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Grimus, W.; Ecker, G.

Vienna Univ. (Austria). Inst. fuer Theoretische Physik

Vienna Univ. (Austria). Inst. fuer Theoretische Physik

AbstractAbstract

[en] We prove two theorems on the simultaneous diagonalizability of a set of complex square matrices by a biunitary transformation. (Author)

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1986; 4 p

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Mahdavi-Hezavehi, M.

International Centre for Theoretical Physics, Trieste (Italy)

International Centre for Theoretical Physics, Trieste (Italy)

AbstractAbstract

[en] Matrix orderings on rings are investigated. It is shown that in the commutative case they are essentially positive cones. This is proved by reducing it to the field case; similarly one can show that on a skew field, matrix positive cones can be reduced to positive cones by using the Dieudonne determinant. Our main result shows that there is a natural bijection between the matrix positive cones on a ring R and the ordered epic R-fields. (author). 7 refs

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Aug 1990; 8 p

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Abbasi, S.J.

International Centre for Theoretical Physics, Trieste (Italy)

International Centre for Theoretical Physics, Trieste (Italy)

AbstractAbstract

[en] This paper was motivated by the question: Does, like the ring case, the process of taking Jacobson Radicals and constructing matrix near rings coincide? We present here, for the class of weakly distributive d.g. near rings, a conditionally affirmative answer to this question. Our main result is as follows: Let R be a weakly distributive d.g. near ring with identity. If J(R) is contained δ

_{1}M_{n}(R), the derived group of M_{n}(R), then J(R)=J(M_{n}(R)) where I-bar is defined as a subnear ring of M_{n}(R) generated by {f^{a}_{ij}; a is an element of I, 1 ≤ i, j ≤ n}. (author). 6 refsPrimary Subject

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Jan 1994; 5 p

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Khan, M.A.

International Centre for Theoretical Physics, Trieste (Italy)

International Centre for Theoretical Physics, Trieste (Italy)

AbstractAbstract

[en] We study the commutativity of certain class of rings, namely rings with unity 1 and right s-unital rings under each of the following properties [yx

^{m}- x^{n}f(y)x^{p},x]=0, [yx^{m}+x^{n}f(y)x^{p},x]=0, where f(t) is a polynomial in t^{2}Z[t] varying with pair of ring elements x,y and m,n,p are fixed non-negative integers. Moreover, the results have been extended to the case when m and n depend on the choice of x and y and the ring satisfies the Chacron's Theorem. (author). 14 refsPrimary Subject

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Aug 1994; 5 p

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[en] The Gauss algorithm for diagonalization of constant matrices is modified for application to polynomial matrices. Due to this modification the diagonal elements become pure polynomials rather than rational functions. (author)

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Oct 1982; 11 p

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Zhang, S.Y.

Brookhaven National Lab., Upton, NY (USA)

Brookhaven National Lab., Upton, NY (USA)

AbstractAbstract

[en] In this paper, we present the systematic realizations for general matrix fraction description G = PQ

^{-1}R, and for the matrix fraction PQ^{-1}and Q^{-1}R. The realizations are based on the Kalman-Fuhrmann realization theory and the dual theory. By choosing the proper basis for the state space of the system, the realizations appear to be very simple. The realizations of PQ^{-1}and Q^{-1}R are just in a similar way to the realizations of single-variable systemsPrimary Subject

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1985; 11 p; 23. annual allerton conference on communication, control, and computing; Champaign-Urbana, IL (USA); 3-5 Oct 1985; CONF-8510226--2; Available from NTIS, PC A02/MF A01 as DE86003370

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El Hassouni, A.; Zakkari, M.

International Centre for Theoretical Physics, Trieste (Italy)

International Centre for Theoretical Physics, Trieste (Italy)

AbstractAbstract

[en] A representation of one parameter deformation of U(1)-Kac Moody and Virasoro algebras is obtained through the infinite matrix algebra a-bar

_{∞}. Their central extensions are also investigated. (author). 19 refsPrimary Subject

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Nov 1995; 7 p

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Abbasi, S.J.

International Centre for Theoretical Physics, Trieste (Italy)

International Centre for Theoretical Physics, Trieste (Italy)

AbstractAbstract

[en] It is known that if R is a near ring with identity then (I,+) is abelian if (I

^{+},+) is abelian and (I,+) is abelian if (I*,+) is abelian [S.J. Abbasi, J.D.P. Meldrum, 1991]. This paper extends these results. We show that if R is a distributively generated near ring with identity then (I,+) is included in Z(R), the center of R, if (I^{+},+) is included in Z(M_{n}(R)), the center of matrix near ring M_{n}(R). Furthermore (I,+) is included in Z(R) if (I*,+) is included in Z(M_{n}(R)). (author). 5 refsPrimary Subject

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Apr 1993; 4 p

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Catoni, Francesco; Cannata, Roberto; Nichelatti, Enrico

ENEA, Centro Ricerche Casaccia, Rome (Italy). Dipt. Energia

ENEA, Centro Ricerche Casaccia, Rome (Italy). Dipt. Energia

AbstractAbstract

[en] Systems of hypercomplex numbers, which had been studied and developed at the end of the last century, are nowadays quite unknown to the scientific community. It is believed that study of their applications ended just before one of the fundamental discoveries of our century, Einstein's equivalence between space and time. Owing to this equivalence, not-defined quadratic forms - which are in a quite strong relationship with hypercomplex numbers possessing divisors of the zero - have got concrete physical meaning. The aim of this work is to study these systems of numbers and to describe them in terms of a familiar mathematical tool, i.e. matrix algebra. Moreover, they will show how hypercomplex numbers possessing divisors of the zero candidate themselves to be the most proper mathematical language for treatment of propagative phenomena

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Rappresentazione matriciale dei numeri ipercomplessi e delle funzioni analitiche di variabile ipercomplessa

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Oct 1997; 29 p; ISSN 0393-6317;

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Urbantke, H.

Vienna Univ. (Austria)

Vienna Univ. (Austria)

AbstractAbstract

[en] An overview of the algebra of two-component spinors and of four-component spinors based on abstract linear algebra is given. The role of spinors for the complex Lorentz group and for all of its real forms is worked out. (G.Q.)

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Die Algebra der 2-Komponenten-Spinoren

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1984; 21 p

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