Spectrofluorimetric flow injection method for the individual and successive determination of L-cysteine and L-cystine in pharmaceutical and urine samples.

A flow injection configuration is proposed for the determination of L-cysteine and L-cystine individually and for mixtures of both analytes. The procedure is based on the rapid oxidation of L-cysteine by thallium(III) with concomitant formation of fluorescent thallium(I). The inclusion of a selecting valve and of a copper-coated cadmium column in the configuration allows the successive determination of two analytes. Linear calibration graphs were obtained between 5 x 10(-6) and 5 x 10(-5) mol dm-3 of L-cysteine and between 2 x 10(-6) and 2 x 10(-5) mol dm-3 of L-cystine. The applicability of the method to the determination of L-cysteine and L-cystine in pharmaceutical preparations was demonstrated by investigating the effect of potential interferents and by the analysis of commercial preparations. The method was successfully applied to the determination of L-cysteine and L-cystine in urine samples.     

Determination of epinephrine, norepinephrine, dopamine and L-dopa in pharmaceuticals by a photokinetic method.

A study of the photochemical reaction of the Rose Bengal (RB)-ethylenediaminetetraacetic acid system in the presence of epinephrine, norepinephrine, dopamine and L-dopa is presented. The rate of photoreduction of RB is dramatically retarded by small amounts of these catecholamines, which have an inhibitory effect on the excited state of RB, which is the activator of the process. Optimum conditions for the determination of catecholamines in the range of concentration between 5 x 10(-6) and 1 x 10(-4) mol dm-3 are described. The proposed method has been applied with excellent results to the determination of catecholamines in pharmaceuticals.     

On the theory of the weighing method for automatic crystal shape control in czochralski growth

We derive the exact analytical expression for the meniscus volume in terms of the crystal radius R, the melt contact angle θ_L, and the meniscus height h for the axisymmetric planar growth interface Czochralski configuration. This relation is applied together with motion and mass balance considerations to find the general rate of change in the force experience by the weighing cell in a standard diameter control arrangement. In contrast to the classical work of Bardsley et al. (1977), which is limited to the close viscinity of stationary right cylinder growth, our results are valid for growth developing any crystal profile. In addition, they also account for the fall of melt level due to finite crucible size. The magnitudes of the capillary contributions to the force, and their implications for diameter servo control, are discussed over a wide range of profile parameters using the Tsivinskii formula for h = h (R, θ_L).     

Hamilton cycles in 3‐out

Let G_3‐out denote the random graph on vertex set [n] in which each vertex chooses three neighbors uniformly at random. Note that G_3‐out has minimum degree 3 and average degree 6. We prove that the probability that G_3‐out is Hamiltonian goes to 1 as n tends to infinity. © 2009 Wiley Periodicals, Inc. Random Struct. Alg., 2009     

Nonequilibrium model for the contact process in an ensemble of constant particle number.

We introduce and analyze numerically a nonequilibrium model with a conserved dynamics which is a realization of the contact process in an ensemble of constant particle number. The model possesses just one process in which particles jump around landing only on empty sites next to an existing particle. Particles are not allowed to land on a vacant site surrounded by empty sites. In contrast with the ordinary contact process, the present model does not have an absorbing state. In spite of lacking an absorbing state, the model displays properties that, in the thermodynamic limit, are identical to those of the ordinary contact process.     

A heuristic algorithm for minimax sensor location in the plane

This paper addresses the problem of locating a finite number of sensors to detect an event in a given planar region. The objective is to minimize the maximum probability of non-detection where the underlying region consists of a convex polygon. The sensor location problem has a multitude of applications, including the location of aircraft detection sensors, the placement of sentries along a border to detect enemy penetration, the detection of nuclear tests, and the detection of natural and hazardous man-made events. The problem is a difficult nonlinear nonconvex programming problem even in the case of two sensors. A fast heuristic based on Voronoi polygons is developed in this paper. The algorithm can quickly generate high-quality solutions. Computational experience is provided.     

Compact Packings of the Plane with Two Sizes of Discs

We consider packings of the plane using discs of radius 1 and r. A packing is compact if every disc D is tangent to a sequence of discs D₁, D₂, ..., D_n such that D_i is tangent to D_i+1. We prove that there are only nine values of r with r < 1 for which such packings are possible. For each of the nine values we describe the possible compact packings.