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Semisimple and semilocal pseudo BL-algebras

Walendziak A., Wojciechowska M.

Demonstratio Mathematica

2009

Vol. 42, nr 3

453-466

The concepts of semisimple and semilocal pseudo BL-algebras are investigated. Many facts corresponding with them are considerated. Moreover, we give a negative answer to the question from [Di Nola, Georgescu and lorgulescu (Multiplae Valued Logic 8: 715-750, 2002), Problem 1.33].

Sylvester inertia law in commutative Leibniz algebras with logarithms

Przeworska-Rolewicz D.

Demonstratio Mathematica

2007

Vol. 40, nr 3

659-669

In algebras with logarithms induced by a given right invertible operator D one can define quadratic forms by means of power mappings induced by logarithmic mapping. Main results of this paper will be concerned with the case when an algebra X under consideration is commutative and has a unit and the operator D satisfies the Leibniz condition, i.e. D(xy) = xDy+yDx for x, y is an element of dom D. If X is an locally m-convex algebra then these forms have the similar properties as quadratic forms in the Euclidian spaces En, including the Sylvester inertia law.

A Functorial Approach to the Behaviour of Multidimensional Control Systems

Pommaret J. F., Quadrat A.

International Journal of Applied Mathematics and Computer Science

2003

Vol. 13, no 1

7-13

We show how to use the extension and torsion functors in order to compute the torsion submodule of a differential module associated with a multidimensional control system. In particular, we show that the concept of the weak primeness of matrices corresponds to the torsion-freeness of a certain module.

An algebraic analysis approach to 2-D discrete problems

Przeworska-Rolewicz D., Wysocki H.

Control and Cybernetics

2001

Vol. 30, no 2

149-158

A model of algebraic analysis for the 2-index sequences (of the type 2-D) is considered. For difference operators of the form D{x_m,n}:= {x_m+1,n+1 - A_m,nX_m,n} the right inverses and the corresponding initial operators are constructed. Having already known the initial operators, one can determine solutions of the corresponding initial value problems.