A time discretization scheme of a characteristics method for a fluid–rigid system with discontinuous density

We propose a new characteristics method for the time discretization of a fluid–rigid system in the case when the densities of the fluid and the solid are different. This method is based on a global weak formulation involving only terms defined on the whole fluid–rigid domain. The main idea is to construct a characteristic function which preserves the rigidity of the solid at the discrete time levels. A convergence result for this semi-discrete scheme is then given.     

Semigroups of transformations restricted by an equivalence

Suppose σ is an equivalence on a set X and let E(X, σ) denote the semigroup (under composition) of all α: X → X such that σ ⊆ α ∘ α ⁻¹. Here we characterise Green’s relations and ideals in E(X, σ). This is analogous to recent work by Sullivan on K(V, W), the semigroup (under composition) of all linear transformations β of a vector space V such that W ⊆ ker β, where W is a fixed subspace of V.     

Admission control for a multi-server queue with abandonment

In a M/M/N+M queue, when there are many customers waiting, it may be preferable to reject a new arrival rather than risk that arrival later abandoning without receiving service. On the other hand, rejecting new arrivals increases the percentage of time servers are idle, which also may not be desirable. We address these trade-offs by considering an admission control problem for a M/M/N+M queue when there are costs associated with customer abandonment, server idleness, and turning away customers. First, we formulate the relevant Markov decision process (MDP), show that the optimal policy is of threshold form, and provide a simple and efficient iterative algorithm that does not presuppose a bounded state space to compute the minimum infinite horizon expected average cost and associated threshold level. Under certain conditions we can guarantee that the algorithm provides an exact optimal solution when it stops; otherwise, the algorithm stops when a provided bound on the optimality gap is reached. Next, we solve the approximating diffusion control problem (DCP) that arises in the Halfin–Whitt many-server limit regime. This allows us to establish that the parameter space has a sharp division. Specifically, there is an optimal solution with a finite threshold level when the cost of an abandonment exceeds the cost of rejecting a customer; otherwise, there is an optimal solution that exercises no control. This analysis also yields a convenient analytic expression for the infinite horizon expected average cost as a function of the threshold level. Finally, we propose a policy for the original system that is based on the DCP solution, and show that this policy is asymptotically optimal. Our extensive numerical study shows that the control that arises from solving the DCP achieves a very similar cost to the control that arises from solving the MDP, even when the number of servers is small.     

Regular path decompositions of odd regular graphs

Kotzig asked in 1979 what are necessary and sufficient conditions for a d‐regular simple graph to admit a decomposition into paths of length d for odd d>3. For cubic graphs, the existence of a 1‐factor is both necessary and sufficient. Even more, each 1‐factor is extendable to a decomposition of the graph into paths of length 3 where the middle edges of the paths coincide with the 1‐factor. We conjecture that existence of a 1‐factor is indeed a sufficient condition for Kotzig's problem. For general odd regular graphs, most 1‐factors appear to be extendable and we show that for the family of simple 5‐regular graphs with no cycles of length 4, all 1‐factors are extendable. However, for d>3 we found infinite families of d‐regular simple graphs with non‐extendable 1‐factors. Few authors have studied the decompositions of general regular graphs. We present examples and open problems; in particular, we conjecture that in planar 5‐regular graphs all 1‐factors are extendable. © 2009 Wiley Periodicals, Inc. J Graph Theory 63: 114–128, 2010     

Experimental and molecular modeling investigation of (E)-N-{2-[(2-hydroxybenzylidene)amino]phenyl}benzenesulfonamide

The Schiff base compound (E)-N-{2-[(2-hydroxybenzylidene)amino]phenyl}benzenesulfonamide has been synthesized and characterized by IR, NMR and Uv-vis spectroscopies, and single-crystal X-ray diffraction technique. In addition, quantum chemical calculations employing density functional theory (DFT) method with the 6–311++G(d,p) basis set were performed to study the molecular, spectroscopic and some electronic structure properties of the title compound, and the results were compared with the experimental findings. There exists a good correlation between experimental and theoretical data. Enol-imine/keto-amine tautomerization mechanism was investigated in the gas phase and in solution phase using the polarizable continuum model (PCM) approximation. The energetic and thermodynamic parameters of the enol-imine?→?keto-amine transfer process show that the single proton exchange is thermodynamically unfavored both in the gas phase and in solution phase. However, the reverse reaction seems to be feasible with a low barrier height and is supported by negative values in enthalpy and free energy changes both in the gas phase and in solution phase. The solvent effect is found to be sizable with increasing polarity of the solvents for the reverse reaction. The predicted nonlinear optical properties of the compound are found to be much greater than those of urea.     

