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Based on the concept of blown‐ups of evolution, introduced by OuYang in 1995, for nonlinear models, the logistic model and its modification of population evolutions are analyzed analytically and numerically. Presents results that imply: (1) There does not exist successive whole evolution of time in both the logistic model and its modifications. (2) The increase or decrease of the population size, caused by unsuccessive evolution, is limited. (3) The discontinuity characteristic realizes the philosophy that “things will develop in the opposite direction when they have reached extremes”. (4) The exponential increase of the population size is a special case, where it is shown that the modified logistic model agrees more with the reality than the original model. At the end, it points out that it is necessary to reconsider the method of reducing the original model into an algebraic equation by changing Δt to a non‐dimensional nonvariable by using difference scheme.

The entropy as a measure of diversity has been used by ecologists to characterize a community by its stability process. After the introduction of the concept of a fuzzy subset by Zadeh (1965), many definitions of entropies were given emphasizing the subjectivity in evaluations. A pioneering work which relates the classical meaning of entropy (Shannon index) with the modern fuzzy theory was due to De Luca and Termini (1972); Knopfmacher (1975) formulated a generalization of the axiomatics given by De Luca and Termini; Batle and Trillas (1979) obtained a result which is essentially analogous to Knopfmacher’s by considering a finite fuzzy measure space and the Sugeno’s integrals; and Trillas and Riera (1978) introduced the concept of fuzzy algebraic entropics. Analyses the continuity properties for these fuzzy entropies and establishes conditions which guarantee the convergence E(f_n) → E(f), where (f_n) is a sequence of fuzzy sets and E is an entropy.

In this paper, we apply the concept of blown‐ups to discuss the laser evolution model. Our first conclusion implies that: after a certain amount of photons have been absorbed under certain conditions, a blown‐up will occur and so some pulse photons will be emitted, whose stability depends on the value of the parameter. Our second implies that: single model laser equation contains no “chaotic” behaviors, which agrees with laboratory experiments and shows why slaving principle becomes invalid.

In the economic design of •‐control charts the two extreme approaches used are that the design parameters are: (i) fixed once determined, and (ii) change from sample to sample. Administrative convenience favours the first approach in practice, although research work indicates, for instance, that constant sampling intervals are not necessarily optimal. This article provides an economic but partially dynamic model where the sampling intervals are of random lengths but other parameters are kept fixed once determined. Random sampling intervals are practical especially in labour‐intensive economies and job‐shop situations where assignable causes are introduced by external factors such as operator skill, fatigue, carelessness and other physical environments. In such work environments, operators have been found to take undue advantage of constant sampling intervals. The model developed here incorporates statistical, economic and administrative considerations in addition to other practical work situations. Some guidelines for implementing the model in the production environment are provided.

Presents the fixed‐point paradigm and its aspects from vector algebra to dynamical systems, not forgetting eigenbehaviours. Then considers the problem of subjects (and objects) in interaction, using the author's concepts of observation operator, pragmatical operator and epistemo‐praxiological loop which give rise to the intervention of a fixed point. More precise conclusions are obtained in the recurrent case. A comparison is made with Heinz von Förster's views on subject and object.

Selects one of Hamaker′s procedures for deriving a “σ” method (i.e. known process standard deviation) double sampling plan and exploits some of its properties to develop a system of “s” method (i.e. unknown process standard deviation) double sampling plans by variables that match the system of single specification limit “s” method single sampling plans of the current edition of the international standard on sampling by variables. ISO 3951: 1989. The new system is presented in two forms, the second of which may also be used for combined double specification limits and multivariate acceptance sampling.

AIRSCREW data for performance estimation, in practical form, is generally acceptable in the design office, and the present charts and notes have been found useful and convenient in use.

This study proposes a new modified discrete preventive maintenance policy where failures of a system can be detected only by inspections and be fixed by minimal repairs. The maximum number of minimal repairs allowed to the system is, however, a prespecified integer, N. Under the proposed policy, inspections are conducted at times T, 2T, ...(T>0) to detect and fix failures by minimal repairs, and the whole system is preventively replaced by a new one when the cumulative number of failures detected becomes equal to an integer, k or more. The expected cost per unit time is formulated under the proposed maintenance policy. The existence of an optimal integer k=k* which minimizes the expected cost is then shown. Numerical examples are also presented to illustrate the theoretical underpinnings of the proposed formulation.

Adomian has developed a numerical technique using special kinds of polynomials for solving non‐linear functional equations. General conditions and a new formulation are proposed for proving the convergence of Adomian's method for the numerical resolution of non‐linear functional equations depending on one or several variables. The methods proposed are applicable to a very wide class of problems.