We prove the ultimate boundedness of solutions of some third order nonlinear ordinary differential equations using the Lyapunov method. The results obtained generalize earlier results of Ezeilo, Tejumola, Reissig, Tunç and others. The Lyapunov function used does not involve the use of signum functions as used by others.
We define an ultra $LI$-ideal of a lattice implication algebra and give equivalent conditions for an $LI$-ideal to be ultra. We show that every subset of a lattice implication algebra which has the finite additive property can be extended to an ultra $LI$-ideal.
A mistake concerning the ultra $LI$-ideal of a lattice implication algebra is pointed out, and some new sufficient and necessary conditions for an $LI$-ideal to be an ultra $LI$-ideal are given. Moreover, the notion of an $LI$-ideal is extended to $MTL$-algebras, the notions of a (prime, ultra, obstinate, Boolean) $LI$-ideal and an $ILI$-ideal of an $MTL$-algebra are introduced, some important examples are given, and the following notions are proved to be equivalent in $MTL$-algebra: (1) prime proper $LI$-ideal and Boolean $LI$-ideal, (2) prime proper $LI$-ideal and $ILI$-ideal, (3) proper obstinate $LI$-ideal, (4) ultra $LI$-ideal.
A systematic study of the ultraviolet spectra of the Algol-like semidetached binary stars is described. Revision of the traditionally accepted spectral types has been found necessary in most cases toward earlier spectral types. Superionized emission lines seen at total eclipses show interesting differences in intensities.
High resolution UV spectroscopic observations of the binary symbiotic star AG Peg obtained with the IUE satellite in the periode 1978-81 are analyzed. The variability of the fluxes and the radial velocities of emission lines accordingto orbital phase are presented, The observaions support a binary model with mass transfer from a hot rotationaly unstable subdvarf to a cool M giant.