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A letter commenting on the article "Tectonic control on development of a Frasnian-Famennian (Late Devonian) palaeokarst surface, Canning Basin reef complexes, northwestern Australia," by N. Chow and colleagues, which appeared in Vol. 51 is presented along with the authors' response.

The model estimates, subject to restrictions, the functional relationship between national sulfur dioxide discharges and investment in control technology development. Estimates may be made for different product demands, allowed cost increases, and clean fuel availabilities. Control technology development may be accelerated by increased investment. Both optimal and sub-optimal solutions are calculated for an example problem. A general computing method is provided. [ABSTRACT FROM AUTHOR]

This section presents a commentary to an article about the application of the population model to interpret randomized block designs. A confusion arises when a linear combination of parameters and random variable is used to describe the data. The assumptions of correlated interaction terms does not seem natural and it is just a consequence of the condition with is a carryover from the overparameterized fixed-effects model.

The objective of this article is to review existing methods for analyzing experimental design models with unbalanced data and to relate them to existing computer programs. The methods are distinguished by the hypotheses associated with the sums of squares which are generated. The choice of a method should be based on the appropriateness of the hypothesis rather than on computational convenience or the orthogonality of the quadratic forms. The sums of squares are described using the R ( ) notation as applied to the over-parameterized linear model, but the hypotheses are stated in terms of the full-rank cell means model. The zero-cell frequency situation is treated briefly. [ABSTRACT FROM AUTHOR]

SUMMARY The optimal sample allocation is determined using convex programming methods for an example of a stratified survey design involving multiple characteristics. Some comparisons are given with alternative methods of allocation. The effect of variations in the variance restrictions can be studied. Some times required for computation are given. [ABSTRACT FROM AUTHOR]

The investment problem in natural gas transmission in a static sense as analyzed by Chenery [1] and Lehn [3] is reconsidered as a discrete time control problem using a formulation developed by Thompson and George [6]. In the model, the objective is to maximize, subject to constraints, the terminal value of the investment in transmission pipe and pumping capacity plus the sum of the terminal value of the net savings and the capitalized value of the dividends paid over a decision-making period of fixed length. The state variables are: pumping capacity, indebtedness outstanding, depreciated value of the transmission pipe, depreciated value of the pumping capacity, and savings. The control parameters are: the inside diameter of the transmission pipe (pipe size), the wall thickness of the pipe (thickness), initial pumping capacity, initial borrowings, and initial savings. The control variables are; investments in pumping capacity and borrowings during the period. [ABSTRACT FROM AUTHOR]

An algorithm based on convex programming is developed for optimum time compression in network scheduling systems. The development allows for the activity time-cost trade-off functions to be any differentiable convex function. Decomposition theory is then applied to reduce the amount of computation necessary. This along with a limited number of rules to structure any incoming vector makes the algorithm amenable to time compression in large project networks. [ABSTRACT FROM AUTHOR]

This paper describes an algorithm for the solution of the convex programming problem using the simplex method. The algorithm is computationally very simple, requiring the solution of a single linear programming problem which can be accomplished with only slight modification of existing computer codes for the revised simplex method. [ABSTRACT FROM AUTHOR]

In this paper a method is developed for estimating the parameters in the multivariate normal distribution in which the missing observations are not restricted to follow certain patterns as in most previous papers. The large sample properties of the estimators are discussed. Equivalence with maximum likelihood estimators has been established for a subclass of problems. The results of some simulation studies are provided to support the theoretical development. [ABSTRACT FROM AUTHOR]

A method is given here for fitting a quadratic subject to restrictions on the location of the extreme point which is conceptually somewhat different from that proposed by Cunia [1]. The solution is presented as a special case of the general quadratic programming problem, that is, minimizing a quadratic function subject to restrictions on the variables. [ABSTRACT FROM AUTHOR]

Background: Testosterone is measured for the investigation of female hyperandrogenism and male hypogonadism. Liquid chromatography-tandem mass spectrometry (tandem MS) is becoming the method of choice but comprehensive reference ranges are lacking. Methods: Testosterone was measured by tandem MS on 90 healthy women, 67 young healthy men and pregnant women (59 first trimester and 60 second trimester). Results: The male, male calculated free, first trimester and second trimester testosterone reference ranges (derived using the antilog of mean±1.96 SD of log transformed data) were 10.6-31.9, 0.23-0.63, 0.6-4.9 and 0.9-4.9 nmol/L, respectively. The female testosterone upper reference range limit, derived non-parametrically from the 97.5th centile, was <1.7 nmol/L. Conclusions: We have derived tandem MS testosterone reference ranges to support clinical services. [ABSTRACT FROM AUTHOR]

The article discusses the possible reasons why fiddler crabs build chimneys or mud mounds around the entrance of their burrow. The study, conducted on Uca capricornis crabs, showed that both male and female crabs make chimneys, but females do them disproportionately more often. It also showed that intruders have a harder time locating burrows with chimneys, indicating that some crabs build chimneys to hide their burrow's entrance and lower the possibility of losing it to intruders.