On two methods for accelerating convergence of series

Summary The Euler-Knopp transformation and a recently considered transformation, effective for entire function of order 1, are applied to series involving completely monotonic coefficients. Some properties of the resulting series are analyzed; these include uniform convergence with respect to the index, a priori and a posteriori estimates of the remainder. For the latter transformation a compact recursive algorithm is established which enables one to make effective use of the transformation. To illustrate the effectiveness of the transformations three applications, with examples, are included.     

Determination of nickel in standard rocks and glasses by photon activation analysis with 30-MeV bremsstrahlung

The determination of nickel in various silicate rocks and glasses by photon activation analysis with a linear electron accelerator is described. Simultaneous irradiation of the sample and comparative standards produces the ⁵⁸Ni(γ, n)⁵⁷Ni reaction, and a post-irradiation chemical separation is used in conjunction with Ge(Li) γ-spectrometry. Nickel abundances for ten standard silicate rocks and two elementally doped glasses are presented and compared with the data previously published. The method is quite simple and gives good reproducible results for nickel down to sub-p.p.m. levels.     

Universal system for liquid stationary phase classification on the basis of thermodynamical data

Summary Equations modifying Rohrschneider's relationship between I and thermodynamical characteristics values are derived. Polarity in chromatography is discussed as a possibility of stationary phases or absorbents to enter into intermolecular interactions and is determined on the basis of the partial molar free energies of solution (G) of six test substances. A simple method for the calculation of stationary phase polarity in terms of G from retention indices and McReynolds constants is given. Equations are presented for the calculation of stationary phase selectivity utilizing G data tabulated for selected test substances. The thermodynamical basis of selecting a reference phase for a unified system expressing the selectivity of stationary phases which can also be applied for adsorbents is suggested. The energy equivalent to an index unit, G_i.u., is discussed.     

On cubature formulae with a minimal number of knots

Summary In this paper an approach is outlined to the two-dimensional analogon of the Gaussian quadrature problem. The main results are necessary and sufficient conditions for the existence of cubature formulae which are exact for all polynomials of degree m and which have a minimal number of 1/2k(k+1) knots,k=[m/2]+1. Ifm is odd, similar results are due to I.P. Mysovskikh ([5, 6]) which will be derived in a new way as a special case of the general characterization given here. Furthermore, it will be shown how this characterization can be used to construct minimal formulae of even degree.     

Error bounds for continued fractionsK(1/b n)

Summary A priori truncation error bounds are obtained for continued fractions of the formK(1/b _n),b _n complex. The error bounds are easily applied to the case whenb _n0 asn. A numerical example involving the complex error function is given.     

Extended iterative methods for the solution of operator equations

Summary Given an iterative methodM ₀, characterized byx ^(k+1=G ₀(x( ^k )) (k0) (x(⁰) prescribed) for the solution of the operator equationF(x)=0, whereF:XX is a given operator andX is a Banach space, it is shown how to obtain a family of methodsM _p characterized byx ^(k+1=G _p (x( ^k )) (k0) (x(⁰) prescribed) with order of convergence higher than that ofM _o. The infinite dimensional multipoint methods of Bosarge and Falb [2] are a special case, in whichM ₀ is Newton's method.Analogues of Theorems 2.3 and 2.36 of [2] are proved for the methodsM _p, which are referred to as extensions ofM ₀. A number of methods with order of convergence greater than two are discussed and existence-convergence theorems for some of them are proved.Finally some computational results are presented which illustrate the behaviour of the methods and their extensions when used to solve systems of nonlinear algebraic equations, and some applications currently being investigated are mentioned.     

Selective determination of uric acid in the presence of ascorbic acid using a penicillamine self-assembled gold electrode

The electrochemical behaviors of uric acid (UA) at the penicillamine (Pen) self-assembled monolayers modified gold electrode (Pen/Au) have been studied. The Pen/Au electrode is demonstrated to promote the electrochemical response of UA by cyclic voltammetry (CV). The diffusion coefficient D of UA is 6.97 × 10⁻⁶ cm² s⁻¹. In differential pulse voltammetric (DPV) measurements, the Pen/Au electrode can separate the UA and ascorbic acid (AA) oxidation potentials by about 120 mV and can be used for the selective determination of UA in the presence of AA. The detection limit was 1 × 10⁻⁶ mol L⁻¹. The modified electrode shows excellent sensitivity, good selectivity and antifouling properties.     

Electroosmosis through a Cation-Exchange Membrane: Effect of an ac Perturbation on the Electroosmotic Flow

Electroosmosis experiments through a cation-exchange membrane have been performed using NaCl solutions in different experimental situations. The influence of an alternating (ac) sinusoidal perturbation, of known angular frequency and small amplitude, superimposed to the usual applied continuous (dc) signal on the electroosmotic flow has been studied. The experimental results show that the presence of the ac perturbation affects the electroosmotic flow value, depending on the frequency of the ac signal and on the solution stirring conditions. In the frequency range studied, two regions have been observed where the electroosmotic flow reaches a maximum value: one at low frequencies (Hz); and another at frequencies of the order of kHz. These regions could be related to membrane relaxation phenomena.     

Application of the JKR Method to the Measurement of Adhesion to Langmuir-Blodgett Cellulose Surfaces

The JKR method has been applied for studying adhesion between poly(dimethylsiloxane) (PDMS) caps and Langmuir–Blodgett cellulose surfaces including the substrate, hydrophobized mica, and two flat mineral surfaces, bare mica and glass. The self-adhesion of PDMS caps and oxidized PDMS caps are included as a reference to compare with literature data. The results of the measurements have been compared with previous studies using the surface force apparatus and similar systems. A satisfactory agreement is obtained for simple systems showing no, or very limited, hysteresis between loading and unloading curves. In several cases, however, a large hysteresis is found between loading and unloading curves, with a larger adhesion measured from the pull-off force than from the JKR-curve determined on loading. This is, for instance, the case for PDMS against cellulose. The situation is analogous to that found in wetting studies showing a large hysteresis between advancing and receding contact angles.     

Synthesis,characterization and antimicrobial studies on 13-membered-N6-macrocyclic transition metal complexes containing trimethoprim

Asymmetrical macrocyclic complexes of Mn^II, Co^II, Ni^II, Cu^II and Zn^II have been synthesized by the template process using bis(benzil)ethylenediamine as precursor. Bis(benzil)ethylenediamine reacts with transition metal chlorides and trimethoprim in a 1:1:1 molar ratio in methanol to give several solid metal complexes of the general composition [M(L)X₂] (M = Mn^II, Co^II, Ni^II, Cu^II and Zn^II, L = ligand and X = Cl^?). They were characterized by physicochemical and spectroscopic techniques. Based on analytical, spectral and magnetic moments, all the complexes are identified as distorted octahedral structures. All the complexes are of the [M(L)X₂] type. The shifts of the ν(CN) (azomethine) stretches have been monitored. To find out the donor sites of the ligands, the activity data show that the metal complexes are more potent than the parent ligand. The [M(L)X₂] complexes showed a broad spectrum of antimicrobial activity in vitro against both gram-positive and gram-negative human pathogenic bacterial isolates and the antimicrobial spectrum enhanced only with a combination of metal chlorides and trimethoprim complex. From the results it is imperative that the synthesized macrocyclic [M(L)X₂] complexes exhibit potent broad spectrum antibacterial activity.