Geometry

1810 Submissions

[8] viXra:1810.0421 [pdf] submitted on 2018-10-26 02:32:17

Derivative-Based Numerical Method for Penalty-Barrier Nonlinear Programming

Authors: Martin Peter Neuenhofen
Comments: 16 Pages.

We present an NLP solver for nonlinear optimization with quadratic penalty terms and logarithmic barrier terms. The method is suitable for large sparse problems. Each iteration has a polynomial time-complexity. The method has global convergence and local quadratic convergence, with a convergence radius that depends little on our method but rather on the geometry of the problem.
Category: Geometry

[7] viXra:1810.0379 [pdf] submitted on 2018-10-24 03:13:11

От ошибки Гильберта к исчислению сфер

Authors: Франц Герман
Comments: 9 Pages.

Что такое след проективной плоскости и как можно его увидеть рассказывается в этой заметке.
Category: Geometry

[6] viXra:1810.0324 [pdf] replaced on 2018-10-23 10:40:48

Exact and Intuitive Geometry Explanation: Why Does a Half-angle-rotation in Spin or Quaternion Space Correspond to the Whole-angle-rotation in Normal 3D Space?

Authors: Hongbing Zhang
Comments: 18 Pages. Please Indicate This Source From Hongbing Zhang When Cite the Contents in Works of Sience or Popular Sience

Why does a half-angle-rotation in quaternion space or spin space correspond to a whole-angle-rotation in normal 3D space? The question is equivalent to why a half angle in the representation of SU(2) corresponds to a whole angle in the representation of SO(3). Usually we use the computation of the abstract mathematics to answer the question. But now I will give an exact and intuitive geometry-explanation on it in this paper.
Category: Geometry

[5] viXra:1810.0295 [pdf] submitted on 2018-10-18 09:47:40

К вопросу о представлении дельта-функции Дирака

Authors: Франц Герман
Comments: Pages.

В данной заметке мы покажем представление дельта-функции Дирака, которое будем назвать естественным. Существующие способы представления дельта-функции Дирака носят в общем-то искусственный характер.
Category: Geometry

[4] viXra:1810.0283 [pdf] submitted on 2018-10-17 05:53:48

Smoothing using Geodesic Averages

Authors: Jan Hakenberg
Comments: 10 Pages.

Geodesic averages have been used to generalize curve subdivision and Bézier curves to Riemannian manifolds and Lie groups. We show that geodesic averages are suitable to perform smoothing of sequences of data in nonlinear spaces. In applications that produce temporal uniformly sampled manifold data, the smoothing removes high-frequency components from the signal. As a consequence, discrete differences computed from the smoothed sequence are more regular. Our method is therefore a simpler alternative to the extended Kalman filter. We apply the smoothing technique to noisy localization estimates of mobile robots.
Category: Geometry

[3] viXra:1810.0171 [pdf] replaced on 2018-10-14 11:00:59

The Seiberg-Witten Equations for Vector Fields

Authors: Antoine Balan
Comments: 2 pages, written in english

By similarity with the Seiberg-Witten equations, we propose two differential equations, depending of a spinor and a vector field, instead of a connection. Good moduli spaces are espected as a consequence of commutativity.
Category: Geometry

[2] viXra:1810.0068 [pdf] submitted on 2018-10-06 02:12:13

An Introduction to Non-Commutative (Pseudo) Metric Geometry.

Authors: Johan Noldus
Comments: 11 Pages.

We introduce the reader to the problematic aspects of formulating in concreto a suitable notion of geometry. Here, we take the canonical approach and give some examples.
Category: Geometry

[1] viXra:1810.0057 [pdf] submitted on 2018-10-04 09:55:33

Теорема о поляре треугольника

Authors: Франц Герман
Comments: Pages.

Сформулирована и доказана теорема, ранее не встречавшаяся в литературе по проективной геометрии. На основании «теоремы о поляре трёхвершинника» открывается целый класс задач на построение. Теорема может быть полезна студентам математических факультетов педагогических вузов, а также учителям математики средней школы для проведения факультативных занятий.
Category: Geometry