In this paper, we analyse the iterated collocation method for Hammerstein equations with smooth and weakly singular kernels. The paper expands the study which began in [ 161 concerning the superconvergence of the iterated Galerkin method for Hammerstein equations. We obtain in this paper a similar superconvergence result for the iterated collocation method for Hammerstein equations. We also discuss the discrete collocation method for weakly singular Hammerstein equations. Some discrete collocation methods for Hammerstein equations with smooth kernels were given previously in [3, 181.

The implementation of an all‐volunteer force in 1974 sparked academic interest in U.S. Army recruiting. During the past three decades Moskos's (1977) Institution/ Occupation (I/O) thesis has dominated this literature. Moskos held that the U.S. Army was becoming less of an institution and more of an occupation. He warned about the danger of offering monetary incentives for enlistment which, he believed, threatened to transform a patriotic duty into a mere job and might also undermine motivation to fight during wartime. This study examines recruiting theme trends through an analysis of recruitment posters from 1915 to 1953. (In a companion article, we extend the examination from 1954 to 1990.) Findings indicate that the I/O thesis was not borne out (Janowitz 1977) and that military changes, including the emergence of an elite military culture, influenced recruitment themes.

First, in this paper, a general theory for the iterated operator approximation is developed.Some of the known results of the superconvergence of the various iterated schemes can be formulated as special cases of this theory. The method is then subsequently used to prove the superconvergence of the iterated degenerate kernel method for the Fredholm equations of the second kind. A similar result of the superconvergence of the degenerate kernel method for the Hammerstein equations is also given.

A prototype fault-tolerant clock synchronization system is designed t o a proven correct formal specification. T h e specification is derived from Schneider's general paradigm for Byzantine resilient clock synchronization. One addition to the formal theory is a mechanism for proven recovery from a bounded number of transient faults. A description of a four-clock implementation which satisfies the requirements of the formal theory is presented. In addition, the design provides options for initialization which enable recovery from some correlated transient failures. Extra logic is included to provide experimental control of these options. Simulation results are presented.

SUMMARYIn this note, we make a few comments concerning the paper of Hughes and Akin (Int. J. Numer. Meth. Engng., 15, 733-751 (1980)). Our primary goal is to demonstrate that the rate of convergence of numerical solutions of the ÿnite element method with singular basis functions depends upon the location of additional collocation points associated with the singular elements. Copyright ? 1999 John Wiley & Sons, Ltd.KEY WORDS: ÿnite element method with singular basis functions; the collocation method; singular interpolation elements FINITE ELEMENT METHOD WITH SINGULAR BASIS FUNCTIONSIn the paper [1], Hughes and Akin made an interesting observation concerning the ÿnite element analysis that incorporates singular element functions. A need for introducing some singular elements as part of basis functions in certain ÿnite element analysis arises out of the following considerations. The solution of certain problems, such as a ÿeld problem [2], exhibits highly singular behaviour due to geometric features of the spatial domain. On the other hand, in other circumstances, the solution is overwhelmingly a ected by the nature of loading and the problem of singularity can be ignored. To satisfy both situations just described, it is thought that an incorporation of singular elements that emulate the solution with the standard polynomial elements may perhaps be desirable. This is the point that was exploited by Hughes and Akin [1]. In order to make the computations of the ÿnite element method with singular elements more e cient, they consider the following algorithm for constructing interpolation functions. A construction of such algorithm was motivated by the idea that 'it is of practical interest to develop techniques for systematically deÿning shape functions for singularity modeling (and for developing special elements in general), which circumvent the interpolation problem ' [3; p:176]. The algorithm that they developed is as follows: