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In this paper, the generalization of pre-topological spaces called bipretopological spaces (briefly, π-pre-topology) depending on two pre-topologies on an arbitrary universal set has been introduced. New kinds of separations axioms on π-pre-topological spaces are established and some of their properties are investigated. A comparison between four separation axioms on π-pre-topological spaces and pre-topological spaces with different sorts of counterexamples are presented. The topological property for some π-pre-separation axioms are satisfied and its relation with disubgraphs are discussed. A human heart will be studied through it is generated digraph. It is noted that all separation axioms for human heart are not all satisfied. [ABSTRACT FROM AUTHOR]

Pot experiment was conducted to evaluate the effect of chitosan or brassinolide applications on morphology and physiology parameters of Azadirachta indica grown under water deficient stress. The plants received different irrigation intervals, and were sprayed monthly with either chitosan or brassinolide each at concentrations of 50, 100 and 200 ppm, while the control plants were sprayed only with tap water. The results showed that water stress reduced all growth parameters, chemical constituents of pigments content, total carbohydrates, N, P, and K%, total indoles, while proline and total phenols content were increased. Instead, the plants sprayed with the higher concentrations of chitosan or brassinolide resulted in significant increase in growth parameters, pigments content, total carbohydrates, proline content, N, P and K%, total indoles while reduced total phenols content. Based on the obtained results it can be concluded that, foliar application of chitosan or brassinolide at 200 ppm can alleviate the adverse effects of water deficient stress on the growth and physiology parameters of Azadirachta indica. [ABSTRACT FROM AUTHOR]

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The breakup of a thin non-evaporating liquid film that is either flowing down or climbing on a vertical or inclined surface and subject to cocurrent or countercurrent interfacial shear (or gas flow) is investigated analytically. Analytical expressions for the dimensionless liquid film thickness, $\Delta_{\hbox{\scriptsize\it min}}$, and wetting rate, $\Gamma_{\hbox{\scriptsize\it min}}$, at breakup are derived based on the minimization of the total energy of a stable rivulet, formed following the film breakup. For a downflowing liquid film, increasing the cocurrent interfacial shear (or gas velocity) or decreasing the equilibrium contact angle, $\theta_{o}$, decreases both $\Delta_{\hbox{\scriptsize\it min}}$ and $\Gamma _{\hbox{\scriptsize\it min}}$, below their values with zero interfacial shear. Conversely, increasing the countercurrent interfacial shear or $\theta_{o}$, increases both $\Delta_{\hbox{\scriptsize\it min}}$ and $\Gamma_{\hbox{\scriptsize\it min}}$, above their values with zero interfacial shear. The predictions of $\Delta _{\hbox{\scriptsize\it min}}$ and $\Gamma _{\hbox{\scriptsize\it min}}$ for a climbing water film on a vertical surface are in good agreement with reported experimental data for a wide range of cocurrent gas velocities. [ABSTRACT FROM AUTHOR]