Solving unsteady Korteweg–de Vries equation and its two alternatives

This paper aims to present the generalized Kudryashov method to find the exact traveling wave solutions transmutable to the solitary wave solutions of the ubiquitous unsteady Korteweg–de Vries equation and its two famed alternatives, namely, the regularized long‐wave equation and the time regularized long‐wave equation. The exact analytic solutions of the studied equations are constructed explicitly in three forms, namely, hyperbolic, trigonometric, and rational function. The validity of our solutions is verified with MAPLE by putting them back into the original equation and found correct. Moreover, it has shown that the generalized Kudryashov method is an easy and reliable technique over the existing methods. Copyright © 2016 John Wiley & Sons, Ltd.     

A mathematical model to characterise effects of liquid hold-up on bosh silicon transport in the dripping zone of a blast furnace

A first principle based mathematical model has been developed to characterise the effect of total liquid hold-up on the bosh silicon distribution behaviour in the dripping zone of a blast furnace. Two specific cases of hold-up behaviour have been investigated, namely, hold-up in the absence and in the presence of counter current gas flow conditions. The model exemplifies coupled phenomenon of chemical kinetics, transport processes and liquid hold-up to characterise the silicon behaviour in the dripping zone. The present modelling investigation shows that the bosh silicon level diminishes with the enhanced liquid hold-up in the dripping zone. Further, the influence of counter current gas flow on the hold-up is not significant. However, it has been observed that the liquid phase temperature reduces with increased liquid hold-up in dripping zone under steady state operating conditions. The model predictions of bosh silicon distribution have been validated with the published literatures (bulk values) and found to be in good agreement.     

On doubly warped product Finsler manifolds

In this paper, we introduce horizontal and vertical warped product Finsler manifolds. We prove that every C-reducible or proper Berwaldian doubly warped product Finsler manifold is Riemannian. Then, we find the relation between Riemannian curvatures of doubly warped product Finsler manifold and its components, and consider the cases that this manifold is flat or has scalar flag curvature. We define the doubly warped Sasaki-Matsumoto metric for warped product manifolds and find a condition under which the horizontal and vertical tangent bundles are totally geodesic. We obtain some conditions under which a foliated manifold reduces to a Reinhart manifold. Finally, we study an almost complex structure on the tangent bundle of a doubly warped product Finsler manifold.     

Global existence and nonexistence results for a class of semilinear hyperbolic systems

In this paper, we investigate the Cauchy problem for a class of the system of semilinear hyperbolic equations with damping. With the use of the L_p → L_q type estimation for the corresponding linear problem and the method of comparison of functional, the existence and nonexistence criteria of global solutions are found. Copyright © 2012 John Wiley & Sons, Ltd.     

Computational explorations to gain insight into the structural features of TNF-α receptor I inhibitors

TNF-α is a crucial cytokine in the process of inflammatory diseases. The adverse effect of TNF-α is mostly mediated by interaction of TNF-α with TNF-α receptor type I (TNFR1); therefore, discovery of molecules which can bind to TNFR1 preventing TNF-α-receptor complex formation would be of great interest. In the current study, using GRID/GOLPE program, a 3D-QSAR study was conducted on a series of synthetic TNFR1 binders, which resulted in a 3D-QSAR model with appropriate power of predictivity in internal (r²?=?0.94 and q²_LOO?=?0.74) and external (r²?=?0.66 and SDEP?=?0.42) validations. The structural features of TNFR1 inhibitors essential for exerting activity were explored by analyzing the contour maps of the 3D-QSAR model showing that steric interactions and hydrogen bonds are responsible for exerting TNFR1 inhibitory activity. To propose potential chemical entities for TNFR1 inhibition, PubChem database was searched and the selected compounds were virtually tested for anti-TNFR1 activity using the generated model, resulting in two potential anti-TNFR1 compounds. Finally, the possible interactions of the compounds with TNFR1 were investigated using docking studies. The findings in the current work can pave the way for designing more potent anti-TNFR1 inhibitors.     

New nickel(II), copper(II), platinum(II) and palladium(II) complexes of a multidentate sulfur–nitrogen chelating agent

A new, potentially polydentate sulfur–nitrogen chelating agent, 2,6–bis(N-methyl-S-methyldithiocarbazato)pyridine (L) has been synthesized and characterized. With nickel(II) salts, the ligand yields complexes of empirical formula NiLX2·nH2O (X=Cl−, NCS− or NO3−; n=0 or 1) in which it behaves as a quadridentate NSSN chelating agent, coordinating to the nickel(II) ion via the two amino nitrogen atoms and the two sulfur atoms. Magnetic and spectral evidence support a distorted octahedral structure for these complexes. The ligand reacts with copper(II), platinum(II) and palladium(II) salts to yield homo-binuclear complexes of general formula [M2LX4]·nSol (M=CuII, PtII or PdII; X=Cl− or Br−; n=0.5, 1 or 2; Sol=H2O, MeOH or MeCOMe), in which each of the metal ions is in a square-planar environment. These complexes have been characterized by a variety of physicochemical techniques. This revised version was published online in June 2006 with corrections to the Cover Date.     

Selenium Alleviates the Adverse Effect of Drought in Oilseed Crops Camelina (Camelina sativa L.) and Canola (Brassica napus L.)

Drought poses a serious threat to oilseed crops by lowering yield and crop failures under prolonged spells. A multi-year field investigation was conducted to enhance the drought tolerance in four genotypes of Camelina and canola by selenium (Se) application. The principal aim of the research was to optimize the crop yield by eliciting the physio-biochemical attributes by alleviating the adverse effects of drought stress. Both crops were cultivated under control (normal irrigation) and drought stress (skipping irrigation at stages i.e., vegetative and reproductive) conditions. Four different treatments of Se viz., seed priming with Se (75 μM), foliar application of Se (7.06 μM), foliar application of Se + Seed priming with Se (7.06 μM and 75 μM, respectively) and control (without Se), were implemented at the vegetative and reproductive stages of both crops. Sodium selenite (Na₂SeO₃), an inorganic compound was used as Se sources for both seed priming and foliar application. Data regarding physiochemical, antioxidants, and yield components were recorded as response variables at crop maturity. Results indicated that WP, OP, TP, proline, TSS, TFAA, TPr, TS, total chlorophyll contents, osmoprotectant (GB, anthocyanin, TPC, and flavonoids), antioxidants (APX, SOD, POD, and CAT), and yield components (number of branches per plant, thousand seed weight, seed, and biological yields were significantly improved by foliar Se + priming Se in both crops under drought stress. Moreover, this treatment was also helpful in boosting yield attributes under irrigated (non-stress) conditions. Camelina genotypes responded better to Se application as seed priming and foliar spray than canola for both years. It has concluded that Se application (either foliar or priming) can potentially alleviate adverse effects of drought stress in camelina and canola by eliciting various physio-biochemicals attributes under drought stress. Furthermore, Se application was also helpful for crop health under irrigated condition.