A Euclidean Invariants Based Study of Circular Surfaces With Fixed Radius

2007 ◽  
Author(s):  
Lei Cui ◽  
Delun Wang
Keyword(s):  
Complete System ◽  
Distribution Parameter ◽  
Moving Frame ◽  
Necessary Condition ◽  
Spherical Indicatrix ◽  
Circular Surface ◽  
Fixed Radius ◽  
Curvature And Torsion ◽  
The Relationship ◽  
Sufficient And Necessary Condition

In this paper a complete system of Euclidean invariants is presented to study circular surfaces with fixed radius. The study of circular surfaces is simplified to the study of two curves: the spherical indicatrix of the unit normals of circle planes and the spine curve. After the geometric meanings of these Euclidean invariants are explained, the distribution parameter of a circular surface is defined. If the value of the distribution parameter of a circular surface is 0, the circular surface is a sphere. Then the relationship between the moving frame {E1, E2, E3} and the Frenet frame {t, n, b} of the spine curve is investigated, and the expressions of the curvature and torsion of the spine curve are obtained based on these Euclidean invariants. The fundamental theorem of circular surfaces is first proved. Next the first and second fundamental forms of circular surfaces are computed. The last part of this paper is devoted to constraint circular surfaces. The sufficient and necessary condition for a general circular surface to be one that can be generated by a series-connected C’R, HR, RR, or PR mechanism is proved.

scholarly journals Research on the Relationship between Shared Leadership and Individual Creativity-Qualitative Comparative Analysis on the Basis of Clear Set

2021 ◽  
Vol 13 (10) ◽  
pp. 5445
Author(s):  
Muyun Sun ◽  
Jigan Wang ◽  
Ting Wen
Keyword(s):  
Comparative Analysis ◽  
Environmental Factors ◽  
Shared Leadership ◽  
Management Practices ◽  
Qualitative Comparative Analysis ◽  
Necessary Condition ◽  
The Individual ◽  
The Impact ◽  
The Relationship ◽  
Sufficient And Necessary Condition

Creativity is the key to obtaining and maintaining competitiveness of modern organizations, and it has attracted much attention from academic circles and management practices. Shared leadership is believed to effectively influence team output. However, research on the impact of individual creativity is still in its infancy. This study adopts the qualitative comparative analysis method, taking 1584 individuals as the research objects, underpinned by a questionnaire-based survey. It investigates the influence of the team’s shared leadership network elements and organizational environmental factors on the individual creativity. We have found that there are six combination of conditions of shared leadership and organizational environmental factors constituting sufficient combination of conditions to increase or decrease individual creativity. Moreover, we have noticed that the low network density of shared leadership is a sufficient and necessary condition of reducing individual creativity. Our results also provide management suggestions for practical activities during the team management.

A study on timelike circular surfaces in Minkowski 3-space

2020 ◽  
Vol 17 (06) ◽  
pp. 2050074
Author(s):  
Rashad A. Abdel-Baky ◽  
Nadia Alluhaibi ◽  
Akram Ali ◽  
Fatemah Mofarreh
Keyword(s):  
Geodesic Curvature ◽  
Parameter Family ◽  
Lines Of Curvature ◽  
Constant Radius ◽  
Spherical Indicatrix ◽  
New Type ◽  
Circular Surface ◽  
Fixed Radius

This paper studies a smooth one-parameter family of standard Lorentzian circles with fixed radius. Such a surface is called a timelike circular surface with constant radius. We call each circle a generating circle. A new type of timelike circular surfaces was identified and coined as the timelike tangent circular surface. The new timelike tangent circular surface has the property of all generating circles being lines of curvature and its Gaussian and mean curvatures being independent of the geodesic curvature of the spherical indicatrix.

Kinematic Geometry of Circular Surfaces With a Fixed Radius Based on Euclidean Invariants

2009 ◽  
Vol 131 (10) ◽  
Author(s):  
Lei Cui ◽  
Delun Wang ◽  
Jian S. Dai
Keyword(s):  
Mechanism Analysis ◽  
Necessary And Sufficient Condition ◽  
Principal Curvatures ◽  
Lines Of Curvature ◽  
Kinematic Geometry ◽  
Circular Surface ◽  
Fixed Radius ◽  
Necessary And Sufficient ◽  
First Time ◽  
The Relationship

A circular surface with a fixed radius can be swept out by moving a circle with its center following a curve, which acts as the spine curve. Based on a system of Euclidean invariants, the paper identifies those circular surfaces taking lines of curvature as generating circles and further explores the properties of the principal curvatures and Gaussian curvature of the tangent circular surfaces. The paper then applies the study to mechanism analysis by proving the necessary and sufficient condition for a circular surface to be generated by a serially connected C′R, HR, or RR mechanism, where C′ joint can be visualized as a special H joint with a variable pitch of one degree of freedom. Following the analysis, this paper reveals for the first time the relationship between the invariants of a circular surface and the commonly used D-H parameters of C′R, HR, and RR mechanisms.

