Empty spaces and perfect fluids with homothetic transformation

A class of Lorentzian metrics in one variable that admits homothetic transformation is introduced. Solutions of Einstein's empty space equations are presented. The case of perfect fluids is discussed.     

Symmetries of second-order ordinary differential equations and Elie Cartan's method of equivalence

We show how the differential invariants generated by Elie Cartan's method of equivalence may be used in determining the symmetry groups of second-order ordinary differential equations. This result is then applied to a series of equations which arise in various aspects of mathematical physics.     

Associated primes of local cohomology modules

Let be an ideal of a commutative Noetherian ring and a finitely generated -module. Let be a natural integer. It is shown that there is a finite subset of , such that is contained in union with the union of the sets , where and . As an immediate consequence, we deduce that the first non- -cofinite local cohomology module of with respect to has only finitely many associated prime ideals.

     

Quasi-exact solvability beyond the <Emphasis Type="Italic">sl</Emphasis>(2) algebraization

We present evidence to suggest that the study of one-dimensional quasi-exactly solvable (QES) models in quantum mechanics should be extended beyond the usual sl(2) approach. The motivation is twofold: We first show that certain quasi-exactly solvable potentials constructed with the sl(2) Liealgebraic method allow for a new larger portion of the spectrum to be obtained algebraically. This is done via another algebraization in which the algebraic Hamiltonian cannot be expressed as a polynomial in the generators of sl(2). We then show an example of a new quasi-exactly solvable potential which cannot be obtained within the Lie algebraic approach. The text was submitted by the authors in English.     

Mathematical modeling for facilitated transport of Ge(IV) through supported liquid membrane containing Alamine 336

A mathematical model was developed for the germanium-facilitated transport from a medium containing tartaric acid using Alamine 336 as a carrier. Modeling was carried out based on the extraction constant (K _ext) obtained from the liquid–liquid extraction (LLX) modeling. The LLX data were achieved from experiments with conditions being Alamine 336 concentrations of 0.1–10% v/v from a solution containing about 1.378 mmol/L Ge (100 mg/L) and tartaric acid as an anionic complexant. The LLX model was attained using the equilibrium-based procedure and fitted to extraction experimental data for various carrier concentrations. This model presented an accurate extraction constant (K _ext = 0.02) used in the facilitated transport modeling. The flat sheet supported liquid membrane (FSSLM) experiments were conducted in the condition of 1.378 mmol/L Ge (100 mg/L), tartaric acid concentration of 2.760 mmol/L, 1 M HCl as a stripping phase and various Alamine 336 concentrations in the range of 0–35% v/v. The FSSLM model was developed according to the Fick’s law, the diffusional transport, and equilibrium equations. According to the model, mass transfer and diffusion coefficients for various concentrations of the carrier were found. In addition, the calculated and experimental values had a good correlation with together showing the validity of the model. This model can be used in the further process simulation such as hollow fiber SLMs.     

Graphitization of Carbon Particles in a Non-thermal Plasma Reactor

The production of nanomaterials using non-thermal plasmas remains the focus of ongoing investigations due to advantageous properties of this class of processes, most notably the intense plasma-induced heating arising from energetic recombination events occurring at the surface of nanoparticles, which allows for the tailored synthesis of crystalline nanoparticles. In this work, the authors discuss an in situ, in-flight Fourier Transform Infrared absorption spectroscopy technique to investigate the temperature variation of carbon nanoparticles during their synthesis in an acetylene–argon–hydrogen non-thermal RF plasma. Based on the FTIR measurements, decreasing hydrogenation levels and the progressive onset of an incandescence signal were observed at increasing RF input power. In the high RF power region, the carbon particle temperature, derived by fitting the corresponding FTIR spectra with a modified Planck’s law, shows values above 2000 K. The corresponding ex situ characterization of the synthesized materials by Transmission Electron Microscopy and Raman Spectroscopy displays the production of highly graphitic particles and loss of bonded hydrogen from the material, hence supporting the substantial nanoparticle heating derived from the FTIR measurements.     

New natural product -an efficient antimicrobial applications of new newly synthesized pyrimidine derivatives by the electrochemical oxidation of hydroxyl phenol in the presence of 2-mercapto-6-(trifluoromethyl) pyrimidine-4-ol as nucleophile

Some new pyrimidine derivatives have been synthesised by electrochemical oxidation of catechol (1a) in the existence of 2-mercapto-6-(trifluoromethyl) pyrimidine-4-ol (3) as a nucleophile in aqueous solution using Cyclic Voltammetric and Controlled Potential Coulometry. The catechol has been oxidised to o-quinone through electrochemical method and participative in Michael addition reaction, leading to the development of some new pyrimidine derivatives. The products were achieved in good yield with high pureness. The mechanism of the reaction has been conformed from the Cyclic Voltammetric data and Controlled Potential Coulometry. After purification, the compounds were characterised using modern techniques. The synthesised materials were screened for antimicrobial actions using Gram positive and Gram negative strain of bacteria. These new synthesised pyrimidine derivatives showed very good antimicrobial activity.     

Pt/oxide nanocatalysts synthesized via the ultrasonic spray pyrolysis process: engineering metal–oxide interfaces for enhanced catalytic activity

We show that Pt nanoparticles synthesized on oxide nanocatalysts exhibit catalytic activity enhancement depending on the type of the oxide support. To synthesize the Pt/oxide nanocatalysts, we employed a versatile synthesis method using Pt nanoparticles (NPs) supported on various metal oxides (i.e., SiO₂, CeO₂, Al₂O₃, and FeAl₂O₄) utilizing ultrasonic spray pyrolysis. Catalytic CO oxidation was carried out on these catalysts, and it was found that the catalytic activity of the Pt NPs varied depending on the supporting oxide. While Pt/CeO₂ exhibited the highest metal dispersion and active surface area, Pt/FeAl₂O₄ exhibited the lowest active surface area. Among the Pt/oxide nanocatalysts, Pt NPs supported on CeO₂ showed the highest catalytic activity. We ascribe the enhancement in turnover frequency of the Pt/CeO₂ nanocatalysts to strong metal–support interactions due to charge transport between the metal catalysts and the oxide support. Such Pt/oxide nanocatalysts synthesized via spray pyrolysis offer potential possibilities for large-scale synthesis of tailored catalytic systems for technologically relevant applications.     

Magnetic Field Treatments Improves Sunflower Yield by Inducing Physiological and Biochemical Modulations in Seeds

Magnetic seed enhancement has been practicing as a promising tool to improve germination and seedling growth of low vigor seeds stored under suboptimal conditions, but there is still ambiguity regarding the prospects for magnetism in oilseeds. Present study elucidates the potential of magnetic seed stimulation to improve sunflower germination, growth and yield. Germination and emergence tests were performed to optimize the strength of the magnetic field to sunflower seed enhancement. The seeds were directly exposed to magnetic field strengths of 50, 100 and 150 millitesla (mT) for 5, 10 and 15 min (min) and then standard germination tests were performed. Secondly, the emergence potential of untreated seeds was compared with seed exposed to hydropriming, priming with 3% moringa leaf extract (MLE), priming with magnetically treated water (MTW) for 10 min and priming with 3% MLE solution prepared in magnetically treated water (MTW + MLE). Germination, emergence, seedling growth and seed biochemical properties were used to select the best treatment for field evaluation. The results of the study revealed that magnetic seed treatment with 100 mT for 10 min and seed priming with 3% MLE solution in magnetically treated water (MTW + MLE) significantly improved emergence, crop growth rate and sunflower yield.