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Page 7614 of Mathematical Reviews Vol. , Issue 98M [page]

1998 Mathematical Reviews  
It is shown that any weakly self-dual normal basis is a multiple c -. of a self-dual normal basis for some c € F,, i.e. it is a trace orthogonal normal basis.”  ...  Summary: “In this paper weakly self-dual normal bases of the field extension F,» over F, are characterized.  ... 

A New Aspect of Dual Basis for Efficient Field Arithmetic [chapter]

Chang -Hyi Lee, Jong -In Lim
1999 Lecture Notes in Computer Science  
no additional work load as basis changing(from standard to the dual basis or from the dual basis to standard basis as the conventional dual based arithmetic does), (3) the eld squaring is only bit-by-bit  ...  In this manuscript we consider the special type of dual basis for nite elds, GF(2 m ), where the variants of m are presented in the following contents.  ...  basis(or optimal normal basis), where m is the eld extending dimension over GF (2) Note that our dual basis is not a self-dual normal basis 11] .  ... 
doi:10.1007/3-540-49162-7_2 fatcat:as2meng7uzenno3ga32phaa2wy

Looijenga's Conjecture via Integral-affine Geometry [article]

Philip Engel
2018 arXiv   pre-print
A cusp singularity is an elliptic surface singularity whose minimal resolution is a cycle of smooth rational curves meeting transversely. Cusp singularities come in naturally dual pairs.  ...  This paper provides an alternative proof of Looijenga's conjecture based on a combinatorial criterion for smoothability given by Friedman and Miranda in 1983.  ...  Because i S has no boundary, we immediately triangulate it into basis triangles, and construct the simple normal crossings surface i X 0 whose dual complex is i S.  ... 
arXiv:1409.7676v2 fatcat:ls5katy3fja3hjffqzwiardg6q

CURVATURE STRUCTURE OF SELF-DUAL 4-MANIFOLDS

NOVICA BLAŽIĆ, PETER GILKEY, STANA NIKČEVIĆ, IVA STAVROV
2008 International Journal of Geometric Methods in Modern Physics (IJGMMP)  
We obtain a new characterization of the Weyl curvature tensor of an (anti-)self-dual manifold and we prove some new results regarding (Jordan) Osserman manifolds.  ...  We then apply this algebraic result to certain classes of pseudo-Riemannian manifolds of signature (2,2).  ...  A 4-dimensional oriented pseudo-Riemannian manifold is conformally Osserman if and only if it is self-dual or anti-self-dual.  ... 
doi:10.1142/s0219887808003259 fatcat:jyoboi2xm5f3xd3syjooj4ibt4

Machine Reading Comprehension Framework Based on Self-training for Domain Adaptation

Hyeon-gu Lee, Youngjin Jang, Harksoo Kim
2021 IEEE Access  
Hence, we propose a self-training framework for MRC. The proposed framework is composed of a pseudo-answer extractor, a pseudo-question generator, and an MRC system.  ...  During the mutual self-training, the pseudo-question generator provides new training data to the MRC system and obtains rewards from the MRC system for reinforcement learning.  ...  R-Net [3] first used self-attention to analyze the relationships between words in a certain context. These two models have been used as the basis for many early MRC studies.  ... 
doi:10.1109/access.2021.3054912 fatcat:5vjfedeqdncy5komjdm5oik6ta

Polynomial extensions of skew fields

Jan Treur
1990 Journal of Pure and Applied Algebra  
An extension L/K of skew fields is called a leftpolynomialextension with polynomial generator 0 if it has a left basis of the form 1, i3, ti', 0022-4049/90/$03.50 0 1990 -Elsevier Science Publishers B.V  ...  In fact, the standard construction of dual extensions as given in [lo, Appendix] provides such one. This implies that the notion of a polynomial extension is self-dual in some weak sense.  ...  A normalizing element of L/K is an element 0~ L* such that 8-'K6'= K; a normalizing basis is a basis that consists of normalizing elements. K(B) -+ K(q).  ... 
doi:10.1016/0022-4049(90)90164-d fatcat:77fc3pgu3zhmfm5gmsxads7u2u

Page 404 of Mathematical Reviews Vol. 39, Issue 2 [page]

1970 Mathematical Reviews  
One says that g, is involutive if there exists a basis ¢,, ---, t, of T (the dual of 7'*) which is quasi-regular for g,.  ...  proofs of certain identities, construction of an infinitely differentiable non-analytic function, expansions using the Haar and Walsh ortho- normal systems, and asymptotic formulae for Stirling numbers  ... 

