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.

A logic-mathematical point of view of the truth: Reality, perception, and language

In this article, the authors propose a theory of the truth value of propositions from a logic-mathematical point of view. The work that the authors present is an attempt to address this question from an epistemological, linguistic, and logical-mathematical point of view. What is it to exist and how do we define existence? The main objective of this work is an approach to the first of these questions. We leave a more thorough treatment of the problem of existence for future works.

A structural model of cognitive-motivational variables as explanatory factors of academic achievement in Spanish Language and Mathematics

In recent years, several explanatory models have been developed which attempt to analyse the predictive worth of various factors in relation to academic achievement, as well as the direct and indirect effects that they produce. The aim of this study was to examine a structural model incorporating various cognitive and motivational variables which influence student achievement in the two basic core skills in the Spanish curriculum: Spanish Language and Mathematics. These variables included differential aptitudes, specific self-concept, goal orientations, effort and learning strategies. The sample comprised 341 Spanish students in their first year of Compulsory Secondary Education. Various tests and questionnaires were used to assess each student, and Structural Equation Modelling (SEM) was employed to study the relationships in the initial model. The proposed model obtained a satisfactory fit for the two subjects studied, and all the relationships hypothesised were significant. The variable with the most explanatory power regarding academic achievement was mathematical and verbal aptitude. Also notable was the direct influence of specific self-concept on achievement, goal-orientation and effort, as was the mediatory effect that effort and learning strategies had between academic goals and final achievement.

Diversity for Texts Builds in Language L(MT): Indexes Based in Theory of Information

If one has a distribution of words (SLUNs or CLUNS) in a text written in language L(MT), and is adjusted one of the mathematical expressions of distribution that exists in the mathematical literature, some parameter of the elected expression it can be considered as a measure of the diversity. But because the adjustment is not always perfect as usual measure; it is preferable to select an index that doesn't postulate a regularity of distribution expressible for a simple formula. The problem can be approachable statistically, without having special interest for the organization of the text. It can serve as index any monotonous function that has a minimum value when all their elements belong to the same class, that is to say, all the individuals belong to oneself symbol, and a maximum value when each element belongs to a different class, that is to say, each individual is of a different symbol. It should also gather certain conditions like they are: to be not very sensitive to the extension of the text and being invariant to certain number of operations of selection in the text. These operations can be theoretically random. The expressions that offer more advantages are those coming from the theory of the information of Shannon-Weaver. Based on them, the authors develop a theoretical study for indexes of diversity to be applied in texts built in modeling language L(MT), although anything impedes that they can be applied to texts written in natural languages.

A Theorical Point of View of Reality, Perception, and Language

It is possible to view the relations between mathematics and natural language from different aspects. This relation between mathematics and language is not based on just one aspect. In this article, the authors address the role of the Subject facing Reality through language. Perception is defined and a mathematical theory of the perceptual field is proposed. The distinction between purely expressive language and purely informative language is considered false, because the subject is expressed in the communication of a message, and conversely, in purely expressive language, as in an exclamation, there is some information. To study the relation between language and reality, the function of ostensibility is defined and propositions are divided into ostensives and estimatives.

Myth, Language, and Complex Ideologies

Ideologies use for their conservation and propagation persuasive methods of communication: rhetoric. Rhetoric is analyzed from the semiotic and logical-mathematical points of view. The following hypotheses are established: (1) language L is a self-explanatory system, mediated by a successive series of systems of cultural conventions, (2) connotative significances of an ideological advertising rhetoric must be known, and (3) the notion of ideological information is a neutral notion that does not imply the valuation of ideology or its conditions of veracity or falsification. Rhetorical figures like metonymy, metaphor, parable analogy, and allegory are defined as relations. Metaphor and parable are order relations. Operations of metonymic and metaphoric substitution are defined and several theorems derived from these operations have been deduced.

Diversity for Texts Builds in Language L(MT) II: Indexes Based in Abundances

One saw previously that indications of diversity IT and the one of Shannon permits to characterize globally by only one number one fundamental aspects of the text structure. However a more precise knowledge of this structure requires specific abundance distributions and the use, to represent this one, of a suitable mathematical model. Among the numerous models that would be either susceptible to be proposed, the only one that present a real convenient interest are simplest. One will limit itself to study applied three of it to the language L(MT): the log-linear, the log-normal and Mac Arthur's models very used for the calculation of the diversity of the species of ecosystems, and used, we believe that for the first time, in the calculation of the diversity of a text written in a certain language, in our case L(MT). One will show advantages and inconveniences of each of these model types, methods permitting to adjust them to text data and in short tests that permit to decide if this adjustment is acceptable.

Systematic Improvement of Density Functionals through Parameter-Free Hybridization Schemes

It is suggested here that the ultimate accuracy of DFT methods arises from the type of hybridization scheme followed. This idea can be cast into a mathematical formulation utilizing an integrand connecting the noninteracting and the interacting particle system. We consider two previously developed models for it, dubbed as HYB0 and QIDH, and assess a large number of exchange-correlation functionals against the AE6, G2/148, and S22 reference data sets. An interesting consequence of these hybridization schemes is that the error bars, including the standard deviation, are found to markedly decrease with respect to the density-based (nonhybrid) case. This improvement is substantially better than variations due to the underlying density functional used. We thus finally hypothesize about the universal character of the HYB0 and QIDH models.