scholarly journals To every rule there is an exception: A rational extension of Loewenstein’s rule

2020 ◽  
Author(s):  
Magnus Fant ◽  
Mattias Ångqvist ◽  
Anders Hellman ◽  
Paul Erhart
Keyword(s):  
Rational Extension

scholarly journals To every rule there is an exception: A rational extension of Loewenstein’s rule

2020 ◽  
Author(s):  
Magnus Fant ◽  
Mattias Ångqvist ◽  
Anders Hellman ◽  
Paul Erhart
Keyword(s):  
Rational Extension

scholarly journals $U$-rational extension of a ring

1976 ◽  
Vol 5 (2) ◽  
pp. 227-231 ◽  
Author(s):  
Kenji NISHIDA
Keyword(s):  
Rational Extension

The Maximal Co-Rational Extension by a Module

1966 ◽  
Vol 18 ◽  
pp. 953-962 ◽  
Author(s):  
R. C. Courter
Keyword(s):  
Projective Module ◽  
Unit Element ◽  
Projective Cover ◽  
Arbitrary Ring ◽  
Rational Extension ◽  
Image Position

Modules are S-modules where S is an arbitrary ring with or without a unit element. We consider a projective module P having a submodule K such that K + Y = P implies that the submodule Y is P (P, then, is a projective cover of P/K (Definition 4 in this section)) and we define the submodule X of P byOur main result states that up to isomorphism P/X is the maximal co-rational extension over P/K (by P/K, in the more precise wording of the title).

Extended Velocity–Enthalpy Relations for Wall-Bounded and Free Shear Layers

2005 ◽  
Vol 127 (6) ◽  
pp. 1205-1209 ◽  
Author(s):  
B. W. van Oudheusden
Keyword(s):  
Shear Flow ◽  
Prandtl Number ◽  
Shear Layers ◽  
Turbulent Shear ◽  
Turbulent Shear Flow ◽  
Total Enthalpy ◽  
Rational Extension ◽  
Free Shear Layers ◽  
Steady Shear Flow ◽  
The Subject

The relation between the velocity and the enthalpy in steady shear flow is expressed by the Crocco–Busemann relation, which states that for adiabatic conditions the total enthalpy remains constant throughout the shear layer when the Prandtl number is one. The subject of the present Technical Brief is the rational extension of this concept in case the Prandtl number differs from one. The comparison between wall-bounded and free shear flows is studied in particular, as well as the possible application of the concept in turbulent shear flow.

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