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.     

Reduction of soluble colloidal MnO<Subscript>2</Subscript> by <Emphasis Type="SmallCaps">DL</Emphasis>-malic acid in the absence and presence of nonionic TritonX-100

Kinetics of oxidation of DL-malic acid by water soluble colloidal MnO₂ (prepared from potassium permanganate and sodium thiosulfate solutions) have been studied spectrophotometrically in the absence and presence of nonionic Triton X-100 surfactant. The reaction is autocatalytic and manganese(II) (reduction product of the colloidal MnO₂) may be the autocatalyst. The order of the reaction is first in colloidal [MnO₂] as well as in [malic acid] both in the absence and presence of the surfactant. The reaction has acid-dependent and acid-independent paths and, in the former case, the order is fractional in [H⁺]. The effect of externally added manganese(II) is complex. The results show that the rate constant increases as the manganese(II) concentration is increased. It is not possible to predict the exact dependence of the rate constants on manganese(II) concentration, which has a series of reactions with other reactants. In the presence of TX-100, the observed effect on k is catalytic up to a certain [TX-100]; thereafter, an inhibitory effect follows. The catalytic effect is explained in terms of the mathematical model proposed by Tuncay et al. (in Colloids Surf A Physicochem Eng Aspects 149:279 3). Activation parameters associated with the observed rate constants (k_obs/k) have also been evaluated and discussed.     

Effect of ionic and non-ionic surfactants on the reduction of water soluble colloidal MnO<Subscript>2</Subscript> by glycolic acid

Kinetics of the redox reaction between colloidal MnO₂ and glycolic acid have been studied spectrophotometrically by monitoring the decay in the absorbance of colloidal MnO₂ in absence and presence of surfactants. Anionic sodium dodecyl sulfate has no effect, non-ionic Triton X-100 catalyzed the reaction and experiments were not possible in presence of cationic cetyltrimethylammonium bromide due to the precipitation of MnO₂.The reaction followed the same type of kinetic behavior, i.e., fractional-, first- and fractional-order dependencies, respectively, in [glycolic acid], [MnO₂] and [H⁺ ] in both the media. Effects of gum arabic and manganese(II) have also been studied and discussed. Mechanisms in accordance with the experimental data are proposed for the reaction.     

Mn(Ⅱ)和Ce(Ⅳ)离子对铬酸氧化乳酸的影响

The kinetics and mechanism of lactic acid oxidation in the presence of Mn(II)and Ce(IV)ions by chromic acid were studied spectrophotometrically.The oxidation of lactic acid by Cr(VI)was found to proceed in two measurable steps,both of which gave pyruvic acid as the primary product in the absence of Mn(II).2Cr(VI) 2CH3CHOHCOOH→2CH3COCOOH Cr(V) Cr(III)Cr(V) CH3CHOHCOOH→Cr(III) CH3COCOOH The observed kinetics was explained due to the catalytic and inhibitory effects of Mn(II)and Ce(IV)on the lactic acid oxidation by Cr(VI).The reactivity of lactic acid depends upon the experimental conditions.It acts as a two-or three-equivalent reducing agent in the absence or presence of Mn(II).It was examined that Cr(III)products resulting from the direct reduction of Cr(VI)by three-equivalent reducing agents.The oxidation of lactic acid follows the complex order kinetics with respect to [lactic acid].The activation parameters Ea,ΔH#,and ΔS# were calculated and discussed.