Elasticity of a magnetic lattice near the magnetic critical point

The isothermal elastic constants and the coefficient of anomalous thermal expansion of a magnetic lattice are discussed. The spin system is described by the Ising model with an exchange coupling depending on lattice spacing. A behavior of the elastic constants and the coefficient of thermal expansion is found which is in qualitative agreement with experiments. The isothermal compressibility remains positive nearT _c and no thermo-mechanical instability occurs (which would lead to a first-order phase transitions), in contrast to earlier theories.     

A central cutting plane algorithm for the convex programming problem

An algorithm is developed for solving the convex programming problem which iteratively proceeds to the optimum by constructing a cutting plane through the center of a polyhedral approximation to the optimum. This generates a sequence of primal feasible points whose limit points satisfy the Kuhn—Tucker conditions of the problem. Additionally, we present a simple, effective rule for dropping prior cuts, an easily calculated bound on the objective function, and a rate of convergence.     

γ-Lactam analogues of penicillanic and carbapenicillanic acids

Synthesis and biological activity of γ-lactam analogues of penicillanic and carboapenicillanic acids, and the sodium periodate mediated rearrangement of pyrrolidine-2,3-diones are described. 1,3- Dipolar addition of cyclic nitrone (6) and methyl acrylate afforded the bicyclic adducts (7a) and (7b). Reductive cleavage of the N-O bond and subsequent cyclisation of a regioisomer (11a) gave the γ-lactams (12a) and (12b) in a ratio of 85 : 15. They are transformed to the carbapenam analogues (1)-(4). Their stereochemistry was assigned according to the X-ray structure of the γ-lactam (12b). Benzyl 6-oxopenicillanate (20) was directly transformed to the γ-lactam analogue (5) $\text{via}$ a novel ring expansion. These synthetic analogues did not show antibiotic activity or β-lactamase inhibition. Treatment of pyrro1idine-2,3-diones (25a) and (25b) with sodium periodate gave ring contracted β-lactams (26a) and (26b) respectively. Similar treatment of (27) followed by diazomethane afforded an unexpected spiro epoxide.     

Sessions of the seminar “algebra i logika”

Sessions of the seminar algebra i logika     

Sets associated with the farthest point problem

LetS be a convex compact set in a normed linear spaceX. For each cardinal numbern, defineS _n = {x X:x has exactlyn farthest points inS} andT _n = _kn S _k. It is shown that ifX =E thenT ₃ is countable andT ₂ is contractible to a point. Properties of associated level curves are given.     

The Fermat—Weber location problem revisited

The Fermat—Weber location problem requires finding a point in ^N that minimizes the sum of weighted Euclidean distances tom given points. A one-point iterative method was first introduced by Weiszfeld in 1937 to solve this problem. Since then several research articles have been published on the method and generalizations thereof. Global convergence of Weiszfeld's algorithm was proven in a seminal paper by Kuhn in 1973. However, since them given points are singular points of the iteration functions, convergence is conditional on none of the iterates coinciding with one of the given points. In addressing this problem, Kuhn concluded that whenever them given points are not collinear, Weiszfeld's algorithm will converge to the unique optimal solution except for a denumerable set of starting points. As late as 1989, Chandrasekaran and Tamir demonstrated with counter-examples that convergence may not occur for continuous sets of starting points when the given points are contained in an affine subspace of ^N . We resolve this open question by proving that Weiszfeld's algorithm converges to the unique optimal solution for all but a denumerable set of starting points if, and only if, the convex hull of the given points is of dimensionN.     

Investigation of EDTA anticoagulant in plasma to improve the throughput of liquid chromatography/tandem mass spectrometric assays

In this study, EDTA and heparin are compared as anticoagulants with respect to their efficiency in preventing clot formation in plasma samples that were subsequently analyzed by liquid chromatography/tandem mass spectrometry (LC/MS/MS). A pilot in vivo pharmacokinetic study for the drug chlorpheniramine was conducted in which both EDTA and heparin plasma samples were collected simultaneously. All conditions except the anticoagulant were held constant during the pharmacokinetic study. Bioanalytical results were compared from samples transferred by manual pipette and by an automated liquid handler workstation. The concentration of chlorpheniramine in samples was determined by LC/MS/MS. Results from the analysis of variances (ANOVA) of log-transformed plasma chlorpheniramine concentrations were used to calculate 90% confidence intervals for the ratio least-squares mean values for anticoagulants and for transfer methods. Analytical concentrations of the drug chlorpheniramine were equivalent in heparin- and EDTA-containing plasma. Results suggest that the failure rate for transfer of EDTA plasma (50 micro L by automated workstation or manually) is less than that for heparinized plasma. As a consequence of these results, the vast majority of plasma samples in our laboratories are now collected in EDTA, which allows for use of automated sample transfer resulting in a three-fold timesaving over manual transfer using a single-channel pipette. The ability to use automation has resulted in improved efficiency and cost savings.