Galerkin-wavelet methods for two-point boundary value problems

Summary Anti-derivatives of wavelets are used for the numerical solution of differential equations. Optimal error estimates are obtained in the applications to two-point boundary value problems of second order. The orthogonal property of the wavelets is used to construct efficient iterative methods for the solution of the resultant linear algebraic systems. Numerical examples are given.This work was supported by National Science Foundation     

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.     

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.     

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.     

Compact High-Order Finite Differences for Interface Problems in One Dimension

This paper is concerned with the construction and analysis ofcompact finite difference approximations to the model linearsource problem –(pu')' + qu = f where the functions p,q, and f can have jump discontinuities at a finite number ofpoints. Explicit formulae that give O(h²) O(h³) and O(h⁴) accuracyare derived, and a procedure for computing three-point schemesof any prescribed order of accuracy is presented. A rigoroustruncation and discretization error analysis is offered. Numericalresults are also given.     

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.     

Investigation of selenium-containing root exudates of Brassica juncea using HPLC-ICP-MS and ESI-qTOF-MS

Selenium-containing root exudates were investigated in a known selenium accumulator model plant. Indian mustard (Brassica juncea) plants were grown hydroponically and supplemented with selenite (SeO(3)(2-)) in a 25% Hoagland's nutrient solution. Additive concentrations were 0, 1, 5 and 20 microg mL(-1) Se with five replicate plants per treatment level. Plants were exposed to the respective Se solutions for two weeks, then placed in deionized water for two more weeks. The hydroponic solutions were collected for analysis after the first two weeks of selenium supplementation (day 14) and twice during the deionized water period (days 21 and 28). Separation by ion-pairing high performance liquid chromatography was followed by inductively coupled plasma-mass spectrometry (ICP-MS) for selenium specific detection. Chromatographic peaks unable to be identified by retention-time matching were collected for analysis by electrospray ionization mass spectrometry (ESI-MS). Additional chemical experiments were performed for structural elucidation. Several selenium-containing compounds were identified in the exudate-containing solution and two were identified as selenocystine and the selenosulfate (SSeO(3)(2-)) ion. The presence of dimethylselenide (CH(3)SeCH(3)) is also observed but cannot be attributed exclusively to plant exudation because plants were not grown in sterile conditions. Further, the incorporation of fortified selenoamino acids into peptide structures was found to occur under neutral pH conditions, suggesting that exuded enzymes might facilitate such a reaction. Finally, physiological differences resulting from selenium supplementations were noted and discussed.