Mesoscopic tube model of fluids composed of worm-like micelles

Rheological model of fluids involving Brownian relaxation, reptation, diffusion, and scission–recombination processes as relaxation mechanisms is formulated. Numerical solution of a particular example of the model displays the S-shape form of the shear rate versus shear stress curves observed in worm-like micellar solutions.     

Inequalities and bounds for the eigenvalues of the sub-Laplacian on a strictly pseudoconvex CR manifold

We establish inequalities for the eigenvalues of the sub-Laplace operator associated with a pseudo-Hermitian structure on a strictly pseudoconvex CR manifold. Our inequalities extend those obtained by Niu and Zhang (Pac J Math 208(2):325–345, 2003 [26]) for the Dirichlet eigenvalues of the sub-Laplacian on a bounded domain in the Heisenberg group and are in the spirit of the well known Payne–Pólya–Weinberger and Yang universal inequalities.     

Regime-switching stochastic volatility model: estimation and calibration to VIX options

We develop and implement a method for maximum likelihood estimation of a regime-switching stochastic volatility model. Our model uses a continuous time stochastic process for the stock dynamics with the instantaneous variance driven by a Cox–Ingersoll–Ross process and each parameter modulated by a hidden Markov chain. We propose an extension of the EM algorithm through the Baum–Welch implementation to estimate our model and filter the hidden state of the Markov chain while using the VIX index to invert the latent volatility state. Using Monte Carlo simulations, we test the convergence of our algorithm and compare it with an approximate likelihood procedure where the volatility state is replaced by the VIX index. We found that our method is more accurate than the approximate procedure. Then, we apply Fourier methods to derive a semi-analytical expression of S&P500 and VIX option prices, which we calibrate to market data. We show that the model is sufficiently rich to encapsulate important features of the joint dynamics of the stock and the volatility and to consistently fit option market prices.     

Existence Results for Critical Semi-linear Equations on Heisenberg Group Domains

Following the work of G. Citti and F. Uguzzoni who studied Yamabe type problems on Heisenberg group domains, we consider here the following critical semi-linear equation on domains of the Heisenberg group ${{\mathbb{H}^1}}$ : $$(P) \left\{\begin{array}{lll}-{\Delta_{H}}u\quad =\quad K{u^{3}}\quad\,{\rm in}\,\,\Omega,\\ \quad\quad\,{u}\quad > \quad0\qquad\,\,\,\,{\rm in}\,\,\Omega,\\ \quad\quad\,{u}\quad = \quad 0 \quad\quad\,\,\,{\rm on}\,\partial \Omega, \end{array}\right. $$ where Δ _H is the sublaplacian on ${{\mathbb{H}^1}}$ and K is a C ³ positive function defined on Ω. Using a version of the Morse Lemma at infinity, we give necessary conditions on K to insure the existence of solutions for (P).     

Random walks on highly symmetric graphs

We consider uniform random walks on finite graphs withn nodes. When the hitting times are symmetric, the expected covering time is at least 1/2n logn-O(n log logn) uniformly over all such graphs. We also obtain bounds for the covering times in terms of the eigenvalues of the transition matrix of the Markov chain. For distance-regular graphs, a general lower bound of (n-1) logn is obtained. For hypercubes and binomial coefficient graphs, the limit law of the covering time is obtained as well.     

ab-initio investigations of electronic and magnetic properties of the tetragonal chalcopyrite BeTiTe2 compound: DFT + U study

The spin-polarised structural, electronic, and magnetic properties of the chalcopyrite BeTiTe₂ compound in tetragonal structure (Be_0.50Ti_0.50Te) have been studied by employing first-principles full-potential linearised augmented plane wave plus local orbitals (FP-L/APW?+?lo) method within the density functional theory (DFT) and implemented in WIEN2k code. The exchange and correlation energy are described in two frameworks of GGA (generalised gradient approximation) and GGA?+?U (U is the Hubbard term). The structural analysis confirms that the ferromagnetic phase of the tetragonal BeTiTe₂ compound (Be_0.50Ti_0.50Te) is energetically more favourable; also different equilibrium lattice parameters, such as lattice constants (a₀ and c₀), bulk modulus (B₀), and its first-pressure derivative (B?) have been evaluated in both paramagnetic and ferromagnetic phases. The electronic results of the tetragonal BeTiTe₂ compound show a complete half-metallic behaviour. Moreover, the computed total magnetic moment of this compound is close to 4 μ_B, confirming its half-metallic ferromagnetic nature.     

Effect of some physical and chemical parameters on fluoride removal by nanofiltration

In natural waters, fluoride ions are necessary and beneficial for the human being. At higher level of F⁻ in water, it is toxic and detrimental to human health, leading to serious problems such as dental and skeleton fluorosis. According to the World Health Organization, the acceptable concentrations of fluoride in potable water are in the range of 0.7–1.5 mg L⁻¹. Various treatment technologies for fluoride removal from water have been used such as ion exchange, adsorption and membrane processes. In the present study, removal of fluoride ions from aqueous solutions was investigated using a polyamide thin film composite nanofiltration membrane denoted as HL 2514 T from Osmonics Company. Through this membrane, the mechanism of transport was investigated. The Kedem–Katchelsky model was applied in order to determine phenomenological parameters σ and P _s, respectively, the reflection coefficient of the membrane and the solute permeability of ions. The convective and diffusive parts of the mass transfer were quantified. The retention of monovalent and bivalent salts by this membrane shows that it is negatively charged. In the second part, retention of fluoride anions was investigated. Results show that the retention of fluoride by HL membrane exceeds 80%. The influence of the chemical parameters (feed concentration and ionic strength) and the physical parameters (applied pressure and recovery) on the elimination of fluoride was studied.     

Signal-levelling agents for eliminating the interferences of iron,aluminium, barium and calcium in the determination of lead by flame atomic absorption spectrometry

The interferences of iron, aluminium, barium and calcium on the determination of lead by flame atomic absorption spectrometry are discussed; a titration procedure was used. Ascorbic acid, citric acid, EDTA and nitric acid were used successfully for levelling the interfering effects from the cations.