Completely discrete schemes for 2D Sobolev equations with Burgers’ type nonlinearity

Numerical Algorithms - Inthis paper, we discuss two first-order completely discrete schemes based on Backward Euler and its linearized variant methods for the 2D Sobolev equations with...     

Thermophysical properties of neat and radiolytically degraded acidic extractants present in room temperature ionic liquid

In the present work, radon concentrations were measured in surface and underground water samples in Faridabad District of Southern Haryana, India using an active radon monitor based on alpha scintillation technique and results have been inter-compared. The average radon concentration in the underground water samples was observed to be 4 times higher than in the surface water samples. The estimated annual effective dose varied from 5.7 to 58.5 μSvy^?1 with an average of 24.2 μSvy^?1 for underground water samples and 1.1 to 12.5 μSvy^?1 with an average of 6.7 μSvy^?1 for surface water samples. The estimated annual effective dose for both type of samples was found to be less than 0.1 mSvy^?1, which is the safe limit as suggested by World Health Organisation and EU Council.

     

The ABC of Insulin: The Organic Chemistry of a Small Protein

Insulin is a small protein crucial for regulating the blood glucose level in all animals. Since 1922 it has been used for the treatment of patients with diabetes. Despite consisting of just 51 amino acids, insulin contains 17 of the proteinogenic amino acids, A- and B-chains, three disulfide bridges, and it folds with 3 α-helices and a short β-sheet segment. Insulin associates into dimers and further into hexamers with stabilization by Zn²⁺ and phenolic ligands. Selective chemical modification of proteins is at the forefront of developments in chemical biology and biopharmaceuticals. Insulin's structure has made it amenable to organic and inorganic chemical reactions. This Review provides a synthetic organic chemistry perspective on this small protein. It gives an overview of key chemical and physico-chemical aspects of the insulin molecule, with a focus on chemoselective reactions. This includes N-acylations at the N-termini or at Lys^B29 by pH control, introduction of protecting groups on insulin, binding of metal ions, ligands to control the nano-scale assembly of insulin, and more.     

Coordination and Hydroboration of Ru(II)-Borate Complexes: Dihydridoborate vs. Bis(dihydridoborate)

Treatment of [Cp*RuCl₂]₂, 1 , [(COD)IrCl]₂, 2 or [(p-cymene)RuCl₂]_2, 3 (Cp*=η⁵-C₅Me_5, COD= 1,5-cyclooctadiene and p-cymene=η⁶-ⁱPrC₆H₄Me) with heterocyclic borate ligands [Na[(H₃B)L], L₁ and L₂ ( L₁ : L=amt, L₂ : L=mp; amt=2-amino-5-mercapto-1,3,4-thiadiazole, mp=2-mercaptopyridine) led to the formation of borate complexes having uncommon coordination. For example, complexes 1 and 2 on reaction with L₁ and L₂ afforded dihydridoborate species [L^AM(μ-H)₂BHL] 4 – 6 ( 4 : L^A=Cp*, M=Ru, L=amt; 5 : L^A=Cp*, M=Ru, L=mp; 6 : L^A=COD, M=Ir, L=mp). On the other hand, treatment of 3 with L₂ yielded cis- and trans-bis(dihydridoborate) species, [Ru{(μ-H)₂BH(mp)}₂], cis- 7 and trans- 7 . The isolation and structural characterization of fac- and mer-[Ru{(μ-H)₂BH(mp)}{(μ-H)BH(mp)₂}], 8 from the same reaction offered an insight into the behaviour of these dihydridoborate species in solution. Fascinatingly, despite having reduced natural charges on Ru centres both at cis-and trans- 7 , they underwent hydroboration reaction with alkynes that yielded both Markovnikov and anti-Markovnikov addition products, 10 a – d .     

Quantitative estimations of bivariate summation‐integral–type operators

In this paper, we study the approximation properties of bivariate summation‐integral–type operators with two parameters . The present work deals within the polynomial weight space. The rate of convergence is obtained while the function belonging to the set of all continuous and bounded function defined on ([0],∞)(×[0],∞) and function belonging to the polynomial weight space with two parameters, also convergence properties, are studied. To know the asymptotic behavior of the proposed bivariate operators, we prove the Voronovskaya type theorem and show the graphical representation for the convergence of the bivariate operators, which is illustrated by graphics using Mathematica. Also with the help of Mathematica, we discuss the comparison by means of the convergence of the proposed bivariate summation‐integral–type operators and Szász‐Mirakjan‐Kantorovich operators for function of two variables with two parameters to the function. In the same direction, we compute the absolute numerical error for the bivariate operators by using Mathematica and is illustrated by tables and also the comparison takes place of the proposed bivariate operators with the bivariate Szász‐Mirakjan operators in the sense of absolute error, which is represented by table. At last, we study the simultaneous approximation for the first‐order partial derivative of the function.     

