Operational Matrix of Fractional Integration Based on the Shifted Second Kind Chebyshev Polynomials for Solving Fractional Differential Equations

This paper is devoted to studying a computational method for solving multi-term differential equations based on new operational matrix of shifted second kind Chebyshev polynomials. The properties of the operational matrix of fractional integration are exploited to reduce the main problem to an algebraic equation. We present an upper bound for the error in our estimation that leads to achieve the convergence rate of O(M ^−κ). Numerical experiments are reported to demonstrate the applicability and efficiency of the proposed method.

     

Nandrolone decanoate increases the volume but not the length of the proximal and distal convoluted tubules of the mouse kidney

Anabolic androgenic steroids are widely used by athletes for increasing their muscle mass. These drugs are also used by some patients with chronic renal disease. But the effect of these drugs on the renal structure has received less attention. To investigate which parts of the kidney are affected by these drugs, mice kidneys were studied stereologically after injection of nandrolone decanoate (ND), an anabolic androgenic steroid. The treated group received nandrolone decanoate intraperitoneally (solved in olive oil) in doses of 3mg/kg of body weight and administered in one, two and three doses, respectively, in the first, second and third week of treatment. The mice in the control group received an olive oil solution. One week after the last injection, the mice were anaesthetized and their kidney removed. The analysis of data revealed that the weight of kidney was increased approximately 30% (p < or = 0.006) and its volume increased approximately 25% (p < or = 0.02) in ND treated mice in comparison with the control group. The volume of the cortex increased in ND treated animals approximately 44% (p < or = 0.006). Proximal convoluted tubules (PCT) and distal convoluted tubules (DCT) volume increased approximately 25% (p < or = 0.02) and approximately 68% (p < or = 0.02) in ND treated mice. The volume of glomeruli, other ducts, connective tissues, vessels and the length of PCT, DCT, collecting and Henle's ducts and vessels did not show significant differences. CONCLUSION: ND can increase the volume of the renal cortex and its two main parts, i.e. PCT and DCT in mice.     

Silica-bonded S-sulfonic acid as a recyclable catalyst for chemoselective synthesis of 1,1-diacetates

A simple and efficient procedure for the preparation of silica-bonded S-sulfonic acid (SBSSA) by reaction of 3-mercaptopropylsilica (MPS) and chlorosulfonic acid in chloroform is described. This solid acid is employed as a recyclable catalyst for the synthesis of 1,1-diacetates from aromatic aldehydes and acetic anhydride under mild and solvent-free conditions at room temperature.     

C-20 ketone reduction of hydrocortisone by rice field microalga <Emphasis Type="Italic">Chlorella vulgaris</Emphasis> MCCS 013

A unicellular microalga, Chlorella vulgaris, was isolated from rice field and applied in the biotransformation experiment of hydrocortisone (1). This strain has not been previously tested for hydrocortisone bioconversion. Fermentation was carried out in BG-11 medium supplemented with 0.05% substrate at 25°C for 14 days incubation. The products obtained were chromatographically purified followed by their characterization using spectroscopic methods. 11β,17α,20β,21-Tetrahydroxypregn-4-en-3-one (2), 11β,17β-dihydroxyandrost-4-en-3-one (3), and 11β-hydroxyandrost-4-ene-3,17-dione (4) were the main bioproducts in the hydrocortisone bioconversion. Bioreaction characteristics observed were 20-ketone reduction for accumulation of compound 2 and side chain degradation of the substrate to prepare compounds 3 and 4. Time course study showed the accumulation of the product 2 from the second day of the fermentation and 3 as well as 4 from the third day. All the metabolites reached their maximum concentration in seven days. Microalgal 18S rRNA gene was also amplified by PCR. PCR products were sequenced to confirm their authenticity as 18S rRNA gene of microalgae. The result of PCR blasted with other sequenced microalgae in NCBI showed 100% homology to the 18S small subunit rRNA of six strains of Chlorella vulgaris.     

An improved electrochemical method for the synthesis of some benzofuran derivatives

Electrochemical oxidation of catechol and some 3-substituted catechols (1a--c) has been studied in the presence of 2-chloro-5,5-dimethyl-1,3-cyclohexanedione (3) in aqueous solution using cyclic voltammetry and controlled-potential coulometry. The results indicate that the quinones derived from catechols (1a--c) participate in a Michael addition reaction with 2-chloro-5,5-dimethyl-1,3-cyclohexanedione (3) with consumption of only two electrons per molecule of (1a--c) to from the corresponding benzoforans (10a--c). The electrochemical synthesis of benzofurans has been successfully performed at a carbon rod electrode and in an undivided cell with high yields and purity.     

