Chebanov law and Vakar formula in mathematical models of complex systems

Ecological models written in a mathematical language L(M) or model language, with a given style or methodology can be considered as a text. It is possible to apply statistical linguistic laws and the experimental results demonstrate that the behaviour of a mathematical model is the same of any literary text of any natural language. A text has the following characteristics: (a) the variables, its transformed functions and parameters are the lexic units or LUN of ecological models; (b) the syllables are constituted by a LUN, or a chain of them, separated by operating or ordering LUNs; (c) the flow equations are words; and (d) the distribution of words (LUM and CLUN) according to their lengths is based on a Poisson distribution, the Chebanov's law. It is founded on Vakar's formula, that is calculated likewise the linguistic entropy for L(M). We will apply these ideas over practical examples using MARIOLA model. In this paper it will be studied the problem of the lengths of the simple lexic units composed lexic units and words of text models, expressing these lengths in number of the primitive symbols, and syllables. The use of these linguistic laws renders it possible to indicate the degree of information given by an ecological model.

Ideological Complex Systems: Mathematical Theory

The goal of this article is to build an abstract mathematical theory rather than a computational one of the process of transmission of ideology. The basis of much of the argument is Patten's Environment Theory that characterizes a system with its double environment (input or stimulus and output or response) and the existing interactions among them. Ideological processes are semiotic processes, and if in Patten's theory, the two environments are physical, in this theory ideological processes are physical and semiotic, as are stimulus and response.

Integration of different models in the design of chemical processes: Application to the design of a power plant

With advances in the synthesis and design of chemical processes there is an increasing need for more complex mathematical models with which to screen the alternatives that constitute accurate and reliable process models. Despite the wide availability of sophisticated tools for simulation, optimization and synthesis of chemical processes, the user is frequently interested in using the ‘best available model’. However, in practice, these models are usually little more than a black box with a rigid input–output structure. In this paper we propose to tackle all these models using generalized disjunctive programming to capture the numerical characteristics of each model (in equation form, modular, noisy, etc.) and to deal with each of them according to their individual characteristics. The result is a hybrid modular–equation based approach that allows synthesizing complex processes using different models in a robust and reliable way. The capabilities of the proposed approach are discussed with a case study: the design of a utility system power plant that has been decomposed into its constitutive elements, each treated differently numerically. And finally, numerical results and conclusions are presented.

Saint Mathew Law and Bonini Paradox in Textual Theory of Complex Models

The mathematical models of the complex reality are texts belonging to a certain literature that is written in a semi-formal language, denominated L(MT) by the authors whose laws linguistic mathematics have been previously defined. This text possesses linguistic entropy that is the reflection of the physical entropy of the processes of real world that said text describes. Through the temperature of information defined by Mandelbrot, the authors begin a text-reality thermodynamic theory that drives to the existence of information attractors, or highly structured point, settling down a heterogeneity of the space text, the same one that of ontologic space, completing the well-known law of Saint Mathew, of the General Theory of Systems and formulated by Margalef saying: “To the one that has more he will be given, and to the one that doesn't have he will even be removed it little that it possesses.