In this work, join and meet algebraic structure which exists in non-near-linear finite geometry are discussed. Lines in non-near-linear finite geometry 2  d were expressed as products of lines in near-linear finite geometry 2 p () Π d with variables in  d and a finite system from the subsets of the set of divisors of d is established.

A quantum system Σ(n) with variables in Z(n), where n = Q pi (with pi prime numbers), is considered. The non-near-linear geometry G(n) of the phase space Z(n) × Z(n), is studied. The lines through the origin are factorized in terms of 'prime factor lines' in Z(pi)×Z(pi). Weak mutually unbiased bases (WMUB) which are products of the mutually unbiased bases in the 'prime factor Hilbert spaces' H(pi), are also considered. The factorization of both lines and WMUB is analogous to the factorization of integers in terms of prime numbers. The duality between lines and WMUB is discussed. It is shown that there is a partial order in the set of subgeometries of G(n), isomorphic to the partial order in the set of subsystems of Σ(n).

In this study we investigate the sharp radius of starlikeness of subclasses of Ma and Minda class for the ratio of analytic functions which are related to limaçon functions. This survey is connected also to the first-order differential subordinations. In this context, we get the condition on β for which certain differential subordinations associated with limaçon functions imply Ma and Minda starlike functions. Simple corollaries are provided for certain examples of our results. Finally, we present several geometries related to our study.

In this article, we introduce the q-analogue of functions characterized by the lemniscate of Bernoulli in the right-half plane and define the class $\mathbb{L}^{\ast}_{q}(A, B)$. Furthermore, we study the geometric properties of this class, which include coefficient inequalities, subordination factor sequence property, radii results and Fekete-Szeg$\ddot{\textup{o}}$ problems. Some deductions of our results show relevant connections between this present work and the existing ones in many literature. It is worthy of note that some of our results are sharp.

This study focuses on the anti-protozoan activities of Stachytarpheta angustifolia (Tarkajiya; Hausa, Devil’s coach whip; English) on haematological parameters of Albino Wistar rats which is an unexplored study area. The work is aimed at the determination of the effects of S. angustifolia on Wistar Rats, when exposed to herbal extract on the haematological parameters of Wistar Rats infected with E. tenella Biomarkers. The plant was obtained whole; dried under the shade, made into a powdered form and aqueous extraction method carried by maceration technique. After infecting the experimental animals with the parasites; E. tenella, the following respective doses of 750 mg and 1500 mg were administered to the rats in groups of 3 and 4. Results obtained were analyzed using Analysis of Variance (ANOVA). It was discovered that no significant harmful effect on the rats was recorded, but 60 % of the parasites were killed. This work demonstrated that the herbal extract killed the parasites but induced minimal stress to the animals as shown by the low haematological parameters in the study.