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

1999
*
Lecture Notes in Computer Science
*

no additional work load as

doi:10.1007/3-540-49162-7_2
fatcat:as2meng7uzenno3ga32phaa2wy
*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] . ...##
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Looijenga's Conjecture via Integral-affine Geometry
[article]

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. ...

##
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CURVATURE STRUCTURE OF SELF-DUAL 4-MANIFOLDS

2008
*
International Journal of Geometric Methods in Modern Physics (IJGMMP)
*

We obtain

doi:10.1142/s0219887808003259
fatcat:jyoboi2xm5f3xd3syjooj4ibt4
*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*. ...##
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Machine Reading Comprehension Framework Based on Self-training for Domain Adaptation

2021
*
IEEE Access
*

Hence, we propose

doi:10.1109/access.2021.3054912
fatcat:5vjfedeqdncy5komjdm5oik6ta
*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. ...##
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Polynomial extensions of skew fields

1990
*
Journal of Pure and Applied Algebra
*

An extension L/K of skew fields is called

doi:10.1016/0022-4049(90)90164-d
fatcat:77fc3pgu3zhmfm5gmsxads7u2u
*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). ...##
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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 ...##
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Anti-Self-Dual Conformal Structures in Neutral Signature
[article]

2010
*
arXiv
*
pre-print

We review the subject of four dimensional anti-

arXiv:math/0610280v5
fatcat:253xdmdro5fglpnhngxfdq2jhm
*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*. ...##
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Non-Crossing Frameworks with Non-Crossing Reciprocals

2004
*
Discrete & Computational Geometry
*

We study non-crossing frameworks in the plane

doi:10.1007/s00454-004-1139-x
fatcat:che6rcal2jdyxjwbwuwnsfbh7q
*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. ...##
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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

2017
*
Journal of Mathematical Physics
*

Our

doi:10.1063/1.5002689
fatcat:zdgbjpufmvfvfjz4lwfhkuzklu
*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*. ...##
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Constructing an explicit AdS/CFT correspondence with Cartan geometry

2018
*
Nuclear Physics B
*

An explicit AdS/CFT correspondence is shown

doi:10.1016/j.nuclphysb.2018.02.006
fatcat:fbwnuhvunzcsznsn3perfyqp44
*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. ...##
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Einstein gravity in almost Kähler and Lagrange–Finsler variables and deformation quantization

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. ...

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

2007
*
Protein Peptide Letters
*

Based on such

doi:10.2174/092986607781483778
pmid:17979824
fatcat:h7p26rwc55es7k4jeg4nuc7zly
*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 ...##
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An efficient procedure for the development of optimized Projector Augmented Wave basis functions
[article]

2010
*
arXiv
*
pre-print

In the Projector Augmented Wave (PAW)

arXiv:1008.0681v1
fatcat:mplvfzleyrdijleg5rntbmfn6m
*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. ...
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