An acceleration condition for b-incomplete timelike curves

1981 ◽  
Vol 90 (1) ◽  
pp. 191-193 ◽  
Author(s):  
C. T. J. Dodson ◽  
L. J. Sulley ◽  
P. M. Williams
Keyword(s):  
Smooth Manifold ◽  
Linear Connection ◽  
Timelike Curve ◽  
Acceptable Method ◽  
Proper Length ◽  
Lorentz Norm

AbstractThe b-completion of a smooth manifold with linear connection was introduced by Schmidt (6). He pointed out that, in a spacetime, an inextensible timelike curve of finite proper length and bounded acceleration has an endpoint on the b-boundary. However, it is not clear in what sense boundedness was meant. Geroch(1) suggested that any acceptable method of completing a spacetime should have this property with boundedness interpreted through the Lorentz norm. This result for the b-completion was given by Rosso(4), based on his earlier paper (3), which, however, contains some arguments that we do not accept. We give another proof of the result and improve it by weakening the condition of boundedness of the acceleration.

scholarly journals Lifts of connections to the bundle of (1,1) type tensor frames

2021 ◽  
pp. 177-183
Author(s):  
Habil FATTAYEV
Keyword(s):  
Smooth Manifold ◽  
Linear Connection ◽  
Sasaki Metric ◽  
Geodesic Lines ◽  
Complete Lift

In this paper we consider the bundle of (1,1) type tensor frames over a smooth manifold, define the horizontal and complete lifts of symmetric linear connection into this bundle. Also we study the properties of the geodesic lines corresponding to the complete lift of the linear connection and investigate the relations between Sasaki metric and lifted connections on the bundle of (1,1) type tensor frames.

scholarly journals Parabolic conformally symplectic structures I; definition and distinguished connections

2018 ◽  
Vol 30 (3) ◽  
pp. 733-751 ◽  
Author(s):  
Andreas Čap ◽  
Tomáš Salač
Keyword(s):  
Lie Algebra ◽  
Geometric Structure ◽  
Tangent Bundle ◽  
Smooth Manifold ◽  
Symplectic Structure ◽  
Linear Connection ◽  
Underlying Structure ◽  
Normalization Condition ◽  
Lie Algebra Cohomology ◽  
First Order

AbstractWe introduce a class of first order G-structures, each of which has an underlying almost conformally symplectic structure. There is one such structure for each real simple Lie algebra which is not of type {C_{n}} and admits a contact grading. We show that a structure of each of these types on a smooth manifold M determines a canonical compatible linear connection on the tangent bundle {\mathrm{TM}}. This connection is characterized by a normalization condition on its torsion. The algebraic background for this result is proved using Kostant’s theorem on Lie algebra cohomology. For each type, we give an explicit description of both the geometric structure and the normalization condition. In particular, the torsion of the canonical connection naturally splits into two components, one of which is exactly the obstruction to the underlying structure being conformally symplectic. This article is the first in a series aiming at a construction of differential complexes naturally associated to these geometric structures.

Banach Lie Algebroids

2011 ◽  
Vol 57 (2) ◽  
pp. 409-416
Author(s):  
Mihai Anastasiei
Keyword(s):  
Differential Equations ◽  
Smooth Manifold ◽  
Vector Bundles ◽  
Second Order ◽  
Lie Algebroids ◽  
Second Order Differential Equations

Banach Lie AlgebroidsFirst, we extend the notion of second order differential equations (SODE) on a smooth manifold to anchored Banach vector bundles. Then we define the Banach Lie algebroids as Lie algebroids structures modeled on anchored Banach vector bundles and prove that they form a category.

Comparison of two air sampling methods to monitor operating room air quality and assessment of air quality in two operating rooms with different ventilation systems in the national hospital of Sri Lanka

2016 ◽  
Vol 12 (3) ◽  
Author(s):  
Tshokey Tshokey ◽  
Pranitha Somaratne ◽  
Suneth Agampodi
Keyword(s):  
Air Quality ◽  
Sri Lanka ◽  
Operating Room ◽  
Ventilation System ◽  
Surgical Site Infections ◽  
National Hospital ◽  
Air Contamination ◽  
Acceptable Method ◽  
The Difference ◽  
Laminar Air Flow

