inference r scripts are provided that implement our methods supplementary materials for this article are available online

barycentric interpolation collocation methods for solving linear and nonlinear high dimensional fredholm integral equations abstract in this article two barycentric interpolation collocation methods are proposed for solving linear and nonlinear high dimensional f r e d h o l m integral equations of the second kind the approaches respectively utilize the modified weighted l a g r a n g e functions and the novel rational functions as the interpolation basis functions they are effective schemes for evaluating the multidimensional undetermined function through the numerical strategies and some composite quadrature formulas the linear and nonlinear f r e d h o l m integral equations are transformed into the corresponding linear and nonlinear algebraic equations further we prove that the discrete collocation methods are equivalent to the n y s t r o m quadrature methods then the convergence analysis is established by the collectively compact theory moreover the error estimation of the approximate solution and the exact solution are also provided numerical examples are presented to illustrate the capability and efficiency of the techniques by compared with the classic l a g r a n g e interpolation collocation method and other methodologies

a 4 node finite shell element for the implementation of general hyperelastic 3d elasticity at finite strains abstract in this paper a finite shell element for large deformations is presented based on extensible director kinematics the essential feature is an interface to arbitrary three dimensional material laws the non linear lagrangian formulation is based on the three field variational principle parametrized with the displacement vector enhanced green lagrangian strain tensor and second piola kirchhoff stress tensor the developed quadrilateral shell element is characterized by a course mesh accuracy and distortion insensitivity compared with bilinear displacement approaches furthermore plane stress response is approximately recovered in the asymptotic case of vanishing thickness a number of example problems investigating large deformation as well as finite strain applications are presented compressible and incompressible hyperelastic materials of the st venant kirchhoff neo hookean and mooney rivlin type are particularly used

fast and stable rational interpolation in roots of unity and chebyshev points a new method for interpolation by rational functions of prescribed numerator and denominator degrees is presented when the interpolation nodes are roots of unity or chebyshev points the algorithm is particularly simple and relies on discrete fourier transform matrices which results in a fast implementation using the fast fourier transform the method is generalized for arbitrary grids which requires the construction of polynomials orthogonal on the set of interpolation nodes the appearance of common factors in the numerator and denominator due to finite precision arithmetic is explained by the behavior of the singular values of the linear system associated with the rational interpolation problem the new algorithm has connections with other methods particularly the work of jacobi and kronecker berrut and mittelmann and egecioglu and koc short matlab codes and numerical experiments are included

superconvergence and a posteriori error estimates of the dg method for scalar hyperbolic problems on cartesian grids in this paper we analyze the discontinuous galerkin dg finite element method for the steady two dimensional transport reaction equation on cartesian grids we prove the l2 stability and optimal l2 error estimates for the dg scheme we identify a special numerical flux for which the l2 norm of the solution is of order p 1 when tensor product polynomials of degree at most p are used we further prove superconvergence towards a particular projection of the directional derivative the order of superconvergence is proved to be p 1 2 we also provide a very simple derivative recovery formula which is o h p 1 superconvergent approximation to the directional derivative moreover we establish an o h 2 p 1 global superconvergence for the solution flux at the outflow boundary of the domain these results are used to construct asymptotically exact a posteriori error estimates for the directional derivative approximation by solving a local problem on each element finally we prove that the proposed a posteriori dg error estimates converge to the true errors in the l2 norm at o h p 1 rate and that the global effectivity index converges to unity at o h rate our results are valid without the flow condition restrictions we perform numerical experiments to demonstrate that theoretical rates proved in this paper are optimal

a three dimensional non linear timoshenko beam based on the core congruential formulation a three dimensional geometrically non linear two node timoshenko beam element based on the total lagrangian description is derived the element behaviour is assumed to be linear elastic but no restrictions are placed on the magnitude of finite rotations the resulting element has twelve degrees of freedom six translational components and six rotational vector components the formulation uses the green lagrange strains and second piola kirchhoff stresses as energy conjugate variables and accounts for bending stretching and bending torsional coupling effects without special provisions the core congruential formulation ccf is used to derive the discrete equations in a staged manner core equations involving the internal force vector and tangent stiffness matrix are developed at the particle level a sequence of matrix transformations carries these equations to beam cross sections and finally to the element nodal degrees of freedom the choice of finite rotation measure is made in the next to last transformation stage and the choice of over the element interpolation in the last one the tangent stiffness matrix is found to retain symmetry if the rotational vector is chosen to measure finite rotations an extensive set of numerical examples are presented to test and validate the present element

the set of unattainable points for the rational hermite interpolation problem abstract we describe geometrically and algebraically the set of unattainable points for the rational hermite interpolation problem i e those points where the problem does not have a solution we show that this set is a union of equidimensional complete intersection varieties of odd codimension the number of them being equal to the minimum between the degrees of the numerator and denominator of the problem each of these equidimensional varieties can be further decomposed as a union of as many rational irreducible varieties as input data points we exhibit algorithms and equations defining all these objects

diffusion models with blow up a number of physical situations including chemical reactions electrical heating and fluid flow give rise to nonlinear diffusion problems in this paper models are derived and results relating to the blow up of the solutions are given some of the proofs are outlined and the physical significance of the results is noted

non linear strain displacement equations exactly representing large rigid body motions part i timoshenko mindlin shell theory abstract the precise representation of arbitrarily large rigid body motions in the displacement patterns of curved timoshenko mindlin tm shell elements is considered this consideration requires the development of the strain displacement relationships of the finite deformation tm shell theory with regard to their consistency with the large rigid body motions for this purpose a refined tm theory of multilayered anisotropic shells undergoing finite deformations is elaborated the transverse shear and transverse normal deformation response and bending extension coupling are included the fundamental unknowns consist of six displacements and 11 strains of the bottom and top surfaces of the shell and 11 stress resultants on the basis of this theory the simple and efficient mixed models are developed by using the incremental total lagrangian formulation in conjunction with the newton raphson method the elemental arrays are derived applying the hu washizu mixed variational principle numerical results are presented to demonstrate the high accuracy and effectiveness of the developed four node shell elements and to compare their performance with other non linear finite elements reported in the literature

