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A characterization of weakly J(n)-rings

Danchev P. V.

Journal of Mathematics and Applications

2018

Vol. 41

53--61

A ring R is called a J(n)-ring if there exists a natural number n ≥ 1 such that for each element r ∈ R the equality r (n+1) = r holds and a weakly J(n)-ring if there exists a natural number n ≥ 1 such that for each element r ∈ R the equalities r (n+1) = r or r(n+1) = -r hold. We completely describe both classes of these rings R for any n, thus considerably extending some well-known results in the subject, especially that of V. Perić in Publ. Inst. Math. Beograd (1983) as well as, in particular, the classical description of Boolean rings when n = 1.

Dynamic projection operator method in the theory of hyperbolic systems of partial differential equations with variable coefficients

Leble S., Vereshchagina I.

TASK Quarterly : scientific bulletin of Academic Computer Centre in Gdansk

2017

Vol. 21, No 2

109--120

We consider a generalization of the projection operator method for the case of the Cauchy problem in 1D space for systems of evolution differential equations of first order with variable coefficients. It is supposed that the dependence of coefficients on the only variable χ is weak, that is described by the introduction of a small parameter. Such problem corresponds, for example, to the case of wave propagation in a weakly inhomogeneous medium. As an example, we specify the problem to adiabatic acoustics in waveguides with a variable cross-section. Projection operators are constructed for the Cauchy problem to fix unidirectional modes. The method of successive approximations (perturbation theory) is developed and based on the pseudodifferential operators theory. The application of projection operators adapted for the case under consideration allows deriving approximate evolution equations corresponding to the separated directed waves.

Note on logics of idempontents

Katrnoška F.

Demonstratio Mathematica

2004

Vol. 37, nr 2

267--274

The main result of this paper is the characterization of certain logics of idempotents by Boolean semirings. Moreover some interesting examples are likewise added.