Air contamination in the operating room (OR) is an important contributor for surgical site infections. Air quality should be assessed during microbiological commissioning of new ORs and as required thereafter. Despite many modern methods of sampling air, developing countries mostly depended on conventional methods. This was studied in two ORs of the National Hospital of Sri Lanka (NHSL) with different ventilation system; a conventional ventilation (CV) and a laminar air flow (LAF). Both ORs were sampled simultaneously by two different methods, the settle plate and sampler when empty and during use for a defined time period. Laboratory work was done in the Medical Research Institute. The two methods of sampling showed moderate but highly significant correlation. The OR with CV was significantly more contaminated than LAF when empty as well as during use by both methods. Overall, the difference in contamination was more significant when sampled by the sampler. Differences in contamination in empty and in-use ORs were significant in both ORs, but significance is less in LAF rooms. The consistent and significant correlation between settle plate and sampler showed that the settle plate is an acceptable method. The LAF theatre showed less contamination while empty and during use as expected. Air contamination differences were more significant when sampled with sampler indicating that it is a more sensitive method. Both CV and LAF ORs of the NHSL did not meet the contamination standards for empty theatres but met the standards for in-use indicating that the theatre etiquette was acceptable.

scholarly journals Missing the point in noncommutative geometry

Synthese ◽  
2021 ◽  
Author(s):  
Nick Huggett ◽  
Fedele Lizzi ◽  
Tushar Menon
Keyword(s):  
Scalar Field ◽  
Noncommutative Geometry ◽  
Smooth Manifold ◽  
Operational Definition ◽  
Spectral Triple ◽  
Fundamental Quantity

AbstractNoncommutative geometries generalize standard smooth geometries, parametrizing the noncommutativity of dimensions with a fundamental quantity with the dimensions of area. The question arises then of whether the concept of a region smaller than the scale—and ultimately the concept of a point—makes sense in such a theory. We argue that it does not, in two interrelated ways. In the context of Connes’ spectral triple approach, we show that arbitrarily small regions are not definable in the formal sense. While in the scalar field Moyal–Weyl approach, we show that they cannot be given an operational definition. We conclude that points do not exist in such geometries. We therefore investigate (a) the metaphysics of such a geometry, and (b) how the appearance of smooth manifold might be recovered as an approximation to a fundamental noncommutative geometry.

scholarly journals Gauging the higher-spin-like symmetries by the Moyal product

2021 ◽  
Vol 2021 (6) ◽  
Author(s):  
M. Cvitan ◽  
P. Dominis Prester ◽  
S. Giaccari ◽  
M. Paulišić ◽  
I. Vuković
Keyword(s):  
Linear Connection ◽  
Covariant Formulation ◽  
Formal Similarity ◽  
Commutative Field ◽  
Gauge Transformations ◽  
Yang Mills ◽  
Higher Derivative ◽  
Novel Approach ◽  
Emergent Geometry ◽  
Higher Spin

Abstract We analyze a novel approach to gauging rigid higher derivative (higher spin) symmetries of free relativistic actions defined on flat spacetime, building on the formalism originally developed by Bonora et al. and Bekaert et al. in their studies of linear coupling of matter fields to an infinite tower of higher spin fields. The off-shell definition is based on fields defined on a 2d-dimensional master space equipped with a symplectic structure, where the infinite dimensional Lie algebra of gauge transformations is given by the Moyal commutator. Using this algebra we construct well-defined weakly non-local actions, both in the gauge and the matter sector, by mimicking the Yang-Mills procedure. The theory allows for a description in terms of an infinite tower of higher spin spacetime fields only on-shell. Interestingly, Euclidean theory allows for such a description also off-shell. Owing to its formal similarity to non-commutative field theories, the formalism allows for the introduction of a covariant potential which plays the role of the generalised vielbein. This covariant formulation uncovers the existence of other phases and shows that the theory can be written in a matrix model form. The symmetries of the theory are analyzed and conserved currents are explicitly constructed. By studying the spin-2 sector we show that the emergent geometry is closely related to teleparallel geometry, in the sense that the induced linear connection is opposite to Weitzenböck’s.

