Existence of multiple positive periodic solutions for delay differential equation whose order is a multiple of 4

This article shows the existence of positive periodic solutions for retarded, advanced, neutral, and ordinary differential equations whose order is a multiple of 4. First, we find a positive Green’s function explicitly. Then assuming that the coefficient of the unknown in the linear part of the equation is bounded above and below by positive constants, we find one and then three solutions by applying the Krasnoselskii and Legget–William fixed point theorems.     

Thermodynamics of the silver—silver thiocyanate electrode in urea—water mixtures

E.m.f. measurements on cells of the type Ag(s), AgCNS(s), KCNS(c)//KCl(c), AgCl(s), Ag(s) in four different composition of urea—water mixtures at seven different temperatures from 5 to 35°C have been made to determine the standard potentials of the silver—silver thiocyanate electrode in these media. These values have been used to evaluate the transfer thermodynamic quantities accompanying the transfer of 1 g ion of CNS^? ion from the standard state in water to the standard state in urea—water mixtures.     

Photoisomerization and proton-coupled electron transfer (PCET) promoted water oxidation by mononuclear cyclometalated ruthenium catalysts

Photoisomeric transformations in ruthenium polypyridyl complexes have been rarely reported. Herein we report the geometrical transformation of cyclometalated trans-[Ru(tpy)(PAD)(OH(2))](+) ([1](+)) to the cis-[Ru(tpy)(PAD)(OH(2))](+) ([1a](+)) (tpy = 2,2';6',2"-terpyridine, PAD = 2-(pyrid-2'-yl)acridine) isomer upon irradiation of visible light (λ ≥420 nm). Due to a proton-induced tautomeric equilibrium between the Ru-C bond and Ru═C coordination, the π* energy levels of PADH are lower than those of tpy by 12.61 and 12.24 kcal mol(-1), respectively, in [1](+) and [1a](+). Isomers [1](+) and [1a](+) both act as catalytic oxygen-evolving complexes (OECs) chemically as well as electrochemically.     

Comparative Study of C(∧)N and N(∧)C Type Cyclometalated Ruthenium Complexes with a NAD(+)/NADH Function

Cyclometalated ruthenium complexes having C(∧)N and N(∧)C type coordinating ligands with NAD(+)/NADH function have been synthesized and characterized by spectroscopic methods. The variation of the coordinating position of σ-donating carbon atom leads to a drastic change in their properties. Both the complex Ru(phbn)(phen)(2)]PF(6) ([1]PF(6)) and [Ru(pad)(phen)(2)]PF(6) ([2]PF(6)) reduced to Ru(phbnHH)(phen)(2)]PF(6) ([1HH]PF(6)) and [Ru(padHH)(phen)(2)]PF(6) ([2HH]PF(6)) by chemical and electrochemical methods. Complex [1]PF(6) photochemically reduced to [1HH]PF(6) in the presence of the sacrificial agent triethylamine (TEA) upon irradiation of visible light (λ ≥ 420 nm), whereas photochemical reduction of [2]PF(6) was not successful. Both experimental results and theoretical calculations reveal that upon protonation the energy level of the π* orbital of either of the ligands phbn or pad is drastically stabilized compared to the nonprotonated forms. In the protonated complex [Ru(padH)(phen)(2)](PF(6))(2) {[2H](PF(6))(2)}, the Ru-C bond exists in a tautomeric equilibrium with Ru═C coordination and behaves as a remote N-heterocyclic carbene (rNHC) compex; on the contrary, this behavior could not be observed in protonated complex [Ru(phbnH)(phen)(2)](PF(6))(2) {[1H](PF(6))(2)}.     

Oscillation of neutral delay difference equations of second order with positive and negative coefficients

This paper is concerned with a class of neutral difference equations of second order with positive and negative coefficients of the forms

Directional compton profile studies of GaP

59.54 keV gamma ray Compton profiles (CP) of GaP along (100) and (1 1 1) directions are reported. The measured anisotropy has qualitatively similar features as given by the recent pseudopotential calculations for other III–V compound semiconductors. The average valence profile is found to be more peaked compared to that of the pure covalent semiconductors Si and Ge. This suggests that inonicity has the effect of making the valence-electron wave functions of compound semiconductors more diffused. Theoretical calculations on the directional Compton profiles of GaP will be of great use for an exact comparision with the present data, which will help in detailed understanding of the electronic structure of GaP.     

Standard potentials of the silver—silver tungstate,silver—silver phosphate,and silver—silver arsenate electrodes in water—dioxane and water—urea mixtures and related thermodynamic functions

The standard potentials of the silver—silver tungstate, silver—silver phosphate and silver—silver arsenate electrodes in four different compositions of water—dioxane and water—urea mixtures at seven different temperatures from 5 to 35°C have been determined from EMF measurements of cells of the type Ag(s), AgCl(s), NaCl(c)//Na_xZ(c/x), Ag_xZ(s), Ag(s), where x is 2 or 3, and Z is WO₄, PO₄ or AsO₄. These values have been used to evaluate the transfer thermodynamic quantities accompanying the transfer of 1 g ion of WO^2?₄. PO^3?₄ or AsO^3?₄ ion from the standard state in water to the standard state in water—dioxane or water—urea mixtures.     

Deracemisation of β-hydroxy esters using immobilised whole cells of Candida parapsilosis ATCC 7330: substrate specificity and mechanistic investigation

Deracemisation of aryl substituted β-hydroxy esters by immobilised whole cells of Candida parapsilosis ATCC 7330 gave >99% ee and up to 75% yield of their corresponding (S)-enantiomers. Mechanistic investigation of the deracemisation reaction carried out using a deuterated substrate, ethyl 3-deutero-3-hydroxy-3-phenyl propanoate revealed that while the (S)-enantiomer remains unreacted the (R)-enantiomer undergoes enantioselective oxidation to its corresponding ketoester, which on complementary enantiospecific reduction gives the (S)-enantiomer in high yield and % ee.     

Synthesis,structure, thermal studies on Zn(II), Cd(II) complexes of N-(2-pyridylmethyl)pyridine-2-carbaldimine and N-(2-pyridylmethyl)pyridine-2-methylketimine

The bivalent zinc and cadmium complexes of two Schiff bases N-(2-pyridylmethyl)pyridine-2-carbaldimine (L1), N-(2-pyridylmethyl)pyridine-2-methylketimine (L2), tridentate ligands with an N₃ chromophore and coordinating with two five-membered chelate rings, were synthesized. Complexes [Zn(L1)(NO₃)₂] (1), [Zn(L2)(NO₃)₂] (2), [Cd(L1)(NO₃)₂(H₂O)] (3) and [Cd(L2)(NO₃)₂(CH₃OH)] (4) were characterized by X-ray crystallography. In 1 and 2, Zn(II) has a distorted square-pyramidal geometry where as in 3 and 4, Cd(II) possesses a pseudo-pentagonal-bipyramidal geometry. The following trends in the bond lengths are observed: M–N_im < M–N_py; Zn–N > Zn–O; Cd–N < Cd–O. The final residues from the thermogravimetric analysis are ZnO and CdO, the SEM studies revealed, respectively, their porous and spherical natures. The average activation energy (E) for the loss of pyridine rings obtained from the Friedman fitting of the DSC data, for 1, 2, 3, and 4 are 193.8(2), 114.5(3), 127.1(4), and 63.7(3) kJ mol⁻¹ and their logarithmic pre-exponential factor (A) are 11.22, 5.31, 6.88, and 2.09, respectively.