Determination of work functions near melting points of refractory metals by using a direct-current arc

A direct-current arc in argon at atmospheric pressure was used to determine effective work functions of refractory metals, including tantalum, tungsten, molybdenum, and niobium. The procedure is experimentally advantageous because surface cleanliness of the specimen is not critical, high vacuum is not required, and the anode-cathode spacing is not critical. The experimental procedure involves striking an arc to a metal wire cathode to form a melted ball having an emitting area defined by its diameter. The literature melting point of the metal is taken as the emitting temperature. By using these parameters and the known arc current, effective work functions were calculated from the Richardson-Dushman equation. The calculated work functions agree with recommended handbook values to within about 0.1 V and have typical repeatabilities of 0.02 V. By varying the arc current, Richardson plots can be made over a temperature range from a few hundred degrees below the melting point to about 50° over the melting point of the test metal. A Richardson plot over this temperature range is presented for tantalum.     

Some aerodynamic and acoustic characteristicsof acute laryngitis

The purpose of the present study was to describe the effects ofacute laryngitis on some aerodynamic, acoustic, and perceptual measures. Eleven subjects with diagnosed acute laryngitis due to upper respiratory infection were recorded during a laryngitic episode and 1 week to 10 days after amelioration of the laryngitic condition. Fundamental frequency values, collapsed across the five vowels, were significantly reduced in the laryngitic compared with the normal speaking condition. The decrease in fundamental frequency associated with acute laryngitis suggests an increase in the mass of the vocal folds. In addition, aerodynamic values differed significantly for the laryngitic condition compared with the normal speaking condition, suggesting the presence of laryngeal hypofunction. Perceptual data indicated that speakers in the laryngitic condition were judged to have a hoarse voice when compared with the normal speaking condition.     

An adaptive large neighborhood search heuristic for the Pollution-Routing Problem

The Pollution-Routing Problem (PRP) is a recently introduced extension of the classical Vehicle Routing Problem with Time Windows which consists of routing a number of vehicles to serve a set of customers, and determining their speed on each route segment so as to minimize a function comprising fuel, emission and driver costs. This paper presents an adaptive large neighborhood search for the PRP. Results of extensive computational experimentation confirm the efficiency of the algorithm.     

Nonconvergence of the plain Newton-min algorithm for linear complementarity problems with a P-matrix

The plain Newton-min algorithm to solve the linear complementarity problem (LCP for short) can be viewed as a semismooth Newton algorithm without globalization technique to solve the system of piecewise linear equations min(x, Mx + q) = 0, which is equivalent to the LCP. When M is an M-matrix of order n, the algorithm is known to converge in at most n iterations. We show in this paper that this result no longer holds when M is a P-matrix of order ≥ 3, since then the algorithm may cycle. P-matrices are interesting since they are those ensuring the existence and uniqueness of the solution to the LCP for an arbitrary q. Incidentally, convergence occurs for a P-matrix of order 1 or 2.     

Asymptotic analysis of Daubechies polynomials

To study wavelets and filter banks of high order, we begin with the zeros of . This is the binomial series for , truncated after terms. Its zeros give the zeros of the Daubechies filter inside the unit circle, by . The filter has additional zeros at , and this construction makes it orthogonal and maximally flat. The dilation equation leads to orthogonal wavelets with vanishing moments. Symmetric biorthogonal wavelets (generally better in image compression) come similarly from a subset of the zeros of . We study the asymptotic behavior of these zeros. Matlab shows a remarkable plot for . The zeros approach a limiting curve in the complex plane, which is the circle . All zeros have , and the rightmost zeros approach (corresponding to ) with speed . The curve gives a very accurate approximation for finite . The wide dynamic range in the coefficients of makes the zeros difficult to compute for large . Rescaling by allows us to reach by standard codes.

     

Multiobjective routing problems

Summary Many network routing problems, particularly where the transportation of hazardous materials is involved, are multiobjective in nature; that is, it is desired to optimise not only physical path length but other features as well. Several such problems are defined here and a general framework for multiobjective routing problems is proposed. The notion of “efficient solution” is defined and it is demonstrated, by means of an example, that a problem may have very many solutions which are efficient. Next, potentially useful solution methods for multiobjective routing problems are discussed with emphasis being placed on the use of shortest/k-shortest path techniques. Finally, some directions for possible further research are indicated. Invited by B. Pelegrin     

The propagation problem and far-field patterns in a stratified finite-depth ocean

In this paper we investigate the direct problem associated with the scattering of ‘plane waves’ from an object submerged in an ocean of finite depth. An integral representation for the Dirichlet problem is found, from which a formula for the far-field pattern evolves. A density theorem is established concerning the set of all far-field patterns. This theorem is essential for the reconstruction of the submerged object, the ‘inverse’ problem [2], [4], [5].     

A Multiresolution Method for Numerical Reduction and Homogenization of Nonlinear ODEs

The multiresolution analysis (MRA) strategy for the reduction of a nonlinear differential equation is a procedure for constructing an equation directly for the coarse scale component of the solution. The MRA homogenization process is a method for building a simpler equation whose solution has the same coarse behavior as the solution to a more complex equation. We present two multiresolution reduction methods for nonlinear differential equations: a numerical procedure and an analytic method. We also discuss one possible appproach to the homogenization method.