scholarly journals Invariants in Separated Variables: Yang-Baxter, Entwining and Transfer Maps

2019 ◽  
Author(s):  
Pavlos Kassotakis ◽  
Keyword(s):  
Transfer Maps ◽  
Separated Variables

scholarly journals Dual separated variables and scalar products

2020 ◽  
Vol 806 ◽  
pp. 135494 ◽  
Author(s):  
Nikolay Gromov ◽  
Fedor Levkovich-Maslyuk ◽  
Paul Ryan ◽  
Dmytro Volin
Keyword(s):  
Scalar Products ◽  
Separated Variables

scholarly journals Integrable Derivations and Stable Equivalences of Morita Type

2018 ◽  
Vol 61 (2) ◽  
pp. 343-362 ◽  
Author(s):  
Markus Linckelmann
Keyword(s):  
Hochschild Cohomology ◽  
Block Theory ◽  
Discrete Valuation Rings ◽  
Symmetric Algebras ◽  
Valuation Rings ◽  
Transfer Maps ◽  
Stable Equivalences ◽  
Morita Type

AbstractUsing that integrable derivations of symmetric algebras can be interpreted in terms of Bockstein homomorphisms in Hochschild cohomology, we show that integrable derivations are invariant under the transfer maps in Hochschild cohomology of symmetric algebras induced by stable equivalences of Morita type. With applications in block theory in mind, we allow complete discrete valuation rings of unequal characteristic.

Elastodynamic Local Fields for a Crack Running in an Orthotopic Medium

1991 ◽  
Vol 58 (4) ◽  
pp. 982-987 ◽  
Author(s):  
A. Piva ◽  
E. Radi
Keyword(s):  
Dynamic Stress ◽  
Equations Of Motion ◽  
Local Fields ◽  
Stress Fields ◽  
Orthotropic Materials ◽  
Displacement Fields ◽  
First Order ◽  
Stress And Displacement Fields ◽  
Order Elliptic System ◽  
Separated Variables

The dynamic stress and displacement fields in the neighborhood of the tip of a crack propagating in an orthotropic medium are obtained. The approach deals with the methods of linear algebra to transform the equations of motion into a first-order elliptic system whose solution is sought under the assumption that the local displacement field may be represented under a scheme of separated variables. The analytical approach has enabled the distinction between two kinds of orthotropic materials for which explicit espressions of the near-tip stress fields are obtained. Some results are presented graphically also in order to compare them with the numerical solution given in a quoted reference.

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