scholarly journals On Characterizing a Three-Dimensional Sphere

Mathematics ◽  
2021 ◽  
Vol 9 (24) ◽  
pp. 3311
Author(s):  
Nasser Bin Turki ◽  
Sharief Deshmukh ◽  
Gabriel-Eduard Vîlcu

In this paper, we find a characterization of the 3-sphere using 3-dimensional compact and simply connected trans-Sasakian manifolds of type (α,β).

Mathematics ◽  
2020 ◽  
Vol 8 (5) ◽  
pp. 718
Author(s):  
Dong-Soo Kim ◽  
Young Ho Kim ◽  
Jinhua Qian

We characterize spheres and the tori, the product of the two plane circles immersed in the three-dimensional unit sphere, which are associated with the Laplace operator and the Gauss map defined by the elliptic linear Weingarten metric defined on closed surfaces in the three-dimensional sphere.


2000 ◽  
Vol 109 (5) ◽  
pp. 505-513 ◽  
Author(s):  
Corey W. Mineck ◽  
Roger Chan ◽  
Niro Tayama ◽  
Ingo R. Titze

The biomechanics of vocal fold abduction and adduction during phonation, respiration, and airway protection are not completely understood. Specifically, the rotational and translational forces on the arytenoid cartilages that result from intrinsic laryngeal muscle contraction have not been fully described. Anatomic data on the lines of action and moment arms for the intrinsic laryngeal muscles are also lacking. This study was conducted to quantify the 3-dimensional orientations and the relative cross-sectional areas of the intrinsic abductor and adductor musculature of the canine larynx. Eight canine larynges were used to evaluate the 3 muscles primarily responsible for vocal fold abduction and adduction: the posterior cricoarytenoid, the lateral cricoarytenoid, and the interarytenoid muscles. Each muscle was exposed and divided into discrete fiber bundles whose coordinate positions were digitized in 3-dimensional space. The mass, length, relative cross-sectional area, and angle of orientation for each muscle bundle were obtained to allow for the calculations of average lines of action and moment arms for each muscle. This mapping of the canine laryngeal abductor and adductor musculature provides important anatomic data for use in laryngeal biomechanical modeling. These data may also be useful in surgical procedures such as arytenoid adduction.


2005 ◽  
Vol 07 (02) ◽  
pp. 145-165 ◽  
Author(s):  
ALICE FIALOWSKI ◽  
MICHAEL PENKAVA

We consider versal deformations of 0|3-dimensional L∞ algebras, also called strongly homotopy Lie algebras, which correspond precisely to ordinary (non-graded) three-dimensional Lie algebras. The classification of such algebras is well-known, although we shall give a derivation of this classification using an approach of treating them as L∞ algebras. Because the symmetric algebra of a three-dimensional odd vector space contains terms only of exterior degree less than or equal to three, the construction of versal deformations can be carried out completely. We give a characterization of the moduli space of Lie algebras using deformation theory as a guide to understanding the picture.


2018 ◽  
Author(s):  
Yifu Ding ◽  
Daniel J. Vanselow ◽  
Maksim A. Yakovlev ◽  
Spencer R. Katz ◽  
Alex Y. Lin ◽  
...  

AbstractHistological studies providing cellular insights into tissue architecture have been central to biological discovery and remain clinically invaluable today. Extending histology to three dimensions would be transformational for research and diagnostics. However, three-dimensional histology is impractical using current techniques. We have customized sample preparation, synchrotron X-ray tomographic parameters, and three-dimensional image analysis to allow for complete histological phenotyping using whole larval and juvenile zebrafish. The resulting digital zebrafish can be virtually sectioned and visualized in any plane. Whole-animal reconstructions at subcellular resolution also enable computational characterization of the zebrafish nervous system by region-specific detection of cell nuclei and quantitative assessment of individual phenotypic variation. Three-dimensional histological phenotyping has potential use in genetic and chemical screens, and in clinical and toxicological tissue diagnostics.One Sentence SummarySynchrotron X-ray micro-tomography can be used to rapidly create 3-dimensional images of fixed and stained specimens without sectioning, enabling computational histological phenotyping at cellular resolution.


