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.     

Growth mechanism and optical property of CdS nanoparticles synthesized using amino-acid histidine as chelating agent under sonochemical process

Using amino-acid histidine as chelating agent, CdS nanoparticles have been synthesized by sonochemical method. It is found that by varying the ultrasonic irradiation time, we can tune the band gap and particle size of CdS nanoparticles. The imidazole ring of histidine captures the Cd ions from the solution, and prevents the growth of the CdS nanoparticles. The deviation in the linear relation in between cube of radius of nanoparticles and ultrasonic irradiation time confirms the growth of CdS nanoparticles occur via two process; one is the diffusion process of the reactants as well as reaction at the surface of the crystallite. CdS nanoparticles synthesized using histidine as organic chelating agent have band edge emission at 481 nm and have greater photoluminescence intensity with blue-shift to higher energy due to typical quantum confinement effect.     

Hypersurfaces of a Finsler space with a special (<Emphasis Type="Italic">α</Emphasis>, <Emphasis Type="Italic">β</Emphasis>)-metric

In the present paper we study the Finslerian hypersurfaces of a Finsler space with a special (α, β) metric, and examine the hypersurfaces of this special metric as a hyperplane of first, second and third kinds.     

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.     

An efficient, one-pot synthesis of trithiocarbonates from the corresponding thiols using the Mitsunobu reagent

A novel Mitsunobu-based protocol has been developed for the synthesis of a variety of symmetrical and unsymmetrical trithiocarbonates from primary, secondary and tertiary thiols using carbon disulfide, in good to excellent yields. This protocol is mild and efficient compared to other reported methods.     

Renner-Teller and spin-orbit vibronic coupling effects in linear triatomic molecules with a half-filled pi shell

The vibronic and spin-orbit-induced interactions among the (3)Sigma(-), (1)Delta, and (1)Sigma(+) electronic states arising from a half-filled pi orbital of a linear triatomic molecule are considered, employing the microscopic (Breit-Pauli) spin-orbit coupling operator. The 6 x 6 Hamiltonian matrix is derived in a diabatic spin-orbital electronic basis set, including terms up to fourth order in the expansion of the molecular Hamiltonian in the bending normal coordinate about the linear geometry. The symmetry properties of the Hamiltonian are analyzed. Aside from the nonrelativistic fourth-order Renner-Teller vibronic coupling within the (1)Delta state and the second-order nonrelativistic vibronic coupling between the (1)Sigma(+) and (1)Delta states, there exist zeroth-order, first-order, as well as third-order vibronic coupling terms of spin-orbit origin. The latter are absent when the phenomenological expression for the spin-orbit coupling operator is used instead of the microscopic form. The effects of the nonrelativistic and spin-orbit-induced vibronic coupling mechanisms on the (3)Sigma(-), (1)Delta, and (1)Sigma(+) adiabatic potential energy surfaces as well as on the spin-vibronic energy levels are discussed for selected parameter values.     

On the formation of hydrogen peroxide in water microdroplets

Recent reports on the formation of hydrogen peroxide (H₂O₂) in water microdroplets produced via pneumatic spraying or capillary condensation have garnered significant attention. How covalent bonds in water could break under such mild conditions challenges our textbook understanding of physical chemistry and water. While there is no definitive answer, it has been speculated that ultrahigh electric fields at the air–water interface are responsible for this chemical transformation. Here, we report on our comprehensive experimental investigation of H₂O₂ formation in (i) water microdroplets sprayed over a range of liquid flow-rates, (shearing) air flow rates, and air composition, and (ii) water microdroplets condensed on hydrophobic substrates formed via hot water or humidifier under controlled air composition. Specifically, we assessed the contributions of the evaporative concentration and shock waves in sprays and the effects of trace O₃(g) on the H₂O₂ formation. Glovebox experiments revealed that the H₂O₂ formation in water microdroplets was most sensitive to the air–borne ozone (O₃) concentration. In the absence of O₃(g), we could not detect H₂O₂(aq) in sprays or condensates (detection limit ≥250 nM). In contrast, microdroplets exposed to atmospherically relevant O₃(g) concentration (10–100 ppb) formed 2–30 µM H₂O₂(aq), increasing with the gas–liquid surface area, mixing, and contact duration. Thus, the water surface area facilitates the O₃(g) mass transfer, which is followed by the chemical transformation of O₃(aq) into H₂O₂(aq). These findings should also help us understand the implications of this chemistry in natural and applied contexts.

