scholarly journals Almost symplectic structures on the linear frame bundle from linear connection

2009 ◽  
Vol 63 (1) ◽  
Author(s):  
Anna Bednarska
Keyword(s):  
Linear Connection ◽  
Frame Bundle ◽  
Symplectic Structures

scholarly journals Prolongations of linear connections to the frame bundle

1983 ◽  
Vol 28 (3) ◽  
pp. 367-381
Author(s):  
Luis A. Cordero ◽  
Manuel de Leon
Keyword(s):  
Linear Connection ◽  
Frame Bundle ◽  
Linear Connections ◽  
Complete Lift

In this paper we construct the prolongation of a linear connection Γ on a manifold Μ to the bundle space of its frame bundle, and show that such prolongated connection coincides with the so-called complete lift of Γ to .

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.

Embeddings of Butterflies into Hypermeshes

1998 ◽  
Vol 08 (03) ◽  
pp. 337-350
Author(s):  
Sook-Yeon Kim ◽  
Oh-Heum Kwon ◽  
Kyung-Yong Chwa
Keyword(s):  
Aspect Ratio ◽  
Interconnection Network ◽  
Linear Connection ◽  
Parallel Computers ◽  
Multiple Copies

Hypermeshes have been given much attention as a versatile interconnection network of parallel computers. A hypermesh is obtained from a mesh by replacing each linear connection with a hyperedge. In this paper, we show how to embed a butterfly or multiple copies of a butterfly into a hypermesh. First, a butterfly B(s) of (s + 1)2s nodes is embedded into a 2s × X hypermesh where X = 2⌊ log 2 s ⌋+ 1. Second, the butterfly B(s) is embedded into a square hypermesh. Third, multiple copies of the butterfly B(s) are embedded into a hypermesh of variable aspect ratio. The efficiency of these embeddings is measured by alignment cost, congestion, and expansion. The alignment cost of all of these embeddings is optimal. The congestion of the first and third embedding is optimal. The expansion of the first and third embedding is one if s = 2k - 1 for some integer k, otherwise, less than two. The expansion of the second embedding is 2 + ∊ (s) where ∊(s) = (2 log (s + 1) + 2)/(s + 1).

scholarly journals Effectiveness Testing of an Inverse Method for Balancing Nonlinear Rotordynamic Systems

2018 ◽  
Author(s):  
Sergio G. Torres Cedillo ◽  
Philip Bonello ◽  
Ghaith Ghanim Al-Ghazal ◽  
Jacinto Cortés Pérez ◽  
Alberto Reyes Solis
Keyword(s):  
Inverse Problem ◽  
Inverse Method ◽  
Linear Connection ◽  
The Other ◽  
Squeeze Film ◽  
Squeeze Film Damper ◽  
Operational Conditions ◽  
Non Invasive ◽  
Highly Nonlinear ◽  
Aero Engine

Modern aero-engine structures typically have at least two nested rotors mounted within a flexible casing via squeeze-film damper (SFD) bearings. The inaccessibility of the HP rotor under operational conditions motivates the use of a non-invasive inverse problem procedure for identifying the unbalance. Such an inverse problem requires prior knowledge of the structure and measurements of the vibrations at the casing. Recent work by the authors reported a non-invasive inverse method for the balancing of rotordynamic systems with nonlinear squeeze-film damper (SFD) bearings, which overcomes several limitations of earlier works. However, it was not applied to a common practical configuration wherein the HP rotor is mounted on the casing via just one weak linear connection (retainer spring), with the other connections being highly nonlinear SFDs. The analysis of the present paper considers such a system. It explores the influence of the condition number and how it is affected as the number of sensors and/or measurement speeds is increased. The results show that increasing the number of measurement speeds has a far more significant impact on the conditioning of the problem than increasing the number of sensors. The balancing effectiveness is reasonably good under practical noise level conditions, but significantly lower than obtained for the previously considered simpler configurations.

Vertical Chern Type Classes on Complex Finsler Bundles

2011 ◽  
Vol 57 (2) ◽  
pp. 377-386
Author(s):  
Cristian Ida
Keyword(s):  
Differential Forms ◽  
Linear Connection ◽  
Curvature Form ◽  
Cohomology Groups ◽  
Finsler Manifolds ◽  
Invariance Properties ◽  
Type Classes

Vertical Chern Type Classes on Complex Finsler BundlesIn the present paper, we define vertical Chern type classes on complex Finsler bundles, as an extension of thev-cohomology groups theory on complex Finsler manifolds. These classes are introduced in a classical way by using closed differential forms with respect to the conjugated vertical differential in terms of the vertical curvature form of Chern-Finsler linear connection. Also, some invariance properties of these classes are studied.

scholarly journals Gibbs' States for Moser-Calogero Potentials

1997 ◽  
Vol 11 (01n02) ◽  
pp. 203-211 ◽  
Author(s):  
K. L. Vaninsky
Keyword(s):  
Phase Space ◽  
Equation Of State ◽  
Gibbs States ◽  
Symplectic Structures ◽  
Classical Particles

We present two independent approaches for computing the thermodynamics for classical particles interacting via the Moser-Calogero potential Combining the results we conjecture the form of equation of state or, what is equivalent, the asymptotics of the Jacobian between volume elements corresponding to two symplectic structures on the phase space.

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