the linear rational collocation method we introduce the collocation method based on linear rational interpolation for solving general hyperbolic problems prove its stability and its convergence in weighted norms and give numerical examples for its use

optimized point shifts and poles in the linear rational pseudospectral method for boundary value problems due to their rapid often exponential convergence as the number n of interpolation collocation points is increased polynomial pseudospectral methods are very efficient in solving smooth boundary value problems however when the solution displays boundary layers and or interior fronts this fast convergence will merely occur with very large n to address this difficulty we present a method which replaces the polynomial ansatz with a rational function r and considers the physical domain as the conformal map g of a computational domain g shifts the interpolation points from their classical position in the computational domain to a problem dependent position in the physical domain starting from a map by bayliss and turkel we have constructed a shift that can in principle accomodate an arbitrary number of fronts its parameters as well as the poles of r are optimized numerical results demonstrate how g best accomodates interior fronts while the poles also handle boundary layers

efficient hypersingular line and surface integrals direct evaluation by complex variable differentiation method abstract we present an efficient numerical scheme to evaluate hypersingular integrals appeared in boundary element methods the hypersingular integrals are first separated into regular and singular parts in which the singular integrals are defined as limits around the singularity and their values are determined analytically by taking the finite part values the remaining regular integrals can be evaluated using rational interpolatory quadrature or complex variable differentiation cvdm for the regular function when machine precision like accuracy is required the proposed method is then generalised for evaluating hypersingular surface integrals in which the inner integral is treated as the hypersingular line integral via coordinate transformations the procedure is implemented into 8 node rectangular boundary element and 6 node triangular element for numerical evaluation finally several numerical examples are presented to demonstrate the efficiency of the present method to the best of our knowledge the proposed method is more accurate faster and more generalised than other methods available in the literature to evaluate hypersingular integrals

local sensitivity approximations for selectivity bias summary observational data analysis is often based on tacit assumptions of ignorability or randomness the paper develops a general approach to local sensitivity analysis for selectivity bias which aims to study the sensitivity of inference to small departures from such assumptions if m is a model assuming ignorability we surround m by a small neighbourhood at defined in the sense of kullback leibler divergence and then compare the inference for models in iv with that for m interpretable bounds for such differences are developed applications to missing data and to observational comparisons are discussed local approximations to sensitivity analysis are model robust and can be applied to a wide range of statistical problems

on the lebesgue constant of barycentric rational hermite interpolants at equidistant nodes abstract barycentric rational floater hormann interpolants compare favourably to classical polynomial interpolants in the case of equidistant nodes because the lebesgue constant associated with these interpolants grows logarithmically in this setting in contrast to the exponential growth experienced by polynomials in the hermite setting in which also the first derivatives of the interpolant are prescribed at the nodes the same exponential growth has been proven for polynomial interpolants and the main goal of this paper is to show that much better results can be obtained with a recent generalization of floater hormann interpolants after summarizing the construction of these barycentric rational hermite interpolants we study the behaviour of the corresponding lebesgue constant and prove that it is bounded from above by a constant several numerical examples confirm this result

moving mesh methods based on moving mesh partial differential equations several versions of a moving mesh method are developed based on a mesh spatial smoothing technique and on the moving mesh pdes derived in a previous paper these versions are quite simple and easy to program they are applied to three bench mark one dimensional problems which show different solution behaviour the numerical results clearly demonstrate that the present methods are capable of accurately tracking rapid spatial and temporal transitions

the finite deformation theory for beam plate and shell part i the two dimensional beam theory a finite deformation theory is proposed that can describe precisely the nonlinear geometric behavior of a two dimensional beam structure unlike the existing nonlinear theories this theory does away with simplifications such as the assumptions of small displacement small normal or shearing strain small rotation as well as small loading step the finite element method and its formulation of this theory are deduced numerical examples performed by the theory proved it valid and computed results obtained by the theory are independent of loading steps

a novel method for a class of parameterized singularly perturbed boundary value problems in this paper a novel approach is presented for solving parameterized singularly perturbed two point boundary value problems with a boundary layer by the boundary layer correction technique the original problem is converted into two non singularly perturbed problems which can be solved using traditional numerical methods such as runge kutta methods several non linear problems are solved to demonstrate the applicability of the method numerical experiments indicate the high accuracy and the efficiency of the new method

a kinematically exact finite element formulation of planar elastic plastic frames a finite element formulation of finite deformation static analysis of plane elastic plastic frames subjected to static loads is presented in which the only function to be interpolated is the rotation of the centroid axis of the beam one of the advantages of such a formulation is that the problem of the field consistency does not arise exact non linear kinematic relationships of the finite strain beam theory are used which assume the bernoulli hypothesis of plane cross sections finite displacements and rotations as well as finite extensional and bending strains are accounted for the effects of shear strains and non conservative loads are at present neglected yet they can simply be incorporated in the formulation because the potential energy of internal forces does not exist with elastic plastic material the principle of virtual work is introduced as the basis of the finite element formulation a generalized principle of virtual work is proposed in which the displacements rotation extensional and bending strains and the lagrangian multipliers are independent variables by exploiting the special structure of the equations of the problem the displacements the strains and the multipliers are eliminated from the generalized principle of virtual work a novel principle is obtained in which the rotation becomes the only function to be approximated in its finite element implementation it is shown that n 1 point numerical integration must be employed in conjunction with n node interpolation polynomials for the rotation and the lobatto rule is recommended regarding the integration over the cross section it is demonstrated by numerical examples that due to discontinuous integrands no integration order defined as computationally efficient yet accurate enough could be suggested the theoretical findings and a nice performance of the derived finite elements are illustrated by numerical examples

