Renormalized Solutions of Nonlinear Parabolic Equations in Weigthed Variable-Exponent Space

This article is devoted to study the existence of renormalized solutions for the nonlinear p(x)-parabolic problemin the Weighted-Variable-Exponent Sobolev spaces, without the sign condition and the coercivity condition.     

Existence of Renormalized Solutions of Nonlinear Elliptic Problems in Weighted Variable-Exponent Space

In this article, we study a general class of nonlinear degenerated elliptic problems associated with the differential inclusion $β(u)-div(a(x,Du)+F(u)) ∋ f$ in $Ω$ where $f ∈ L^1(Ω).$ A vector field $a(.,.)$ is a Carathéodory function. Using truncation techniques and the generalized monotonicity method in the framework of weighted variable exponent Sobolev spaces, we prove existence of renormalized solutions for general $L^1$-data.     

Angular dependence of the critical current density and the temperature scaling of the flux pinning force in YBCO thin film

In this paper, the critical current J_c(Θ) have been investigated as a function of magnetic-field angle Θ. Θ is the angle between the c-axis and the applied magnetic field direction. This investigation concerned three temperature values (60?K, 78?K and 81?K). The normalized pinning force f_p versus the normalized magnetic field h was also studied (f_p?=?F_p / F_pmax and h?=?H / H_max). The F_p expression was determined based on the Kramer model.The studied sample was a single crystal of YBaCuO thin film deposited by the ablation laser method on the surface (100) of a SrTiO₃ substrate.The results of this work show the existence of point core pinning of the normal centers in the low field regime and the occurrence of the flux creep in high field regime.     

RESPONSE OF MICROPOLAR THERMOELASTIC SOLID WITH VOIDS DUE TO VARIOUS SOURCES UNDER GREEN NAGHDI THEORY

Green-Naghdi (G-N) theory of thermoelasticity is employed to study the deformation of micropolar thermoelastic solid with voids considering the influence of varions sources acting on the plane surface....     

Theoretical Density Functional Theory insights into the nature of chalcogen bonding between CX2 (X = S,Se, Te) and diazine from monomer to supramolecular complexes

Chalcogen bonding is a noncovalent interaction, highly similar to halogen and hydrogen bonding, occurring between a chalcogen atom and a nucleophilic region. Two density functional theory (DFT) approaches B3LY-D3 and B97-D3 were performed on a series of complexes formed between CX₂ (X = S, Se, Te) and diazine (pyridazine, pyrimidine and pyrazine). Chalcogen atoms prefer interacting with the lone pair of a nitrogen atom rather than with the π-cloud of an aromatic ring. CTe₂ and CSe₂ form a stronger chalcogen bond than CS₂. The electrostatic potential of CX₂ (X = S, Se and Te) reveals the presence of two equivalent σ-holes, one on each chalcogen atom. These CX₂ molecules interact with diazine giving rise to supramolecular interactions. Wiberg bond index and second-order perturbation theory analysis in NBO were performed to better understand the nature of the chalcogen bond interaction.     

Hemisynthesis,crystal structure and inhibitory effect of sesquiterpenic thiosemicarbazones and thiazolidin‐4‐ones on the corrosion behaviour of stainless steel in 1 M H2SO4 solution

Treatment of thiosemicarbazones prepared from sesquiterpenes with ethyl 2‐bromoacetate in the presence of sodium acetate afforded the corresponding thiazolidin‐4‐ones. The structures of all the newly synthesized compounds were established by considering spectral and single‐crystal X‐ray diffraction data. The title compound, ethyl 2‐((Z)‐2‐{(Z)‐[(1aR,5aR,9aS)‐1,1‐dichloro‐1a,5,5,7‐tetramethyl‐1a,2,3,4,5,5a,8,9‐octahydro‐1H‐benzo[a]cyclopropa[b][7]annulen‐8‐ylidene]hydrazono}‐4‐oxothiazolidin‐3‐yl)acetate, C₂₃H₃₁Cl₂N₃O₃S, 5 , crystallizes in the orthorhombic noncentrosymmetric space group P2₁2₁2₁ with Z = 4. Within the molecule in the crystal structure, the cyclohexene ring has an envelope conformation and the cycloheptane ring, to which it is fused, has a boat conformation. In the crystal, molecules are linked by C—H…Cl hydrogen bonds forming chains propagating along the b‐axis direction. The absolute configuration of the molecule in the crystal could be fully confirmed from anomalous dispersion effects [Flack parameter = ?0.04 (2)]. Thiosemicarbazones 1 and 2 are efficient inhibitors for steel corrosion in 1 M H₂SO₄ solution, with a maximum efficiency of 92.28% at 10^?3 M. Furthermore, thiosemicarbazone compounds were found to be more efficient than thiazolidin‐4‐one derivatives. In addition, cyclic voltammetry was used to characterize the tested molecules, as well to estimate the experimental value of the energy band gap.     

