Pharmaceutical counterfeiting

Pharmaceutical counterfeiting is becoming a serious problem both in developed and developing countries. This paper considers the extent of the problem and provides several examples of drugs which have been counterfeited. Additionally, the effects of counterfeit products on consumers, health care providers, drug manufacturers and governments are discussed. Several of the currently used methods of detection are described and these include near-infrared spectroscopy, Raman spectroscopy, isotopic characterization, tensiography, chromatographic and mass spectrometric approaches. Finally, anti-counterfeiting measures such as the use of holograms, tracers and taggants and electronic tracking are summarized.     

Invariant manifolds of singularly perturbed ordinary differential equations

For singularly perturbed systems of ODE's satisfying a certain stability assumption the existence of an asymptotically stable (unstable) invariant manifold is proved. This invariant manifold is -close to the so-called reduced manifold of such a system. As an illustrative example a 3-dimensional autonomous system describing a model in biochemistry is considered.

---

Zusammenfassung Für singulär gestörte Differentialgleichungssysteme, die einer gewissen Stabilitätsbedingung genügen, wird die Existenz einer asymptotisch stabilen (instabilen) invarianten Mannigfaltigkeit nachgewiesen, die in einer -Umgebung der sogenannten reduzierten Mannigfaltigkeit eines solchen Systems liegt. Als Anschauungsbeispiel wird ein dreidimensionales autonomes System betrachtet, welches ein biochemisches Modell beschreibt.

     

Stability and length of computations in the variational-difference method

The article considers a stable algorithm for computing the matrix and the righthand side of a variational-difference system of equations for one-dimensional nonsingular problems with a differential operator of order 2k. Since usually such systems are O(h^–2k) conditioned, an error in the coefficients in general leads to an asymptotic error O(h^–2k) in the solution of the system. A matrix subspace is identified in which an error leads to an error C in the solution of the system (in the energy norm) the constant C is independent of h), and then an algorithm is proposed which leaves the matrix computation error in this subspace. An approximate solution is represented as a sequence (a word) of elementary arithmetic operations, and a bound on the computation length is derived. A measure of the computation length is a nonnegative functional defined on the set of words of some alphabet which has certain desirable properties. Particular instances of this functional include the number of operations, the weighted average number of macroinstructions of different types, the computation time, etc.Translated from Zapiski Nauchnykh Seminarov Leningradskogo Otdeleniya Matematicheskogo Instituta im. V. A. Steklova AN SSSR, Vol. 80, pp. 5–29, 1978.     

Structure investigations on the hot-working behaviour of steel

Structure changes occurring in hot-deformation of the austenite of steel, the - phase transformation of which takes place above room temperature, cannot directly be studied with quenched specimens. However, within certain limits a microstructure characterization is possible by means of investigation of carefully selected model alloys and/or by analysis of the microstructure inheritance associated with a martensitic - transition of the hot-worked austenite. Application of both procedures is demonstrated with results which were obtained in investigations of the hot-working behaviour of low-alloy spring steel and an Fe-Ni-C model alloy.     

Crossover critical correlation function

The anomalous dimension index assumes its critical value for small momenta and vanishes for large momenta. We provide, in the form of a quadrature, a momentum dependent (k) which interpolates between the above limits. High- and low-momentum expansions for the spectral function are obtained, leading to a Padé approximant from which (k) is determined, thereby giving a crossover critical correlation function.Dedicated to B. Mühlschlegel on the occasion of his 60th birthday     

Resonant generation of even-order harmonics in metal vapors

Generation of the second- and fourth-order harmonics of laser radiation is reported in Mg vapor at the forbidden 3s ²¹ S _o–4s ¹ S _o transition. The conversion efficiency for the second-order harmonics has been measured to be 10^–2% and for the fourth one 10^–8%.