barycentric formulae for cardinal sinc interpolants we present a barycentric representation of cardinal interpolants as well as a weighted barycentric formula for their efficient evaluation we also propose a rational cardinal function which in some cases agrees with the corresponding cardinal interpolant and in other cases is even more accurate in numerical examples we compare the relative accuracy of those various interpolants with one another and with a rational interpolant proposed in former work

assessment of the extent of corroboration of an elaborate theory of a causal hypothesis using partial conjunctions of evidence factors an elaborate theory of predictions of a causal hypothesis consists of several falsifiable statements derived from the causal hypothesis statistical tests for the various pieces of the elaborate theory help to clarify how much the causal hypothesis is corroborated in practice the degree of corroboration of the causal hypothesis has been assessed by a verbal description of which of the several tests provides evidence for which of the several predictions this verbal approach can miss quantitative patterns in this paper we develop a quantitative approach we first decompose these various tests of the predictions into independent factors with different sources of potential biases support for the causal hypothesis is enhanced when many of these evidence factors support the predictions a sensitivity analysis is used to assess the potential bias that could make the finding of the tests spurious along with this multiparameter sensitivity analysis we consider the partial conjunctions of the tests these partial conjunctions quantify the evidence supporting various fractions of the collection of predictions a partial conjunction test involves combining tests of the components in the partial conjunction we find the asymptotically optimal combination of tests in the context of a sensitivity analysis our analysis of an elaborate theory of a causal hypothesis controls for the familywise error rate

new representations of pade pade type and partial pade approximants pade approximants are rational functions with a denominator which does not vanish at zero and whose series expansion match a given series as far as possible these approximants are usually written under a rational form in this paper we will show how to write them also under two different barycentric forms and under a partial fraction form depending on free parameters according to the choice of these parameters pade type approximants can be obtained under a barycentric or a partial fraction form

boundary layer resolving pseudospectral methods for singular perturbation problems pseudospectral methods are investigated for singularly perturbed boundary value problems for ordinary differential equations odes which possess boundary layers it is well known that if the boundary layer is very small then a very large number of spectral collocation points is required to obtain accurate solutions we introduce here a new effective procedure based on coordinate stretching and the chebyshev pseudospectral method to resolve the boundary layers stable and accurate results are obtained for very thin boundary layers with a fairly small number of spectral collocation points

sensitivity analysis for multiple comparisons in matched observational studies through quadratically constrained linear programming abstracta sensitivity analysis in an observational study assesses the robustness of significant findings to unmeasured confounding while sensitivity analyses in matched observational studies have been well addressed when there is a single outcome variable accounting for multiple comparisons through the existing methods yields overly conservative results when there are multiple outcome variables of interest this stems from the fact that unmeasured confounding cannot affect the probability of assignment to treatment differently depending on the outcome being analyzed existing methods allow this to occur by combining the results of individual sensitivity analyses to assess whether at least one hypothesis is significant which in turn results in an overly pessimistic assessment of a study s sensitivity to unobserved biases by solving a quadratically constrained linear program we are able to perform a sensitivity analysis while enforcing that unmeasured confounding must have the same impact on the treatm

a uniformly convergent difference method for the periodical boundary value problem abstract the periodical boundary value problem for linear second order ordinary differential equation with small parameter by the first and second derivatives is considered by the method of integral identities with the use of exponential basis functions and interpolating quadrature rules with weight and remainder term in integral form an exponentially fitted difference scheme is constructed in a uniform mesh which gives first order uniform convergence in the discrete maximum norm numerical experiments support these theoretical results

a fast algorithm for rational interpolation via orthogonal polynomials l algorithme propose genere un ensemble de polynomes orthogonaux par la relation de recurrence a trois termes et ensuite utilise l interpolation de newton pour determiner les polynomes au numerateur et au denominateur de la fonction rationnelle d interpolation

on a rational differential quadrature method in irregular domains for problems with boundary layers abstract a rational differential quadrature method in irregular domains rdqmid is investigated to deal with a kind of singularly perturbed problems with boundary layers through a transformation the boundary layer which may be not straight is transformed into a segment of a line parallel to one of the cartesian axes the rational differential quadrature method rdqm is applied to discretize the governing equation finally a direct expansion method of the boundary conditions dembc is raised to deal with the boundary conditions numerical experiments show that rdqmid is of high accuracy efficiency and easy to programme

a method for directly finding the denominator values of rational interpolants in this paper we give an algorithm for directly finding the denominator values of rational interpolants at the nodes and present an expression for the corresponding rational interpolant when the latter exists with these denominator values our method also provides information concerning the existence of the interpolant and the presence of unattainable points and poles

pade type rational and barycentric interpolation in this paper we consider the particular case of the general rational hermite interpolation problem where only the value of the function is interpolated at some points and where the function and its first derivatives agree at the origin thus the interpolants constructed in this way possess a pade type property at 0 numerical examples show the interest of the procedure the interpolation procedure can be easily modified to introduce a partial knowledge on the poles and the zeros of the function to approximated a strategy for removing the spurious poles is explained a formula for the error is proved in the real case applications are given