A. Gallo Jr, H. Mishra et al., pinpoint the origins of the spontaneous H₂O₂ formation in water microdroplets formed via spraying or condensation, i.e., without the addition of electrical energy, catalyst, or co-solvent.     

Synthesis of 4a-carba-alpha-D-lyxofuranose from 2,3-O-isopropylidene-L-erythruronolactone via Tebbe-mediated cascade reaction

A new, efficient and highly diastereoselective approach for the synthesis of 1,2,3,5-tetraacetylcarba-alpha-D-lyxofuranose from D-ribose is reported via one-pot conversion of to using Tebbe reagent which involves a cascade reaction sequence of methylenation, cleavage of isopropyl group, carbocyclization and again methylenation.     

Reactivity of triazolyl Schiff bases with Ru(II)-2,2′-bipyridyl: Synthesis,spectroscopic characterization of isomers and their photo-physical properties

The condensation of 3-amino-1H-1,2,4-triazole with benzaldehyde and terephthalaldehyde provides the bidentate and tetradentate Schiff bases 1,2,4-triazolo-3-imino-benzene L¹H and 1,4-bis(1,2,4-triazolo-3-imino)benzene L²H₂, respectively. The well characterized Schiff bases were allowed to react with cis-Ru(bpy)₂Cl₂ · 2H₂O. Isomers of the mononuclear complexes Ru(bpy)₂L¹]PF₆ · NH₄PF₆ (1a, N4) and [Ru(bpy)₂L¹]PF₆ · 0.5NH₄PF₆ (1b, N2), and the dinuclear Ru(II) complexes [Ru(bpy)₂L²Ru(bpy)₂](PF₆)₂ · NH₄PF₆ (2a, N4N4), [Ru(bpy)₂L²Ru(bpy)₂](PF₆)₂ · NH₄PF₆ · 2H₂O (2b, N2N2) and [Ru(bpy)₂L²Ru(bpy)₂](PF₆)₃ · NH₄PF₆ (2c, Ru(II)-Ru(III)) were separated by column chromatography and characterized by their elemental analysis, FAB mass and spectral (IR, NMR, UV–Vis) data. The data obtained suggest that the ligands are bound to the metal centre via the N4 and N2 atoms of the triazole moiety along with the N (imine) atom. The complexes display metal-to-ligand charge-transfer (MLCT) transitions in the visible region from the dπ(Ru^II) → π^∗L transition. Highly intense ligand-based π→π^∗ transitions are observed in the UV region. A dual emission occurs from the N2 and N2N2 isomers.     

Formation of 8-nitroguanine and 8-oxoguanine due to reactions of peroxynitrite with guanine

Reactions of peroxynitrite with guanine were investigated using density functional theory (B3LYP) employing 6-31G** and AUG-cc-pVDZ basis sets. Single point energy calculations were performed at the MP2/AUG-cc-pVDZ level. Genuineness of the calculated transition states (TS) was tested by visually examining the vibrational modes corresponding to the imaginary vibrational frequencies and applying the criterion that the TS properly connected the reactant and product complexes (PC). Genuineness of all the calculated TS was further ensured by intrinsic reaction coordinate (IRC) calculations. Effects of aqueous media were investigated by solvating all the species involved in the reactions using the polarizable continuum model (PCM). The calculations reveal that the most stable nitro-product complex involving the anion of 8-nitroguanine and a water molecule i.e. 8NO(2)G(-) + H(2)O can be formed according to one reaction mechanism while there are two possible reaction mechanisms for the formation of the oxo-product complex involving 8-oxoguanine and anion of the NO(2) group i.e. 8OG + NO(2)(-). The calculated relative stabilities of the PC, barrier energies of the reactions and the corresponding enthalpy changes suggest that formation of the complex 8OG + NO(2)(-) would be somewhat preferred over that of the complex 8NO(2)G(-) + H(2)O. The possible biological implications of this result are discussed.