Electrokinetic Potential for Characterization of Nanosctructured Solid Flat Surfaces

2013 ◽  
Vol 25 ◽  
pp. 31-39 ◽  
Author(s):  
Zdeňka Kolská ◽  
Nikola Slepičková Kasálková ◽  
Jakub Siegel ◽  
Václav Švorčík
Keyword(s):  
Zeta Potential ◽  
Isoelectric Point ◽  
Electrokinetic Potential ◽  
Characteristic Parameter ◽  
Metal Nanostructures ◽  
Gold Deposition ◽  
Fast Analysis ◽  
Flat Surfaces ◽  
Acceptable Method ◽  
Point Determination

Electrokinetic potential (zeta potential) is a characteristic parameter for description of the surface chemistry of solid flat materials and it can be used for a fast analysis of materials modified by different chemical or physical methods. Due to its sensitivity, zeta potential is able to distinguish surface modified by coating with monolayers of various materials or nanostructures created after plasma treatment. Also metal nanostructures deposited on surfaces can be characterized by zeta potential. It can also be used for isoelectric point determination of materials. We present data on zeta potential in 0.001 mol/dm3 KCl at constant pH7.0 and also in pH range (2.5-7.0) for isoelectric point determination for pristine polymers PET, PTFE, PS, LDPE, HDPE, PLLA, PVF, PVDF, PMP and polyimides (Upilex R, Upilex S, Kapton). The zeta potential of selected polymers, modified by plasma and by chemical coatings (e.g. by biphenyldithiol or polyethyleneglycol) or by gold deposition was measured too. Zeta potentials of these modified materials were also studied to confirmation that electrokinetic analysis is acceptable method for their fast description.

Evaluation of Microbially Influenced Degradation as a Method for the Decontamination of Radio Actively Contaminated Concrete

1996 ◽  
Vol 465 ◽  
Author(s):  
R. D. Rogers ◽  
M. A. Hamilton ◽  
L. O. Nelson ◽  
J. Benson ◽  
M. Green
Keyword(s):  
Pilot Scale ◽  
Field Application ◽  
Department Of Energy ◽  
Laboratory Evaluation ◽  
Concrete Slabs ◽  
Initial Field ◽  
Acceptable Method ◽  
Application Data ◽  
The Cost ◽  
The U.S

ABSTRACTBecause there are literally square kilometers of radioactively contaminated concrete surfaces within the U.S. Department of Energy (DOE) complex, the task (both scope and cost) of decontamination is staggering. Complex-wide cleanup using conventional methodology does not appear to be feasible for every facility because of prioritization, cost, and manual effort required.We are investigating the feasibility of using microbially influenced degradation (MID) of concrete as a unique, innovative approach for the decontamination of concrete. Currently, work is being conducted to determine the practicality and cost effectiveness of using this environmentally acceptable method for decontamination of large surface concrete structures. Under laboratory conditions, the biodecontamination process has successfully been used to remove 2 mm of the surface of concrete slabs. Subsequently, initial field application data from an ongoing pilot-scale demonstration have shown that an average of 2 mm of surface can be removed from meter-square areas of contaminated concrete. The cost for the process has been estimated as $1.29/m2. Methodologies for field application of the process are being developed and will be tested. This paper provides information on the MID process, laboratory evaluation of its use for decontamination, and results from the pilot field application.

scholarly journals Pseudoinversion of degenerate metrics

2003 ◽  
Vol 2003 (55) ◽  
pp. 3479-3501 ◽  
Author(s):  
C. Atindogbe ◽  
J.-P. Ezin ◽  
Joël Tossa
Keyword(s):  
Differential Geometry ◽  
Large Class ◽  
Smooth Manifold ◽  
Differential Operators ◽  
Type Operator ◽  
Lorentzian Space ◽  
Lightlike Hypersurface ◽  
Definition Of ◽  
Lightlike Hypersurfaces ◽  
Theoretical Results

Let(M,g)be a smooth manifoldMendowed with a metricg. A large class of differential operators in differential geometry is intrinsically defined by means of the dual metricg∗on the dual bundleTM∗of 1-forms onM. If the metricgis (semi)-Riemannian, the metricg∗is just the inverse ofg. This paper studies the definition of the above-mentioned geometric differential operators in the case of manifolds endowed with degenerate metrics for whichg∗is not defined. We apply the theoretical results to Laplacian-type operator on a lightlike hypersurface to deduce a Takahashi-like theorem (Takahashi (1966)) for lightlike hypersurfaces in Lorentzian spaceℝ1n+2.

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