A procedure to construct exact solutions of nonlinear evolution equations

In this paper, we implemented the functional variable method for the exact solutions of the Zakharov?CKuznetsov-modified equal-width (ZK-MEW), the modified Benjamin?CBona?CMahony (mBBM) and the modified KdV?CKadomtsev?CPetviashvili (KdV?CKP) equations. By using this scheme, we found some exact solutions of the above-mentioned equations. The obtained solutions include solitary wave solutions, periodic wave solutions and combined formal solutions. The functional variable method presents a wider applicability for handling nonlinear wave equations.     

Refraction-based photonic crystal diode

A system composed of air holes in a dielectric host to form two square photonic crystals, with the same orientation and lattice constant but different scatterer radii, making an interface along their body diagonals, is numerically demonstrated to facilitate unidirectional light transmission. Band structure computations are carried out via the plane wave expansion method, whereas finite-difference time-domain simulations are carried out to investigate the transient behavior. Unidirectional light transmission is achieved over two adjacent stop bands along the ΓX direction, which are circumvented in the forward direction by scaling down the wave vector and rotating the surface normal. Contrast ratios as high as 0.9 are attained within the lower stop band.     

Exact Solutions for Fractional Differential-Difference Equations by (G′/G)-Expansion Method with Modified Riemann-Liouville Derivative

In this paper, the ($G′/G$)-expansion method is suggested to establish new exact solutions for fractional differential-difference equations in the sense of modified Riemann–Liouville derivative. The fractional complex transform is proposed to convert a fractional partial differential difference equation into its differential difference equation of integer order. With the aid of symbolic computation, we choose nonlinear lattice equations to illustrate the validity and advantages of the algorithm. It is shown that the proposed algorithm is effective and can be used for many other nonlinear lattice equations in mathematical physics and applied mathematics.     

Effects of Sorafenib and Quercetin Alone or in Combination in Treating Hepatocellular Carcinoma: In Vitro and In Vivo Approaches

Sorafenib is the first drug approved to treat advanced hepatocellular carcinoma (HCC) and continues as the gold-standard therapy against HCC. However, acquired drug resistance represents a main concern about sorafenib therapy. The flavanol quercetin found in plants has shown great anti-cancer and anti-inflammatory properties. In this work, quercetin was used as a therapeutic agent alone or in combination with a sorafenib chemotherapy drug to improve the routine HCC treatment with sorafenib. The in vitro and in vivo results presented here confirm that quercetin alone or in combination with sorafenib significantly inhibited HCC growth, induced cell cycle arrest and induced apoptosis and necrosis. Further molecular data shown in this report demonstrate that quercetin alone or combined with sorafenib downregulated key inflammatory, proliferative and angiogenesis-related genes (TNF-α, VEGF, P53 and NF-κB). Combined quercetin/sorafenib treatment markedly improved the morphology of the induced liver damage and showed significant antioxidant and anti-tumor effects. The advantage of combined treatment efficacy reported here can be attributed to quercetin’s prominent effects in modulating cell cycle arrest, apoptosis, oxidative stress and inflammation.     

Symbolic computation of conservation laws and exact solutions of a coupled variable-coefficient modified Korteweg–de Vries system

In this paper we study a generalized coupled variable-coefficient modified Korteweg–de Vries (CVCmKdV) system that models a two-layer fluid, which is applied to investigate the atmospheric and oceanic phenomena such as the atmospheric blockings, interactions between the atmosphere and ocean, oceanic circulations and hurricanes. The conservation laws of the CVCmKdV system are derived using the multiplier approach and a new conservation theorem. In addition to this, a similarity reduction and exact solutions with the aid of symbolic computation are computed.     

Torsion in equivariant cohomology

Partially supported by an NSF grant.     

Solid-state fermentation of agricultural wastes into food through pleurotus cultivation

The technical feasibility of using agricultural wastes (mango and date industry wastes) as a substrate for the cultivation ofPleurotus ostreatus NRRL-0366 is evaluated. When comparing the biological efficiency of mushroom production, the highest yield of fruiting bodies was obtained using a mixture of date waste and rice straw at a ratio (1:1) (11.96%), followed by a mixture 3:1 (11.16%). The lowest one was the mixture 2:1 (9.19%). FungusPleurotus ostreatus NRRL-0366 can also be cultivated on mango waste supplemented with rice straw at a different ratio. The best one was the 1:1 mixture (10.18%), whereas the lowest was a mixture 3:1 (6.4%). Comparing the results obtained favored the use of date waste as a substrate for growingPleurotus ostreatus NRRL-0366. Spawn was cultured on three different substrates as follows: Date waste alone (I); 1:1 (by wt) date waste and rice straw (II); 1:1:1 date waste, rice straw, and corncobs (III). Final dry weight and composition of the fruiting bodies are tabulated for the three sets of conditions. Date waste and rice straw mixture (II) is a good source of nonstarchy carbohydrate (67%) and protein (27.44%) containing amounts of essential amino acids, especially lysine and low RNA (3.81%). Elemental analysis were studied in the fruit bodies of the three media.     

The effect of carbonaceous contamination on the investigation of the surface oxide on silicon by angle-resolved XPS

The carbon-contaminated native oxide layer on a standard silicon wafer was investigated by angle-resolved signal ratio X-ray photoelectron spectroscopy (AR/SR/XPS). The results, based on intensity measurements of C_1s , O_1s , Si _2p ⁴⁺ and Si^elemental _2p showed the carbon to be ingested into the oxide to a mean depth of 0.4 nm, and the oxide to consist of a fully oxidized layer ( 1 nm) on top, followed by a suboxidic layer (0.8 nm). The conclusions are that the depth location of the carbonaceous contamination is of cardinal importance for the correct interpretation of the oxidic data, and that for well studied systems routine measurements at two take-off angles suffice for quantitative results.Dedicated to Professor Günther Tölg on the occasion of his 60th birthday     

Synthesis and reactions of 2-[α-(3,4-disubstituted phenacyl)-p-substituted styryl]-4H-3,1-benzoxazin-4-ones

Science Department, Faculty of Teachers, P.O.Box 2313, Al Hasa, 31982, Saudi Arabia Faculty of Engineering, Ain Shames University, EgyptChemistry Department, Faculty of Science, Ain Shames University, Egypt     

A simple and selective flow-injection spectrophotometric determination of copper(II) by using acetylsalicylhydroxamic acid

A new simple, and rapid flow-injection spectrophotometric method is developed for the determination of trace amounts of Cu(II) by using a new chromogenic reagent acetylsalicylhydroxamic acid (AcSHA). The method is based on the formation of colored Cu(II)-(AcSHA)₂ complex. The optimum conditions for the chromogenic reaction of Cu(II) with AcSHA is studied and the colored (green) complex is selectively monitored at λ_max 700 nm. With the reagent carrier solvent (dimethylsulfoxide (DMSO) and acetate buffer, pH 4.2) flow-rate of 1 ml min⁻¹, a detection limit (2S) of 1 μg l⁻¹ Cu(II) was obtained at a sampling rate of 80 sample h⁻¹. The calibration graph was linear in the Cu(II) concentration range 5-120 μg l⁻¹. The relative standard deviation (n=10) was 0.64% for a sample containing 60 μg l⁻¹ Cu(II). The detailed study of various interferences confirmed the high selectivity of the developed method. The method was successfully applied to determine trace amounts of copper(II) in river and seawater samples. The accuracy of the method was demonstrated by the analysis of standard reference materials C12X3500 and C14XHS 50.