Synthesis and characterization of dimeric μ-oxidovanadium complexes as the functional model of vanadium bromoperoxidase

Two vanadium (IV) complexes [V^IVO(Haeae-sal)(MeOH)]⁺ ( 1 ) and [V^IVO(Haeae-hyap)(MeOH)]⁺ ( 2 ) were prepared by reacting [VO(acac)₂] with ligands [H₂aeae-sal] ( I ) and [H₂aeae-hyap] ( II ) respectively. Condensation of 2-(2-aminoethylamino)ethanol with salicylaldehyde and 2-hydroxyacetophenone produces the ligands ( I ) and ( II ) respectively. Both vanadium complexes 1 and 2 are sensitive towards aerial oxygen in solution and rapidly convert into vanadium(V) dioxido species. Vanadium(V) dioxido species crystalizes as the dimeric form in the solid-state. Single-crystal XRD analysis suggests octahedral geometry around each vanadium center in the solid-state. To access the benefits of heterogeneous catalysis, vanadium(V) dioxido complexes were anchored into the polymeric chain of chloromethylated polystyrene. All the synthesized neat and supported vanadium complexes have been studied by a number of techniques to confirm their structural and functional properties. Bromoperoxidase activity of the synthesized vanadium(V) dioxido complexes 3 and 4 was examined by carrying out oxidative bromination of salicylaldehyde and oxidation of thioanisole. In the presence of hydrogen peroxide, 3 shows 94.4% conversion ( TOF value of 2.739 × 10² h⁻¹) and 4 exhibits 79.0% conversion (TOF value of 2.403 × 10² h⁻¹) for the oxidative bromination of salicylaldehyde where 5-bromosalicylaldehyde appears as the major product. Catalysts 3 and 4 also efficiently catalyze the oxidation of thioanisole in the presence of hydrogen peroxide where sulfoxide is observed as the major product. Covalent attachment of neat catalysts 3 and 4 into the polymer chain enhances substrate conversion (%) and their catalytic efficiency increases many folds, both in the oxidative bromination and oxidation of thioether. Polymer supported catalysts 5 displayed 98.8% conversion with a TOF value of 1.127 × 10⁴ h⁻¹ whereas catalyst 6 showed 95.7% conversion with a TOF value of 4.675 × 10³ h⁻¹ for the oxidative bromination of salicylaldehyde. These TOF values are the highest among the supported vanadium catalysts available in the literature for the oxidative bromination of salicylaldehyde.     

Effective removal of 4-Aminophenol from aqueous environment by pea (Pisum sativum) shells activated with sulfuric acid: Characterization,isotherm, kinetics and thermodynamics

The threat of phenol contamination in aquatic ecosystems is significant for the health of the earth's water systems as well as all humans on it. The present study was conducted to synthesize a cost-effective adsorbent (pea shells activated with sulfuric acid, PSASA) from agriculture waste (pea shells) and its use for effective removal of toxic 4-Aminophenol (4-AP). Newly designed PSASA exhibited significant adsorption of 4-AP which was confirmed by SEM, FT-IR, and XRD analysis. Surface topography confirmed high unevenness of the PSASA surface and the macroporous feature of the PSASA was confirmed by BET analysis. . Multiple testing was done to see how various factors affected adsorption such as adsorbent dose, temperature, pH, PZC, the effect of KCl and urea addition and the effect of the initial concentration of 4-AP. A drop in adsorption uptake of 4-AP was observed as the temperature increases from 25 °C to 45 °C. Maximum adsorption uptake (q_m) was found to be 106.11 mg/g at an optimum pH of 7.0 and 25 °C. Among various adsorption isotherm models tested, Langmuir Isotherm gave the best explanation with high R² values of experimental data. The pseudo-first-order model was found to explain the kinetics of adsorption well. The thermodynamic finding confirms the adsorption process was physical and exothermic. The adsorption of 4-AP was primarily governed by electrostatic interaction, hydrogen-bonding and π-π exchange mechanism. Because of the positive outcomes of the present research, we can use the PSASA as a cost-effective adsorbent for removing phenolic compounds.     

On nonsmooth V-invexity and vector variational-like inequalities in terms of the Michel–Penot subdifferentials

In this paper, we establish some results which exhibit an application for Michel–Penot subdifferential in nonsmooth vector optimization problems and vector variational-like inequalities. We formulate vector variational-like inequalities of Stampacchia and Minty type in terms of the Michel–Penot subdifferentials and use these variational-like inequalities as a tool to solve the vector optimization problem involving nonsmooth V-invex function. We also consider the corresponding weak versions of the vector variational-like inequalities and establish various results for the weak efficient solutions.     

A summation‐integral type modification of Szász–Mirakjan operators

In this paper, we introduced a summation‐integral type modification of Szász–Mirakjan operators. Calculation of moments, density in some space, a direct result and a Voronvskaja‐type result, are obtained. Copyright © 2016 John Wiley & Sons, Ltd.     

Further study of alternating iterations for rectangular matrices

Theory of matrix splittings is a useful tool in the analysis of iterative methods for solving systems of linear equations. When two splittings are given, it is of interest to compare the spectral radii of the corresponding iteration matrices. This helps to arrive at the conclusion that which splitting should one choose so that one can reach the desired solution of accuracy or the exact solution in a faster way. In the case of many splittings are provided, the comparison of the spectral radii is time-consuming. Such a situation can be overcome by introducing another iteration scheme which converges to the same solution of interest in a much faster way. In this direction, the theory of alternating iterations for real rectangular matrices is recently proposed. In this note, some more results to the theory of alternating iterations are added. A comparison result of two different alternating iteration schemes is then presented which will help us to choose the iteration scheme that will guarantee the faster convergence of the alternating iteration scheme. In addition to these results, a comparison result for proper weak regular splittings is also obtained.