Some algorithms for hemiequilibrium problems

In this paper, we suggest and analyze a class of iterative methods for solving hemiequilibrium problems using the auxiliary principle technique. We prove that the convergence of these new methods either requires partially relaxed strongly monotonicity or pseudomonotonicity, which is a weaker condition than monotonicity. Results obtained in this paper include several new and known results as special cases.     

Modified Householder iterative method free from second derivatives for nonlinear equations

In this paper, we suggest and analyze a new two-step predictor–corrector type iterative method free from second derivatives for solving nonlinear equations of the type f(x)=0. This new method includes the two-step Newton method as a special case. We prove that the new iterative method is of fourth-order. Several examples are given to illustrate the efficiency of this new method and its comparison with other iterative methods. This method can be considered as a significant improvement of the Newton method and its variant forms.     

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.     

Annihilation contributions in B→K<Subscript>1</Subscript>γ decay in next-to-leading order in LEET and CP-asymmetry

The effect of weak annihilation and u-quark penguin contribution on the branching ratio B→K₁γ at next-to-leading order of α_s are calculated using the LEET approach. It is shown that the value of the LEET form factor remains the same in the range of the unitarity triangle phase α favored by the standard model. The CP-asymmetry for the above mentioned decay has been calculated, and its suppression due to the hard-spectator correction has also been incorporated. In addition, the sensitivity of the CP-asymmetry on the underlying parameters has been discussed.     

SINGLE- and DOUBLE-STRAND BREAK FORMATION IN DOUBLE-STRANDED DNA UPON NANOSECOND LASER-INDUCED PHOTOIONIZATION

Double-stranded (ds) calf thymus DNA (0.4 mM), excited by 20 ns laser pulses at 248 nm, was studied in deoxygenated aqueous solution at room temperature and pH 6.7 in the presence of a sodium salt (10 mM). The quantum yields for the formation of hydrated electrons (phi c-), single-strand breaks (phi ssb) and double-strand breaks (phi dsb) were determined for various laser pulse intensities (IL). phi c- and phi ssb increase linearly with increasing IL; however, phi ssb has a tendency to reach saturation at high IL (greater than 5 X 10(6) Wcm-2). The ratio phi ssb/phi c-, representing the number of ssb per radical cation, is about 0.08 at IL less than or equal to 5 X 10(6) Wcm-2. For comparison, the number of ssb per OH radical reacting with dsDNA is 0.22. On going from argon to N2O saturation, phi ssb and phi dsb become larger by factors of approximately 5 and 10-15, respectively. This enhancement is produced by attack on DNA bases by OH radicals generated by N2O-scavenging of the photoelectrons. While phi ssb is essentially independent of the dose (Etot), phi dsb depends linearly on Etot in both argon- and N2O-saturated solutions. The linear dependence of phi dsb implies a square dependence of the number of dsb on Etot. This portion of dsb formation is explained by the occurrence of two random ssb, generated within a critical distance (h) in opposite strands. For both argon- and N2O-saturated solutions h was found to be of the order of 40-70 phosphoric acid diester bonds. On addition of electron scavengers such as 2-chloroethanol (or N2O plus t-butanol), phi dsb is similar to that in neat, argon-saturated solutions. Thus, hydrated electrons are not involved in the chemical pathway leading to laser-pulse-induced dsb of DNA.     

Group generated by two elements of orders 2 and 4 acting on real quadratic fields

Coset diagrams for the orbit of the groupG=〈x,y∶x ²=y ⁴ =1〉 acting on real quadratic fields give some interesting information. By using these coset diagrams, we show that in the orbitpG, where , the non-square positive integern does not change its value and the real quadratic irrational numbers of the formp, wherep and its algebraic conjugate have different signs, are finite in number and that part of the coset diagram containing such numbers forms a single closed path, which is the only closed path in the orbit ofp.     

Trioxatriangulenium (TOTA+) as a robust carbon-based Lewis acid in frustrated Lewis pair chemistry

We report the reactivity between the water stable Lewis acidic trioxatriangulenium ion (TOTA⁺) and a series of Lewis bases such as phosphines and N-heterocyclic carbene (NHC). The nature of the Lewis acid–base interaction was analyzed via variable temperature (VT) NMR spectroscopy, single-crystal X-ray diffraction, UV-visible spectroscopy, and DFT calculations. While small and strongly nucleophilic phosphines, such as PMe₃, led to the formation of a Lewis acid–base adduct, frustrated Lewis pairs (FLPs) were observed for sterically hindered bases such as P(^tBu)₃. The TOTA⁺–P(^tBu)₃ FLP was characterized as an encounter complex, and found to promote the heterolytic cleavage of disulfide bonds, formaldehyde fixation, dehydrogenation of 1,4-cyclohexadiene, heterolytic cleavage of the C–Br bonds, and interception of Staudinger reaction intermediates. Moreover, TOTA⁺ and NHC were found to first undergo single-electron transfer (SET) to form [TOTA]·[NHC]˙⁺, which was confirmed via electron paramagnetic resonance (EPR) spectroscopy, and subsequently form a [TOTA–NHC]⁺ adduct or a mixture of products depending the reaction conditions used.

Frustration at carbon! Herein, we present a frustrated Lewis pair system derived from a water stable carbon-based Lewis acid, trioxatriangulene (TOTA⁺), and a variety of Lewis bases, which successfully promotes bond cleavage and molecule fixation.     

Spectral and Mechanistic Investigation of Oxidation of Rizatriptan by Silver Third Periodate Complex in Aqueous Alkaline Medium

The oxidation of Rizatriptan by diperiodatoargentate(III) has been studied by spectrophotometry at neutral pH. The kinetics of the reaction of Rizatriptan has been shown to principle of non-complementary oxidation steps. The initial step involves the deprotonated of the diperiodatoargentate(III) with the alkali; this rearranges during the displacement of a ligand to give free periodate and takes up another ligand monoperiodateargentate(III), combines with a substrate to endow with an intermediate complex which decomposes within a slow step to provide the final product in the following step with a first-order rate constant. The main product was identified by spot test, Fourier- transform infrared spectroscopy, Nuclear magnetic resonance and Liquid chromatography-mass spectrometry spectrum. A conceivable mechanism including pre equilibrium of adducts development between the complex and reductant was planned from the kinetics study. The rate conditions got from system can clarify all exploratory phenomena, and the activation parameters alongside rate constants of the rate determining step were ascertained.