scholarly journals New Type Direction Curves in 3-Dimensional Compact Lie Group

Symmetry ◽  
2019 ◽  
Vol 11 (3) ◽  
pp. 387 ◽  
Author(s):  
Ali Çakmak
Keyword(s):  
Lie Group ◽  
Three Dimensional ◽  
Normal Direction ◽  
General Definition ◽  
Compact Lie Group ◽  
3 Dimensional ◽  
New Type ◽  
Definition Of

In this paper, new types of associated curves, which are defined as rectifying-direction, osculating-direction, and normal-direction, in a three-dimensional Lie group G are achieved by using the general definition of the associated curve, and some characterizations for these curves are obtained. Additionally, connections between the new types of associated curves and the curves, such as helices, general helices, Bertrand, and Mannheim, are given.

scholarly journals Correction: Çakmak, A. New Type Direction Curves in 3-Dimensional Compact Lie Group Symmetry 2019, 11, 387

Symmetry ◽  
2020 ◽  
Vol 12 (2) ◽  
pp. 284
Author(s):  
Ali Çakmak
Keyword(s):  
Lie Group ◽  
Group Symmetry ◽  
Compact Lie Group ◽  
3 Dimensional ◽  
New Type ◽  
Lie Group Symmetry

The authors wish to make the following corrections to their paper [...]

Three-Dimensional Magneto-Optical Recording

2004 ◽  
Vol 834 ◽  
Author(s):  
Akiyoshi Itoh
Keyword(s):  
Storage System ◽  
Three Dimensional ◽  
Optical Recording ◽  
High Density ◽  
The Novel ◽  
National Project ◽  
3 Dimensional ◽  
Disk Storage ◽  
High Density Recording ◽  
New Type

ABSTRACTIn this report, the newly developed three-dimensional magneto-optical (MO) recording scheme and the experimental results are reported. A part of this work has been done as the national project of 3D-MO (3-dimensional MO) project. It started at September 1998 and ended March 2002 as a part of the national project “Nanometer-Scale Optical High Density Disk Storage System” and aimed at achieving 100 Gb/in2 in storage density. Three-dimensional MO recording is one of the prosperous candidates of next generation ultra high density recording. Magnetic amplifying MO system (MAMMOS) is employed for achieving the novel three-dimensional MO recording. Double-MAMMOS scheme consists of 2-recording layers of differing compensation temperature (Tcomp ) and one readout layer was proposed and discussed.With write/read test it is succeeded to show the results corresponding to a 100 Gb/in2 (50 Gb/in2 × 2) recording density. We also proposed and showed results of simulations of a new type of Double-MAMMOS in which the recording layers can hold quadri-valued information by single writing process.

scholarly journals On a general definition of the set of native conformations for globular polypeptides

2016 ◽  
Author(s):  
Imadol V Jeff-Eke
Keyword(s):  
Protein Folding ◽  
Functional Activity ◽  
Common Knowledge ◽  
General Definition ◽  
Native Conformation ◽  
3 Dimensional ◽  
Definition Of

Here we question the generality of the conventional definition of a native conformation –as the 3-dimensional conformation of an entire globular polypeptide molecule. Although considered common knowledge, and thus not explicitly stated in modern writings, this definition of native conformations has a history as old as the protein folding problem. We attempt a more applicable definition that better correlates with functional activity and thus may be a more suitable substitute for the current convention.

scholarly journals The index of symmetry of three-dimensional Lie groups with a left-invariant metric

2018 ◽  
Vol 18 (4) ◽  
pp. 395-404 ◽  
Author(s):  
Silvio Reggiani
Keyword(s):  
Lie Groups ◽  
Constant Curvature ◽  
Lie Group ◽  
Dimensional Space ◽  
Three Dimensional ◽  
Invariant Metric ◽  
3 Dimensional ◽  
Space Of Constant Curvature ◽  
Positive Index

Abstract We determine the index of symmetry of 3-dimensional unimodular Lie groups with a left-invariant metric. In particular, we prove that every 3-dimensional unimodular Lie group admits a left-invariant metric with positive index of symmetry. We also study the geometry of the quotients by the so-called foliation of symmetry, and we explain in what cases the group fibers over a 2-dimensional space of constant curvature.

THREE-DIMENSIONAL DEFINITION OF LEAF MORPHOLOGICAL TRAITS OF ARABIDOPSIS IN SILICO PHENOTYPIC ANALYSIS

2005 ◽  
Vol 03 (02) ◽  
pp. 401-414 ◽  
Author(s):  
ELI KAMINUMA ◽  
NAOHIKO HEIDA ◽  
YUKO TSUMOTO ◽  
MIKI NAKAZAWA ◽  
NOBUHARU GOTO ◽  
...  
Keyword(s):  
In Silico ◽  
Morphological Traits ◽  
Three Dimensional ◽  
In Silico Analysis ◽  
Phenotypic Analysis ◽  
3 Dimensional ◽  
Functional Studies ◽  
Phenotypic Alteration ◽  
Definition Of ◽  
Leaf Morphological Traits

