on the biregular geometry of the fulton macpherson compactification abstract let x n be the fulton macpherson compactification of the configuration space of n ordered points on a smooth projective variety x we prove that if either n 2 or dim x 2 then the connected component of the identity of aut x n is isomorphic to the connected component of the identity of aut x when x c is a curve of genus g c 1 we classify the dominant morphisms c n c r and thanks to this we manage to compute the whole automorphism group of c n namely aut c n s n aut c for any n 2 while aut c 2 s 2 aut c aut c furthermore we extend these results on the automorphisms to the case where x c 1 c r is a product of curves of genus g c i 2 finally using the techniques developed to deal with fulton macpherson spaces we study the automorphism groups of some kontsevich moduli spaces m 0 n p n d

a solution condition for complementarity problems with an application to spatial price equilibrium a sufficient condition is developed for the existence of solutions to complementarity problems which is applicable to all continuous functions in addition it is shown to imply a number of simpler conditions including the well known coerciveness condition finally this condition is applied to an existence problem in spatial price equilibrium where it is shown to yield not only a more general result but also a simpler method of proof

an existence condition for open set nonlinear complementarity problems with an application to a closed economic system a sufficient condition for the existence of solutions to open set nonlinear complementarity problems oncp is developed this condition is applied to an existence problem in a closed general economic equilibrium system

hermite birkhoff interpolation on scattered data on the sphere and other manifolds abstract the hermite birkhoff interpolation problem of a function given on arbitrarily distributed points on the sphere and other manifolds is considered each proposed interpolant is expressed as a linear combination of basis functions the combination coefficients being incomplete taylor expansions of the interpolated function at the interpolation points the basis functions depend on the geodesic distance are orthonormal with respect to the point evaluation functionals and have all derivatives equal zero up to a certain order at the interpolation points a remarkable feature of such interpolants which belong to the class of partition of unity methods is that their construction does not require solving linear systems numerical tests are given to show the interpolation performance

reconstruction of a function from hermite birkhoff data abstract birkhoff or lacunary interpolation is an extension of polynomial interpolation that appears when observation gives irregular information about some function and its derivatives a birkhoff interpolation problem is not always solvable even in the appropriate polynomial or rational space in this paper we split up the initial problem in subproblems having a unique polynomial solution and use multinode rational basis functions in order to obtain a global interpolant

on a nonlinear 4 point ternary and non interpolatory subdivision scheme eliminating the gibbs phenomenon abstract a nonlinear ternary 4 point non interpolatory subdivision scheme is presented it is based on a nonlinear perturbation of the 4 point subdivision scheme studied in 16 the convergence of the scheme and the regularity of the limit function are analyzed it is shown that the gibbs phenomenon that is classical in linear schemes is eliminated we also establish the stability of the subdivision scheme that is not a consequence of its convergence due to its non linearity to the best of our knowledge this is the first ternary non interpolatory subdivision scheme that can be found in the literature

family of a point b ary subdivision schemes with bell shaped mask in this paper we present a generalized refine smooth algorithm to design a family of a point b ary approximating subdivision schemes with bell shaped mask where a 3 and b 2 we use the combination of corner cutting b ary subdivision scheme and weighted average of b 1 points to construct the proposed family we demonstrate that the proposed family has smaller complexity and support width and higher continuity than the existing refine smooth subdivision schemes we also study the shape preserving properties of the proposed family in addition it is observed that the proposed family is suitable for fitting the locally noisy oscillatory and irregular data

non uniform interpolatory subdivision surface abstract this paper presents an interpolatory subdivision scheme with non uniform parametrization for arbitrary polygon meshes with arbitrary manifold topology this is the first attempt to generalize the non uniform four point interpolatory curve subdivision to surface with extraordinary points the scheme is constructed from the inspiration of the relation between the non uniform four point interpolatory subdivision scheme and the non uniform b spline refinement rule numerical examples and comparisons with the uniform interpolatory subdivision schemes indicate that the quality of the limit surface can be improved by using non uniform parameter values for non uniform initial data

approximation of parametric curves by moving least squares method in this work we propose a method to approximate a parametric curve in r d some distinct points in r d are given we assume that these points belong to a parametric curve and our aim is to approximate these data by moving least squares method we mention several applications of the proposed method to emphasize the importance of the work also root mean squares errors and hausdorff distances between the exact curve and its approximation are presented to demonstrate the efficiency and reliability of the method

exchange price equilibria and variational inequalities the aim of this paper is to show the relevance of the concept and the theory of variational inequalities in the study of economic equilibria

