On the Bergman Theory for Solenoidal and Irrotational Vector Fields, I: General Theory

2010 ◽  
pp. 79-106 ◽  
Author(s):  
José Oscar González-Cervantes ◽  
María Elena Luna-Elizarrarás ◽  
Michael Shapiro
Keyword(s):  
General Theory ◽  
Vector Fields

Field Approach for General Relativity

2021 ◽  
Vol 5 (1) ◽  
Author(s):  
Ali Rıza ŞAHİN ◽  
Keyword(s):  
General Relativity ◽  
General Theory ◽  
Vector Fields ◽  
Einstein Equations ◽  
Light Deflection ◽  
Theory Of Relativity ◽  
General Theory Of Relativity ◽  
Metric Tensor ◽  
Perihelion Precession ◽  
Field Approach

The general theory of relativity is based on expressing gravity by means of the metric tensor and its elements instead of some fields as in electrodynamics. This work starts with by defining some vector fields for metric or metric tensor. After metric and metric tensor are expressed in terms of these fields, the geodesic equations and Einstein equations are derived for these fields. Finally, perihelion precession and light deflection are recalculated, as two different applications of the introduced fields.

scholarly journals Multiresolution and wavelets

1994 ◽  
Vol 37 (2) ◽  
pp. 271-300 ◽  
Author(s):  
Rong-Qing Jia ◽  
Zuowei Shen
Keyword(s):  
General Theory ◽  
Vector Fields ◽  
Scaling Function ◽  
Necessary And Sufficient Condition ◽  
Intrinsic Properties ◽  
Orthogonal Wavelets ◽  
Shift Invariant Spaces ◽  
Necessary And Sufficient ◽  
Invariant Spaces ◽  
The Scaling Function

Multiresolution is investigated on the basis of shift-invariant spaces. Given a finitely generated shift-invariant subspace S of L2(ℝd), let Sk be the 2k-dilate of S (k∈ℤ). A necessary and sufficient condition is given for the sequence {Sk}k∈ℤ to fom a multiresolution of L2(ℝd). A general construction of orthogonal wavelets is given, but such wavelets might not have certain desirable properties. With the aid of the general theory of vector fields on spheres, it is demonstrated that the intrinsic properties of the scaling function must be used in constructing orthogonal wavelets with a certain decay rate. When the scaling function is skew-symmetric about some point, orthogonal wavelets and prewavelets are constructed in such a way that they possess certain attractive properties. Several examples are provided to illustrate the general theory.

Extreme self-sacrifice beyond fusion: Moral expansiveness and the special case of allyship

2018 ◽  
Vol 41 ◽  
Author(s):  
Daniel Crimston ◽  
Matthew J. Hornsey
Keyword(s):  
General Theory ◽  
Biological Markers ◽  
Natural Environment ◽  
Relevant Dimension ◽  
Special Case

AbstractAs a general theory of extreme self-sacrifice, Whitehouse's article misses one relevant dimension: people's willingness to fight and die in support of entities not bound by biological markers or ancestral kinship (allyship). We discuss research on moral expansiveness, which highlights individuals’ capacity to self-sacrifice for targets that lie outside traditional in-group markers, including racial out-groups, animals, and the natural environment.

Normal Forms and Bifurcation of Planar Vector Fields

1994 ◽  
Author(s):  
Shui-Nee Chow ◽  
Chengzhi Li ◽  
Duo Wang
Keyword(s):  
Vector Fields ◽  
Normal Forms ◽  
Planar Vector Fields ◽  
Planar Vector

Review of A General Theory of Crime.

1992 ◽  
Vol 37 (11) ◽  
pp. 1225-1225
Author(s):  
No authorship indicated
Keyword(s):  
General Theory ◽  
General Theory Of Crime ◽  
Theory Of Crime
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