dimensional euclidean space
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Axioms ◽  
2022 ◽  
Vol 11 (1) ◽  
pp. 26
Author(s):  
Erhan Güler ◽  
Ömer Kişi

We introduce the real minimal surfaces family by using the Weierstrass data (ζ−m,ζm) for ζ∈C, m∈Z≥2, then compute the irreducible algebraic surfaces of the surfaces family in three-dimensional Euclidean space E3. In addition, we propose that family has a degree number (resp., class number) 2m(m+1) in the cartesian coordinates x,y,z (resp., in the inhomogeneous tangential coordinates a,b,c).


2022 ◽  
Vol 40 ◽  
pp. 1-7
Author(s):  
Muhammed T. Sariaydin ◽  
Talat Korpinar ◽  
Vedat Asil

In this paper, it is investigated Ruled surfaces according to modified orthogonal frame with curvature in 3-dimensional Euclidean space. Firstly, we give apex angle, pitch and drall of closed ruled surface in E³. Then,  it characterized the relationship between these invariant of parallel p-equidistant ruled surfaces.


2021 ◽  
Vol 66 (4) ◽  
pp. 757-768
Author(s):  
Ioannis K. Argyros ◽  
◽  
Santhosh George ◽  
Kedarnath Senapati ◽  
◽  
...  

We present the local convergence of a Newton-type solver for equations involving Banach space valued operators. The eighth order of convergence was shown earlier in the special case of the k-dimensional Euclidean space, using hypotheses up to the eighth derivative although these derivatives do not appear in the method. We show convergence using only the rst derivative. This way we extend the applicability of the methods. Numerical examples are used to show the convergence conditions. Finally, the basins of attraction of the method, on some test problems are presented.


Author(s):  
Hassan Al-Zoubi

In this paper, we consider surfaces of revolution in the 3-dimensional Euclidean space E3 with nonvanishing Gauss curvature. We introduce the finite Chen type surfaces with respect to the third fundamental form of the surface. We present a special case of this family of surfaces of revolution in E3, namely, surfaces of revolution with R is constant, where R denotes the sum of the radii of the principal curvature of a surface.


Mathematics ◽  
2021 ◽  
Vol 9 (23) ◽  
pp. 3106
Author(s):  
Samundra Regmi ◽  
Christopher I. Argyros ◽  
Ioannis K. Argyros ◽  
Santhosh George

We develop a unified convergence analysis of three-step iterative schemes for solving nonlinear Banach space valued equations. The local convergence order has been shown before to be five on the finite dimensional Euclidean space assuming Taylor expansions and the existence of the sixth derivative not on these schemes. So, the usage of them is restricted six or higher differentiable mappings. But in our paper only the first Frèchet derivative is utilized to show convergence. Consequently, the scheme is expanded. Numerical applications are also given to test convergence.


2021 ◽  
Vol 36 (2) ◽  
pp. 241-278
Author(s):  
Valeriu Soltan

This is a survey on support and separation properties of convex sets in the n-dimensional Euclidean space. It contains a detailed account of existing results, given either chronologically or in related groups, and exhibits them in a uniform way, including terminology and notation. We first discuss classical Minkowski’s theorems on support and separation of convex bodies, and next describe various generalizations of these results to the case of arbitrary convex sets, which concern bounding and asymptotic hyperplanes, and various types of separation by hyperplanes, slabs, and complementary convex sets.


2021 ◽  
Vol 17 (4) ◽  
pp. 1-23
Author(s):  
Yi Zhang ◽  
Zheng Yang ◽  
Guidong Zhang ◽  
Chenshu Wu ◽  
Li Zhang

Extensive efforts have been devoted to human gesture recognition with radio frequency (RF) signals. However, their performance degrades when applied to novel gesture classes that have never been seen in the training set. To handle unseen gestures, extra efforts are inevitable in terms of data collection and model retraining. In this article, we present XGest, a cross-label gesture recognition system that can accurately recognize gestures outside of the predefined gesture set with zero extra training effort. The key insight of XGest is to build a knowledge transfer framework between different gesture datasets. Specifically, we design a novel deep neural network to embed gestures into a high-dimensional Euclidean space. Several techniques are designed to tackle the spatial resolution limits imposed by RF hardware and the specular reflection effect of RF signals in this model. We implement XGest on a commodity mmWave device, and extensive experiments have demonstrated the significant recognition performance.


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