scholarly journals Geometric interpretation and classification of global solutions in generalized dilaton gravity

1996 ◽  
Vol 53 (10) ◽  
pp. 5609-5618 ◽  
Author(s):  
M. O. Katanaev ◽  
W. Kummer ◽  
H. Liebl
Keyword(s):  
Global Solutions ◽  
Geometric Interpretation ◽  
Dilaton Gravity

Embeddings of locally compact abelian p-groups in Hawaiian groups

2021 ◽  
Vol 0 (0) ◽  
Author(s):  
Yanga Bavuma ◽  
Francesco G. Russo
Keyword(s):  
Algebraic Topology ◽  
Geometric Interpretation ◽  
Locally Compact Groups ◽  
Compact Groups ◽  
Locally Compact ◽  
Locally Compact Abelian Groups ◽  
Compact Abelian Groups ◽  
Hawaiian Earring ◽  
Path Connected

Abstract We show that locally compact abelian p-groups can be embedded in the first Hawaiian group on a compact path connected subspace of the Euclidean space of dimension four. This result gives a new geometric interpretation for the classification of locally compact abelian groups which are rich in commuting closed subgroups. It is then possible to introduce the idea of an algebraic topology for topologically modular locally compact groups via the geometry of the Hawaiian earring. Among other things, we find applications for locally compact groups which are just noncompact.

SATANIC AND THELEMIC CIRCLES ON KNOTS

2013 ◽  
Vol 22 (05) ◽  
pp. 1350017 ◽  
Author(s):  
G. FLOWERS
Keyword(s):  
Geometric Interpretation ◽  
Second Order ◽  
Geometric Properties ◽  
Vassiliev Invariants ◽  
Vassiliev Invariant ◽  
Knot Diagrams

While Vassiliev invariants have proved to be a useful tool in the classification of knots, they are frequently defined through knot diagrams, and fail to illuminate any significant geometric properties the knots themselves may possess. Here, we provide a geometric interpretation of the second-order Vassiliev invariant by examining five-point cocircularities of knots, extending some of the results obtained in [R. Budney, J. Conant, K. P. Scannell and D. Sinha, New perspectives on self-linking, Adv. Math. 191(1) (2005) 78–113]. Additionally, an analysis on the behavior of other cocircularities on knots is given.

Characteristic tetrahedron of wrench singularities for parallel manipulators with three legs

2002 ◽  
Vol 216 (1) ◽  
pp. 81-93 ◽  
Author(s):  
I Ebert-Uphoff ◽  
J-K Lee ◽  
H Lipkin
Keyword(s):  
Parallel Manipulators ◽  
Stewart Platform ◽  
Geometric Interpretation ◽  
Mobile Platform ◽  
Line Geometry ◽  
Important Theorem ◽  
Parallel Platform

A new analysis of wrench singularities is presented for spatial parallel platform manipulators consisting of three legs, with up to two actuators each, and connected to the mobile platform by spherical joints. The analysis also applies to some related manipulators with six legs, such as the 6-3 Gough-Stewart platform. The characteristic tetrahedron is introduced to identify wrench singularities, i.e. configurations where the platform can move infinitesimally with all actuators locked. An important theorem is presented that provides a geometric interpretation of wrench singularities: a manipulator is at a wrench singularity if and only if the characteristic tetrahedron is singular. All cases in which the tetrahedron becomes singular are enumerated, which leads to a classification of wrench singularities. This method is easy to visualize and presents an alternative to standard approaches using line geometry.

scholarly journals Classification of stringlike solutions in dilaton gravity

2002 ◽  
Vol 65 (6) ◽  
Author(s):  
Y. Verbin ◽  
S. Madsen ◽  
A. L. Larsen ◽  
M. Christensen
Keyword(s):  
Dilaton Gravity

scholarly journals Properties of the free boundary near the fixed boundary of the double obstacle problems

