scholarly journals Two-fold branched covers

2014 ◽  
Vol 23 (03) ◽  
pp. 1430001 ◽  
Author(s):  
David Auckly
Keyword(s):  
Finite Number ◽  
Three Dimensional ◽  
Dehn Surgery ◽  
Dimensional Sphere ◽  
Branched Covers ◽  
Additional Symmetries ◽  
Branched Cover

Many three-dimensional manifolds are two-fold branched covers of the three-dimensional sphere. However, there are some that are not. This paper includes exposition about two-fold branched covers and includes many examples. It shows that there are three-dimensional homology spheres that do not two-fold branched cover any manifold, ones that only two-fold branched cover the three-dimensional sphere, ones that just two-fold branched cover a non-trivial manifold, and ones that two-fold branched cover both the sphere and non-trivial manifolds. When a manifold is surgery on a knot, the possible quotients via involutions generically correspond to quotients of the knot. There can, however, be a finite number of surgeries for which there are exceptional additional symmetries. The included proof of this result follows the proof of Thurston's Dehn surgery theorem. The paper also includes examples of such exceptional symmetries. Since the quotients follow the behavior of knots, a census of the behavior for knots with less than 11 crossings is included.

Criteria and Methods for Reliable Three-Dimensional Image Reconstruction

1974 ◽  
Vol 32 ◽  
pp. 330-331
Author(s):  
R. A. Crowther
Keyword(s):  
Image Reconstruction ◽  
Finite Number ◽  
Density Distribution ◽  
Electron Micrographs ◽  
Mathematical Problem ◽  
Three Dimensional ◽  
Ideal Case ◽  
Dimensional Image ◽  
General Object ◽  
The Ideal

The reconstruction of a three-dimensional image of a specimen from a set of electron micrographs reduces, under certain assumptions about the imaging process in the microscope, to the mathematical problem of reconstructing a density distribution from a set of its plane projections.In the absence of noise we can formulate a purely geometrical criterion, which, for a general object, fixes the resolution attainable from a given finite number of views in terms of the size of the object. For simplicity we take the ideal case of projections collected by a series of m equally spaced tilts about a single axis.

Center of Mass Theorem and the Separation of Variables for Two-Body System on a Three-Dimensional Sphere

2020 ◽  
Vol 23 (3) ◽  
pp. 306-311
Author(s):  
Yu. Kurochkin ◽  
Dz. Shoukavy ◽  
I. Boyarina
Keyword(s):  
Constant Curvature ◽  
Jacobi Equation ◽  
Separation Of Variables ◽  
Center Of Mass ◽  
Three Dimensional ◽  
Relative Distance ◽  
Dimensional Sphere ◽  
Body System ◽  
Spaces Of Constant Curvature ◽  
Hamilton Jacobi Equation

The immobility of the center of mass in spaces of constant curvature is postulated based on its definition obtained in [1]. The system of two particles which interact through a potential depending only on the distance between particles on a three-dimensional sphere is considered. The Hamilton-Jacobi equation is formulated and its solutions and trajectory equations are found. It was established that the reduced mass of the system depends on the relative distance.

EXCITON INSULATOR STATES IN MATERIALS WITH ‘MEXICAN HAT’ BAND STRUCTURE DISPERSION AND IN GRAPHENE

2015 ◽  
Vol 11 (1) ◽  
pp. 2927-2949
Author(s):  
Lyubov E. Lokot
Keyword(s):  
Band Structure ◽  
Three Dimensional ◽  
Dimensional Sphere ◽  
Electron Hole ◽  
Dinger Equation ◽  
Fermi Sphere ◽  
Zinc Blende ◽  
Bulk Gan ◽  
Structure Dispersion ◽  
Excitonic States

In the paper a theoretical study the both the quantized energies of excitonic states and their wave functions in grapheneand in materials with "Mexican hat" band structure dispersion as well as in zinc-blende GaN is presented. An integral twodimensionalSchrödinger equation of the electron-hole pairing for a particles with electron-hole symmetry of reflection isexactly solved. The solutions of Schrödinger equation in momentum space in studied materials by projection the twodimensionalspace of momentum on the three-dimensional sphere are found exactly. We analytically solve an integral twodimensionalSchrödinger equation of the electron-hole pairing for particles with electron-hole symmetry of reflection. Instudied materials the electron-hole pairing leads to the exciton insulator states. Quantized spectral series and lightabsorption rates of the excitonic states which distribute in valence cone are found exactly. If the electron and hole areseparated, their energy is higher than if they are paired. The particle-hole symmetry of Dirac equation of layered materialsallows perfect pairing between electron Fermi sphere and hole Fermi sphere in the valence cone and conduction cone andhence driving the Cooper instability. The solutions of Coulomb problem of electron-hole pair does not depend from a widthof band gap of graphene. It means the absolute compliance with the cyclic geometry of diagrams at justification of theequation of motion for a microscopic dipole of graphene where >1 s r . The absorption spectrums for the zinc-blendeGaN/(Al,Ga)N quantum well as well as for the zinc-blende bulk GaN are presented. Comparison with availableexperimental data shows good agreement.

