Special linear PA circuit considerations for ET

2015 ◽  
pp. 187-223
Author(s):  
Earl McCune
Keyword(s):  
Special Linear

scholarly journals Irreducible modules with highest weight vectors over modular Witt and special Lie superalgebras

2019 ◽  
Vol 17 (1) ◽  
pp. 1381-1391
Author(s):  
Keli Zheng ◽  
Yongzheng Zhang
Keyword(s):  
Lie Superalgebras ◽  
Arbitrary Field ◽  
Special Linear ◽  
Highest Weight ◽  
Irreducible Modules

Abstract Let 𝔽 be an arbitrary field of characteristic p > 2. In this paper we study irreducible modules with highest weight vectors over Witt and special Lie superalgebras of 𝔽. The same irreducible modules of general and special linear Lie superalgebras, which are the 0-th part of Witt and special Lie superalgebras in certain ℤ-grading, are also considered. Then we establish a certain connection called a P-expansion between these modules.

(ANTI)COMMUTATIVITY OF THE HARMONIC CREATION AND ANNIHILATION OPERATORS

2006 ◽  
Vol 20 (11n13) ◽  
pp. 1808-1818
Author(s):  
S. KUWATA ◽  
A. MARUMOTO
Keyword(s):  
Irreducible Representation ◽  
Harmonic Oscillator ◽  
Linear Algebra ◽  
Commutation Relation ◽  
Complex Number ◽  
Single Mode ◽  
Equation Of Motion ◽  
Sufficient Condition ◽  
Special Linear ◽  
Creation And Annihilation Operators

It is known that para-particles, together with fermions and bosons, of a single mode can be described as an irreducible representation of the Lie (super) algebra 𝔰𝔩2(ℂ) (2-dimensional special linear algebra over the complex number ℂ), that is, they satisfy the equation of motion of a harmonic oscillator. Under the equation of motion of a harmonic oscillator, we obtain the set of the commutation relations which is isomorphic to the irreducible representation, to find that the equation of motion, conversely, can be derived from the commutation relation only for the case of either fermion or boson. If Nature admits of the existence of such a sufficient condition for the equation of motion of a harmonic oscillator, no para-particle can be allowed.

scholarly journals Invariants of Surface Indicatrix in a Special Linear Transformation

2019 ◽  
Vol 7 (4) ◽  
pp. 106-115
Author(s):  
A. Artykbaev ◽  
B. M. Sultanov
Keyword(s):  
Linear Transformation ◽  
Special Linear

scholarly journals Link theorem and distributions of solutions to uncertain Liouville-Caputo difference equations

2021 ◽  
Vol 0 (0) ◽  
pp. 0
Author(s):  
Hari Mohan Srivastava ◽  
Pshtiwan Othman Mohammed ◽  
Juan L. G. Guirao ◽  
Y. S. Hamed
Keyword(s):  
Uniqueness Theorem ◽  
Difference Equations ◽  
Special Linear ◽  
Uncertain Variables ◽  
Important Theorem ◽  
Special Case ◽  
The Uniqueness Theorem

<p style='text-indent:20px;'>We consider a class of initial fractional Liouville-Caputo difference equations (IFLCDEs) and its corresponding initial uncertain fractional Liouville-Caputo difference equations (IUFLCDEs). Next, we make comparisons between two unique solutions of the IFLCDEs by deriving an important theorem, namely the main theorem. Besides, we make comparisons between IUFLCDEs and their <inline-formula><tex-math id="M1">\begin{document}$ \varrho $\end{document}</tex-math></inline-formula>-paths by deriving another important theorem, namely the link theorem, which is obtained by the help of the main theorem. We consider a special case of the IUFLCDEs and its solution involving the discrete Mittag-Leffler. Also, we present the solution of its <inline-formula><tex-math id="M2">\begin{document}$ \varrho $\end{document}</tex-math></inline-formula>-paths via the solution of the special linear IUFLCDE. Furthermore, we derive the uniqueness of IUFLCDEs. Finally, we present some test examples of IUFLCDEs by using the uniqueness theorem and the link theorem to find a relation between the solutions for the IUFLCDEs of symmetrical uncertain variables and their <inline-formula><tex-math id="M3">\begin{document}$ \varrho $\end{document}</tex-math></inline-formula>-paths.</p>

scholarly journals O Ensino de Álgebra Linear para Engenharias utilizando o Scilab: aspectos matemáticos e computacionais / Teaching of Linear Algebra to Engineering Students using Scilab: mathematical and computational aspects

2017 ◽  
Vol 6 (1) ◽  
Author(s):  
Marcos Rodrigues Pinto
Keyword(s):  
Equilibrium Point ◽  
Linear Algebra ◽  
Learning Process ◽  
Engineering Students ◽  
Algebraic Thinking ◽  
The Other ◽  
Personal Computers ◽  
Special Linear ◽  
Computational Aspects ◽  
Teaching Learning

ABSTRACTThe teaching of Algebra, in special Linear Algebra, to engineering students, come changing its focus since the popularization of personal computers. Various specialized softwares has been developed and has become feasible to pay more attention in the algebraic thinking to solve problems and minus attention in the calculus itself. But one needs to be careful to not go to the extreme of this teaching-learning process. The teaching of Algebra using computational software must not mean the teaching of a sequence of commands and its syntaxes. On the other hand, it must not mean to memorize a sequence of definitions and theorems. So we propose a equilibrium point based on our experience with students of engineering that attended in our lessons of Algebra with Scilab software.RESUMOO ensino de álgebra, especialmente álgebra linear (AL), para estudantes de engenharia, vem mudando seu foco desde a populariozação dos computadores pessoais. Diversos softwares especializados têm sido desenvolvidos e tornado possível prestar mais atenção ao pensamento algébrico para a solução de problemas do que ao cálculo em si. Mas é necessário ter-se cuidado para não ocupar os extremos nesse processo de ensino-aprendizagem. O ensino de álgebra usando softwares não deve significar ensinar uma sequência de comandos e suas sintaxes. Também não deve significar memorizar uma sequência de definições e teoremas. Assim, propõe-se um ponto de equilíbrio baseado na experiência com estudantes de engenharia que participaram das aulas de AL utilizando o Scilab.

Some homomorphisms of general and special linear groups

1986 ◽  
Vol 103 (3-4) ◽  
pp. 287-291
Author(s):  
A. W. Mason
Keyword(s):  
Linear Groups ◽  
Special Linear ◽  
Special Linear Groups ◽  
Natural Way

SynopsisA ring epimorphism θ:A →B extends in a natural way to a homomorphism γn: GLn(A)→GLn(B) and, when A is commutative, to a homomorphism σn:SLn(A)→SLn(B), where n ≧ 1. In this paper we consider the question: when are γn and σn surjective (or non-surjective)?

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