Curvature Invariant and Generalized Canonical Operator Models – I

Curvature invariant and generalized canonical operator models – II

Journal of Functional Analysis ◽

10.1016/j.jfa.2013.07.005 ◽

2014 ◽

Vol 266 (4) ◽

pp. 2486-2502 ◽

Cited By ~ 7

Author(s):

Ronald G. Douglas ◽

Yun-Su Kim ◽

Hyun-Kyoung Kwon ◽

Jaydeb Sarkar

Keyword(s):

Curvature Invariant ◽

Canonical Operator

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Oscillation of Second-Order Differential Equations with Multiple and Mixed Delays under a Canonical Operator

Mathematics ◽

10.3390/math9121323 ◽

2021 ◽

Vol 9 (12) ◽

pp. 1323

Author(s):

Shyam Sundar Santra ◽

Rami Ahmad El-Nabulsi ◽

Khaled Mohamed Khedher

Keyword(s):

Differential Equations ◽

Necessary Conditions ◽

Second Order ◽

Multiple Delays ◽

Mixed Delays ◽

Neutral Differential Equations ◽

Canonical Operator ◽

Second Order Differential Equations ◽

The Future ◽

Sufficient And Necessary Conditions

In this work, we obtained new sufficient and necessary conditions for the oscillation of second-order differential equations with mixed and multiple delays under a canonical operator. Our methods could be applicable to find the sufficient and necessary conditions for any neutral differential equations. Furthermore, we proved the validity of the obtained results via particular examples. At the end of the paper, we provide the future scope of this study.

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Application of the canonical operator in thermodynamics

Doklady Mathematics ◽

10.1134/s1064562406060020 ◽

2006 ◽

Vol 74 (3) ◽

pp. 791-794

Author(s):

V. P. Maslov ◽

V. E. Nazaikinskii

Keyword(s):

Canonical Operator

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Properties of a scalar curvature invariant depending on two planes

manuscripta mathematica ◽

10.1007/s00229-006-0056-0 ◽

2006 ◽

Vol 122 (1) ◽

pp. 59-72 ◽

Cited By ~ 22

Author(s):

S. Haesen ◽

L. Verstraelen

Keyword(s):

Scalar Curvature ◽

Curvature Invariant

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Isotropic exact solutions in $$F(R,Y,\phi )$$ gravity via Noether symmetries

The European Physical Journal C ◽

10.1140/epjc/s10052-021-08917-z ◽

2021 ◽

Vol 81 (2) ◽

Author(s):

Saira Waheed ◽

Iqra Nawazish ◽

M. Zubair

Keyword(s):

Scalar Field ◽

Exact Solutions ◽

Field Potential ◽

Noether Symmetries ◽

Dynamical Equations ◽

Curvature Invariant ◽

Gauge Symmetries ◽

Cosmic Evolution ◽

Fluid Matter ◽

Alpha Beta

AbstractThe present article investigates the existence of Noether and Noether gauge symmetries of flat Friedman–Robertson–Walker universe model with perfect fluid matter ingredients in a generalized scalar field formulation namely $$f(R,Y,\phi )$$ f ( R , Y , ϕ ) gravity, where R is the Ricci scalar and Y denotes the curvature invariant term defined by $$Y=R_{\alpha \beta }R^{\alpha \beta }$$ Y = R α β R α β , while $$\phi $$ ϕ represents scalar field. For this purpose, we assume different general cases of generic $$f(R,Y,\phi )$$ f ( R , Y , ϕ ) function and explore its possible forms along with field potential $$V(\phi )$$ V ( ϕ ) by taking constant and variable coupling function of scalar field $$\omega (\phi )$$ ω ( ϕ ) . In each case, we find non-trivial symmetry generator and its related first integrals of motion (conserved quantities). It is seen that due to complexity of the resulting system of Lagrange dynamical equations, it is difficult to find exact cosmological solutions except for few simple cases. It is found that in each case, the existence of Noether symmetries leads to power law form of scalar field potential and different new types of generic function. For the acquired exact solutions, we discuss the cosmology generated by these solutions graphically and discuss their physical significance which favors the accelerated expanding eras of cosmic evolution.

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Stresses in a Multilayer Thin Film/Substrate System Subjected to Nonuniform Temperature

Journal of Applied Mechanics ◽

10.1115/1.2755178 ◽

2008 ◽

Vol 75 (2) ◽

Cited By ~ 33

Author(s):

X. Feng ◽

Y. Huang ◽

A. J. Rosakis

Keyword(s):

Thin Film ◽

Field Measurements ◽

Film Stress ◽

Effect Of Temperature ◽

Multilayer Thin Film ◽

Nonuniform Temperature ◽

Curvature Invariant ◽

Full Field ◽

Curvature Measurements ◽

Film Substrate

Current methodologies used for the inference of thin film stress through curvature measurements are strictly restricted to uniform film stress and system curvature states over the entire system of a single thin film on a substrate. By considering a circular multilayer thin film/substrate system subjected to nonuniform temperature distributions, we derive relations between the stresses in each film and temperature, and between the system curvatures and temperature. These relations featured a “local” part that involves a direct dependence of the stress or curvature components on the temperature at the same point, and a “nonlocal” part, which reflects the effect of temperature of other points on the location of scrutiny. We also derive relations between the film stresses in each film and the system curvatures, which allow for the experimental inference of such stresses from full-field curvature measurements in the presence of arbitrary nonuniformities. These relations also feature a “nonlocal” dependence on curvatures making full-field measurements of curvature a necessity for the correct inference of stress. The interfacial shear tractions between the films and between the film and substrate are proportional to the gradient of the first curvature invariant, and can also be inferred experimentally.

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