The Fundamental Equations of Electrodynamics.

1988 ◽  
Vol 1 (3) ◽  
pp. 171-175
Author(s):  
D. E. McLennan
Keyword(s):  
Equations Of Electrodynamics ◽  
Fundamental Equations

On submersions of the complex indicatrix

Filomat ◽  
2017 ◽  
Vol 31 (16) ◽  
pp. 5081-5092
Author(s):  
Elena Popovicia
Keyword(s):  
Fixed Point ◽  
Complex Projective Space ◽  
Finsler Space ◽  
Hermitian Manifold ◽  
Almost Hermitian Manifold ◽  
Codimension One ◽  
Real Submanifold ◽  
Fundamental Equations ◽  
Complex Projective ◽  
Extrinsic Sphere

In this paper we study the complex indicatrix associated to a complex Finsler space as an embedded CR - hypersurface of the holomorphic tangent bundle, considered in a fixed point. Following the study of CR - submanifolds of a K?hler manifold, there are investigated some properties of the complex indicatrix as a real submanifold of codimension one, using the submanifold formulae and the fundamental equations. As a result, the complex indicatrix is an extrinsic sphere of the holomorphic tangent space in each fibre of a complex Finsler bundle. Also, submersions from the complex indicatrix onto an almost Hermitian manifold and some properties that can occur on them are studied. As application, an explicit submersion onto the complex projective space is provided.

Stresses in a Metal Tube Under Both High Radial Temperature Variation and Internal Pressure

1954 ◽  
Vol 21 (2) ◽  
pp. 101-108
Author(s):  
Chieh-Chien Chang ◽  
Wen-Hwa Chu
Keyword(s):  
Stress Distribution ◽  
Temperature Variation ◽  
Modulus Of Elasticity ◽  
Coefficient Of Thermal Expansion ◽  
Metal Tube ◽  
Radial Temperature ◽  
Variation Of Parameters ◽  
Effects Of Temperature ◽  
Fundamental Equations ◽  
Very High

Abstract The paper treats the stress distribution in a metal tube which is subject to a very high radial temperature variation and pressure. The radial temperature distribution across the tube wall and the variations of the modulus of elasticity and the coefficient of thermal expansion are obtained from experimental data, and all these effects of temperature are taken into account in the calculations. The fundamental equations in the case of plane strain and plane stress can be formulated as the nonhomogeneous Whittaker differential equations. The corresponding solutions are obtained by the method of variation of parameters and in terms of Kummer series. An example is shown, and the stress distribution across the wall is given. For comparison, the stress distribution of the case of constant modulus of elasticity and coefficient of expansion is included.

Local Scale Covariance and Its Radical Implications for Cosmology

Galaxies ◽  
2021 ◽  
Vol 9 (4) ◽  
pp. 76
Author(s):  
Yehonatan Knoll
Keyword(s):  
Local Scale ◽  
Covariant Theory ◽  
De Sitter ◽  
Cosmological Redshift ◽  
Physical Limit ◽  
Scale Covariance ◽  
The Status ◽  
Scale Motion ◽  
Fundamental Equations ◽  
Conceptual Foundations

Local scale covariance posits that no privileged length scales should appear in the fundamental equations of local, Minkowskian physics—why should nature have scale, but not position preferences?—yet, they clearly do. A resolution is proposed wherein scale covariance is promoted to the status of Poincaré covariance, and privileged scales emerge as a result of `scale clustering’, similarly to the way privileged positions emerge in a translation covariant theory. The implied ability of particles to `move in scale’ has recently been shown by the author to offer a possible elegant solution to the missing matter problem. For cosmology, the implications are: (a) a novel component of the cosmological redshift, due to scale-motion over cosmological times; (b) a radically different scenario for the early universe, during which the conditions for such scale clustering are absent. The former is quantitatively analyzed, resulting in a unique cosmological model, empirically coinciding with standard Einstein–de-Sitter cosmology, only in some non-physical limit. The latter implication is qualitatively discussed as part of a critique of the conceptual foundations of ΛCDM which ignores scale covariance altogether.

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