Al~tract--By employing the second-order Noether's theorem, several new invariant integrals have been derived for the non-linear shallow shell--the Marguerre-von K~irm~in shell. The dynamic effect is considered in the derivations. These invariant integrals are path-independent over the projection image of the middle surface of the shell in a Cartesian plane, in which the projection area of the m...

Many image-rotation invariant texture classification approaches have been presented. However, image rotation is not necessarily the same as surface rotation. This paper proposes a novel scheme that is surface-rotation invariant. It uses magnitude spectra of the partial derivatives of the surface obtained using photometric stereo. Unfortunately the partial derivative operator is directional. It ...

Khovanov introduced a cohomology theory for oriented classical links whose graded Euler characteristic is the Jones polynomial. Since Khovanov’s theory is functorial for link cobordisms between classical links, we obtain an invariant of a surface-knot, called the Khovanov-Jacobsson number, by considering the surface-knot as a link cobordism between empty links. In this paper, we define an invar...

Stereoscopic VISIon delivers a sparse map of the range to various "matched" points or contours, in the field of view. This paper addresses the problem of explicitly reconstructing a smooth surface that interpolates those points and contours. It is argued that any scheme for surface reconstruction should be viewpoint-invariant; otherwise the reconstructed surface would "wobble" as the viewpoint ...

We present efficient and accurate numerical methods for computing invariant manifolds of maps which arise in the study of dynamical systems. In order to decrease the number of points needed to compute a given surface, we propose using higher-order approximation techniques developed for the field of computer-aided geometric design (CAGD). We use Bézier curves and triangles, fundamental objects i...

Given a noncompact quasi-Fuchsian surface in a finite volume hyperbolic 3–manifold, we introduce a new invariant called the cusp thickness, that measures how far the surface is from being totally geodesic. We relate this new invariant to the width of a surface, which allows us to extend and generalize results known for totally geodesic surfaces. We also show that checkerboard surfaces provide e...

An invariant local descriptor of smooth object surfaces is Gaussian curvature. We present an object signature which is a condensed representation related to the object’s Gaussian curvature distribution over visible points. An invariant related to Gaussian curvature at an object point is developed based upon the covariance matrix of photometric values related to surface normals within a local ne...

We show that the algebra of equi-affine differential invariants of a suitably generic surface S ⊂ R is entirely generated by the third order Pick invariant via invariant differentiation. The proof is based on the new, equivariant approach to the method of moving frames. The goal of this paper is to prove that, in three-dimensional equi-affine geometry, all higher order differential invariants o...

bifurcations leading to chaos have been investigated in a number of one dimensional dynamical systems by varying the parameters incorporated within the systems. the property hyperbolicity has been studied in detail in each case which has significant characteristic behaviours for regular and chaotic evolutions. in the process, the calculations for invariant set have also been carried out. a bro...

let g_1 and g_2 be simple connected graphs with disjoint vertex sets v(g_1) and v(g_2), respectively. for given vertices a_1in v(g_1) and a_2in v(g_2), a splice of g_1 and g_2 by vertices a_1 and a_2 is defined by identifying the vertices a_1 and a_2 in the :union: of g_1 and g_2. in this paper, we present exact formulas for computing some vertex-degree-based graph invariants of splice of graphs.