Optical solitons in $$$$-dimensions under anti-cubic law of nonlinearity by analytical methods

The present study emphasis to look for new closed form exact solitary wave solutions for the \((n+1)\)-dimensional nonlinear Schrödinger equation using the extended trial equation method (ETEM) and the \(\exp (-\Omega (\eta ))\)-expansion method (EEM) with the help of symbolic computation package maple. As a consequence, the ETEM and EEM are successfully employed and acquired some new exact solitary wave solutions in terms of exponential based functions, hyperbolic based functions, trigonometric based functions and rational based functions. All solutions have been verified back into its corresponding equation with the aid of maple package program. Finally, we believe that the executed method is robust and efficient than other methods and the obtained solutions in this paper can help us to understand the variation of solitary waves in the field of nonlinear optic.     

Analytical treatments of the space–time fractional coupled nonlinear Schrödinger equations

Under investigation in this work is a (\(2+1\))-dimensional the space–time fractional coupled nonlinear Schrödinger equations, which describes the amplitudes of circularly-polarized waves in a nonlinear optical fiber. With the aid of conformable fractional derivative and the fractional wave transformation, we derive the analytical soliton solutions in the form of rational soliton, periodic soliton, hyperbolic soliton solutions by four integration method, namely, the extended trial equation method, the \(\exp (-\,\Omega (\eta ))\)-expansion method and the improved \(\tan (\phi (\eta )/2)\)-expansion method and semi-inverse variational principle method. Based on the the extended trial equation method, we derive the several types of solutions including singular, kink-singular, bright, solitary wave, compacton and elliptic function solutions. Under certain condition, the 1-soliton, bright, singular solutions are driven by semi-inverse variational principle method. Based on the analytical methods, we find that the solutions give birth to the dark solitons, the bright solitons, combine dark-singular, kink, kink-singular solutions with fractional order for nonlinear fractional partial differential equations arise in nonlinear optics.     

Wave solutions for variants of the KdV–Burger and the K(n,n)–Burger equations by the generalized G′/G‐expansion method

An application of the ‐expansion method to search for exact solutions of nonlinear partial differential equations is analyzed. This method is used for variants of the Korteweg–de Vries–Burger and the K(n,n)–Burger equations. The generalized ‐expansion method was used to construct periodic wave and solitary wave solutions of nonlinear evolution equations. This method is developed for searching exact traveling wave solutions of nonlinear partial differential equations. It is shown that the generalized ‐expansion method, with the help of symbolic computation, provides a straightforward and powerful mathematical tool for solving nonlinear problems. Copyright © 2017 John Wiley & Sons, Ltd.     

Molecular docking study on platelet-activating factor antagonistic activity of bioactive compounds isolated from Guttiferae and Ardisia species

A handful of bioactive compounds from plants have been reported to possess platelet-activating factor (PAF) antagonist activity. However, their mode of action is not well understood. Selected bioactive compounds that exhibit PAF antagonist activity and synthetic PAF antagonists were subjected to docking simulations using the MOE 2007.09 software package. The docking study of PAF antagonists was carried out on the PAF receptor (PAFR) protein which involves in various pathological responses mediated by PAF. The docking results revealed that amentoflavone (3) showed good interactions with the PAFR model where the flavone and phenolic moieties were mostly involved in these interactions. Knowledge on PAF antagonists' interactions with the PAFR model is a useful screening tool of potential PAF antagonists prior to performing PAF inhibitory assay.     

Inhibitory effect of lactone fractions and individual components from three species of the Achillea millefolium complex of Bulgarian origin on the human neutrophils respiratory burst activity

Achillea species are widely used in folk medicine for treatment of inflammatory diseases. The inhibitory effect on the human neutrophils respiratory burst activity of total extracts, their fractions and some main constituents of the flower heads from Achillea asplenifolia, A. collina and A. distans belonging to A. millefolium complex of Bulgarian origin, were tested by the modified method of Tan and Berridge. Seven from the investigated fractions showed activity similar or higher than that of indomethacine and might be evaluated as nonsteroidal anti-inflammatory agents.     

A Simple Efficient Procedure for the Synthesis of Benzopyrano[2,3‐c]pyrazoles

A one‐step procedure is proposed for synthesizing 2‐acyl benzopyrano[2,3‐c]pyrazoles and 2‐aryl benzopyrano[2,3‐c]pyrazoles. The method is based on the condensation of 2‐iminocoumarin‐3‐carbonitriles with hydrazides and hydrazines in acid as catalysts. A mechanism of reaction is proposed. All prepared compounds are identified by FTIR, ¹H NMR, ¹³C NMR, mass spectroscopy, and elemental analysis.     

New measurements concerning a non-resonant photo-activation cross-section for Cd

A ⁶⁰Co source of high activity has been used to photo-activate the 396 keV isomeric level (T_1/248.6 min) of ¹¹¹Cd. Present results support the existence of a non-resonant contribution to the photo-activation cross-section, the magnitude of our current estimate comparing favourably with measurements obtained by a number of other workers.     

Quantum Walk on the Generalized Birkhoff Polytope Graph

We study discrete-time quantum walks on generalized Birkhoff polytope graphs (GBPGs), which arise in the solution-set to certain transportation linear programming problems (TLPs). It is known that quantum walks mix at most quadratically faster than random walks on cycles, two-dimensional lattices, hypercubes, and bounded-degree graphs. In contrast, our numerical results show that it is possible to achieve a greater than quadratic quantum speedup for the mixing time on a subclass of GBPG (TLP with two consumers and m suppliers). We analyze two types of initial states. If the walker starts on a single node, the quantum mixing time does not depend on m, even though the graph diameter increases with it. To the best of our knowledge, this is the first example of its kind. If the walker is initially spread over a maximal clique, the quantum mixing time is O(m/ϵ), where ϵ is the threshold used in the mixing times. This result is better than the classical mixing time, which is O(m1.5/ϵ).     

A chaotic map with infinite number of equilibria in a bounded domain

The European Physical Journal Special Topics - Although chaotic flows with special properties in their equilibria have been investigated widely, such an effort about chaotic maps has been...