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The singularly perturbed parabolic differential equations with integral boundary conditions and a large negative shift in the space variable are studied in this paper. The implicit Euler method for the temporal direction and the cubic spline method for the spatial direction on a piecewise uniform mesh (Shishkin mesh) are applied to formulate a parameter-uniform numerical method. To handle the integral boundary condition, the composite Simpson's rule is used. The proposed scheme has been shown to be uniformly convergent with order of convergence O Δ t + N − 2 ln 2 N . The maximum absolute errors and rate of convergence for various perturbation parameters and mesh size values are tabulated for two model problems, which agrees with the theoretical estimates and the method is more accurate than the results of some methods existing in the literature. [ABSTRACT FROM AUTHOR]

The article presents an example of a tricky linear algebra. It states that the trick starts when the instructor writes the number 65 on a paper and the instructor announces his psychic ability to predict sums in advance. Moreover, the numbers from 1-25 are then written consecutively in a 5-by-5 arrangement and a student is asked to choose any five numbers from this with the restriction that no two numbers can lie in the same column or row. It is further instructed that these numbers are then added together by the student before the instructor shows the paper with the number 65 written on it.

This paper presents a review of the numerical analysis of composite steel-concrete beams, with particular attention on the modelling of composite beams containing deep trapezoidal slabs cast onto profiled steel sheeting. It is concluded that while robust algorithms are available, there is considerable scope for improvement of these models as an alternative to undertaking expensive testing programs in order to formulate practical design procedures. This is of particular relevance to Australian practice, as timely revisions of its composite structures standard are needed [ABSTRACT FROM AUTHOR]

Viewing truth and beauty as a compromise also is appealing because today many data analysts prefer to use an adjustable Ockham's straight or electric razor, that is, digital computer. Conceptualization of the bump or outlier detection problem in terms of the odds that each bump would be present in a sample of infinite size has certain mathematical advantages. Most scientists also feel that it is usually not enough to demonstrate simple existence, but instead they must also explain the nature of the beast causing a bump. For this reason, before directly commenting on Good and Gaskins's excellent paper, it seems appropriate to illustrate the process of associating apparent anomalies with explanatory factors. Field trials with the primitive form of roughness penalty described before indicated that the scientific the expansion was terminated when the first term failed to satisfy the term-inclusion rule.

Longley [10] proposed a set of data for use in testing regression programs. This paper shows that the numerically accurate solution in this example was probably an unreasonable estimate of the regression coefficients. This is true because the accuracy of the data and appropriateness of the model may affect the solution more than the computational method. An easily computed index is derived that can be used to indicate such computational instability. The basic conclusion is that a concern about highly accurate computational methods must be tempered with a concern for whether the data are accurate enough to make the results meaningful. [ABSTRACT FROM AUTHOR]

This paper describes admissible hypothesis tests for Markov order, the tests being defined on certain conditioned variables. In the spirit of classical hypothesis testing, the tests have the following appealing properties: The power function is constant on the hypothesis set (and, therefore, the level is not pessimistic), and the test is asymptotically most powerful within the class of tests based on regular estimators. Application of the tests herein derived to simulated and actual hydrologic data indicates that our test is superior to the usual chi-square test for Markov order, and that with moderate amounts of data, conclusions with significant physical import can be gleaned. [ABSTRACT FROM AUTHOR]

This contribution to the literature on density estimation is a welcome sequel to Good and Gaskins's previous papers on the subject. Certainly the penalized-likelihood approach to curve estimation is of considerable appeal, not least because of its ability to provide a unified approach to various different smoothing problems. Therefore, it would appear that some adjustment should be made to the weight of evidence of a bump to take this fact into account. One possible approach that would deal with this automatically would be to introduce an extra bump-penalty term into the penalized likelihood, either instead of or in addition to the roughness-penalty term. It may be an advantage to avoid direct consideration of the density altogether and instead consider only the second derivative of the density, since the values of the density itself are really of only peripheral interest most of the concern is with points of inflection and senses of curvature. It may be an advantage to avoid direct consideration of the density altogether and instead consider only the second derivative of the density, since the values of the density itself are really of only peripheral interest most of the concern is with points of inflection and senses of curvature.

Statistical researcher M. Stone continues in his diligent search for flaws in the Bayesian theory of statistical inference. In the present paper he considers two examples in which Bayesian strong inconsistency can occur with a flat prior. Only a relatively few statisticians believe that a single theory of inference can be the answer for all of statistics. The committed Bayesian's, however, are prominent among such believers. There are, of course, substantial arguments against the Bayesian theory as a single theory of inference, a summary of these arguments may be may be found in D.A.S. Fraser. These arguments are not primarily concerned with the Bayesian method as a tool in the statistician's tool bag rather, they are concerned with the catholic claim for Bayesian theory and with the meaning and consequences of the theory in scientific contexts. The two examples considered by Stone are some what remote from Bayesian theory in a scientific context indeed, the theory will not rise or fall on the basis of the examples. Nevertheless the examples are extremely interesting they are concerned with implications of the theory, and they are presented with the attractive flair that we expect from Stone.