We interpret the finite Zariski tangent spaces Ta(X,Fqm) to an affine variety X ⊂ Fq n as linear codes. If the degree ofX is relatively prime to the characteristic p = charFq, we show that the minimum distance of Ta(X,Fqm) stabilizes while varying a ∈ X(Fqm) := X ∩ Fnqm and m ∈ N. The article provides a pseudocode for obtaining the generic minimum distance of a tangent code and points, at which...

Based on the geometry of a radial function, sequence approximations for arcsine, arccosine and arctangent are detailed. The arcsine sharp at points zero one. Convergence is proved convergence significantly better than Taylor series arguments approaching established can be utilized as basis Newton-Raphson iteration analytical approximations, modest complexity, with relative error bounds order 10...

In this paper we study the tangent spaces of the smooth nested Hilbert scheme Hilb n,n−1 (A 2) of points in the plane, and give a general formula for computing the Euler characteristic of a T 2-equivariant locally free sheaf on Hilb n,n−1 (A 2). Applying our result to a particular sheaf, we conjecture that the result is a polynomial in the variables q and t with non-negative integer coefficient...

A direct search method for the class of problems considered by Lewis and Torczon [SIAM J. Optim., 12 (2002), pp. 1075-1089] is developed. Instead of using an augmented Lagrangian method, a simplicial approximation method to the feasible set is implicitly employed. This allows the points our algorithm considers to conveniently remain within an a priori specified distance of the feasible set. In ...

Let η be a line bundle on a smooth curve X with η^2=0 such that π_η, the double covering induced by η is an etale morphism. Assume also that X_η be the Prym-canonical model of X associated to K_X.η and Q is a rank 4 quadric containing X_η. After stablishing the projective normality of the prym-canonical models of curves X with Clifford index 2, we obtain in this paper a sufficient condition for...

We prove non-existence of C-smooth embeddings of n-dimensional discs to R such that the tangent spaces at distinct points are pairwise disjoint.

Introduction. The object of this note is to present a short and simple proof of the following two theorems. Theorem 1. Suppose that C is a closed rectifiable Jordan curve in the complex l-plane and that C has a continuously turning tangent in a neighborhood of one of its points, XoSuppose, furthermore, that the tangent angle t(s) as function of the arc length s has a modulus of continuity (¡)(t...

Let a smooth manifold M be equipped with a smoothly varying positive definite quadratic form on a distribution-subbundle V of the tangent bundle TM. One assumes that V is completely nonintegrable, equivalently all sections of V together with all brackets between them generate TM at each point of M. Then by the well-known theorem of Rashevski-Chow [3] it is possible to connect any two points (in...

In this paper we consider continuity of the set of fixed points and approximate fixed points for parameterized set-valued mappings. Continuity properties are provided for the fixed points of general multivalued mappings, with additional results shown for contraction mappings. Further analysis is provided for the continuity of the approximate fixed points of set-valued functions. Additional resu...