2021 ◽  
Author(s):  
Jinwan Park
Keyword(s):  
Free Boundary ◽  
Obstacle Problem ◽  
Nonlinear Operator ◽  
Main Idea ◽  
Global Solutions ◽  
Obstacle Problems ◽  
Local Regularity ◽  
Fixed Boundary ◽  
New Type

In this paper, we study the tangential touch and [Formula: see text] regularity of the free boundary near the fixed boundary of the double obstacle problem for Laplacian and fully nonlinear operator. The main idea to have the properties is regarding the upper obstacle as a solution of the single obstacle problem. Then, in the classification of global solutions of the double problem, it is enough to consider only two cases for the upper obstacle, [Formula: see text] The second one is a new type of upper obstacle, which does not exist in the study of local regularity of the free boundary of the double problem. Thus, in this paper, a new type of difficulties that come from the second type upper obstacle is mainly studied.

A GEOMETRIC INTERPRETATION FOR THE TORSION CONSTRAINTS OF (2,0) HETEROTIC WORLDSHEET SUPERGRAVITY

1991 ◽  
Vol 06 (36) ◽  
pp. 3341-3347 ◽  
Author(s):  
SURESH GOVINDARAJAN ◽  
BURT A. OVRUT
Keyword(s):  
Geometric Interpretation

We present a geometric interpretation for the torsion constraints in (2,0) supergravity using G-structures. This leads to a classification of the constraints as given by Ref. 1. We also present the essential torsion constraints for (p,q) geometry.

scholarly journals Biharmonic curves in Minkowski3-space

2003 ◽  
Vol 2003 (21) ◽  
pp. 1365-1368 ◽  
Author(s):  
Jun-Ichi Inoguchi
Keyword(s):  
Geometric Interpretation ◽  
Biharmonic Curves

We give a differential geometric interpretation for the classification of biharmonic curves in semi-Euclidean3-space due to Chen and Ishikawa (1991).

scholarly journals Geometric Interpretation and General Classification of Three-Dimensional Polarization States through the Intrinsic Stokes Parameters

Photonics ◽  
2021 ◽  
Vol 8 (8) ◽  
pp. 315
Author(s):  
José J. Gil
Keyword(s):  
Three Dimensional ◽  
Geometric Interpretation ◽  
Stokes Parameters ◽  
Geometric Representation ◽  
Systematic Classification ◽  
Quadric Hypersurface ◽  
Complicated Form ◽  
Polarization States ◽  
Rotationally Invariant

In contrast with what happens for two-dimensional polarization states, defined as those whose electric field fluctuates in a fixed plane, which can readily be represented by means of the Poincaré sphere, the complete description of general three-dimensional polarization states involves nine measurable parameters, called the generalized Stokes parameters, so that the generalized Poincaré object takes the complicated form of an eight-dimensional quadric hypersurface. In this work, the geometric representation of general polarization states, described by means of a simple polarization object constituted by the combination of an ellipsoid and a vector, is interpreted in terms of the intrinsic Stokes parameters, which allows for a complete and systematic classification of polarization states in terms of meaningful rotationally invariant descriptors.

scholarly journals Asymptotic and quenching behaviors of semilinear parabolic systems with singular nonlinearities

2021 ◽  
Vol 0 (0) ◽  
pp. 0
Author(s):  
Qi Wang ◽  
Yanyan Zhang
Keyword(s):  
Global Solutions ◽  
Parabolic Systems ◽  
First Eigenvalue ◽  
Variational Characterization ◽  
Semilinear Parabolic Systems ◽  
Singular Nonlinearities ◽  
New Ideas ◽  
Semilinear Parabolic

<p style='text-indent:20px;'>In this paper, we consider a family of parabolic systems with singular nonlinearities. We study the classification of global existence and quenching of solutions according to parameters and initial data. Furthermore, the rate of the convergence of the global solutions to the minimal steady state is given. Due to the lack of variational characterization of the first eigenvalue to the linearized elliptic problem associated with our parabolic system, some new ideas and techniques are introduced.</p>

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