Almost Contact Lagrangian Submanifolds of Nearly Kaehler 6-Sphere

For a Lagrangian submanifold M of S ⁶ with nearly Kaehler structure, we provide conditions for a canonically induced almost contact metric structure on M by a unit vector field, to be Sasakian. Assuming M contact metric, we show that it is Sasakian if and only if the second fundamental form annihilates the Reeb vector field ξ, furthermore, if the Sasakian submanifold M is parallel along ξ, then it is the totally geodesic 3-sphere. We conclude with a condition that reduces the normal canonical almost contact metric structure on M to Sasakian or cosymplectic structure.     

Evaluation of antioxidant activities of the edible and medicinal Acacia albida organs related to phenolic compounds

This study compared phenolic contents and antioxidant activity in different organs of Acacia albida (leaves and bark) and focuses on identification of phenolic compounds of leaves by HPLC-DAD. The analysed organs exhibited differences in total polyphenol contents (100 and 59.5 mg GAE g^? 1 DW). Phenolic contents of leaves were two times higher than those in bark. Ethanolic extracts exhibited good antioxidant activities with IC₅₀ = 26 μg mL^? 1 for DPPH and EC₅₀ = 50 μg mL^? 1 for FRAP. Identification by HPLC-DAD revealed the presence of nine phenolic compounds known for their high antioxidant activity. The results suggested that this species can be used as source of natural antioxidants.     

Geometry of warped product pseudo-slant submanifolds of Kenmotsu manifolds

In this paper, we study pseudo-slant submanifolds and their warped products in Kenmotsu manifolds. We obtain the necessary conditions that a pseudoslant submanifold is locally a warped product and establish an inequality for the squared norm of the second fundamental form in terms of the warping function. The equality case is also considered.     

A note on slant submanifolds of nearly trans-Sasakian manifolds

The geometry of slant submanifolds of a nearly trans-Sasakian manifold is studied when the tensor field Q is parallel. It is proved that Q is not parallel on the submanifold unless it is anti-invariant and thus the result of [CABRERIZO, J. L.—CARRIAZO, A.—FERNANDEZ, L. M.—FERNANDEZ, M.: Slant submanifolds in Sasakian manifolds, Glasg. Math. J. 42 (2000), 125–138] and [GUPTA, R. S.—KHURSHEED HAIDER, S. M.—SHARFUDIN, A.: Slant submanifolds of a trans-Sasakian manifold, Bull. Math. Soc. Sci. Math. Roumanie (N.S.) 47 (2004), 45–57] are generalized.     

B.-Y. Chen’s Inequality for Bi-warped Products and Its Applications in Kenmotsu manifolds

In this paper, we establish a sharp inequality for the squared norm of the second fundamental form of bi-warped product submanifolds of Kenmotsu manifolds. The equality case is also considered. We also provide a non-trivial example and some applications of derived inequality.     

Evaluation and modeling of the mechanical properties of graphite nanoplatelets based rubber nanocomposites for pressure sensing applications

Acrylonitrile butadiene rubber (NBR) compounds filled with different concentrations of graphite nanoplatelets were experimentally investigated. The stress–strain curves of the nanocomposites were studied, which suggest good filler–matrix adhesion. The large reinforcement effect of the filler followed the Guth model for non‐spherical particles. The effect of graphite nanoplatelets on the cyclic fatigue and hysteresis was also examined. The loading and unloading stress–strain relationships for any cycle were described by applying Ogden's model for rubber nanocomposites. With this model for incompressible materials, expressions may be developed to predict the stress–strain relationship for any given cycle. The dissipated energy increased with graphite nanoplatelets concentrations and decrease with number of cycles. The rate of damage accumulation becomes marginal after first ten cycles. The rate of damage increases as the amount of graphite nanoplatelets increase into the rubber matrix. Copyright © 2011 John Wiley & Sons, Ltd.     

Warped Product Bi-slant Immersions in Kaehler Manifolds

A submanifold M of an almost Hermitian manifold \((\widetilde{M},g,J)\) is called slant, if for each point \(p\in M\) and \(0\ne X\in T_p M\), the angle between JX and \(T_p M\) is constant (see Chen in Bull Aust Math Soc 41:135–147, 1990). Later, Carriazo (in: Proceedings of the ICRAMS 2000, Kharagpur, 2000) defined the notion of bi-slant immersions as an extension of slant immersions. In this paper, we study warped product bi-slant submanifolds in Kaehler manifolds and provide some examples of warped product bi-slant submanifolds in some complex Euclidean spaces. Our main theorem states that every warped product bi-slant submanifold in a Kaehler manifold is either a Riemannian product or a warped product hemi-slant submanifold.