Magnetocaloric Effect in Anisotropic Mixed Spin ½—1 System: Pair Approximation Method

We use the Pair Approximation method to analyze the magnetic and magnetocaloric behaviors of diluted mixed spin ${\rm S_A}$=1 and spin ${\rm S_B}$=1/2 with the anisotropic Heisenberg model, on a cubic lattice with coordination number $z$=6. Our system is described in presence of an external magnetic field; the phase diagram and thermodynamic properties related to the concentration of magnetic atom (A or B) and the single ion anisotropy are constructed and discussed. Special attention is paid to magnetocaloric properties provided by isothermal entropy change as well as the cooling capacity. These cooling power keys are plotted and discussed as a function of interaction anisotropy and magnetic component concentration of two sublattices ions A and B. Numerical results show a double peak structure in the entropy change curve and the inverse magnetocaloric effect related to the presence of the negative single-ion anisotropy.     

Effect of phosphatidylserine content on the partition coefficients of diazepam and flurazepam between phosphatidylcholine-phosphatidylserine bilayer of small unilamellar vesicles and water studied by second derivative spectrophotometry

The affinity of the psychotropic benzodiazepine drugs diazepam (DZ) and flurazepam (FZ) to phosphatidylserine (PS) was examined since PS is abundantly contained in brain membranes. The effect of PS content on the partition coefficients (K(p)s) of these drugs between phosphatidylcholine (PC)-PS bilayer membranes of small unilamellar vesicles (SUV) and water was measured using second derivative spectrophotometry. The second derivative spectra of DZ and FZ measured in the solutions containing various amounts of PC-PS SUV clearly showed derivative isosbestic points and a distinct derivative intensity change depending on the amount of the SUV added. The derivative intensity differences (AD) of the drugs before and after addition of the SUV suspension were measured at a specific wavelength. Using the AD values, the Kp values were calculated and obtained with relative standard deviation of below 10%. The Kp values of both drugs increased according to the PS content in the PS-PC bilayer membranes of the SUV proving that both have higher affinity to the PC-PS bilayer membranes than to PC membranes. The effect was much larger for FZ, i.e., the Kp value of FZ at 30 mol% PS content increased to about five times the value for the PC SUV. This can be explained by the fact that at the experimental pH of 7.4, 80% of FZ molecules are in a cationic form (pKa=8.1), so that these molecules are highly accessible to the negatively charged PS molecules. The results support the rapid and high distribution of DZ and FZ in the central nervous system after their administration.     

The microdetermination of certain pyrimidine derivatives

N-Bromosuccinimide has been used in a new titrimetric method for the microdetermination of uracil, thymine, and sulfadiazine. The reaction between these compounds and N-bromosuccinimide in dilute aqueous solutions is discussed. The determination is carried out within the limits of 10 mg to 100 μg where the experimental error did not exceed ±2%.     

Factorial preservation

Let A be a Dedekind domain with finite residue fields and with a finite unit group. Let S be an infinite subset of A and f be a polynomial with coefficients in the quotient field of A. We show that if the subsets S and f (S) have the same factorials (in Bhargavas sense), then f is of degree 1. In particular, we answer Gilmer and Smiths question [10] if S and f (S) are polynomially equivalent (in McQuillans sense), then f is of degree 1.Received: 29 March 2004