Search results for "tangent"
showing 10 items of 123 documents
Embeddings of Danielewski surfaces
2003
A Danielewski surface is defined by a polynomial of the form P=x nz −p(y). Define also the polynomial P ′ =x nz −r(x)p(y) where r(x) is a non-constant polynomial of degree ≤n−1 and r(0)=1. We show that, when n≥2 and deg p(y)≥2, the general fibers of P and P ′ are not isomorphic as algebraic surfaces, but that the zero fibers are isomorphic. Consequently, for every non-special Danielewski surface S, there exist non-equivalent algebraic embeddings of S in ℂ3. Using different methods, we also give non-equivalent embeddings of the surfaces xz=(y d n >−1) for an infinite sequence of integers d n . We then consider a certain algebraic action of the orthogonal group $\mathcal O(2)$ on ℂ4 which was…
ON THE INDEX OF VECTOR FIELDS TANGENT TO HYPERSURFACES WITH NON-ISOLATED SINGULARITIES
2002
Let $F$ be a germ of a holomorphic function at $0$ in ${\bb C}^{n+1}$ , having $0$ as a critical point not necessarily isolated, and let $\tilde{X}:= \sum^n_{j=0} X^j(\partial/\partial z_j)$ be a germ of a holomorphic vector field at $0$ in ${\bb C}^{n+1}$ with an isolated zero at $0$ , and tangent to $V := F^{-1}(0)$ . Consider the ${\cal O}_{V,0}$ -complex obtained by contracting the germs of Kahler differential forms of $V$ at $0$ \renewcommand{\theequation}{0.\arabic{equation}} \begin{equation} \Omega^i_{V,0}:=\frac{\Omega^i_{{\bb C}^{n+1},0}}{F\Omega^i_{{\bb C}^{n+1},0}+dF\wedge{\Omega^{i-1}}_{{\bb C}^{n+1}},0} \end{equation} with the vector field $X:=\tilde{X}|_V$ on $V$ : \begin{equa…
Semimodular Locally Projective Lattices of Rank 4 from v.Staudt’s Point of View
1981
We consider groups of projectivities in a certain kind of lattices called “Spaces”,also comprising the circle planes, and give theorems of v.Staudtian type, which characterize those Spaces which can be represented by a sublattice of a projective geometry of rank 4.
A symmetric tangent stiffness approach to cohesive mechanical interfaces in large displacements
2022
The present article proposes a formulation for a cohesive interface element in large displacement conditions. Theoretical and computational aspects, useful for an effective and efficient finite element implementation, are examined in details. A six-node (or higher) isoparametric interface element for two dimensional cohesive fracture propagation problems is developed. The element operators are consistently derived by a variational approach enforced in the current configuration, where a current frame is defined with axes tangential and normal to the middle line of the interface opening displacement gap. Under the constitutive assumption of small value of the modulus of the vector product bet…
Tractional Motion Machines: Tangent-Managing Planar Mechanisms as Analog Computers and Educational Artifacts
2012
Concrete and virtual machines play a central role in the both Unconventional Computing (machines as computers) and in Math Education (influence of artifacts on reaching/producing abstract thought). Here we will examine some fallouts in these fields for the Tractional Motion Machines, planar mechanisms based on some devices used to plot the solutions of differential equations by the management of the tangent since the late 17th century.
Separation properties of continuous maps in codimension 1 and geometrical applications
1992
Abstract Nuno Ballesteros, J.J. and M.C. Romero Fuster, Separation properties of continuous maps in codimension 1 and geometrical applications, Topology and its Applications 46 (1992) 107-111. We show that the image of a proper closed continuous map, f , from an n -manifold X to an ( n + 1)-manifold Y , such that H 1 (Y; Z 2 ) =0 , separates Y into at least two connected components provided the self-intersections set of f is not dense in any connected component of Y . We also obtain some geometrical applications.
Stress-Strain Law for Confined Concrete with Hardening or Softening Behavior
2013
This paper provides a new general stress-strain law for concrete confined by steel, fiber reinforced polymer (FRP), or fiber reinforced cementitious matrix (FRCM), obtained by a suitable modification of the well-known Sargin’s curve for steel confined concrete. The proposed law is able to reproduce stress-strain curve of any shape, having both hardening or softening behavior, by using a single closed-form simple algebraic expression with constant coefficients. The coefficients are defined on the basis of the stress and the tangent modulus of the confined concrete in three characteristic points of the curve, thus being related to physical meaningful parameters. It will be shown that if the v…
Contribution to variational analysis : stability of tangent and normal cones and convexity of Chebyshev sets
2014
The aim of this thesis is to study the following three problems: 1) We are concerned with the behavior of normal cones and subdifferentials with respect to two types of convergence of sets and functions: Mosco and Attouch-Wets convergences. Our analysis is devoted to proximal, Fréchet, and Mordukhovich limiting normal cones and subdifferentials. The results obtained can be seen as extensions of Attouch theorem to the context of non-convex functions on locally uniformly convex Banach space. 2) For a given bornology β on a Banach space X we are interested in the validity of the following "lim inf" formula (…).Here Tβ(C; x) and Tc(C; x) denote the β-tangent cone and the Clarke tangent cone to …
A symmetric nonlocal damage theory
2003
The paper presents a thermodynamically consistent formulation for nonlocal damage models. Nonlocal models have been recognized as a theoretically clean and computationally efficient approach to overcome the shortcomings arising in continuum media with softening. The main features of the presented formulation are: (i) relations derived by the free energy potential fully complying with nonlocal thermodynamic principles; (ii) nonlocal integral operator which is self-adjoint at every point of the solid, including zones near to the solid's boundary; (iii) capacity of regularizing the softening ill-posed continuum problem, restoring a meaningful nonlocal boundary value problem. In the present app…
Invariant approximation results in cone metric spaces
2011
Some sufficient conditions for the existence of fixed point of mappings satisfying generalized weak contractive conditions is obtained. A fixed point theorem for nonexpansive mappings is also obtained. As an application, some invariant approximation results are derived in cone metric spaces.