Section 5. A Cancellation Theorem

1965 ◽  
pp. 45-66
Keyword(s):  
Cancellation Theorem

A global two-dimensional version of Smale’s cancellation theorem via spectral sequences

2015 ◽  
Vol 36 (6) ◽  
pp. 1795-1838 ◽  
Author(s):  
M. A. BERTOLIM ◽  
D. V. S. LIMA ◽  
M. P. MELLO ◽  
K. A. DE REZENDE ◽  
M. R. DA SILVEIRA
Keyword(s):  
Sequence Analysis ◽  
Spectral Sequence ◽  
Matrix Theory ◽  
Chain Complex ◽  
Connection Matrix ◽  
Local Version ◽  
Two Dimensional ◽  
Dimensional Version ◽  
Cancellation Theorem ◽  
Flows On Surfaces

In this article, Conley’s connection matrix theory and a spectral sequence analysis of a filtered Morse chain complex $(C,{\rm\Delta})$ are used to study global continuation results for flows on surfaces. The briefly described unfoldings of Lyapunov graphs have been proved to be a well-suited combinatorial tool to keep track of continuations. The novelty herein is a global dynamical cancellation theorem inferred from the differentials of the spectral sequence $(E^{r},d^{r})$. The local version of this theorem relates differentials $d^{r}$ of the $r$th page $E^{r}$ to Smale’s theorem on cancellation of critical points.

Effective Interatomic Interactions VIA The TB-LMTO Method

1997 ◽  
Vol 491 ◽  
Author(s):  
V. Drchal ◽  
J. Kudrnovský ◽  
A. Pasturel ◽  
I. Turek ◽  
P. Weinberger ◽  
...  
Keyword(s):  
Surface Segregation ◽  
Three Dimensional ◽  
Magnetic Multilayers ◽  
Theoretical Background ◽  
Interlayer Exchange Coupling ◽  
Metallic Multilayers ◽  
Disordered Alloys ◽  
Lmto Method ◽  
Cancellation Theorem ◽  
Interlayer Exchange

ABSTRACTThe energetics of metallic alloys, their surfaces or interfaces, and magnetic multilayers is studied in terms of effective interatomic (or interlayer) interactions that are determined from ab initio electronic structure calculations using the TB-LMTO method combined with the coherent potential approximation and the method of surface Green functions. First the theoretical background (force theorem, Lloyd formula, generalized perturbation method for bulk and surfaces, vertex cancellation theorem, method of infinitesimal rotations) is discussed, and then the applications to the phase stability of bulk alloys, surface segregation in disordered alloys, magnetism-induced ordering in two- and three-dimensional systems, phase diagram of two-dimensional alloys, interlayer exchange coupling in metallic multilayers, and the construction of Heisenberg-like Hamiltonians for magnetic systems are presented.

scholarly journals Quadratic pairs in characteristic2and the Witt cancellation theorem

2003 ◽  
Vol 2003 (70) ◽  
pp. 4389-4397 ◽  
Author(s):  
Mohamed Abdou Elomary
Keyword(s):  
Cancellation Theorem

We define the orthogonal sum of quadratic pairs and we show that there is no Witt cancellation theorem for this operation in characteristic2.

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