scholarly journals Absolutely split metacyclic groups and weak metacirculants

2019 ◽  
Vol 18 (06) ◽  
pp. 1950117 ◽  
Author(s):  
Li Cui ◽  
Jin-Xin Zhou
Keyword(s):  
Automorphism Group ◽  
Prime Power ◽  
Necessary Condition ◽  
Prime Power Order ◽  
Metacyclic Groups ◽  
Vertex Transitive ◽  
Open Question ◽  
Positive Integers ◽  
The Relationship ◽  
Sufficient And Necessary Condition

Let [Formula: see text] be positive integers, and let [Formula: see text] be a split metacyclic group such that [Formula: see text]. We say that [Formula: see text] is absolutely split with respect to[Formula: see text] provided that for any [Formula: see text], if [Formula: see text], then there exists [Formula: see text] such that [Formula: see text] and [Formula: see text]. In this paper, we give a sufficient and necessary condition for the group [Formula: see text] being absolutely split. This generalizes a result of Sanming Zhou and the second author in [Weak metacirculants of odd prime power order, J. Comb. Theory A 155 (2018) 225–243]. We also use this result to investigate the relationship between metacirculants and weak metacirculants. Metacirculants were introduced by Alspach and Parsons in [Formula: see text] and have been a rich source of various topics since then. As a generalization of this class of graphs, Marušič and Šparl in 2008 introduced the so-called weak metacirculants. A graph is called a weak metacirculant if it has a vertex-transitive metacyclic automorphism group. In this paper, it is proved that a weak metacirculant of [Formula: see text]-power order is a metacirculant if and only if it has a vertex-transitive split metacyclic automorphism group. This provides a partial answer to an open question in the literature.

scholarly journals Integrated Analysis of Cell Shape and Movement in Moving Frame

2020 ◽  
Author(s):  
Yusri Dwi Heryanto ◽  
Chin-Yi Cheng ◽  
Yutaka Uchida ◽  
Kazushi Mimura ◽  
Masaru Ishii ◽  
...  
Keyword(s):  
Coordinate System ◽  
Cell Shape ◽  
Parallel Transport ◽  
Cell Movement ◽  
Shape Descriptor ◽  
Moving Frame ◽  
Integrated Analysis ◽  
Movement Data ◽  
Curvature And Torsion ◽  
The Relationship

ABSTRACTThe cell movement and morphological change are two interrelated cellular processes. The integrated analysis is needed to explore the relationship between them. However, it has been challenging to investigate them as a whole. The cell trajectory can be described by its speed, curvature, and torsion. On the other hand, the 3-Dimensional (3D) cell shape can be studied by using a shape descriptor such as Spherical harmonic (SH) descriptor which is an extension of Fourier transform in 3D space.To integrate these shape-movement data, we propose a method to use a parallel-transport (PT) moving frame as the 3D-shape coordinate system. This moving frame is purely determined by the velocity vector. On this moving frame, the movement change will influence the coordinate system for shape analysis. By analyzing the change of the SH coefficients over time in the moving frame, we can observe the relationship between shape and movement.We illustrate the application of our approach using simulational and real datasets in this paper.

scholarly journals Averaging algebras, rewriting systems and Gröbner–Shirshov bases

2018 ◽  
Vol 17 (07) ◽  
pp. 1850130 ◽  
Author(s):  
Xing Gao ◽  
Tianjie Zhang
Keyword(s):  
Necessary Condition ◽  
Rewriting Systems ◽  
Averaging Operator ◽  
Rewriting System ◽  
The Relationship ◽  
Sufficient And Necessary Condition

In this paper, we study the averaging operator by assigning a rewriting system to it. We obtain some basic results on the kind of rewriting system we used. In particular, we obtain a sufficient and necessary condition for the confluence. We supply the relationship between rewriting systems and Gröbner–Shirshov bases based on bracketed polynomials. As an application, we give a basis of the free unitary averaging algebra on a nonempty set.

scholarly journals Cauchy matrix and Liouville formula of quaternion impulsive dynamic equations on time scales

2020 ◽  
Vol 18 (1) ◽  
pp. 353-377 ◽  
Author(s):  
Zhien Li ◽  
Chao Wang
Keyword(s):  
Time Scales ◽  
Quaternion Algebra ◽  
Matrix Exponential ◽  
Dynamic Equations ◽  
Necessary Condition ◽  
Quaternion Matrix ◽  
Exponential Functions ◽  
Cauchy Matrix ◽  
Adjoint Matrix ◽  
Sufficient And Necessary Condition

