On Surfaces of Finite Chen — Type

We investigate some relations concerning the first and the second Beltrami operators corresponding to the fundamental forms I, II, III of a surface in the Euclidean space E³ and we study surfaces which are of finite type in the sense of B.-Y. Chen with respect to the fundamental forms II and III.     

Lie-group method solution for two-dimensional viscous flow between slowly expanding or contracting walls with weak permeability

The non-linear equations of motion describing the laminar, isothermal and incompressible flow in a rectangular domain bounded by two weakly permeable, moving porous walls, which enable the fluid to enter or exit during successive expansions or contractions, are considered. We apply Lie-group method for determining symmetry reductions of partial differential equations. Lie-group method starts out with a general infinitesimal group of transformations under which given partial differential equations are invariant, then, the determining equations are derived. The determining equations are a set of linear differential equations, the solution of which gives the infinitesimals of the dependent and independent variables. After the group has been determined, a solution to the given partial differential equation may be found from the invariant surface condition such that its solution leads to similarity variables that reduce the number of independent variables in the system. Effect of the permeation Reynolds number R_e and the dimensionless wall dilation rate α on self-axial velocity have been studied both analytically and numerically and the results are plotted.     

On Commutativity of Rings With Derivations

Let R be a ring and d : R → R a derivation of R. In the present paper we investigate commutativity of R satisfying any one of the properties (i)d([x,y]) = [x,y], (ii)d(x o y) = xoy, (iii)d(x) o d(y) = 0, or (iv)d(x) o d(y) = x o y, for all x, y in some apropriate subset of R.     

Exact solutions of solid-liquid phase-change heat transfer when subjected to convective boundary conditions

A closed-form expression is presented to find the location of solid-liquid interface motion in convection-dominated solidification and melting problems. In this regard, the solutions are expressed in terms of the generalized representations of error functions,E (u, v) andF (u, v), which are useful to heat-conduction problems with convective-type boundary conditions. It is demonstrated that for constant surface temperature, the interface solution reduces to the classical Neumann solution.     

Iodine‐Catalyzed Friedlander Quinoline Synthesis under Solvent‐Free Conditions

Polyfunctional quinolines were synthesized using Friedlander method catalyzed by molecular iodine in high yields at 60 °C under solvent‐free conditions.     

Identification and Separation of Some Anions on Plain and Mixed Adsorbent Layers Using Water as Eluent

The analytical potential of water as an eluent in thin layer chromatographic separation of various anions on plain adsorbent layers (silica gel "G" alumina, and cellulose) as well as on beds containing different combinations of silica gel, alumina, or cellulose has been investigated. In addition to some important separation of anions, microgram separation of IO⁻₄ from milligram quantities of IO⁻₃, Bro⁻₃, MoO²⁻₄, and Fe (CN)³⁻₆ has been realized. The effect on pH of the sample in the separation of IO⁻₄ from accompanying ions has also been studied. The limits of detection and dilution limits of anions on alumina thin layers have been determined. NO⁻₂ in artificial seawater has been detected. The effect of CaCl₂, MgCl₂, and NaHCO₃ on some ternary separations of analytical importance has been examined.     

Steric effects on nascent vibrational distributions of the HCN product produced in CN radical reactions with ethane, propane and chloroform

Time-resolved IR emission spectroscopy (TRIES) has been used to study infrared emission in the 3400–3100 cm⁻¹ region from HCN molecules produced when CN radicals abstract a hydrogen atom from ethane, propane, and chloroform. From these observations the nascent vibrational distributions of the HCN produced were derived. The nascent vibrational population distributions of the product HCN in all of the reactions are non-statistical and inverted in both the pure CH stretch (00p) and CH stretch—bend (0np) series.     

Colossal magnetoresistance manganites: A new approach

Manganites of the LA_1−x Ca _x MnO₃ family show a variety of new and poorly understood electronic, magnetic and structural effects. Here we outline a new approach recently proposed by us, where we argue that due to strong Jahn-Teller (JT) coupling with phonons the twofold degeneratee _g states at the Mn sites dynamically reorganize themselves into localised, JT polaronsl with exponentially small inter-site hopping, and band-like, nonpolaronic statesb, leading to anew 2-band model for manganites which includes strong Coulomb and Hund’s couplings. We also discuss some results from a dynamical mean-field theory treatment of the model which explains quantitatively a wide variety of experimental results, including insulator-metal transitions and CMR, in terms of the influence of physical conditions on the relative energies and occupation of thel andb states. We argue that this microscopic coexistence of the two types of electronic states, and their relative occupation and spatial correlation is the key to manganite physics. Dedicated to Professor C N R Rao on his 70th birthday     

MgBr2·OEt2 mediated protection of alcohols with hexamethyldisilazane: An efficient catalytic route for the preparation of silyl ethers under solvent-free conditions

Various types of alcohols and phenols were rapidly protected by hexamethyldisilazane in good to excellent yields at room temperature in the presence of catalytic amount of magnesium bromide ethyl etherate under solvent-free conditions. Good to excellent chemoselectivity was demonstrated for competitive protection of primary hydroxyls in the presence of secondary and tertiary alcohols. Highly selective protection of phenols in the presence of aromatic amines was also demonstrated successfully.     

Bis(2-hydroxyacetophenone)ethylenediimine as a neutral carrier in a coated-wire membrane electrode for lead(II).

A coated-wire ion-selective electrode (CWISE), based on a Schiff base as a neutral carrier, was successfully developed for the detection of Pb(II) in aqueous solution. CWISE exhibited a linear response with a Nernstian slope of 29.4 +/- 0.5 mV/decade within the concentration range of 1.0 x 10(-5) - 1.0 x 10(-1) M lead ion. CWISE has shown detection limits of 5.0 x 10(-6) M. The electrode exhibited good selectivity over a number of alkali, alkaline earth, transition and heavy metal ions. This sensor yielded a steady potential within 10 to 20 s at a linear dynamic range. The electrode was suitable for use in aqueous solutions in a pH range of 2.0 to 5.0. Applications of this electrode for the determination of lead in real samples and as indicator electrode for potentiometric titration of Pb2+ ion using K2CrO4 are reported.