a kinematically exact space finite strain beam model finite element formulation by generalized virtual work principle the present paper presents a novel finite element formulation for static analysis of linear elastic spatial frame structures extending the formulation given by simo and vu quoc a geometrically exact rod model incorporating shear and torsion warping deformation int j solids structures 27 3 1991 371 3931 along the lines of the work on the planar beam theory presented by saje a variational principle for finite planar deformation of straight slender elastic beams internat j solids and structures 26 1990 887 9001 we apply exact non linear kinematic relationships of the space finite strain beam theory assuming the bernoulli hypothesis and neglecting the warping deformations of the cross section finite displacements and rotations as well as finite extensional shear torsional and bending strains are accounted for in the formulation a deformed configuration of the beam is described by the displacement vector of the deformed centroid axis and an orthonormal moving frame rigidly attached to the cross section of the beam the position of the moving frame relative to a fixed reference frame is specified by an orthogonal matrix parametrized by the rotational vector which rotates the moving frame from an arbitrary position into the deformed configuration in one step also the incremental rotational vector is introduced which rotates the moving frame from the configuration obtained at the previous iteration step into the current configuration of the beam its components relative to the fixed global coordinate system are taken to be the rotational degrees of freedom at nodal points because in 3 d space both the axial and the follower moments are non conservative not the variational principle but the principle of virtual work has been introduced as a basis for the finite element discretization here we have proposed the generalized form of the principle of virtual work by including exact kinematic equations by means of a procedure similar to that of lagrangian multipliers this makes possible the elimination of the displacement vector field from the principle so that the three components of the incremental rotational vector field remain the only functions to be approximated in the finite element implementation of the principle other researchers on the other hand employ the three components of the incremental rotational vector field and the three components of the incremental displacement vector field as a result more accurate and efficient family of beam finite elements for the non linear analysis of space frames has been obtained a one field formulation results in the fact that in the present finite elements the locking never occurs any combination of deformation states is described equally precisely this is in contrast with the elements developed in literature where in order to avoid the locking a reduced numerical integration has to be applied which unfortunately diminishes the accuracy of the solution polynomials have been chosen for the approximation of the components of the rotational vector in this case the order of the numerical integration can rationally be estimated and the computer program can be coded in such a way that the degree of polynomials need not be limited to a particular value the newton method is used for the iterative solution of the non linear equilibrium equations in an non equilibrium configuration the tangent stiffness matrix obtained by the linearization of governing equations using the directional derivative is non symmetric even for conservative loadings only upon achieving an equilibrium state the tangent stiffness matrix becomes symmetric thus obtained tangent stiffness matrix can be symmetrized without affecting the rate of convergence of the newton method for non conservative loadings however the tangent stiffness matrix is always non symmetric the numerical examples demonstrate capability of the present formulation to determine accurately the non linear behaviour of space frames in numerical examples the out of plane buckling loads are determined and the whole pre and post critical load displacement paths of a cantilever and a right angle frame are traced these in the analysis of space beams standard verification example problems show excellent accuracy of the solution even when employing only one element to describe the displacements of the size of the structure itself the rotations of 2n and extensional strains much beyond the realistic values of linear elastic material

sensitivity of two sample permutation inferences in observational studies abstract in observational studies subjects are not randomly assigned to treatment or control so they may differ in their chances of receiving the treatment a simple method is developed and demonstrated for displaying the sensitivity of conventional two group permutation inferences to departures from random assignment of treatments the unmatched case discussed here differs in certain technical and computational details from the matched case discussed previously however the underlying model and the method for quantifying departures from randomization are the same the method may be applied to wilcoxon s rank sum test the gehan and log rank tests for censored outcomes mantel s test for scored categories and fisher s exact test for binary responses the method embeds the usual randomization reference distribution in a one parameter family of departures involving an unobserved covariate that would have been controlled by adjustments had it been observed as this parameter is varied the sensitivity

a note on a parameterized singular perturbation problem we consider a uniform finite difference method on shishkin mesh for a quasilinear first order singularly perturbed boundary value problem bvp depending on a parameter we prove that the method is first order convergent except for a logarithmic factor in the discrete maximum norm independently of the perturbation parameter numerical experiments support these theoretical results

stable polefinding and rational least squares fitting via eigenvalues a common way of finding the poles of a meromorphic function f in a domain where an explicit expression of f is unknown but f can be evaluated at any given z is to interpolate f by a rational function pq such that r i f i at prescribed sample points i i 1l and then find the roots of q this is a two step process and the type of the rational interpolant needs to be specified by the user many other algorithms for polefinding and rational interpolation or least squares fitting have been proposed but their numerical stability has remained largely unexplored in this work we describe an algorithm with the following three features 1 it automatically finds an appropriate type for a rational approximant thereby allowing the user to input just the function f 2 it finds the poles via a generalized eigenvalue problem of matrices constructed directly from the sampled values f i in a one step fashion and 3 it computes rational approximants p q in a numerically stable manner in that p p q q f with small p q at the sample points making it the first rational interpolation or approximation algorithm with guaranteed numerical stability our algorithm executes an implicit change of polynomial basis by the qr factorization and allows for oversampling combined with least squares fitting through experiments we illustrate the resulting accuracy and stability which can significantly outperform existing algorithms

a continuum based shell theory for non linear applications the paper introduces a non linear shell theory which provides a complete three dimensional state of stress since the theory is derived from simple three dimensional continuum mechanics it is very easy to understand as an example the theory is applied to quadrilateral shell elements which provide only displacement degrees of freedom located at nodes on the outer surfaces and one degree of freedom at the middle surface it is proposed to eliminate this degree of freedom on element level so that the elements have the same layout as the equivalent brick elements but have a better behaviour in bending have stress resultants and are cheaper with respect to computational effort the advantages with respect to implementation in a finite element program as well as in special applications are obvious however well known conditioning problems in thin shell applications must be expected therefore emphasis is put on this issue in the example problems it is shown that the elements can give acceptable answers in engineering applications and offer a potential for material non linear applications which will be considered in a forthcoming paper

polynomial interpolation lagrange versus newton we show that the lagrangian form of the interpolating polynomial can be calculated with the same number of arithmetic operations as the newtonian form

