Formation of the surface charge on silica in mixed solvents

At sufficiently high concentrations of methanol and of alkali salts in aqueous silica dispersions, the negative -potentials of the particles are decreased. This effect is more pronounced with lithium than with other alkali cations, and it is independent on the anion. The NMR spectra indicate lithium adsorption on silica from mixed solvents, but not in the absence of alcohol.Supported by a contract with the XMX Corporation, Burlington, Massachusetts, USA     

Debonding of thin external layer exerted by thermodiffusive fluxes

Summary The stress distributions in a matrix, generated by thermodiffusive fluxes, are determined for the case of a thin, inextensible membrane bonded to the bounding plane over the outer regionr (b>0, ). The problem has been reduced to solving a corresponding system of dual integral equations. There exist singularities in the distribution of contact shear stresses, namely one over square root type atr=b while a logarithmic one at the lines of jumps of temperature and/or mass diffusion.

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Ablösung einer dünner Schicht infolge thermodiffusiver Flüsse

Übersicht Es wird die sich in einer Matrix infolge thermodiffusiver Flüsse einstellende Spannungsverteilung ermittelt wobei auf einen Teil der Grenzfläche (im Bereichr (b>0, )) eine dünne und unverschiebliche Membran aufgebracht ist. Zur Lösung wird das Problem auf ein System von dualen Integralgleichungen reduziert. Die in den Kontaktschubspannungen auftretenden Singularitäten sind einerseits vom reziproken Quadratwurzeltyp am Innenrand, andererseits vom logarithmischen Typ bei Sprüngen in der Temperatur und/oder Massendiffusion.

     

Die Strommer-Zykliden des Flaggenraumes

According to H. BRAUNER a flag space is a three-dimensional affine space with an absolute {,f,F}, wheref is a line in the plane of infinity andF a point onf. A cyclide is a surface of order 4 that intersects only atf. A STROMMER-cyclide is a cyclide generated by translation of a circle in an isotropic plane. In this paper we proof that all STROMMER-cyclides can be generated by translation of an isotropic circle along a divergent Newton-parabola or a conic in a full isotropic plane. We give normal-forms and CAD-pictures of these surfaces. Finaly some geometrical results about STROMMER-cyclides are developed.

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Herrn o.Prof. Dr. Gy. Strommer zum 70. Geburtstag gewidmet.     

On locally optimal nonparametric tests

Summary There is an abundancy of problems in which no parametric model realistically describes the situation and in which, accordingly, we have to resort to nonparametric methods. As the numerical problems connected with nonparametric tests are becoming less and less important, rank tests, permutation tests and the like are becoming more and more part of the standard armatory of applied statisticians. The lack of tabulated critical values, for instance, should no longer be a serious objection against the use of permutation tests in practice; cf. Edgington (1987).The rationale underlying permutation and rank tests has been outlined in quite a number of text books and papers; cf. Fraser (1957), Lehmann (1959), Hájek-Sidák (1967) or Witting (1970). Roughly speaking, permutation tests are constructibel if the data can be condensed by means of a sufficient and complete statistic allowing for the proper kind of conditioning. Rank tests arise if the underlying problem is invariant with respect to (w.r.t.) a large group of transformations which leads to a maximal invariant statistic consisting of (signed) ranks.Most practical nonparametric problems, however, are too complex to be tractable by just one of those approaches. Many of them, however, can be handled by a combination of both techniques. In this paper we outline the logic underlying that combined reduction method and apply it to construct locally most powerful tests. Moreover, we discuss what we label Hoeffding's transfer problem, i.e. the uniformity aspect of locally most powerful tests with respect to the starting point at the boundary. We are concentrating on the discussion of the nonparametric two-sample location and scale problem. Further important problems are mentioned in Section III.This is a written account of an invited lecture delivered by the third author on occasion of the 14th Symposium über Operations Research, Ulm, September 6–8, 1989.     

Electrochemical studies and square-wave voltammetric determination of fenofibrate in pharmaceutical formulations

The electrochemical reduction of fenofibrate at a hanging mercury drop electrode (HMDE) was investigated by cyclic voltammetry, square-wave voltammetry, and chronoamperometry. Different buffer solutions were used over a wide pH range (3.0–10.0). The best definition of the analytical signals was found in borate buffer (pH 9.0)–tetrabutylammonium iodide mixture containing 12.5% (v/v) methanol at –1.2 V (versus Ag/AgCl). According to cyclic voltammetric studies, the reduction was irreversible and diffusion controlled. The diffusion coefficient was 2.38×10^–6 cm² s^–1 as determined by chronoamperometry. Under optimized conditions of square-wave voltammetry, a linear relationship was obtained between 0.146–4.96 g mL^–1 of fenofibrate with a limit of detection of 0.025 g mL^–1. Validation parameters such as sensitivity, accuracy, precision, and recovery were evaluated. The proposed method was applied to the determination of fenofibrate in pharmaceutical formulations. The results were compared with those obtained by a published high-performance liquid chromatography method. No difference was found statistically.     

Distribution of values of σ2 (n) in residue classes

IntegersN for which ₂ (n has weak uniform distribution (modN) are determined.     

Dirichletsche Reihen auf arithmetischen Progressionen

A characterisation of all real Δ≠0 is given, such that $$\overline {f(\sigma + i\Delta \mathbb{N})} = \overline {f(\sigma + i\mathbb{R})} $$ holds for all Dirichlet seriesf(s)=Σa _n n ^?s and all σ greater than the abscissa of absolute convergence off. For only countably many Δ relation (*) is not valid. By using transcendental results it is shown, that (*) holds in the special case, Δ=1.     

On a classical Nicoletti boundary value problem

We shall derive existence, uniqueness and comparison results for the functional differential equationx(t)=f(t, x), a. e.tI, with classical Nicoletti boundary conditionsx _i(t_i)=y _iX, iA, whereI is a real interval,A is a nonempty set andX is a Banach space.     

Sur les séries de Taylor et les transformations de Möbius

Given a non-empty closed subsetF of the unit circle |z|=1, and a Möbius transformationM(z) of the unit disc |z|1, such thatM(0)0, there exists a functionf(z) holomorphic in the unit disc,F being the singular set at the boundary, whose Taylor coefficients tend to zero while the Taylor coefficients off(M(z)), do not tend to zero.