A symmetry analysis of some classes of evolutionary nonlinear (2+1)-diffusion equations with variable diffusivity

In this paper the (2+1)-nonlinear diffusion equation u _t ?div(f(u)grad u)=0 with variable diffusivity is considered. Using the Lie method, a complete symmetry classification of the equation is presented. Reductions, via two-dimensional Lie subalgebras of the equation, to first- or second-order ordinary differential equations are given. In a few interesting cases exact solutions are presented.     

Electrochemical DNA biosensor for the determination of benzo[a]pyrene–DNA adducts

The metabolites of the environmental pollutant, benzo[a]pyrene (BaP) are carcinogenic and mutagenic agents. Thus, the determination of additional products (adducts) of the interaction between DNA and BaP, attracts great interest in cancer research.

In this study, the determination of interaction between BaP and calf thymus double-stranded DNA (dsDNA) was performed by using differential pulse voltammetry (DPV) and constant current chronopotentiometric stripping analysis (PSA) in connection with carbon paste electrode (CPE) or glassy carbon electrode (GCE). As a result of interaction of BaP with dsDNA, the signal obtained from the oxidation of guanine decreased and a new adduct signal at a more positive potential appeared. This new peak is attributed to the formation of an adduct from the interaction of guanine with BaP. The chemically prepared anti-7,8,9,10-tetrahydrobenzo[a]pyrene-7,8-diol-9,10-epoxide (BPDE) adduct by using iodine oxidation was analyzed and the electrochemical signal of the adduct was observed. When the dsDNA modified GCE was immersed into various concentrations of BaP solution, the oxidation peak of guanine decreased and the adduct peak increased with the increasing BaP concentration. The partition coefficient was also obtained from the peak of BaP with dsDNA. The results revealed that the formation of adducts could be determined by using electrochemical DNA biosensors, which are fast, simple and cost-effective devices. Furthermore, this study promises that the analysis of other important adducts would benefit from the introduction of electrochemical methods.     

Lipids and essential oil ofOriganum onites

Neutral lipids, glycolipids, phospholipids, pigments, and essential oil of the above-ground part ofOriganum onites L. (Lamiaceae) are isolated and characterized for the first time. The fatty-acid composition of the lipids and the components of the hydrocarbons, sterols, and essential oil are determined by GC/MS. Linolenic and palmitic acids dominate in the acids of the lipids. The main components of the hydrocarbons are nonacosane; of the sterols, \-sitosterol; of the pigments, chlorophylls a and b. A total of 54 components are identified in the essential oil.Presented at the IIIrd International Symposium on the Chemistry of Natural Compounds, Bukhara, Uzbekistan, 19–22 December, 1998.Translated from Khimiya Prirodnykh Soedinenii, No. 2, pp. 106–109, March–April, 2000.     

Approximate Symmetries and Conservation Laws with Applications

The relationship between the approximateLie-Backlund symmetries and the approximate conservedforms of a perturbed equation is studied. It is shownthat a hierarchy of identities exists by which thecomponents of the approximate conserved vector or theassociated approximate Lie-Backlund symmetries aredetermined by recursive formulas. The results areapplied to certain classes of linear and nonlinear waveequations as well as a perturbed Korteweg-de Vriesequation. We construct approximate conservation laws forthese equations without regard to aLagrangian.     

Computational study of linear and nonlinear optical properties of substituted thiophene imino dyes using long-range corrected hybrid DFT methods

The molecular structures, linear and nonlinear optical properties of a series constituted by four R-substituted thiophene imino dyes, namely A(R?=?SO₂Me), B(R?=?SO₂Ph), C(R?=?NO₂), and D(R?=?C₂(CN)₃) were analysed using CAM-B3LYP, ωB97XD and LC-ωPBE hybrid DFT functionals in combination of the 6-311++G(d,p) standard basis set. The dipole moments, polarisabilities, HOMO-LUMO energy gaps, maximum absorption wavelengths and first hyperpolarisabilities were calculated in the gas phase and the obtained results are in good agreement with experimental NLO activity order A?<?B?<?C. Compared to synthesised dyes A-C, the designed dye D presents a longer maximum absorption wavelength and a lower HOMO-LUMO gap because of the appreciable stabilisation of its LUMO energy. These results were confirmed by the calculation of the total second-order stabilisation energy E⁽²⁾ defined in the context of the NBO population analysis. Consequently, dye D is predicted to exhibit a higher first hyperpolarisability in comparison with dyes A-C. This result can be justified by the enhanced intramolecular charge transfer in dye D due to the stronger electron-withdrawing ability and the cumulative action of the long π-conjugation of the tricyanovinyl moiety. The very high total hyperpolarisability (27 times greater than that of para-nitroaniline) of the designed dye D suggests its promising use in organic NLO devices.     

The single-assignment hub covering problem: Models and linearizations

We study the hub covering problem which, so far, has remained one of the unstudied hub location problems in the literature. We give a combinatorial and a new integer programming formulation of the hub covering problem that is different from earlier integer programming formulations. Both new and old formulations are nonlinear binary integer programs. We give three linearizations for the old model and one linearization for the new one and test their computational performances based on 80 instances of the CAB data set. Computational results indicate that the linear version of the new model performs significantly better than the most successful linearization of the old model both in terms of average and maximum CPU times as well as in core storage requirements.     

Antiferromagnetic Coupling in a New Mn(III) Schiff Base Complex with Open-Cubane Core: Structure,Spectroscopic and Luminescence Properties

A new open-cubane Mn^III, [{(H₂O)Mn^IIIL}{Mn^IIIL}]₂·2(CH₃OH).2(CH₃CH₂OH)·2Cl, 1 where H ₂ L=[N-(2-hydroxyethyl)-3-methoxysalicylaldimine] has been synthesized and characterized by element analysis, FT-IR, solid UV–Vis spectroscopy and single crystal X-ray diffraction. The crystal structure determination shows an open-cubane tetranuclear complex. The Mn1 (Mn1ⁱ) ions is hexacoordinate by NO₅ donor sets while the Mn2 (Mn2ⁱ) is pentacoordinate by NO₄ donor sets. The solid state photoluminescence properties of complex 1 and its ligand H ₂ L have been investigated under UV light at 349 nm in the visible region. H ₂ L exhibits blue emission while complex 1 shows orange-red emission at room temperature. Variable-temperature magnetic susceptibility measurements on the complex 1 in the range 2–300 K indicate an antiferromagnetic interaction.     

Adsorption and diffusion on a phosphorene monolayer: a DFT study

A computational study of the adsorption and diffusion behavior of alkali and alkaline earth metal atoms on a phosphorene monolayer is reported. Our calculations were performed within the framework of density functional theory using the Perdew–Burke–Ernzerhof functional and projector augmented wave potentials, as derived from the generalized gradient approximation. Our binding energy calculations for various potential adsorption sites showed that the site located above the center of a triangle formed by three surface phosphorus atoms is the most attractive to all adatoms. In addition, simulation of the diffusion of adatoms across the surface of the phosphorene monolayer showed that the diffusion is anisotropic, with K having the lowest diffusion barrier (0.02 eV along the zigzag pathway). To the best of our knowledge, this is the lowest diffusion barrier of any metal adatom on a single layer of phosphorene. While phosphorene exhibited significantly better adatom adsorption and diffusion than graphene, it also showed a reduced storage capacity compared to graphene, most probably due to the structural distortion induced by the oversaturated phosphorene surface. This finding strongly suggests that a phosphorene–graphene hybrid system could be employed as a promising high-capacity ion anode.