hodges lehmann point estimates of treatment effect in observational studies abstract a hodges lehmann point estimate of an additive treatment effect is a robust estimate derived from the randomization distribution of a rank test this article shows how to carry out a sensitivity analysis for such an estimate in an observational study where treatments are not randomly assigned two cases are discussed in detail matched pairs and the comparison of two unmatched groups the method uses a model for the distribution of treatment assignments when hidden biases may be present this model has previously been used for sensitivity analysis of significance levels and confidence intervals

an eulerian approach for large displacements of thin shells including geometrical non linearities abstract this paper is devoted to the problem of large displacement of shells the only non linearity being geometrical the geometry of the mid surface of the shell is determined thanks to the knowledge of nodes and normal vectors and is continuously updated stresses are also carried from one configuration to another which enables us to linearize the equilibrium equations it is then possible to build an eulerian formulation moreover some control strategies are proposed in order to find limit points and unstable solutions finally we check in some classical examples the accuracy of this technique

an iterative approach to barycentric rational hermite interpolation in this paper we study an iterative approach to the hermite interpolation problem which first constructs an interpolant of the function values at n 1 nodes and then successively adds m correction terms to fit the data up to the mth derivatives in the case of polynomial interpolation this simply reproduces the classical hermite interpolant but the approach is general enough to be used in other settings in particular we focus on the family of rational floater hormann interpolants which are based on blending local polynomial interpolants of degree d with rational blending functions for this family the proposed method results in rational hermite interpolants which depend linearly on the data with numerator and denominator of degree at most m 1 n 1 1 and m 1 n d respectively they converge at the rate of o h m 1 d 1 as the mesh size h converges to 0 after deriving the barycentric form of these interpolants we prove the convergence rate for m 1 and m 2 and show that the approximation results compare favourably with other constructions

solution of evolutionary partial differential equations using adaptive finite differences with pseudospectral post processing a coordinate transformation approach is described that enables pseudospectral methods to be applied efficiently to unsteady differential problems with steep solutions the work is an extension of a method presented by mulholland huang and sloan for the adaptive pseudospectral solution of steady problems a coarse grid is generated by a moving mesh finite difference method that is based on equidistribution and this grid is used to construct a time dependent coordinate transformation a sequence of spatial transformations may be generated at discrete points in time or a single transformation may be generated as a continuous function of space and time the differential problem is transformed by the coordinate transformation and then solved using a method that combines pseudospectral discretisation in space with a suitable integrator in time numerical results are presented for unsteady problems in one space dimension

lebesgue constant minimizing linear rational interpolation of continuous functions over the interval abstract polynomial interpolation between large numbers of arbitrary nodes does notoriously not in general yield useful approximations of continuous functions following 1 we suggest to determine for each set of n 1 nodes another denominator of degree n and then to interpolate every continuous function by a rational function with that same denominator so that the resulting interpolation process remains a linear projection the optimal denominator is chosen so as to minimize the lebesgue constant for the given nodes it has to be computed numerically for that purpose the barycentric representation of rational interpolants which displays the linearity of the interpolation and reduces the determination of the denominator to that of the barycentric weights is used the optimal weights can then be computed by solving an optimization problem with simple bounds which could not be solved accurately by the first author in 1 we show here how to do so and we present numerical results

a numerical treatment for singularly perturbed differential equations with integral boundary condition we consider a uniform finite difference method on shishkin mesh for a quasilinear first order singularly perturbed boundary value problem bvp with integral boundary condition we prove that the method is first order convergent except for a logarithmic factor in the discrete maximum norm independently of the perturbation parameter the parameter uniform convergence is confirmed by numerical computations

finite rotation elements for the non linear analysis of thin shell structures abstract for the numerical analysis of shells undergoing finite rotations doubly curved finite shell elements are developed via the displacement formulation the derivation starts from a consistent finite rotation shell theory which is transformed by a variational procedure into an incremental formulation thus the non linearity can be treated by an incremental iterative technique the non linear element matrices are obtained by a tensor oriented procedure permitting a direct transformation of the initial equations into efficient numerical models unlike in the usual procedure the kirchhoff love assumption is treated as a subsidiary condition at the element level this computer oriented approach permits the elimination of the dependent rotational degrees of freedom without loss of accuracy finally some examples are presented to demonstrate the ability of the resulting finite elements to deal with finite rotation problems

design sensitivity in observational studies summary outside the field of statistics the literature on observational studies offers advice about research designs or strategies for judging whether or not an association is causal such as multiple operationalism or a dose response relationship these useful suggestions are typically informal and qualitative a quantitative measure design sensitivity is proposed for measuring the contribution such strategies make in distinguishing causal effects from hidden biases several common strategies are then evaluated in terms of their contribution to design sensitivity a related method for computing the power of a sensitivity analysis is also developed

design of barycentric interpolators for uniform and nonuniform sampling grids this paper proposes a method to convert a fixed instant interpolator for band limited signals into a variable instant one which has the form of a barycentric interpolator this interpolator makes it possible to approximate the signal and its derivatives with minimal complexity in a range that surrounds the initial instant and is applicable to uniform and nonuniform sampling grids the barycentric form of the interpolator is derived using two different procedures first by the repeated use of bernstein s inequality and taylor s theorem and second by truncating a lagrange type series these procedures show that the proposed method can be applied to existing fixed instant interpolators and that it can be accurate in long time intervals finally an evaluation procedure for barycentric interpolators and their derivatives is presented that minimizes the number of divisions solving at the same time the numerical problems associated with small denominators this paper includes several numerical examples

