scholarly journals A HYDRODYNAMICAL HOMOTOPY CO-MOMENTUM MAP AND A MULTISYMPLECTIC INTERPRETATION OF HIGHER-ORDER LINKING NUMBERS

2021 ◽  
pp. 1-20
Author(s):  
ANTONIO MICHELE MITI ◽  
MAURO SPERA
Keyword(s):  
Phase Space ◽  
Riemannian Manifolds ◽  
Special Class ◽  
Higher Order ◽  
First Integrals ◽  
Coadjoint Orbits ◽  
Conserved Quantities ◽  
Momentum Map ◽  
Perfect Fluids ◽  
Linking Numbers

Abstract In this paper a homotopy co-momentum map (à la Callies, Frégier, Rogers and Zambon) transgressing to the standard hydrodynamical co-momentum map of Arnol’d, Marsden, Weinstein and others is constructed and then generalized to a special class of Riemannian manifolds. Also, a covariant phase space interpretation of the coadjoint orbits associated to the Euler evolution for perfect fluids, and in particular of Brylinski’s manifold of smooth oriented knots, is discussed. As an application of the above homotopy co-momentum map, a reinterpretation of the (Massey) higher-order linking numbers in terms of conserved quantities within the multisymplectic framework is provided and knot-theoretic analogues of first integrals in involution are determined.

scholarly journals New type of degenerate Daehee polynomials of the second kind

2020 ◽  
Vol 2020 (1) ◽  
Author(s):  
Sunil Kumar Sharma ◽  
Waseem A. Khan ◽  
Serkan Araci ◽  
Sameh S. Ahmed
Keyword(s):  
Generating Function ◽  
Special Class ◽  
Stirling Numbers ◽  
Bernoulli Numbers ◽  
Higher Order ◽  
Bernoulli Numbers And Polynomials ◽  
New Type ◽  
Order Degenerate ◽  
Math Phys

Abstract Recently, Kim and Kim (Russ. J. Math. Phys. 27(2):227–235, 2020) have studied new type degenerate Bernoulli numbers and polynomials by making use of degenerate logarithm. Motivated by (Kim and Kim in Russ. J. Math. Phys. 27(2):227–235, 2020), we consider a special class of polynomials, which we call a new type of degenerate Daehee numbers and polynomials of the second kind. By using their generating function, we derive some new relations including the degenerate Stirling numbers of the first and second kinds. Moreover, we introduce a new type of higher-order degenerate Daehee polynomials of the second kind. We also derive some new identities and properties of this type of polynomials.

Higher order point and continuum mechanics from phase-space action

2002 ◽  
Vol 305 (3-4) ◽  
pp. 93-99 ◽  
Author(s):  
J Shamanna ◽  
B Talukdar ◽  
U Das
Keyword(s):  
Phase Space ◽  
Continuum Mechanics ◽  
Higher Order ◽  
Space Action

Theoretical Analyses of the Universal Approximation Capability of a Class of Higher Order Neural Networks Based on Approximate Identity

2016 ◽  
pp. 1456-1470 ◽  
Author(s):  
Saeed Panahian Fard ◽  
Zarita Zainuddin
Keyword(s):  
Neural Networks ◽  
Approximation Theory ◽  
Special Class ◽  
Higher Order ◽  
Approximate Identity ◽  
Universal Approximation ◽  
Multivariate Functions ◽  
Higher Order Neural Networks ◽  
Approximation Capability ◽  
Theoretical Analyses

One of the most important problems in the theory of approximation functions by means of neural networks is universal approximation capability of neural networks. In this study, we investigate the theoretical analyses of the universal approximation capability of a special class of three layer feedforward higher order neural networks based on the concept of approximate identity in the space of continuous multivariate functions. Moreover, we present theoretical analyses of the universal approximation capability of the networks in the spaces of Lebesgue integrable multivariate functions. The methods used in proving our results are based on the concepts of convolution and epsilon-net. The obtained results can be seen as an attempt towards the development of approximation theory by means of neural networks.

HIGHER ORDER LINKING NUMBERS

1998 ◽  
Vol 07 (03) ◽  
pp. 393-414 ◽  
Author(s):  
W. S. MASSEY
Keyword(s):  
Higher Order ◽  
Linking Numbers

On coadjoint orbits of rotational perfect fluids

1992 ◽  
Vol 33 (3) ◽  
pp. 901-909 ◽  
Author(s):  
Vittorio Penna ◽  
Mauro Spera
Keyword(s):  
Coadjoint Orbits ◽  
Perfect Fluids

scholarly journals Very-High-Eccentricity Librations at Some Higher Order Resonances

1992 ◽  
Vol 152 ◽  
pp. 153-158 ◽  
Author(s):  
J.C. Klafke ◽  
S. Ferraz-Mello ◽  
T. Michtchenko
Keyword(s):  
Phase Space ◽  
Numerical Integration ◽  
Higher Order ◽  
Planar Problem ◽  
High Eccentricity ◽  
Disturbing Potential ◽  
Numerical Exploration ◽  
Numerical Integrations ◽  
Short Period ◽  
Very High

Motions near the 3:1, 4:1 and 5:2 resonances with Jupiter are studied by means of numerical integrations of a semi-analytically averaged Sun-Jupiter-asteroid planar problem. In order to have a model including the very-high-eccentricity regions of the phase space, we adopted a set of local expansions of the disturbing potential, adequate to perform the numerical exploration of regions in the phase space with eccentricities higher than 0.9 (Ferraz-Mello and Klafke, 1991). Individual solutions and qualitative results thus obtained are completely reproduced by numerical integration of the complete equations by filtering off the short-period components of these solutions.

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