Topological phases in Bi/Sb planar and buckled honeycomb monolayers

We investigate topological phases in two-dimensional Bi/Sb honeycomb crystals considering planar and buckled structures, both freestanding and deposited on a substrate. We use the multi-orbital tight-binding model and compare results with density functional theory calculations. We distinguish topological phases by calculating topological invariants, analyzing edge states properties of systems in a ribbon geometry and studying their entanglement spectra. We show that coupling to the substrate induces transition to the $Z_2$ topological insulator phase. It is observed that topological crystalline insulator (TCI) phase, found in planar crystals, exhibits an additional pair of edge states in both energy spectrum and entanglement spectrum. Transport calculations for TCI phase suggest robust quantized conductance even in the presence of crystal symmetry-breaking disorder.     

Scheduling tasks with exponential duration on unrelated parallel machines

This paper introduces a stochastic scheduling problem. In this problem a directed acyclic graphs (DAG) represents the precedence relations among $m$ tasks that $n$ workers are scheduled to execute. The question is to find a schedule $\Sigma$ such that if tasks are assigned to workers according to $\Sigma$, the expected time needed to execute all the tasks is minimized. The time needed to execute task $t$ by worker $w$ is a random variable expressed by a negative exponential distribution with parameter ${\lambda }_{wt}$ and each task can be executed by more than one worker at a time. In this paper, we will prove that the problem in its general form is NP-hard, but when the DAG width is constant, we will show that the optimum schedules can be found in polynomial time.     

Effect of relative humidity on current–voltage characteristics of an electrostatic precipitator

This paper aims at characterizing the behavior of dc corona discharge in wire-to-plane electrostatic precipitators (ESPs) as influenced by the relative humidity (RH) of the inlet air. The current–voltage characteristics and time evolution of the current are analyzed. Experimental results show that discharge current is strongly affected by the RH level of the inlet air. For instance, the time-averaged current is lower at higher RH for a given voltage, except when RH = 99%. Time evolution of the discharge current is affected by the humidity especially in the case of negative corona.     

Solvent influence upon complexation of N-phenylaza-15-crown-5 with UO2 2+ cation in binary mixed non-aqueous solvents

The complexation reaction of N-phenylaza-15-crown-5 (PhA15C5) with UO₂ ²⁺ cation was studied in acetonitrile–methanol (AN–MeOH), acetonitrile–butanol (AN–BuOH), acetonitrile–dimethylformamide (AN–DMF) and methanol–propylencarbonate (MeOH–PC) binary solutions, at different temperatures by conductometry method. The conductance data show that the stoichiometry of the complex formed between PhA15C5 with UO₂ ²⁺ cation in most cases is 1:1 [M:L], but in some solvent systems a 1:2 [M:L₂] complex is formed in solutions. The results revealed that, the stability constant of (PhA15C5·UO₂)²⁺ complex in the binary mixed solvents varies in the order: AN–BuOH>AN–MeOH>AN–DMF. In the case of the pure organic solvents, the sequence of the stability of the complex changes as: AN>PC>BuOH>DMF. A non-linear relationship was observed for changes of logK_f of (PhA15C5·UO₂)²⁺ complex versus the composition of the binary mixed solvents. The corresponding standard thermodynamic parameters (ΔH_c°, ΔS_c°) were obtained from temperature dependence of the stability constant. The results show that the values and also the sign of these parameters are influenced by the nature and composition of the mixed solvents.     

Synthesis and Structure Elucidation of Novel Spirooxindole Linked to Ferrocene and Triazole Systems via [3 + 2] Cycloaddition Reaction

In the present work, a novel heterocyclic hybrid of a spirooxindole system was synthesized via the attachment of ferrocene and triazole motifs into an azomethine ylide by [3 + 2] cycloaddition reaction protocol. The X-ray structure of the heterocyclic hybrid (1″R,2″S,3R)-2″-(1-(3-chloro-4-fluorophenyl)-5-methyl-1H-1,2,3-triazole-4-carbonyl)-5-methyl-1″-(ferrocin-2-yl)-1″,2″,5″,6″,7″,7a″-hexahydrospiro[indoline-3,3″-pyrrolizin]-2-one revealed very well the expected structure, by using different analytical tools (FTIR and NMR spectroscopy). It crystallized in the triclinic-crystal system and the P-1-space group. The unit cell parameters are a = 9.1442(2) Å, b = 12.0872(3) Å, c = 14.1223(4) Å, α = 102.1700(10)°, β = 97.4190(10)°, γ = 99.1600(10)°, and V = 1484.81(7) ų. There are two molecules per unit cell and one formula unit per asymmetric unit. Hirshfeld analysis was used to study the molecular packing of the heterocyclic hybrid. H···H (50.8%), H···C (14.2%), Cl···H (8.9%), O···H (7.3%), and N···H (5.1%) are the most dominant intermolecular contacts in the crystal structure. O···H, N···H, H···C, F···H, F···C, and O···O are the only contacts that have the characteristic features of short and significant interactions. AIM study indicated predominant covalent characters for the Fe–C interactions. Also, the electron density (ρ(r)) at the bond critical point correlated inversely with the Fe–C distances.