an extension of the floater hormann family of barycentric rational interpolants the barycentric rational interpolants introduced by floater and hormann in 2007 are blends of polynomial interpolants of fixed degree d in some cases these rational functions achieve approximation of much higher quality than the classical polynomial interpolants which e g are ill conditioned and lead to runge s phenomenon if the interpolation nodes are equispaced for such nodes however the condition of floater hormann interpolation deteriorates exponentially with increasing d in this paper an extension of the floater hormann family with improved condition at equispaced nodes is presented and investigated the efficiency of its applications such as the approximation of derivatives integrals and primitives of functions is compared to the corresponding results recently obtained with the original family of rational interpolants math subject classification 65d05 65l12 65d32 41a05 41a20 41a25

numerical algorithms based on analytic function values at roots of unity let f z be an analytic or meromorphic function in the closed unit disk sampled at the n th roots of unity based on these data how can we approximately evaluate f z or f m z at a point z in the disk how can we calculate the zeros or poles of f in the disk these questions exhibit in the purest form certain algorithmic issues that arise across computational science in areas including integral equations partial differential equations and large scale linear algebra we analyze some of the possibilities and emphasize the distinction between algorithms based on polynomial or rational interpolation and those based on trapezoidal rule approximations of cauchy integrals we then show how these developments apply to the problem of computing the eigenvalues in the disk of a matrix of large dimension finally we highlight the power of rational in comparison with polynomial approximations for some of these problems

effects attributable to treatment inference in experiments and observational studies with a discrete pivot summary in randomisation and permutation inference pivotal arguments remove the hypothesised treatment effect thereby basing inferences on the null distribution in which the treatment has no effect this is common for instance with additive treatment effects the current paper uses attributable effects to expand substantially the scope of pivotal arguments attributable effects are defined for three cases namely the 2 x 2 contingency table displacement effects and the mann whitney wilcoxon statistic and in each case removing an appropriate attributable effect restores the familiar null randomisation distribution of the associated statistic yielding exact inferences the procedure extends immediately for use in sensitivity analysis in nonrandomised observational studies

spectrally accurate quadratures for evaluation of layer potentials close to the boundary for the 2d stokes and laplace equations dense particulate flow simulations using integral equation methods demand accurate evaluation of stokes layer potentials on arbitrarily close interfaces in this paper we generalize techniques for close evaluation of laplace double layer potentials in j helsing and r ojala j comput phys 227 2008 pp 2899 2921 we create a globally compensated trapezoid rule quadrature for the laplace single layer potential on the interior and exterior of smooth curves this exploits a complex representation a product quadrature in the style of kress for the sawtooth function careful attention to branch cuts and second kind barycentric type formulae for cauchy integrals and their derivatives upon this we build accurate single and double layer stokes potential evaluators by expressing them in terms of laplace potentials we test their convergence for vesicle vesicle interactions for an extensive set of laplace and stokes problems and when applying the system matrix in a boundary value problem solver

a class of reduced order models in the theory of waves and stability this paper presents a class of approximations to a type of wave field for which the dispersion relation is transcendental the approximations have two defining characteristics i they give the field shape exactly when the frequency and wavenumber lie on a grid of points in the frequency wavenumber plane and ii the approximate dispersion relations are polynomials that pass exactly through points on this grid thus the method is interpolatory in nature but the interpolation takes place in frequency wavenumber space rather than in physical space full details are presented for a non trivial example that of antisymmetric elastic waves in a layer the method is related to partial fraction expansions and barycentric representations of functions an asymptotic analysis is presented involving stirling s approximation to the psi function and a logarithmic correction to the polynomial dispersion relation

detecting bias with confidence in observational studies summary in an observational study detecting hidden bias involves checking that treatment effects appear where they should and not elsewhere for instance treated and control groups are often compared with respect to outcomes the treatment should not affect this paper uses such a test for bias to obtain a confidence set for an unobserved covariate the impact of this unobserved covariate is indicated by a sensitivity analysis with the covariate confined to the confidence set in this way a test for bias may indicate either the presence and magnitude of a hidden bias or else a reduction in the sensitivity to bias

parametrized singularly perturbed boundary value problems abstract certain types of singularly perturbed higher order ordinary differential equations depending on parameters are studied lower bounds of the number of parameters are found for which those equations possess a solution for this purpose the nielsen fixed point theory is used

rational spectral collocation and differential evolution algorithms for singularly perturbed problems with an interior layer abstract we are concerned with using high accuracy numerical methods for solving singularly perturbed problems whose solutions exhibit an interior layer a rational spectral collocation method in barycentric form with sinh transformation is firstly applied to find the approximate solution to the given problem the sinh transformation consists of two parameters the location and the width of the interior layer with the tool of the asymptotic analysis the interior layer can be easily located then in determining the width of the interior layer we design a nonlinear unconstrained optimization problem which is solved by using the basic differential evolution de algorithm the feasibility and effectiveness of the proposed method is verified by numerical results the proposed method can also be applied to other singularly perturbed problems

inference for non random samples observational data are often analysed as if they had resulted from a controlled study and yet the tacit assumption of randomness can be crucial for the validity of inference we take some simple statistical models and supplement them by adding a parameter which reflects the degree of non randomness in the sample for a randomized study is known to be 0 we examine the profile log likelihood for and the sensitivity of inference to small non zero values of particular models cover the analysis of survey data with item non response the paired comparison t test and two group comparisons using observational data with covariates some practical examples are discussed allowing for sampling bias increases the uncertainty of estimation and weakens the significance of treatment effects sometimes substantially so

matrices for the direct determination of the barycentric weights of rational interpolation abstract let x0 xn be n 1 interpolation points nodes and 0 n be n 1 interpolation data then every rational function r with numerator and denominator degress n interpolating these values can be written in its barycentric form completely determined by a vector u of n 1 barycentric weights uk finding u is therefore an alternative to the determination of the coefficients in the canonical form of r it is advantageous inasmuch as u contains information about unattainable points and poles in classical rational interpolation the numerator and the denominator of r are made unique up to a constant factor by restricting their respective degrees we determine here the corresponding vectors u by applying a stabilized elimination algorithm to a matrix whose kernel is the space spanned by the u s the method is of complexity o n3 in terms of the denominator degree n it seems on the other hand to be among the most stable ones

