Propionic Anhydride Modification of Cellulosic Kenaf Fibre Enhancement with Bionanocarbon in Nanobiocomposites

The use of chemical modification of cellulosic fibre is applied in order to increase the hydrophobicity, hence improving the compatibility between the fibre and matrix bonding. In this study, the effect of propionic anhydride modification of kenaf fibre was investigated to determine the role of bionanocarbon from oil palm shell agricultural wastes in the improvement of the functional properties of bionanocomposites. The vinyl esters reinforced with unmodified and propionic anhydride modified kenaf fibres bio nanocomposites were prepared using 0, 1, 3, 5 wt% of bio-nanocarbon. Characterisation of the fabricated bionanocomposite was carried out using FESEM, TEM, FT-IR and TGA to investigate the morphological analysis, surface properties, functional and thermal analyses, respectively. Mechanical performance of bionanocomposites was evaluated according to standard methods. The chemical modification of cellulosic fibre with the incorporation of bionanocarbon in the matrix exhibited high enhancement of the tensile, flexural, and impact strengths, for approximately 63.91%, 49.61% and 54.82%, respectively. The morphological, structural and functional analyses revealed that better compatibility of the modified fibre–matrix interaction was achieved at 3% bionanocarbon loading, which indicated improved properties of the bionanocomposite. The nanocomposites exhibited high degradation temperature which signified good thermal stability properties. The improved properties of the bionanocomposite were attributed to the effect of the surface modification and bionanocarbon enhancement of the fibre–matrix networks.     

Pseudoprocesses on a circle and related Poisson kernels

Pseudoprocesses, constructed by means of the solutions of higher-order heat-type equations, have been developed by several authors and many related functionals have been analysed by applying the Feynman–Kac functional or by means of the Spitzer identity. We here examine pseudoprocesses wrapped up on circles and derive their explicit signed density measures. By composing the circular pseudoprocesses with positively skewed stable processes, we arrive at genuine circular processes whose distribution is obtained in the form of Poisson kernels. The distribution of circular even-order pseudoprocesses is similar to the Von Mises (or Fisher) circular normal law and to the wrapped up law of Brownian motion. Time-fractional and space-fractional equations related to processes and pseudoprocesses on the unit radius circumference are introduced and analysed.     

Necessary conditions for optimality for a diffusion with a non-smooth drift

The purpose of this paper is to establish the necessary conditions for optimality of a controlled stochastic differential system without differentiability assumptions on the drift. We use an approximation argument in order to obtain a sequence of smooth control problems, and we apply Ekeland's variational principle to derive the associated adjoint processes. Passing at the Limit with respect to the stable convergence, we obtain a weak adjoint process and the inequality between Hamiltonians. This result is a generalisation of Kushner's maximum principle     

A class of antimagic join graphs

A labeling f of a graph G is a bijection from its edge set E(G) to the set {1, 2, . . . , |E(G)|}, which is antimagic if for any distinct vertices x and y, the sum of the labels on edges incident to x is different from the sum of the labels on edges incident to y. A graph G is antimagic if G has an f which is antimagic. Hartsfield and Ringel conjectured in 1990 that every connected graph other than K 2 is antimagic. In this paper, we show that if G 1 is an n-vertex graph with minimum degree at least r, and G 2 is an m-vertex graph with maximum degree at most 2r-1 (m ≥ n), then G1 ∨ G2 is antimagic.     

In Silico Prediction,Molecular Docking and Dynamics Studies of Steroidal Alkaloids of Holarrhena pubescens Wall. ex G. Don to Guanylyl Cyclase C: Implications in Designing of Novel Antidiarrheal Therapeutic Strategies

The binding of heat stable enterotoxin (STa) secreted by enterotoxigenic Escherichia coli (ETEC) to the extracellular domain of guanylyl cyclase c (ECD_GC-C) causes activation of a signaling cascade, which ultimately results in watery diarrhea. We carried out this study with the objective of finding ligands that would interfere with the binding of STa on ECD_GC-C. With this view in mind, we tested the biological activity of a alkaloid rich fraction of Holarrhena pubescens against ETEC under in vitro conditions. Since this fraction showed significant antibacterial activity against ETEC, we decided to test the screen binding affinity of nine compounds of steroidal alkaloid type from Holarrhena pubescens against extracellular domain (ECD) by molecular docking and identified three compounds with significant binding energy. Molecular dynamics simulations were performed for all the three lead compounds to establish the stability of their interaction with the target protein. Pharmacokinetics and toxicity profiling of these leads demonstrated that they possessed good drug-like properties. Furthermore, the ability of these leads to inhibit the binding of STa to ECD was evaluated. This was first done by identifying amino acid residues of ECD_GC-C binding to STa by protein–protein docking. The results were matched with our molecular docking results. We report here that holadysenterine, one of the lead compounds that showed a strong affinity for the amino acid residues on ECD_GC-C, also binds to STa. This suggests that holadysenterine has the potential to inhibit binding of STa on ECD and can be considered for future study, involving its validation through in vitro assays and animal model studies.     

t-Spread strongly stable monomial ideals*

We introduce the concept of t-spread monomials and t-spread strongly stable ideals. These concepts are a natural generalization of strongly stable and squarefree strongly stable ideals. For the study of this class of ideals we use the t-fold stretching operator. It is shown that t-spread strongly stable ideals are componentwise linear. Their height, their graded Betti numbers and their generic initial ideal are determined. We also consider the toric rings whose generators come from t-spread principal Borel ideals.     

A new proof of the stable manifold theorem for hyperbolic fixed points on surfaces

We introduce a new technique for proving the classical stable manifold theorem for hyperbolic fixed points. This method is much more geometrical than the standard approaches which rely on abstract fixed point theorems. It is based on the convergence of a canonical sequence of “finite time local stable manifolds” which are related to the dynamics of a finite number of iterations.