In this paper, we discuss the usual stochastic‎, ‎likelihood ratio, ‎dispersive and convex transform order between two parallel systems with independent heterogeneous extended generalized exponential components. ‎We also establish the usual stochastic order between series systems from two independent heterogeneous extended generalized exponential samples. ‎Finally, ‎we f...

We study the Lüroth problem for partial differential fields. The main result is following analog of generalized Lüroth's theorem: Let F be a field characteristic 0 with m commuting derivation operators, u=u1,…,un set indeterminates over F. prove that an intermediate G between and F〈u〉 simple extension if only dimension polynomial u form ωu/G(t)=n(t+mm)−(t+m−sm) some s∈N. This generalizes classi...

We prove upper and lower bounds for the leading coefficient of Kolchin dimension polynomial systems partial linear differential equations in case codimension two, quadratic with respect to orders system. A notion typical plays an important role algebra, some its estimations were proved by J. Ritt E. Kolchin; they also advanced several conjectures that later refuted. Our bound generalizes analog...

Our aim in this paper is to introduce some idea about generalized relative Nevanlinna order (α,β) and type of an analytic function with respect another the unit disc where α β are continuous non-negative functions on (-∞,+∞). So we discuss growth properties relating composition two basis as compared their corresponding left right factors.