comparison of a priori and a posteriori meshes for singularly perturbed nonlinear parameterized problems this paper deals with the adaptive mesh generation for singularly perturbed nonlinear parameterized problems with a comparative research study on them we propose an a posteriori error estimate for singularly perturbed parameterized problems by moving mesh methods with fixed number of mesh points the well known a priori meshes are compared with the proposed one the comparison results show that the proposed numerical method is highly effective for the generation of layer adapted a posteriori meshes a numerical experiment of the error behavior on different meshes is carried out to highlight the comparison of the approximated solutions

a brief survey on numerical methods for solving singularly perturbed problems in the present paper a brief survey on computational techniques for the different classes of singularly perturbed problems is given this survey is a continuation of work performed earlier by the first author and contains the literature of the work done by the researchers during the years 2000 2009 however some older important relevant papers are also included in this survey we also mentioned those papers which are not surveyed in the previous survey papers by the first author of this paper see appl math comput 30 1989 223 259 130 2002 457 510 134 2003 371 429 for details thus this survey paper contains a surprisingly large amount of literature on singularly perturbed problems and indeed can serve as an introduction to some of the ideas and methods for the singular perturbation problems

quantiles in nonrandom samples and observational studies abstract in a nonrandom sample or a nonrandomized comparison of treated and control groups methods are developed for displaying the sensitivity of confidence intervals for population quantiles to the magnitude of the departure from random selection quantiles of a single distribution and for a shift in two distributions are both discussed these confidence intervals are based on a new inequality for the distribution of the number of successes in a nonrandom sample or nonrandomized comparison the inequality has additional applications in particular it greatly accelerates the computations in a sensitivity analysis for the mantel haenszel statistic in a 2 2 s contingency table examples include a nonrandom collection of blood samples from a town with comparatively high levels of radon gas an observational study of chromosome damage from mercury and a study of the drug allopurinol as a cause of skin rash the proof of the inequality makes use of savage s lattice for ranks and holley s inequality wh

assessing sensitivity to an unobserved binary covariate in an observational study with binary outcome this paper proposes a simple technique for assessing the range of plausible causal con clusions from observational studies with a binary outcome and an observed categorical covariate the technique assesses the sensitivity of conclusions to assumptions about an unobserved binary covariate relevant to both treatment assignment and response a medical study of coronary artery disease is used to illustrate the technique inevitably the results of clinical studies are subject to dispute in observational studies one basis for dispute is obvious since patients were not assigned to treatments at random patients at greater risk may be over represented in some treatment groups this paper proposes a method for assess ing the sensitivity of causal conclusions to an unmeasured patient characteristic relevant to both treatment assignment and response despite their limitations observational studies will continue to be a valuable source of information and therefore it is prudent to develop appropriate methods of analysis for them our sensitivity analysis consists of the estimation of the average effect of a treatment on a binary outcome variable after adjustment for observed categorical covariates and an unobserved binary covariate u under several sets of assumptions about u both cornfield et al 1959 and bross 1966 have proposed guidelines for determining whether an unmeasured binary covariate having specified properties could explain all of the apparent effect of a treatment that is whether the treatment effect after adjustment for u could be zero our method has two advantages first cornfield et al 1959 and bross 1966 adjust only for the unmeasured binary covariate u whereas we adjust for measured covariates in addition to the unmeasured covariate u second cornfield et al 1959 and bross 1966 1967 only judge whether the effect of the treatment could be zero having adjusted for u where cornfield et al 1959 employ an implicit yet extreme assumption about u in contrast we provide actual estimates of the treatment effect adjusted for both u and the observed categorical covariates under any assumption about u in principle the ith of the n patients under study has both a binary response r1i that would have resulted if he had received the new treatment and a binary response ro0 that would have resulted if he had received the control treatment in this formulation treatment effects are comparisons of r1i and roi such as r1i roi since each patient receives only one treatment either rli or ro0 is observed but not both and therefore comparisons of rli and roi imply some degree of speculation treatment effects defined as comparisons of the two potential responses r1i and roi of individual patients are implicit in fisher s 1953 randomization test of the sharp null

uniform difference method for a parameterized singular perturbation problem we consider a uniform finite difference method on a b mesh is applied to solve a singularly perturbed quasilinear boundary value problem bvp depending on a parameter we give a uniform first order error estimates in a discrete maximum norm numerical results are presented that demonstrate the sharpness of our theoretical analysis

finite rotation analysis and consistent linearization using projectors abstract a systematic procedure is presented that may be used to extend the capabilities of an existing linear finite element to accomodate finite rotation analysis this procedure is a generalization of the work presented in computers and structures volume 30 pp 257 267 the basis of our approach is the element independent co rotational algorithm where the element rigid body motion translations and rotations is separated from the deformational part of its total motion the variation of this co rotational relation results in a projector matrix with the property that a consistent internal force vector is invariant under its action the consistent tangent stiffness matrix is shown to depend on this invariance condition through the derivative of the projector this results in an unsymmetric tangent matrix whose anti symmetric part depends on the out of balance force vector in this paper we prove that using the symmetric part of the tangent matrix the newton iteration retains its quadratic rate of convergence this approach has been used to solve a number of large rotation test example problems the results demonstrate that it is possible to analyze structures undergoing large rotations within a general co rotational framework using simple and economical finite elements the resulting improvements in the performance of these simple elements are brought about through the use of convenient software utilities as pre and post processors to the element routines

