scholarly journals On Sliced Spaces: Global Hyperbolicity Revisited

Symmetry ◽  
2019 ◽  
Vol 11 (3) ◽  
pp. 304 ◽  
Author(s):  
Kyriakos Papadopoulos ◽  
Nazli Kurt ◽  
Basil Papadopoulos
Keyword(s):  
Shift Function ◽  
Global Hyperbolicity ◽  
Globally Hyperbolic ◽  
Topological Condition ◽  
Lapse Function

We give a topological condition for a generic sliced space to be globally hyperbolic without any hypothesis on lapse function, shift function, and spatial metric.

scholarly journals On Sliced Spaces: Global Hyperbolicity Revisited

2019 ◽  
Author(s):  
Kyriakos Papadopoulos ◽  
Nazli Kurt ◽  
Basil K. Papadopoulos
Keyword(s):  
Shift Function ◽  
Global Hyperbolicity ◽  
Globally Hyperbolic ◽  
Topological Condition ◽  
Lapse Function

We give a topological condition for a generic sliced space to be globally hyperbolic, without any hypothesis on the lapse function, shift function and spatial metric.

scholarly journals Solutions with throats in Hořava gravity with cosmological constant

2016 ◽  
Vol 25 (02) ◽  
pp. 1650016 ◽  
Author(s):  
Jorge Bellorín ◽  
Alvaro Restuccia ◽  
Adrián Sotomayor
Keyword(s):  
Cosmological Constant ◽  
Effective Action ◽  
Naked Singularity ◽  
Shift Function ◽  
Coupling Constant ◽  
De Sitter ◽  
Single Side ◽  
Horava Gravity ◽  
Two Sides ◽  
Lapse Function

By combining analytical and numerical methods, we find that the solutions of the complete Hořava theory with negative cosmological constant that satisfy the conditions of staticity, spherical symmetry and vanishing of the shift function are two kinds of geometry: (i) a solution with two sides joined by a throat and (ii) a single side with a naked singularity at the origin. We study the second-order effective action. We consider the case when the coupling constant of the [Formula: see text] term, which is the unique deviation from general relativity (GR) in the effective action, is small. At one side, the solution with the throat acquires a kind of deformed anti-de Sitter (AdS) asymptotia and at the other side, there is an asymptotic essential singularity. The deformation of AdS essentially means that the lapse function [Formula: see text] diverges asymptotically a bit faster than AdS. This can also be interpreted as an anisotropic Lifshitz scaling that the solutions acquire asymptotically.

scholarly journals Fermat Metrics

Symmetry ◽  
2021 ◽  
Vol 13 (8) ◽  
pp. 1422
Author(s):  
Antonio Masiello
Keyword(s):  
Variational Methods ◽  
Morse Theory ◽  
Sagnac Effect ◽  
Variational Theory ◽  
Global Hyperbolicity ◽  
Fermat Principle ◽  
Multiple Image ◽  
Light Rays ◽  
Stationary Spacetimes

In this paper we present a survey of Fermat metrics and their applications to stationary spacetimes. A Fermat principle for light rays is stated in this class of spacetimes and we present a variational theory for the light rays and a description of the multiple image effect. Some results on variational methods, as Ljusternik-Schnirelmann and Morse Theory are recalled, to give a description of the variational methods used. Other applications of the Fermat metrics concern the global hyperbolicity and the geodesic connectedeness and a characterization of the Sagnac effect in a stationary spacetime. Finally some possible applications to other class of spacetimes are considered.

scholarly journals RESONANCES AND SPECTRAL SHIFT FUNCTION FOR THE SEMI-CLASSICAL DIRAC OPERATOR

2007 ◽  
Vol 19 (10) ◽  
pp. 1071-1115 ◽  
Author(s):  
ABDALLAH KHOCHMAN
Keyword(s):  
Dirac Operator ◽  
Upper Bound ◽  
Selfadjoint Operator ◽  
Energy Levels ◽  
Critical Energy ◽  
Spectral Shift ◽  
Approximation Formula ◽  
Shift Function ◽  
Spectral Shift Function ◽  
Electro Magnetic

We consider the selfadjoint operator H = H0+ V, where H0is the free semi-classical Dirac operator on ℝ3. We suppose that the smooth matrix-valued potential V = O(〈x〉-δ), δ > 0, has an analytic continuation in a complex sector outside a compact. We define the resonances as the eigenvalues of the non-selfadjoint operator obtained from the Dirac operator H by complex distortions of ℝ3. We establish an upper bound O(h-3) for the number of resonances in any compact domain. For δ > 3, a representation of the derivative of the spectral shift function ξ(λ,h) related to the semi-classical resonances of H and a local trace formula are obtained. In particular, if V is an electro-magnetic potential, we deduce a Weyl-type asymptotics of the spectral shift function. As a by-product, we obtain an upper bound O(h-2) for the number of resonances close to non-critical energy levels in domains of width h and a Breit–Wigner approximation formula for the derivative of the spectral shift function.

Thermal Error Measurement, Modeling and Compensation for Motorized Spindle and the Research on Compensation Effect Validation

2014 ◽  
Vol 889-890 ◽  
pp. 1003-1008 ◽  
Author(s):  
Yu Qing Fu ◽  
Wei Guo Gao ◽  
Jin Yu Yang ◽  
Qing Zhang ◽  
Da Wei Zhang
Keyword(s):  
Compensation Effect ◽  
Great Influence ◽  
Thermal Characteristics ◽  
Thermal Error ◽  
Shift Function ◽  
Linear Regression Method ◽  
Motorized Spindle ◽  
Verification Method ◽  
Machining Center ◽  
Thermal Error Model

The motorized spindle is a primate part of the machine tool and its thermal characteristics have great influence on the accuracy of the machine tools. The thermal errors of the spindle of a certain type of precision horizontal machining center were measured with PLC acquisition system. By multivariate linear regression method, the axial thermal error model was built. Online real-time error compensation was implemented by applying the FANUC 18i CNC system external machine coordinate system shift function. A verification method was proposed which include three steps: model validation, compensation validation and experimental machining verification. The accuracy of the model was 84.1%, 64.9% and 49.4% respectively. The quantitative analysis results showed the precision was effectively improved and the compensation method was reliable.

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