An indicator for Wiener-Hopf integral equations with invertible analytic symbol

For Wiener-Hopf integral equations with an operator or matrix valued kernel and with an invertible symbol which is analytic on the real line and at infinity an indicator is introduced. In general this indicator is a bounded linear operator, but when the kernel is matrix valued and the symbol is rational it is a (possibly non-square) matrix. From the indicator the invertibility properties and Fredholm characteristics of the integral equation can be read off. The class of Wiener-Hopf equations studied here is also described in terms of growth conditions on the derivatives of the kernel.     

Rings of integral quaternions

A quaternion order derived from an integral ternary quadratic form f = Σa_ijx_ix_j of discriminant d = 4 det (a_ij) is m-maximal if m is not divisible by any prime p such that p² | d, or p 6; d and c_p = 1. If R is m-maximal and m is a product p₁ … p_r of primes, then any primitive element α of R has unique right-divisor ideals of each norm p₁ … p_k (k = 1, …, r). This generalizes Lipschitz's ninety-year-old theorem. We characterize m-maximal orders, study their ideals, and show how the preceding result yields formulas for the number of representations of integers by certain quaternary quadratic forms.     

Generalized criterion of the long-term strength of viscoelastic materials

A long-term strength condition of the same type as the Il'yushin [2] or Moskvitin [1] nonlinear criterion is proposed. A method is suggested for determining the stress and time functions forming part of the proposed criterion from the long-term strength diagrams and from the data of pulsed or stepped loading tests. It is shown, on the basis of the experimental data, that the proposed criterion, which in a particular case is identical with the Moskovitin criterion, describes the experimental results better than the Bailey criterion.     

Liquid chromatographic-mass spectrometric assay for simultaneous pyrimethamine and sulfadoxine determination in human plasma samples

We present a liquid chromatographic-mass spectrometric assay for the simultaneous determination of sulfadoxine and pyrimethamine in human plasma samples. Sample clean-up was achieved by adding acetonitrile for protein precipitation. Gradient elution in only 10 min resulted in high throughput capability. Tandem mass spectrometric detection in multiple reaction monitoring was used for quantification. The developed analytical approach was successfully validated and was applied in the pharmacokinetic evaluation of the bioavailability between two sulfadoxine/pyrimethamine formulations available on the Eastern African market, using a cross-over design.     

Implications of enzymatic, acidic and thermal hydrolysis of DNA on the occurrence of cross-linked melphalan DNA adducts

Calf thymus DNA was treated with melphalan, a nitrogen mustard, and the formation of melphalan cross-linked DNA adducts was investigated. These cross-linked adducts could not be detected either in the enzymatically or in the thermally generated DNA hydrolysates. However, a search for DNA cross-linked adducts in the hydrolysates obtained under acidic conditions revealed the presence of different types of cross-links, mainly containing an adenine moiety. These results are very important because they show that the detection of cross-links is dependent on the hydrolytic procedure used and that these cross-linked adducts are formed under totally different reaction conditions from those in in vivo situations. This can explain the very low abundance or even the absence of cross-linked adducts in nitrogen mustard treated animals. The generally accepted theory that the anti-cancer activity of bifunctional mustards such as melphalan is due to cross-linking of DNA strands remains therefore from our point of view questionable.     

Slim Near Polygons

In this paper we initiate the study of hybrid slim near hexagons. These are near hexagons which are not dense and not a generalized hexagon in which each line is incident with exactly three points. In the present paper, we will emphasize slim near hexagons with at least one W(2)-quad or Q(5, 2)-quad. Such near hexagons are finite if there are no special points, i.e. points which lie at distance at most 2 from any other point. We will determine upper bounds for the number of lines through a fixed point. We will also look at the special case where the near hexagon has an order. We will determine all slim near hexagons with an order which contain at least one (necessarily big) Q(5,2)-quad, or at least one big W(2)-quad.AMS Classification 05B25, 51E12Communicated by: M.J. de ResminiPostdoctoral Fellow of the Research Foundation–Flanders.     

Investigation into the width of the near turbulent wake behind a sphere at M∞=2, Re∞=1.5·106

The results are given of a investigation whose aim was to test the effectiveness of using a correlation coefficient as a criterion for choosing the empirical law of growth of the near turbulent wake behind a sphere at M=2, Re=1.5·10⁶.Translated from Izvestiya Akademii Nauk SSSR, Mekhanika Zhidkosti i Gaza, No. 3, pp. 137–139, May–June, 1980.We are sincerely grateful to G. I. Petrov for discussion and valuable comments and indebted to B. M. Filippov for assistance in the experiments.