2019 ◽  
Vol 16 (01) ◽  
pp. 1950011 ◽  
Author(s):  
Domenico Perrone

The main result of this paper gives a characterization of left-invariant almost [Formula: see text]-coKähler structures on three-dimensional (3D) semidirect product Lie groups [Formula: see text] in terms of the matrix [Formula: see text]. Then, we study the harmonicity of the Reeb vector field [Formula: see text] of a simply connected homogeneous almost [Formula: see text]-coKähler three-manifold, in terms of the Gaussian curvature of the canonical foliation.


Mathematics ◽  
2021 ◽  
Vol 9 (16) ◽  
pp. 1887
Author(s):  
Sharief Deshmukh ◽  
Amira Ishan ◽  
Olga Belova ◽  
Suha B. Al-Shaikh

In this paper, we study 3-dimensional compact and connected trans-Sasakian manifolds and find necessary and sufficient conditions under which these manifolds are homothetic to Sasakian manifolds. First, four results in this paper deal with finding necessary and sufficient conditions on a compact and connected trans-Sasakian manifold to be homothetic to a compact and connected Sasakian manifold, and the fifth result deals with finding necessary and sufficient condition on a connected trans-Sasakian manifold to be homothetic to a connected Sasakian manifold. Finally, we find necessary and sufficient conditions on a compact and simply connected trans-Sasakian manifold to be homothetic to a compact and simply connected Einstein Sasakian manifold.


2009 ◽  
Vol 20 (02) ◽  
pp. 189-208 ◽  
Author(s):  
MIRJANA DJORIĆ ◽  
LUC VRANCKEN

In this paper, we study certain three-dimensional CR-submanifolds M of the nearly Kähler 6-dimensional sphere S6(1). It is well known that there does not exist a three-dimensional totally geodesic proper CR-submanifold in S6(1). In this paper we obtain a classification of the 3-dimensional CR-submanifolds which are the closest possible to totally geodesic submanifolds, i.e. those that admit a one-dimensional nullity distribution.


2021 ◽  
Vol 77 (1) ◽  
Author(s):  
Ameer Al-Abayechi ◽  
Ágota Figula

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.


2007 ◽  
Vol 558-559 ◽  
pp. 751-756 ◽  
Author(s):  
Kristofer Hannesson ◽  
Dorte Juul Jensen

Grain structures in polycrystalline materials are typically three dimensional (3D) structures, but by far the most characterizations of grain structures are done by microscopy and are thus limited to 2D. In the present work 3D grain structures in a well-annealed cylindrical aluminium (AA1050) sample is characterized and analyzed. The characterization is done by 2 methods i) by non-destructive 3-dimensional x-ray diffraction (3DXRD) ii) by serial sectioning and subsequent EBSP mapping of entire circular 2D sample sections; 50 sections are mapped In total 333 grains are reconstructed. It is found that the 3D grain morphologies can be quite complex in particular for the larger grains, the number of neighbours varies significantly and values above 20 are not unusual. When the results from the 2 methods are compared, it is found that the crystallographic agreement is very good and within experimental uncertainties. Slightly more significant differences are found when the reconstructed grain morphologies are compared. Reasons for this are discussed.


2013 ◽  
Vol 63 (6) ◽  
Author(s):  
Sharief Deshmukh ◽  
Mukut Tripathi

AbstractIn this paper, we obtain some sufficient conditions for a 3-dimensional compact trans-Sasakian manifold of type (α, β) to be homothetic to a Sasakian manifold. A characterization of a 3-dimensional cosymplectic manifold is also obtained.


Sign in / Sign up

Export Citation Format

Share Document