Displaying similar documents to “Some Numerical Invariants of Multilinear Identities”

The determinant of oriented rotants

Adam H. Piwocki (2007)

Colloquium Mathematicae

Similarity:

We study the determinant of pairs of rotants of Anstee, Przytycki and Rolfsen. We consider various notions of rotant orientations.

Algebras, Dialgebras, and Polynomial Identities

R. Bremner, Murray (2012)

Serdica Mathematical Journal

Similarity:

2010 Mathematics Subject Classification: Primary 17A30. Secondary 16R10, 17-08, 17A32, This is a survey of some recent developments in the theory of associative and nonassociative dialgebras, with an emphasis on polynomial identities and multilinear operations. We discuss associative, Lie, Jordan, and alternative algebras, and the corresponding dialgebras; the KP algorithm for converting identities for algebras into identities for dialgebras; the BSO algorithm for converting...

Combinatorial Nullstellensatz approach to polynomial expansion

Fedor Petrov (2014)

Acta Arithmetica

Similarity:

Applying techniques similar to Combinatorial Nullstellensatz we prove a lower estimate of |f(A,B)| for finite subsets A, B of a field, and a polynomial f(x,y) of the form f(x,y) = g(x) + yh(x), where the degree of g is greater than that of h.

An analytical approach to Cayley-Hamilton theorem

Luiz C. Martins (1987)

Atti della Accademia Nazionale dei Lincei. Classe di Scienze Fisiche, Matematiche e Naturali. Rendiconti Lincei. Matematica e Applicazioni

Similarity:

Cayley-Hamilton theorem is proved by an analytical approach by recalling certain interesting properties of density. In this process, the classical expressions of the principal invariants follow immediately from the proposed proof's scheme.

q-Leibniz Algebras

Dzhumadil'daev, A. S. (2008)

Serdica Mathematical Journal

Similarity:

2000 Mathematics Subject Classification: Primary 17A32, Secondary 17D25. An algebra (A,ο) is called Leibniz if aο(bοc) = (a ο b)ο c-(a ο c) ο b for all a,b,c ∈ A. We study identities for the algebras A(q) = (A,οq), where a οq b = a ο b+q b ο a is the q-commutator. Let Char K ≠ 2,3. We show that the class of q-Leibniz algebras is defined by one identity of degree 3 if q2 ≠ 1, q ≠−2, by two identities of degree 3 if q = −2, and by the commutativity identity and one identity...

Factorizations related to some numerical triangles

Helmut Prodinger (2017)

Special Matrices

Similarity:

An asymmetric combinatorial matrix with two free parameters is factored in 4 different ways. The results are obtained by a combination of guessing and applying combinatorial identities.

An analytical approach to Cayley-Hamilton theorem

Luiz C. Martins (1987)

Atti della Accademia Nazionale dei Lincei. Classe di Scienze Fisiche, Matematiche e Naturali. Rendiconti

Similarity:

Cayley-Hamilton theorem is proved by an analytical approach by recalling certain interesting properties of density. In this process, the classical expressions of the principal invariants follow immediately from the proposed proof's scheme.

Maps preserving numerical radius distance on C*-algebras

Zhaofang Bai, Jinchuan Hou, Zongben Xu (2004)

Studia Mathematica

Similarity:

We characterize surjective nonlinear maps Φ between unital C*-algebras 𝒜 and ℬ that satisfy w(Φ(A)-Φ(B))) = w(A-B) for all A,B ∈ 𝒜 under a mild condition that Φ(I) - Φ(0) belongs to the center of ℬ, where w(A) is the numerical radius of A and I is the unit of 𝒜.

Free Bicommutative Algebras

Dzhumadil'daev, A. S., Ismailov, N. A., Tulenbaev, K. M. (2011)

Serdica Mathematical Journal

Similarity:

2000 Mathematics Subject Classification: Primary 17A50, Secondary 16R10, 17A30, 17D25, 17C50. Algebras with identities a(bc)=b(ac), (ab)c=(ac)b is called bicommutative. Bases and the cocharacter sequence for free bicommutative algebras are found. It is shown that the exponent of the variety of bicommutaive algebras is equal to 2.

Numerical index with respect to an operator

Mohammad Ali Ardalani (2014)

Studia Mathematica

Similarity:

We introduce new concepts of numerical range and numerical radius of one operator with respect to another one, which generalize in a natural way the known concepts of numerical range and numerical radius. We study basic properties of these new concepts and present some examples.

Numerical integration in the Trefftz finite element method

Rozehnalová, Petra

Similarity:

Using the high order Trefftz finite element method for solving partial differential equation requires numerical integration of oscillating functions. This integration could be performed, instead of classic techniques, also by the Levin method with some modifications. This paper shortly describes both the Trefftz method and the Levin method with its modification.

Central A-polynomials for the Grassmann Algebra

Pereira Brandão Jr., Antônio, José Gonçalves, Dimas (2012)

Serdica Mathematical Journal

Similarity:

2010 Mathematics Subject Classification: 16R10, 16R40, 16R50. Let F be an algebraically closed field of characteristic 0, and let G be the infinite dimensional Grassmann (or exterior) algebra over F. In 2003 A. Henke and A. Regev started the study of the A-identities. They described the A-codimensions of G and conjectured a finite generating set of the A-identities for G. In 2008 D. Gonçalves and P. Koshlukov answered in the affirmative their conjecture. In this paper we...

Remarks on inverse of matrix polynomials

Fischer, Cyril, Náprstek, Jiří

Similarity:

Analysis of a non-classically damped engineering structure, which is subjected to an external excitation, leads to the solution of a system of second order ordinary differential equations. Although there exists a large variety of powerful numerical methods to accomplish this task, in some cases it is convenient to formulate the explicit inversion of the respective quadratic fundamental system. The presented contribution uses and extends concepts in matrix polynomial theory and proposes...