an excursion into large rotations the present discourse develops an enlarged exploration of the matrix formulation of finite rotations in space initiated in 1 it is shown how a consistent but subtle matrix calculus inevitably leads to a number of elegant expressions for the transformation or rotation matrix t appertaining to a rotation about an arbitrary axis also analysed is the case of multiple rotations about fixed or follower axes particular attention is paid to an explicit derivation of a single compound rotation vector equivalent to two consecutive arbitrary rotations this theme is discussed in some detail for a number of cases semitangential rotations for which commutativity holds first proposed in 2 3 are also considered furthermore an elementary geometrical analysis of large rotations is also given finally we deduce in an appendix using a judicious reformulation of quarternions the compound pseudovector representing the combined effect of n rotations in the author s opinion the present approach appears preferable to a pure vectorial scheme and even more so to an indicial formulation and is computationally more convenient

conversions between barycentric rkfun and newton representations of rational interpolants we derive explicit formulas for converting between rational interpolants in barycentric rational krylov rkfun and newton form we show applications of these conversions when working with rational approximants produced by the aaa algorithm y nakatsukasa o sete l n trefethen arxiv preprint 1612 00337 2016 within the rational krylov toolbox and for the solution of nonlinear eigenvalue problems

a rational spectral collocation method for third order singularly perturbed problems a new numerical method is developed for solving a class of third order singularly perturbed boundary value problems first of all the given problem is transformed into a system of two ordinary differential equations odes subject to suitable initial and boundary conditions then the rational spectral collocation method in barycentric form with sinh transformation is applied to solve the system of odes according to the asymptotic analysis the location and width of boundary layer of the given problem which are chosen as parameters in the sinh transformation can be determined ample numerical experiments are presented to illustrate the computational efficiency and accuracy of the our method

sensitivity analysis for the cross match test with applications in genomics the cross match test is an exact distribution free test of no treatment effect on a high dimensional outcome in a randomized experiment the test uses optimal nonbipartite matching to pair 2i subjects into i pairs based on similar outcomes and the cross match statistic a is the number of times that a treated subject was paired with a control rejecting for small values of a if the test is applied in an observational study in which treatments are not randomly assigned then it may be comparing treated and control subjects who are not comparable and thus may falsely reject a true null hypothesis of no treatment effect we develop a sensitivity analysis for the cross match test and apply it in an observational study of the effects of smoking on gene expression levels in addition we develop a sensitivity analysis for several multiple testing procedures using the cross match test and apply it to 1627 molecular function categories in gene ontology

the finite deformation theory for beam plate and shell part iv the fe formulation of mindlin plate and shell based on green lagrangian strain using the kinematic description of the revised mindlin model the lagrangian strain derived by li and the fe formulation of the degenerated 3 d solid we propose an exact finite deformation theory for plate and shell the theory eliminates the need for the restrictions imposed by the existing simplified theories such as small strains small rotations or small loading steps numerical examples are presented to demonstrate the validity and accuracy of the theory compared with 3 d continuum theory

a rational spectral collocation method with adaptively transformed chebyshev grid points a spectral collocation method based on rational interpolants and adaptive grid points is presented the rational interpolants approximate analytic functions with exponential accuracy by using prescribed barycentric weights and transformed chebyshev points the locations of the grid points are adapted to singularities of the underlying solution and the locations of these singularities are approximated by the locations of poles of chebyshev pade approximants numerical experiments on two time dependent problems one with finite time blow up and one with a moving front indicate that the method far outperforms the standard chebyshev spectral collocation method for problems whose solutions have singularities in the complex plane close to 1 1

on the denominator values and barycentric weights of rational interpolants we improve upon the method of zhu and zhu a method for directly finding the denominator values of rational interpolants j comput appl math 148 2002 341 348 for finding the denominator values of rational interpolants reducing considerably the number of arithmetical operations required for their computation in a second stage we determine the points if existent which can be discarded from the rational interpolation problem furthermore when the interpolant has a linear denominator we obtain a formula for the barycentric weights which is simpler than the one found by berrut and mittelmann matrices for the direct determination of the barycentric weights of rational interpolation j comput appl math 78 1997 355 370 subsequently we give a necessary and sufficient condition for the rational interpolant to have a pole

roots of polynomials expressed in terms of orthogonal polynomials a technique is presented for determining the roots of a polynomial p x that is expressed in terms of an expansion in orthogonal polynomials the roots are expressed as the eigenvalues of a nonstandard companion matrix b n whose coefficients depend on the recurrence formula for the orthogonal polynomials and on the coefficients of the orthogonal expansion some questions on the numerical stability of the eigenvalue problem to which they give rise are discussed the problem of finding the roots of a transcendental function f x can be reduced to the problem considered by approximating f x by a chebyshev polynomial we illustrate the effectiveness of this convert to chebyshev strategy by solving several transcendental equations using this plus our new algorithm we analyze the numerical stability through both linear algebra theory and numerical experiments and find that this method is very well conditioned

uniform numerical method for singularly perturbed delay differential equations this paper deals with the singularly perturbed initial value problem for a linear first order delay differential equation a numerical method is constructed for this problem which involves an appropriate piecewise uniform mesh on each time subinterval the difference scheme is shown to converge to the continuous solution uniformly with respect to the perturbation parameter numerical results are presented

the barycentric weights of rational interpolation with prescribed poles abstract we introduce a method for calculating rational interpolants when some but not necessarily all of their poles are prescribed the algorithm determines the weights in the barycentric representation of the rationals it simply consists in multiplying each interpolated value by a certain number computing the weights of a rational interpolant without poles and finally multiplying the weights by those same numbers the supplementary cost in comparison with interpolation without poles is about v 2 n where v is the number of poles and n the number of interpolation points we also give a condition under which the computed rational interpolation really shows the desired poles