<p style='text-indent:20px;'>Let <inline-formula><tex-math id="M2">\begin{document}$ P $\end{document}</tex-math></inline-formula> be a linear, second-order, elliptic operator with real coefficients defined on noncompact Riemannian manifold id="M3">\begin{document}$ M and satisfies id="M4">\begin{document}$ P1 = 0 in id="M5">\begin{document}$ $\end{documen...

In this paper, we introduce the notion order quasi-Cauchy se-quences, downward and upward quasi-cauchy sequences, half Cauchy sequences. Next consider associated idea of continuity namely, ward continuous functions [2] investigated certain intersting results. The entire investigation is perform in (l)-group setting.

In the paper we establish some new results depending on the comparative growth properties of composition of entire functions using relative $L^{ast }$-order (relative $L^{ast }$-lower order) as compared to their corresponding left and right factors where $Lequiv Lleft( rright) $ is a slowly changing function.

Let $L = U_3(9)$ be the simple projective unitary group in dimension 3 over a field  with 92 elements. In this article, we classify groups with the same order and degree pattern as an almost simple group related to $L$. Since $Aut(L)equiv Z_4$ hence almost simple groups related to $L$ are $L$, $L : 2$ or $L : 4$. In fact, we prove that $L$, $L : 2$ and $L : 4$ are OD-characterizable.