scholarly journals Bertrand curves in the three-dimensional sphere

2012 ◽  
Vol 62 (9) ◽  
pp. 1903-1914 ◽  
Author(s):  
Pascual Lucas ◽  
José Antonio Ortega-Yagües
Keyword(s):  
Three Dimensional ◽  
Dimensional Sphere

On the integrability of intermediate distributions for Anosov diffeomorphisms

1995 ◽  
Vol 15 (2) ◽  
pp. 317-331 ◽  
Author(s):  
M. Jiang ◽  
Ya B. Pesin ◽  
R. de la Llave
Keyword(s):  
Finite Number ◽  
Lyapunov Exponents ◽  
Periodic Orbits ◽  
Three Dimensional ◽  
Dimensional Torus ◽  
Anosov Diffeomorphism ◽  
Anosov Diffeomorphisms ◽  
Stable Foliation

AbstractWe study the integrability of intermediate distributions for Anosov diffeomorphisms and provide an example of a C∞-Anosov diffeomorphism on a three-dimensional torus whose intermediate stable foliation has leaves that admit only a finite number of derivatives. We also show that this phenomenon is quite abundant. In dimension four or higher this can happen even if the Lyapunov exponents at periodic orbits are constant.

scholarly journals COMBINATORIAL KNOT FLOER HOMOLOGY AND DOUBLE BRANCHED COVERS

2013 ◽  
Vol 22 (06) ◽  
pp. 1350014
Author(s):  
FATEMEH DOUROUDIAN
Keyword(s):  
Floer Homology ◽  
Combinatorial Proof ◽  
Branched Covers ◽  
Knot Floer Homology ◽  
Branched Cover ◽  
Heegaard Diagram

Using a Heegaard diagram for the pullback of a knot K ⊂ S3 in its double branched cover Σ2(K), we give a combinatorial proof for the invariance of the associated knot Floer homology over ℤ.

scholarly journals GEOMETRIC MOMENTUM IN THE MONGE PARAMETRIZATION OF TWO-DIMENSIONAL SPHERE

2013 ◽  
Vol 10 (03) ◽  
pp. 1220031 ◽  
Author(s):  
D. M. XUN ◽  
Q. H. LIU
Keyword(s):  
Quantum Mechanics ◽  
Laplace Operator ◽  
Three Dimensional ◽  
Dimensional Sphere ◽  
Two Dimensional ◽  
Constrained Motion ◽  
Geometric Invariant ◽  
Gradient Operator ◽  
The Laplace Operator

A two-dimensional (2D) surface can be considered as three-dimensional (3D) shell whose thickness is negligible in comparison with the dimension of the whole system. The quantum mechanics on surface can be first formulated in the bulk and the limit of vanishing thickness is then taken. The gradient operator and the Laplace operator originally defined in bulk converges to the geometric ones on the surface, and the so-called geometric momentum and geometric potential are obtained. On the surface of 2D sphere the geometric momentum in the Monge parametrization is explicitly explored. Dirac's theory on second-class constrained motion is resorted to for accounting for the commutator [xi, pj] = iℏ(δij - xixj/r2) rather than [xi, pj] = iℏδij that does not hold true anymore. This geometric momentum is geometric invariant under parameters transformation, and self-adjoint.

scholarly journals Characterization of Clifford Torus in Three-Spheres

Mathematics ◽  
2020 ◽  
Vol 8 (5) ◽  
pp. 718
Author(s):  
Dong-Soo Kim ◽  
Young Ho Kim ◽  
Jinhua Qian
Keyword(s):  
Laplace Operator ◽  
Unit Sphere ◽  
Three Dimensional ◽  
Gauss Map ◽  
Dimensional Sphere ◽  
Clifford Torus ◽  
Closed Surfaces ◽  
Dimensional Unit ◽  
The Laplace Operator

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.

scholarly journals Topology of Chromosomes 18 and X in Human Blastomeres from 3- to 4-Day-old Embryos

2005 ◽  
Vol 53 (3) ◽  
pp. 273-276 ◽  
Author(s):  
Jan Diblík ◽  
Milan Macek ◽  
Maria-Cristina Magli ◽  
Roman Krejčí ◽  
Luca Gianaroli
Keyword(s):  
Three Dimensional ◽  
Dimensional Sphere ◽  
Chromosome X ◽  
Sphere Model ◽  
Chromosome 18 ◽  
Vitro Fertilization ◽  
Signal Distribution ◽  
Human In Vitro Fertilization

The positions of chromosomes 18 and X fluorescence in situ hybridization signals were analyzed in blastomeres generated from human in vitro fertilization 3- to 4-day-old embryos after preimplantation screening of aneuploidy of chromosomes 13, 16, 18, 21, 22, X, and Y. Fluorescent signal localization compared with a three-dimensional sphere model of random signal distribution revealed significant differences, providing evidence of peripheral localization of chromosome 18 in aneuploid ( p=0.0013) and aneuploid/euploid blastomeres ( p=0.0011). No differences were found in localization of chromosome 18 in euploid and in chromosome X in euploid and aneuploid blastomeres.

Sign in / Sign up

Export Citation Format

Share Document