Abstract The following aspects of multidimensional space are considered in the article. parametrizations hypersurface second order considered, which allow visualizing them process discretization. development principle vector modeling for displaying objects on a two-dimensional plane made it possible to visually display solution problem linear approximation second-order hypersurface. proposed me...

A smooth, nondegenerate hypersurface in projective space contains no linear subvarieties of greater than half its dimension. It can contain linear subvarieties of half its dimension. This note proves that a smooth hypersurface of degree d ≥ 3 contains at most finitely many such subvarieties. Let k be a field. Let X ⊂ Pk be a hypersurface of degree d > 1. For each integer m > 0, denote by Fm(X) ...

In this article we provide a vertical height estimate for compact special Weingarten surfaces of elliptic type in M2(c) × R, i.e. surfaces whose mean curvature H and extrinsic Gauss curvature Ke satisfy H = f(H2 −Ke) with 4x(f ′(x))2 < 1, for all x ∈ [0,+∞). The vertical height estimate generalizes a result by Rosenberg and Sa Earp and applies only to surfaces verifying a height estimate condit...

In this paper we prove some existence and uniqueness results about special Weingarten surfaces in hyperbolic space.

We provide a compact proof of the recent formula of Collins and Matsumoto for the Weingarten matrix of the orthogonal group using Jucys–Murphy elements.

This article presents a new performance measure, the actuation e ciency, which describes isotropy in acceleration capability for non-redundant manipulators. It measures the imbalance between the end-e ector accelerations achievable in di erent directions. Prior to this, no measure of this characteristic was adequate for a six degree-of-freedom manipulator, because its ende ector motions are ref...

This article presents a new performance meamre, the actuation eficiency, which describes isotropy in acceleration capability for non-redundant manipulators. It measures the imbalance between the end-effector accelerations achievable in different directions. Prior to this, no measurre of this characteriStic was adequate for a six dem-of-freedom manipulator, because its endeffector motions are re...

This article presents a new performance measure, the actuation eeciency, which describes isotropy in acceleration capability for non-redundant manipulators. It measures the imbalance between the end-eeector accelerations achievable in diierent directions. Prior to this, no measure of this characteristic was adequate for a six degree-of-freedom manipulator, because its end-eeector motions are re...

Considering the kinematics of the moving frame associated with a constant mean curvature surface immersed in S we derive a linear problem with the spectral parameter corresponding to elliptic sinh-Gordon equation. The spectral parameter is related to the radius R of the sphere S. The application of the Sym formula to this linear problem yields constant mean curvature surfaces in E. Independentl...