The detection of phenotypic alterations of mutants and variants is one of the bottlenecks that hinder systematic gene functional studies of the model plant Arabidopsis. In an earlier study, we have addressed this problem by proposing a novel methodology for phenome analysis based on in silico analysis of polygon models that are acquired by 3-dimensional (3D) measurement and which precisely reconstruct the actual plant shape. However, 3D quantitative descriptions of morphological traits are rare, whereas conventional 2D descriptions have already been studied but may lack the necessary precision. In this report, we focus on six major leaf morphological traits, which are commonly used in the current manual mutant screens, and propose new 3D quantitative definitions that describe these traits. In experiments to extract the traits, we found significant differences between two variants of Arabidopsis with respect to blade roundness and blade epinasty. Remarkably, the detected difference between variants in the blade roundness trait was undetectable when using conventional 2D descriptions. Thus, the result of the experiment indicates that the proposed definitions with 3D description may lead to new discoveries of phenotypic alteration in gene functional studies that would not be possible using conventional 2D descriptions.

scholarly journals Place-Difference-Value Patterns: A Generalization of Generalized Permutation and Word Patterns

Integers ◽  
2010 ◽  
Vol 10 (1) ◽  
Author(s):  
Sergey Kitaev ◽  
Jeffrey Remmel
Keyword(s):  
Partially Ordered Sets ◽  
General Definition ◽  
Permutation Patterns ◽  
Ordered Sets ◽  
Combinatorial Objects ◽  
Permutation Pattern ◽  
New Type ◽  
Number Of Publications ◽  
Definition Of ◽  
Patterns In Permutations

AbstractMotivated by the study of Mahonian statistics, in 2000, Babson and Steingrímsson [Sém. Lothar. Comb] introduced the notion of a “generalized permutation pattern” (GP) which generalizes the concept of “classical” permutation pattern introduced by Knuth in 1969. The invention of GPs led to a large number of publications related to properties of these patterns in permutations and words. Since the work of Babson and Steingrímsson, several further generalizations of permutation patterns have appeared in the literature, each bringing a new set of permutation or word pattern problems and often new connections with other combinatorial objects and disciplines. For example, Bousquet-Mélou et al. [J. Comb. Theory A] introduced a new type of permutation pattern that allowed them to relate permutation patterns theory to the theory of partially ordered sets.In this paper we introduce yet another, more general definition of a pattern, called place-difference-value patterns (PDVP) that covers all of the most common definitions of permutation and/or word patterns that have occurred in the literature. PDVPs provide many new ways to develop the theory of patterns in permutations and words. We shall give several examples of PDVPs in both permutations and words that cannot be described in terms of any other pattern conditions that have been introduced previously. Finally, we discuss several bijective questions linking our patterns to other combinatorial objects.

New Type of PPP-S[T]-PPP Hybrid Cubic Manipulator

2011 ◽  
Vol 181-182 ◽  
pp. 516-521
Author(s):  
Jian Guo Luo ◽  
Jian You Han
Keyword(s):  
Three Dimensional ◽  
Influential Factors ◽  
Degree Of Freedom ◽  
Output Shaft ◽  
Topological Graph ◽  
Rotational Angle ◽  
Working Space ◽  
Hybrid Mechanism ◽  
New Type ◽  
Definition Of

A new type of hybrid cubic manipulator with six degree of freedom(DOF) suggested based on traditional serial manipulator and parallel manipulator, three dimensional translation and rotation of output shaft obtained through lineal driving. Define the description of spacial moving capability of common couples and translation base and rotation base of mechanism, based on the fact of mechanism consists of components, a new description method by topological graph theory of components relationship suggested, new description of serial mechanism and parallel mechanism and hybrid mechanism obtained with this method, description elements include component pane and constrained component pane and component relationship line and constrained component relationship line and spacial relative moving capability between adjacent components. DOF(degree of freedom) of hybrid mechanism analysised with example based on the definition of dimensionity of branch spacial moving capability and mechanism spacial moving capability, necessary and sufficient condition of nonsingularity of mechanism presented. Method of analytic geometry used to find the regular cuboid of the reachable working space shape of mechanism, the volume of the reachable working space rest with the limit of translation of couplers, its influential factors obtained, still the rotational angle limits of output shaft at given configuration analysised through the method of drawing, and limit length of guideway etc. are the primary influential factors.

scholarly journals Topological Loops with Decomposable Solvable Multiplication Groups

2021 ◽  
Vol 77 (1) ◽  
Author(s):  
Ameer Al-Abayechi ◽  
Ágota Figula
Keyword(s):  
Lie Groups ◽  
Lie Group ◽  
Three Dimensional ◽  
Solvable Lie Groups ◽  
3 Dimensional ◽  
Multiplication Group ◽  
Simply Connected ◽  
Solvable Lie Group

AbstractIn this paper we deal with the class $$\mathcal {C}$$ C of decomposable solvable Lie groups having dimension six. We determine those Lie groups in $$\mathcal {C}$$ C and their subgroups which are the multiplication groups Mult(L) and the inner mapping groups Inn(L) for three-dimensional connected simply connected topological loops L. This result completes the classification of the at most 6-dimensional solvable multiplication Lie groups of the loops L. Moreover, we obtain that every at most 3-dimensional connected topological proper loop having a solvable Lie group of dimension at most six as its multiplication group is centrally nilpotent of class two.

scholarly journals Associated Curves of Frenet curves in Three Dimensional Compact Lie Group

2015 ◽  
Vol 16 (2) ◽  
pp. 953-964 ◽  
Author(s):  
Sezai Kızıltuğ ◽  
Mehmet Önder
Keyword(s):  
Lie Group ◽  
Three Dimensional ◽  
Compact Lie Group ◽  
Frenet Curves
Sign in / Sign up

Export Citation Format

Share Document