New modified optimal families of King’s and Traub-Ostrowski’s methods

Based on quadratically convergent Schröder’s method, we derive many new interesting families of fourth-order multipoint iterative methods without memory for obtaining simple roots of nonlinear equations by using the weight function approach. The classical King’s family of fourth-order methods and Traub-Ostrowski’s method are obtained as special cases. According to the Kung-Traub conjecture, these methods have the maximal efficiency index because only three functional values are needed per step. Therefore, the fourth-order family of King’s family and Traub-Ostrowski’smethod are the main findings of the present work. The performance of proposed multipoint methods is compared with their closest competitors, namely, King’s family, Traub-Ostrowski’s method, and Jarratt’s method in a series of numerical experiments. All the methods considered here are found to be effective and comparable to the similar robust methods available in the literature.     

Review of Chemometrics Applied to Spectroscopy: 1985-95, Part 3 — Multi-way Analysis

INTRODUCTION

In this third part of a review on chemometrics in spectroscopy we will describe a recent methodology that has attracted increasing interest in spectroscopy. namely multi-way analysis. The application of multi-way analysis in spectroscopy is still relatively new. hence many methodological improvements are being investigated currently. Part of thls review will also be used to describe the algorithmic improvements gained the last decade.     

Asymptotic behaviour of the ratio of density gradient to electron density for atomic systems

The asymptotic behaviour of the negative ratio of the density gradient to the electron density, q(r), for neutral and singly charged atoms has been investigated. The results show that, for large r, q(r) can approach its limit √8?, where ? is the first ionization potential, from either above or below depending on the specific system considered.     

Oscillatory structure of confined fluids

The confinement of fluids in pores and wedges is associated with exponentially damped oscillatory packing structure, as observed with the surface forces apparatus. This paper reviews the statistical mechanics of confined fluids and then illustrates the results with density functional data for hard-sphere solvent. The free energy of the pore fluid and its functional derivatives with respect to thermodynamic fields all oscillate, as a function of pore width, with a wavelength close to the solvent diameter. In contrast, the density at the centre of pores oscillates with twice this wavelength, as a function of pore width. The development of a unified physics of confined fluids is considered. Approximations based on one-dimensional physics do extraordinarily well in planar symmetry at three-dimensions.     

Exploring complex CIDEP of p-benzosemiquinones with time resolved CW-EPR

The time and magnetic field dependent magnetization of polarized signals in the presence of chemically induced magnetization transfer is described by means of a kinetic matrix incorporated into the Bloch equations. The approach is transformed into a computer algorithm accounting for all hyperfine lines present in the system. Solutions are readily obtained by numerical methods. Calculations are applied to the time resolved EPR (TR-EPR) spectroscopic signals of p-benzoquinone after laser flash photolysis. In an aqueous alcoholic solution at pH 2.0, chemical exchange via intermolecular proton transfer is found present between neutral semiquinones. At pH 8.3, the TR-EPR spectrum shows only a uniform signal of the semiquinone. At pH 5.4, a superposition of neutral and anionic radicals is observed together with a protonation-deprotonation equilibrium. A two-step hydrogen atom transfer, consisting of electron transfer followed by protonation, is proposed to account for the formation of both neutral and anionic semiquinone species prior to observation. Experiments in partly deuterated solvent mixtures indicate the existence of three semiquinone forms: BQH^?, BQ^?-, and BQD^? prior to observation. The origin of the proton/deuteron transferred to the anion radical in the precursor state is discussed.     

Eigenvalues of the difference and product of projections

There is an isomorphism between the matrices over the Boolean algebra of subsets of a k-element set and the k-tuples of Boolean binary (i.e. zero-one) matrices. This isomorphism allows many problems concerning nonbinary Boolean matrices to the referred to the binary ease. However, there are some features of the general (i.e. nonbinary) case that have not been mentioned, although they differ somewhat from the binary case. We exhibit characterizations of the linear operators that preserve several invariants of matrices over finite Boolean algebras to illustrate the differences and similarities of the general vs. the binary cases. We employ a canonical form that is useful in applying the isomorphism.     

A proof of Howard's conjecture in homogeneous parallel shear flows—II: Limitations of Fjortoft's necessary instability criterion

The present paper on the linear instability of nonviscous homogeneous parallel shear flows mathematically demonstrates the correctness of Howard's [4] prediction, for a class of velocity distributions specified by a monotone functionU of the altitudey and a single point of inflexion in the domain of flow, by showing not only the existence of a critical wave numberk _c>0 but also deriving an explicit expression for it, beyond which for all wave numbers the manifesting perturbations attain stability. An exciting conclusion to which the above result leads to is that the necessary instability criterion of Fjortoft has the seeds of its own destruction in the entire range of wave numbersk>k _c—a result which is not at all evident either from the criterion itself or from its derivation and has thus remained undiscovered ever since Fjortoft enunciated [3].     

Ordering of gas bubbles during light ion gas implantation

There have been interesting observations about ordering of microstructures during irradiation. The formation of void lattices is amongst the better known examples. Ordering has also been observed in small gas filled bubbles formed during low energy light ion implantation in the energy range 30–100 keV. The basic underlying mechanism for ordering of gas bubbles has not been clearly understood so far. We identify in this paper a basic instability in the growth kinetics of such bubbles which can develop during irradiation. This instability is shown to be associated with the interstitial production due to the high pressure inside these bubbles and their differential bias due to the strain field interactions with vacancies and interstitials. It is shown that such an instability leads to a selection of a wavelength scale which agrees with the observed lattice parameter.     

Formal hydride transfer mechanism for photoreduction of 3-phenylquinoxalin-2-ones by amines. Association Of 3-phenylquinoxalin-2-one with aliphatic amines

The photophysical and photochemical behavior of 1-methyl-3-phenylquinoxalin-2-one (MeNQ) and 3-phenylquinoxalin-2-one (HNQ) in the presence of amines is reported. While HNQ fluorescence shows an auxochromic effect and a bathochromic shift with added amines, explained by association of HNQ with amine in the ground state and emission from both excited species HNQ and [HNQ-amine], both MeNQ and HNQ are photoreduced efficiently on irradiation in the presence of amines, leading to the semireduced quinoxalin-2-ones, MeNQH(-) and HNQH(-), respectively, via an electron-proton-electron transfer, with unit quantum yields at high amine concentrations. The semireduced quinoxalin-2-ones XNQH(-) (X = H, Me) revert almost quantitatively to the parent XNQ in a dark thermal reaction with an activation free energy for MeNQH(-) of 17.4 and 25.9 kcal/mol in acetonitrile and benzene, respectively. Kinetic and spectroscopic (UV and NMR) evidence supports the proposed reaction mechanism for the reversible photoreduction.