Comparison of glass fragments by neutron activation analysis

A method of comparing glass fragments of potential application to forensic sicence has been developed and evaluated. A representative sample of window glass from England and Wales has been collected and analysed for about 25 elements. An automated radiochemical separation followed by gamma-spectroscopy was used in order to determine the concentration of the maximum number of elements. Frequency distributions of the elemental concentration are shown and used to assess the discrimination of the technique and compare it with the measurement of refractive index. A few simulated cases have been included to demonstrate the possible application to forensic science problems.     

On the convergence of a class of algorithms using linearly independent search directions

Powell has shown that the cyclic coordinate method with exact searches may not converge to a stationary point. In this note we consider a more general class of algorithms for unconstrained minimization, and establish their convergence under the assumption that the objective function has a unique minimum along any line.     

An algorithm for linearly constrained nonlinear programming problems

In this paper an algorithm for solving a linearly constrained nonlinear programming problem is developed. Given a feasible point, a correction vector is computed by solving a least distance programming problem over a polyhedral cone defined in terms of the gradients of the “almost” binding constraints. Mukai's approximate scheme for computing the step size is generalized to handle the constraints. This scheme provides an estimate for the step size based on a quadratic approximation of the function. This estimate is used in conjunction with Armijo line search to calculate a new point. It is shown that each accumulation point is a Kuhn-Tucker point to a slight perturbation of the original problem. Furthermore, under suitable second order optimality conditions, it is shown that eventually only one trial is needed to compute the step size.     

In-situ fractionation—A simple technique for analysis complex mixtures using a routine-gas chromatograph

Summary A simple in-situ fractionation technique, offering several advantages over conventional heart-cutting techniques, is described in which discrete, controlled fractions of effluent from one chromatographic column are transferred sequentially to a second column having diffierent selectively characteristics. Prior to transfer, solutes are stored in-situ on the first column, so that each fraction transferred can be analysed separatley on the second column. In-situ storage and fractionation is achieved using a simple flow-switching arrangement that can be installed in any routine chromatograph without extensive instrument modification. The gas chromatographic determination of aromatics in fuels having final boiling points up to 400° C is used to illustrate the technique. Its potential usefulness in gas chromatography and its possible uses in liquid chromatography are discussed.     

A precise constant-current coulometer

A precise constant-current coulometer is described suitable for manual or automatic coulometric titrations. The apparatus provides II increments of current in the range 250 μA to 200 mA and gives a standard deviation of better than 30 p.p.m. for the total measurement of coulombs.     

Sweet success: Ionic liquids derived from non-nutritive sweeteners

The anions of the sweeteners saccharin and acesulfame form ionic liquids when paired with a variety of organic cations.     

Neutron correlations in the 41K ground state and T = 1 2p-2h states in 40K

Differential cross sections have been measured for ⁴¹(d, t)⁴⁰K and ⁴¹K(p, d)⁴⁰K at 15 MeV using a magnetic spectrograph with electronic detection by proportional-counter-scintillator telescopes or semiconductor detectors. Knowledge of the structure of the ⁴⁰K multiplets ($\text{ν}\text{f}{}_{\mathrm{<mtext>7</mtext><mtext>2</mtext>}}\text{, π}\text{d}{}_{\mathrm{<mtext>3</mtext><mtext>2</mtext>}}{}^{\mathrm{?1}}$) and ($\text{ν}\text{p}{}_{\mathrm{<mtext>3</mtext><mtext>2</mtext>}}\text{, π}\text{d}{}_{\mathrm{<mtext>3</mtext><mtext>2</mtext>}}{}^{\mathrm{?1}}$) permits the determination of amplitudes and relative phases for various configurations and neutron correlations in the ⁴¹K ground state. Spectroscopic factors for neutron pick-up to states in ⁴⁰K are strongly influenced by the interference of transition amplitudes. In the (d, t) reaction T= 1, 2p-2h states are also observed.     

A least-distance programming procedure for minimization problems under linear constraints

In this paper, an algorithm is developed for solving a nonlinear programming problem with linear contraints. The algorithm performs two major computations. First, the search vector is determined by projecting the negative gradient of the objective function on a polyhedral set defined in terms of the gradients of the equality constraints and the near binding inequality constraints. This least-distance program is solved by Lemke's complementary pivoting algorithm after eliminating the equality constraints using Cholesky's factorization. The second major calculation determines a stepsize by first computing an estimate based on quadratic approximation of the function and then finalizing the stepsize using Armijo's inexact line search. It is shown that any accumulation point of the algorithm is a Kuhn-Tucker point. Furthermore, it is shown that, if an accumulation point satisfies the second-order sufficiency optimality conditions, then the whole sequence of iterates converges to that point. Computational testing of the algorithm is presented.