scholarly journals Skew-field of trace-preserving endomorphisms, of translation group in affine plane

2020 ◽  
Vol 39 (4) ◽  
pp. 835-850
Author(s):  
Orgest Zaka ◽  
Mohanad A. Mohammed
Keyword(s):  
Affine Plane ◽  
Translation Group ◽  
Skew Field

Is L2 vocabulary learned better via context or via translation?

2018 ◽  
Vol 2 (1) ◽  
pp. 39-60
Author(s):  
Michael John Alroe ◽  
Heyo Reinders ◽  
Punchalee Wasanasomsithi
Keyword(s):  
Incidental Learning ◽  
Intentional Learning ◽  
Time On Task ◽  
Translation Group ◽  
Gap Filling ◽  
Freshmen Students ◽  
Context Group ◽  
Comprehensible Input ◽  
Post Test ◽  
L2 Vocabulary

Various studies have shown intentional learning of L2 vocabulary to be more efficient than incidental learning from exposure to comprehensible input. Some have argued that such learning may be further enhanced by recourse to L1 translation, particularly for weaker learners. The present study aims to determine if intentional learning of new vocabulary through L1 does indeed confer an advantage over intentional learning from an L2 context. To this end, 403 Thai freshmen students were pre-tested on thirty vocabulary items set for study on their English course. They were then randomly allocated to either a translation or context group to learn those items. Time on task was controlled. A delayed post-test showed that while the translation group was better at matching the thirty English words with Thai translations, albeit marginally so, there was no benefit conferred on the translation group when it came to using the words in a contextual gap-filling exercise. This finding held for both advanced and weaker learners.

scholarly journals A necessary and sufficient condition for simultaneous diagonalization of two hermitian matrices and its application

1970 ◽  
Vol 11 (1) ◽  
pp. 81-83 ◽  
Author(s):  
Yik-Hoi Au-Yeung
Keyword(s):  
Complex Numbers ◽  
Single Element ◽  
Singular Matrix ◽  
Necessary And Sufficient Condition ◽  
Simultaneous Diagonalization ◽  
Hermitian Matrices ◽  
Skew Field ◽  
Conjugate Transpose ◽  
Necessary And Sufficient ◽  
Real Quaternions

We denote by F the field R of real numbers, the field C of complex numbers, or the skew field H of real quaternions, and by Fn an n dimensional left vector space over F. If A is a matrix with elements in F, we denote by A* its conjugate transpose. In all three cases of F, an n × n matrix A is said to be hermitian if A = A*, and we say that two n × n hermitian matrices A and B with elements in F can be diagonalized simultaneously if there exists a non singular matrix U with elements in F such that UAU* and UBU* are diagonal matrices. We shall regard a vector u ∈ Fn as a l × n matrix and identify a 1 × 1 matrix with its single element, and we shall denote by diag {A1, …, Am} a diagonal block matrix with the square matrices A1, …, Am lying on its diagonal.

A METHOD OF DESCRIPTION OF MAGNETIC OSCILLATIONS IN MESOSCOPIC SYSTEMS

1996 ◽  
Vol 10 (27) ◽  
pp. 1333-1338
Author(s):  
STANISLAW WALCERZ
Keyword(s):  
Experimental Investigation ◽  
Magnetic Properties ◽  
Translation Group ◽  
Mesoscopic Systems ◽  
Group Approach ◽  
Proposed Model ◽  
Planar Systems ◽  
Magnetic Translation ◽  
Onsager Theory ◽  
Magnetic Oscillations

A model for calculation of magnetic properties of small planar systems is proposed. The model combines the Onsager theory of de Haas-van Alphen oscillations with the magnetic translation group approach. The proposed model suggests a method for both theoretical and experimental investigation of magnetic properties of mesoscale systems.

On a conjecture of Hughes

1967 ◽  
Vol 63 (3) ◽  
pp. 647-652 ◽  
Author(s):  
Judita Cofman
Keyword(s):  
Projective Plane ◽  
Permutation Group ◽  
Translation Plane ◽  
Collineation Group ◽  
Affine Plane ◽  
Finite Projective Plane ◽  
Transitive Permutation Group ◽  
Condition C

D. R. Hughes stated the following conjecture: If π is a finite projective plane satisfying the condition: (C)π contains a collineation group δ inducing a doubly transitive permutation group δ* on the points of a line g, fixed under δ, then the corresponding affine plane πg is a translation plane.

Bayesian Nash Equilibrium in Electricity Spot Markets: An Affine-Plane Approximation Approach

2021 ◽  
pp. 1-1
Author(s):  
Pranjal Pragya Verma ◽  
Mohammad Hesamzadeh ◽  
Ross Baldick ◽  
Darryl Biggar ◽  
K. Shanti Swarup ◽  
...  
Keyword(s):  
Nash Equilibrium ◽  
Affine Plane ◽  
Spot Markets ◽  
Approximation Approach ◽  
Bayesian Nash Equilibrium ◽  
Electricity Spot Markets

Mathematical aspects of molecular replacement. IV. Measure-theoretic decompositions of motion spaces

2017 ◽  
Vol 73 (5) ◽  
pp. 387-402 ◽  
Author(s):  
Gregory S. Chirikjian ◽  
Sajdeh Sajjadi ◽  
Bernard Shiffman ◽  
Steven M. Zucker
Keyword(s):  
General Theory ◽  
Rigid Body ◽  
Three Dimensional ◽  
Molecular Replacement ◽  
Translation Group ◽  
Common Occurrence ◽  
Space Group ◽  
Space Groups ◽  
Relevant Case ◽  
The Subject

In molecular-replacement (MR) searches, spaces of motions are explored for determining the appropriate placement of rigid-body models of macromolecules in crystallographic asymmetric units. The properties of the space of non-redundant motions in an MR search, called a `motion space', are the subject of this series of papers. This paper, the fourth in the series, builds on the others by showing that when the space group of a macromolecular crystal can be decomposed into a product of two space subgroups that share only the lattice translation group, the decomposition of the group provides different decompositions of the corresponding motion spaces. Then an MR search can be implemented by trading off between regions of the translation and rotation subspaces. The results of this paper constrain the allowable shapes and sizes of these subspaces. Special choices result when the space group is decomposed into a product of a normal Bieberbach subgroup and a symmorphic subgroup (which is a common occurrence in the space groups encountered in protein crystallography). Examples of Sohncke space groups are used to illustrate the general theory in the three-dimensional case (which is the relevant case for MR), but the general theory in this paper applies to any dimension.

An example of a skew field without a trace

1989 ◽  
Vol 17 (9) ◽  
pp. 2303-2307 ◽  
Author(s):  
L. Makar-Limanov
Keyword(s):  
Skew Field
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