Abstract In this study, we obtain the scalar and matrix exponential functions through a series of quaternion-valued functions on time scales. A sufficient and necessary condition is established to guarantee that the induced matrix is real-valued for the complex adjoint matrix of a quaternion matrix. Moreover, the Cauchy matrices and Liouville formulas for the quaternion homogeneous and nonhomogeneous impulsive dynamic equations are given and proved. Based on it, the existence, uniqueness, and expressions of their solutions are also obtained, including their scalar and matrix forms. Since the quaternion algebra is noncommutative, many concepts and properties of the non-quaternion impulsive dynamic equations are ineffective, we provide several examples and counterexamples on various time scales to illustrate the effectiveness of our results.

scholarly journals Sufficient and necessary conditions for oscillation of linear fractional-order delay differential equations

2021 ◽  
Vol 2021 (1) ◽  
Author(s):  
Qiong Meng ◽  
Zhen Jin ◽  
Guirong Liu
Keyword(s):  
Differential Equation ◽  
Fractional Order ◽  
Sufficient Conditions ◽  
Necessary Condition ◽  
Multiple Delays ◽  
All Solutions ◽  
Sufficient And Necessary Conditions ◽  
Delay Differential ◽  
T Tau ◽  
Sufficient And Necessary Condition

AbstractThis paper studies the linear fractional-order delay differential equation $$ {}^{C}D^{\alpha }_{-}x(t)-px(t-\tau )= 0, $$ D − α C x ( t ) − p x ( t − τ ) = 0 , where $0<\alpha =\frac{\text{odd integer}}{\text{odd integer}}<1$ 0 < α = odd integer odd integer < 1 , $p, \tau >0$ p , τ > 0 , ${}^{C}D_{-}^{\alpha }x(t)=-\Gamma ^{-1}(1-\alpha )\int _{t}^{\infty }(s-t)^{- \alpha }x'(s)\,ds$ D − α C x ( t ) = − Γ − 1 ( 1 − α ) ∫ t ∞ ( s − t ) − α x ′ ( s ) d s . We obtain the conclusion that $$ p^{1/\alpha } \tau >\alpha /e $$ p 1 / α τ > α / e is a sufficient and necessary condition of the oscillations for all solutions of Eq. (*). At the same time, some sufficient conditions are obtained for the oscillations of multiple delays linear fractional differential equation. Several examples are given to illustrate our theorems.

scholarly journals A nonlocal game for witnessing quantum networks

2019 ◽  
Vol 5 (1) ◽  
Author(s):  
Ming-Xing Luo
Keyword(s):  
Computational Complexity ◽  
Main Idea ◽  
Bell Inequalities ◽  
Theoretical Computer Science ◽  
Graph Representation ◽  
Necessary Condition ◽  
Quantum Networks ◽  
Theoretical Computer ◽  
Sufficient And Necessary Condition ◽  
Unified Method

Abstract Nonlocal game as a witness of the nonlocality of entanglement is of fundamental importance in various fields. The well-known nonlocal games or equivalent linear Bell inequalities are only useful for Bell networks consisting of single entanglement. Our goal in this paper is to propose a unified method for constructing cooperating games in network scenarios. We propose an efficient method to construct multipartite nonlocal games from any graphs. The main idea is the graph representation of entanglement-based quantum networks. We further specify these graphic games with quantum advantages by providing a simple sufficient and necessary condition. The graphic games imply a linear Bell testing of the nonlocality of general quantum networks consisting of EPR states. It also allows generating new instances going beyond CHSH game. These results have interesting applications in quantum networks, Bell theory, computational complexity, and theoretical computer science.

Some Uses of Justification in Jewish Education

AJS Review ◽  
1977 ◽  
Vol 2 ◽  
pp. 1-44 ◽  
Author(s):  
Walter I. Ackerman
Keyword(s):  
Jewish Education ◽  
Modern Society ◽  
Necessary Condition ◽  
School Systems ◽  
Coercive Power ◽  
Educational Issues ◽  
Rational Control ◽  
The Relationship ◽  
Educational Enterprise

The justification of plans and programs is a necessary condition of the relationship between systems of education, both obligatory and voluntary, and the publics they serve. Those who are responsible for the conduct of the educational enterprise in general and the schooling of the young in particular must provide those who support the system, financially and otherwise, with acceptable and defensible reasons for the efforts and activities of the schools. The idea of justification in education rests on the assumption that the process of schooling, whatever its form and content, is subject to rational control and that the authority for the conduct of schools is derived from the principles inherent in the justification offered. A proferred justification is most effective and likely of acceptance when the positions it generates on educational issues fit the general fabric of ideals and aspirations of the society to which it is addressed. If, as we believe, justification is a necessary part of the rhetoric which surrounds legislatively determined and state maintained school systems—i.e., systems whose right to existence is not subject to question or doubt in any modern society and where attendance is required by law—then it follows that it is of even greater significance for voluntary school systems which lack the coercive power of their governmental counterparts—i.e., Jewish education.

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