Anti-Self-Dual Conformal Structures in Neutral Signature [article]

Maciej Dunajski, Simon West
2010 arXiv   pre-print
We review the subject of four dimensional anti-self-dual conformal structures with signature (+ + - -). Both local and global questions are discussed.  ...  Some of the results - e.g. the Lax pair characterisation of the scalar-flat Kahler condition and a twistor construction of a conformal structure with twisting null Killing vector - are new.  ...  For instance, any Riemannian anti-self-dual conformal structure must be analytic by the twistor construction.  ... 
arXiv:math/0610280v5 fatcat:253xdmdro5fglpnhngxfdq2jhm

Non-Crossing Frameworks with Non-Crossing Reciprocals

David Orden, G�nter Rote, Francisco Santos, Brigitte Servatius, Herman Servatius, Walter Whiteley
2004 Discrete & Computational Geometry  
We study non-crossing frameworks in the plane for which the classical reciprocal on the dual graph is also non-crossing.  ...  For a singular (i.e., non-generic) pseudo-triangulation embedding of a planar Laman circuit, the reciprocal is still non-crossing and a pseudo-triangulation, but its underlying graph may not be a Laman  ...  The normals to these tangent planes track the reciprocal polygon, with a reciprocal vertex for the normal to each of the faces.  ... 
doi:10.1007/s00454-004-1139-x fatcat:che6rcal2jdyxjwbwuwnsfbh7q

Page 386 of Mathematical Reviews Vol. , Issue 80A [page]

1980 Mathematical Reviews  
Each of these may be either self-dual or anti-self- dual, and when one of these cases occurs, a corresponding part of the curvature vanishes.  ...  The four cases correspond to an Einstein space, or a space in which either the totally self-dual or the totally anti-self-dual part of the curvature vanishes.  ... 

Exact description of coalescing eigenstates in open quantum systems in terms of microscopic Hamiltonian dynamics

Kazuki Kanki, Savannah Garmon, Satoshi Tanaka, Tomio Petrosky
2017 Journal of Mathematical Physics  
Our method relies on the Brillouin-Wigner-Feshbach projection method according to which we can obtain a finite dimensional effective Hamiltonian that shares the discrete sector of the spectrum with the  ...  for which it is straightforward to obtain the Jordan form.  ...  on the basis of the Brillouin-Wigner-Feshbach formalism how to construct the Jordan basis.  ... 
doi:10.1063/1.5002689 fatcat:zdgbjpufmvfvfjz4lwfhkuzklu

Constructing an explicit AdS/CFT correspondence with Cartan geometry

Jeffrey S. Hazboun
2018 Nuclear Physics B  
An explicit AdS/CFT correspondence is shown for the Lie group SO(4,2). The Lie symmetry structures allow for the construction of two physical theories through the tools of Cartan geometry.  ...  These "extra" four dimensions have the degrees of freedom used to construct a Yang-Mills theory.  ...  I would also like to thank Derek Wise for a private communication concerning Cartan curvatures and Charles Torre for discussions about gravitational instantons.  ... 
doi:10.1016/j.nuclphysb.2018.02.006 fatcat:fbwnuhvunzcsznsn3perfyqp44

Einstein gravity in almost Kähler and Lagrange–Finsler variables and deformation quantization

Sergiu I. Vacaru
2010 Journal of Geometry and Physics  
A geometric procedure is elaborated for transforming (pseudo) Riemanian metrics and connections into canonical geometric objects (metric and nonlinear and linear connections) for effective Lagrange, or  ...  a quantum model of Einstein manifolds.  ...  Acknowledgement: The work is performed during a visit at Fields Institute. The author is very obliged to C. Castro Perelman for reading the manuscript and valuable discussions.  ... 
doi:10.1016/j.geomphys.2010.05.001 fatcat:digmkwlohvfwtgeeasei2kytfe

Prediction of Protein Structure Classes with Pseudo Amino Acid Composition and Fuzzy Support Vector Machine Network

Yong-Sheng Ding, Tong-Liang Zhang, Kuo-Chen Chou
2007 Protein Peptide Letters  
Based on such a framework, a dual-layer fuzzy support vector machine (FSVM) network is proposed to predict protein structural classes.  ...  It is a critical challenge to develop automated methods for fast and accurately determining the structures of proteins because of the increasingly widening gap between the number of sequence-known proteins  ...  ACKNOWLEDGEMENTS This work was supported in part by Program for New Century Excellent Talents  ... 
doi:10.2174/092986607781483778 pmid:17979824 fatcat:h7p26rwc55es7k4jeg4nuc7zly

An efficient procedure for the development of optimized Projector Augmented Wave basis functions [article]

R. J. Snow and A. F. Wright and C. Y. Fong
2010 arXiv   pre-print
In the Projector Augmented Wave (PAW) method, a local potential, basis functions, and projector functions form an All-Electron (AE) basis for valence wave functions in the application of Density Functional  ...  We have developed a procedure that improves the ease and efficiency of construction of PAW basis sets.  ...  Sandia is a multiprogram laboratory operated by Sandia Corporation, a Lockheed Martin Company, for the United States Department of Energy's National Nuclear Security Administration under Contract No.  ... 
arXiv:1008.0681v1 fatcat:mplvfzleyrdijleg5rntbmfn6m
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