modified moving least squares with polynomial bases for scattered data approximation one common problem encountered in many fields is the generation of surfaces based on values at irregularly distributed nodes to tackle such problems we present a modified robust moving least squares mls method for scattered data smoothing and approximation the error functional used in the derivation of the classical mls approximation is augmented with additional terms based on the coefficients of the polynomial base functions this allows quadratic base functions to be used with the same size of the support domain as linear base functions resulting in better approximation capability the increased robustness of the modified mls method to irregular nodal distributions makes it suitable for use across many fields the analysis is supported by several univariate and bivariate examples

curve and surface fitting models based on the diagonalizable differential systems abstract curve and surface fitting is an important problem in computer aided geometric design including many methods such as the b spline method the nurbs method and so on however many curves and surfaces in the natural or engineering fields need to be described by differential equations in this paper we propose a new curve and surface fitting method based on the homogeneous linear differential systems in order to approximate general curves or surfaces well the diagonalizable differential systems with variable coefficients are adopted which have explicit solutions the fitting algorithms are presented for curves and surfaces from discrete points some numerical examples show that the two algorithms can obtain good fitting accuracy as the b spline method

on the birational geometry of spaces of complete forms ii skew forms abstract moduli spaces of complete skew forms are compactifications of spaces of skew symmetric linear maps of maximal rank on a fixed vector space where the added boundary divisor is simple normal crossing in this paper we compute their effective nef and movable cones the generators of their cox rings and for those spaces having picard rank two we give an explicit presentation of the cox ring furthermore we give a complete description of both the mori chamber and stable base locus decompositions of the effective cone of some spaces of complete skew forms having picard rank at most four

convergence analysis of generalized iteratively reweighted least squares algorithms on convex function spaces the computation of robust regression estimates often relies on minimization of a convex functional on a convex set in this paper we discuss a general technique for a large class of convex functionals to compute the minimizers iteratively which is closely related to majorization minimization algorithms our approach is based on a quadratic approximation of the functional to be minimized and includes the iteratively reweighted least squares algorithm as a special case we prove convergence on convex function spaces for general coercive and convex functionals f and derive geometric convergence in certain unconstrained settings the algorithm is applied to total variation tv penalized quantile regression and is compared with a step size corrected newton raphson algorithm it is found that typically in the first steps the iteratively reweighted least squares algorithm performs significantly better whereas the newton type method outpaces the former only after many iterations finally in the setting of bivariate regression with unimodality constraints we illustrate how this algorithm allows one to utilize highly efficient algorithms for special quadratic programs in more complex settings

families of non linear subdivision schemes for scattered data fitting and their non tensor product extensions abstract in this article families of non linear subdivision schemes are presented that are based on univariate polynomials up to degree three these families of schemes are constructed by using dynamic iterative re weighed least squares method these schemes are suitable for fitting noisy data with outliers the codes are designed in a python environment to numerically fit the given data points although these schemes are non interpolatory but have the ability to preserve the shape of the initial polygon in case of non noisy initial data the numerical examples illustrate that the schemes constructed by non linear polynomials give better performance than the schemes that are constructed by linear polynomials mustafa et al 2015 moreover the numerical examples show that these schemes have the ability to reproduce polynomials and do not cause over and under fitting of the data furthermore families of non linear bivariate subdivision schemes are also presented that are based on linear and non linear bivariate polynomials

on images of mori dream spaces the purpose of this paper is to study the geometry of images of morphisms from mori dream spaces first we prove that a variety which admits a surjective morphism from a mori dream space is again a mori dream space secondly we introduce a natural fan structure on the effective cone of mori dream spaces we show that it encodes the information of zariski decompositions which in turn is equivalent to the information of the variation of git quotients of their cox rings finally we show that under a surjective morphism between mori dream spaces the fan of the target space coincides with the restriction of the fan of the source

construction of hermite subdivision schemes reproducing polynomials abstract the aim of this study is to present a new class of quasi interpolatory hermite subdivision schemes of order two with tension parameters this class extends and unifies some of well known hermite subdivision schemes including the interpolatory hermite schemes acting on a function and the associated first derivative values each scheme in this class reproduces polynomials up to a certain degree depending on the size of stencil this is desirable property since the reproduction of polynomials up to degree d leads to the approximation order d 1 the smoothness analysis has been performed by using the factorization framework of subdivision operators lastly we present some numerical examples to demonstrate the performance of the proposed hermite schemes