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In this paper, we obtain some new Lyapunov-type inequalities for a class of even-order linear differential equations, the results are new and generalize and improve some early results in this field. [ABSTRACT FROM AUTHOR]

In this paper we discuss some linear algebra issues concerning the implementation of blended implicit methods (J. Comput. Appl. Math. 2000; 116:41–62, Appl. Numer. Math. 2002; 42:29–45, J. Comput. Appl. Math. 2004; 164–165:145–158, In Recent Trends in Numerical Analysis, Trigiante D (ed.), Nova Science Publication Inc.: New York, 2001; 81–105) for the numerical solution of ODEs. In particular, we describe the strategies, used in the numerical code BiM (J. Comput. Appl. Math. 2004; 164–165:145–158), for deciding whether re-evaluating the Jacobian and/or the factorization involved in the non-linear splitting for solving the discrete problem. Copyright © 2004 John Wiley & Sons, Ltd. [ABSTRACT FROM AUTHOR]

In this paper we define the polyadic Pavelka algebras as algebraic structures for Rational Pavelka predicate calculus (RPL∀). We prove two representation theorems which are the algebraic counterpart of the completness theorem for RPL∀. [ABSTRACT FROM AUTHOR]