Molecular structure, spectroscopic properties and DFT calculations of 2-(methylthio)nicotinic acid

The analyses of possible conformations, molecular structures, vibrational and electronic properties of 2-(methylthio)nicotinic acid molecule, C₇H₇NO₂S, with the synonym 2-(methylsulfanyl)nicotinic acid have been first presented theoretically. At the same time, FT-IR and micro-Raman spectra of 2-(methylthio)nicotinic acid were recorded in the regions 400–4000 cm^?1 and 100–4000 cm^?1, respectively. In our calculations, the DFTB3LYP method with 6–311G(d, p) basis set was used to have the structural and spectroscopic data about the mentioned molecule in the ground state and the results obtained were compared with experimental values. Furthermore, gauge invariant atomic orbital (GIAO) ¹H and ¹³C NMR chemical shifts in different solvents, UV-vis TD-DFT calculations, the highest occupied molecular orbitals (HOMO-2, HOMO-1, HOMO), lowest unoccupied molecular orbital (LUMO), molecular electrostatic potantial (MEP) surface, atomic charges and thermodynamic properties of molecule have been theoretically verified and simulated at the mentioned level. The energetic behavior of title molecule in different solvent media was investigated by using DFT/B3LYP method with 6–311G(d, p) basis set in terms of integral equation formalism polarizable continuum model (IEFPCM). In addition, the calculated infrared intensities, Raman activities, reduce masses and force constants of the compound under study have been also reported.     

Nonlinear Optical Properties of Benzylic Amide [2] Catenanes: A Novel Versatile Photonic Material

Abstract

Benzylic amide catenanes are a class of synthetically-accessible interlocked molecular rings which can rotate one through the other depending on the nature of the local environment. The rings contain four phenyl units each and interlocking also affords their packing in novel, highly interacting ways that may lead to unexpected properties thus opening up the possibility of developing new materials. Third harmonic generation in benzylic amide catenane solutions was measured at a wavelength of γ = 1064 nm, with the fundamental and the harmonic wavelengths in the region of transparency of the material. The thoroughly non resonant value of the hyperpolarisability γ(-3ω; ω, ω, ω) was found to be (6.5 ± 0.7) × 10^?35 esu with a negligible imaginary part, in agreement with the value of (6.8 ± 0.9) × 10^?35 esu calculated from a bond-additivity model of hyperpolarisability. The static second order hyperpolarisability predicted by a Molecular Orbital model was about a factor four less than the experimental value. Second hyperpolarizability values of several solvents were also measured at the fundamental wavelength of γ = 1064 nm.     

Sample Preparation for the Determination of Metals in Food Samples Using Spectroanalytical Methods—A Review

Abstract

The present article gives an overview of recent publications and modern techniques of sample preparation for food analysis employing atomic and inorganic mass spectrometric techniques, such as flame atomic absorption spectrometry, chemical vapor generation atomic absorption and atomic fluorescence spectrometry, graphite furnace atomic absorption spectrometry, inductively coupled plasma optical emission spectrometry, and inductively coupled plasma mass spectrometry. Among the most frequently applied sample preparation techniques for food analysis are dry ashing, usually with the addition of an ashing aid, and acid digestion, preferably with the assistance of microwave energy. Slurry preparation, particularly with the assistance of ultrasound, is increasingly used to reduce acid consumption and sample preparation time. Direct analysis of solid samples is gaining importance in the field of food analysis as it offers the highest sensitivity, avoids the use of acids and other aggressive reagents, makes possible the analysis of micro‐samples, and can be applied for fast screening analysis, e.g., of fresh meat.     

Controle de l'enrichissement de l'uranium metallique a l'aide du nitrate de cellulose

Abstract

Le nitrate de cellulose permet d'enregistrer le passage de particules α done de mesurer l'activité spécifique d'une source radioactive épaisse. Nous utilisons cette propriété pour mesurer le taux d'eorichissement en uranium 235 d'un éhantillon d'uranium métallique. Afin de faciliter la mesure et de s'affranchir de la lecture du nombre de traces au microscope optique, les échantillons sont révélés dans un bain spécial et le nombre de traces α par unité de surface est évalué en fonction du pouvoir réflecteur de l'échantillon.

Les moyens et le temps nécessaires pour une mesure sont, ainsi que le prix de revient, très réduits.

Cellulose nitrate can be used for the registration of α-tracks and therefore for the measurement of the specific activity of thick radioactive sources. This characteristic is applied to the determination of ²³⁵U enrichment rate of metallic uranium samples. For the measurement of track density a method is developed which replaces the counting procedure under a microscope. The samples are etched in special solutions and track density is evaluated from the diffuse reflecting power of the samples.

The main advantages of this method are its rapidity, easiness and low cost.     

Radioactivity concentrations in topsoil samples from the Thrace region of Turkey and assessment of radiological hazard

The activity concentrations of gamma emitting radionuclides were measured in surface soil samples from the Thrace region. ²³²Th, ²³⁸U, ²²⁶Ra, ⁴⁰K and ¹³⁷Cs activities and physico-chemical parameters of the soil samples were determined in samples collected from 73 sampling stations. Radionuclide concentrations measured were compared with those found in the samples from other locations of Turkey and from different countries. The average activity concentrations of ²³²Th, ²³⁸U, ²²⁶Ra, ⁴⁰K and ¹³⁷Cs were found to be 24.71 ± 8.79, 22.30 ± 7.93, 32.09±12.44, 509.00±160.05, 32.74±29.24 Bq kg^?1, respectively. The mean value of the annual effective dose equivalent from the outdoor terrestrial gamma radiation was calculated as 57.2 μ Sv.