Some results on dual third-order Jacobsthal quaternions

Some New Results on Stochastic Orderings between Generalized Order Statistics

In this paper we specify the conditions on the parameters of pairs of gOS’s under which the corresponding generalized order statistics are ordered according to usual stochastic ordering, hazard rate ordering, likelihood ratio ordering and dispersive ordering. We consider this problem in one-sample as well as two-sample problems. We show that some of the results obtained by Franco et al. ...

On Some Identities of k-Jacobsthal-Lucas Numbers

In this paper we present the sequence of the k-Jacobsthal-Lucas numbers that generalizes the Jacobsthal-Lucas sequence introduced by Horadam in 1988. For this new sequence we establish an explicit formula for the term of order n, the well-known Binet’s formula, Catalan’s and d’Ocagne’s Identities and a generating function. Mathematics Subject Classification 2010: 11B37, 11B83

Some Instability Results on Certain Third Order Nonlinear Vector Differential Equations

In this paper, we obtain some sufficient conditions under which the zero solution of a certain third order non-linear ordinary vector differential equation is unstable. Our results include and improve some well-known results exist in the literature.

New Results on the Nonoscillation of Solutions of Some Nonlinear Differential Equations of Third Order

We give sufficient conditions so that all solutions of differential equations r t y′′ t ′ q t k y′ t p t y g t f t , t ≥ t0, and r t y′′ t ′ q t k y′ t p t h y g t f t , t ≥ t0, are nonoscillatory. Depending on these criteria, some results which exist in the relevant literature are generalized. Furthermore, the conditions given for the functions k and h lead to studying more general differentia...

Some Notes on Unit Quaternions and Rotation