Stability switches in a first-order complex neutral delay equation

Stability of the first-order neutral delay equation x’ (t) + ax’ (t – τ) = bx(t) + cx(t – τ) with complex coefficients is studied, by analyzing the existence of stability switches.

A note on the periodic orbits of a self excited rigid body

The aim of the present paper is to study the periodic orbits of a perturbed self excited rigid body with a fixed point. For studying these periodic orbits we shall use averaging theory of first order.

Ecosustainability as Ideology

In this paper, the authors settle down a systemic theory of the ideologies in one first approach, distinguishing between the Structural Base and the Superstructure, settling down projections and images between both. Distinction between material structure (Structural Base SB) and ideal or cultural Superstructure is common. This dichotomy translates to social sphere the old religious and philosophical dualism between the body and the soul. In fact, such separation between body and soul, between material structure and ideal and cultural superstructure does not exist. It is a cybernetic process with mathematical and logical images and projections. We consider the Eco-sustainability as an ediodynamic ideology in according to Waldorf’s classification.

The curricular value of mathematics in non-mathematics degree

Higher education should provide the acquisition of skills and abilities that allow the student to play a full and active role in society. The educational experience should offer a series of conceptual, procedural and attitudinal contents that encourage “learning to know, learning to do, learning to be and learning to live together”. It is important to consider the curricular value of mathematics in the education of university undergraduates who do not intend to study mathematics but for whom the discipline will serve as an instrumental. This work discusses factors that form part of the debate on the curricular value of mathematics in non-mathematics degrees.

Do first-year university students understand the language of mathematics?

The aim of the project is to determine if the understanding of the language of Mathematics of students starting university is propitious to the development of an appropriate cognitive structure. The objective of this current work was to analyse the ability of first-year university students to translate the registers of verbal or written expressions and their representations to the registers of algebraic language. Results indicate that students do not understand the basic elements of the language of Mathematics and this causes them to make numerous errors of construction and interpretation. The students were not able to associate concepts with definitions and were unable to offer examples.

Exàmens resolts de FMI 2, Grau en Enginyeria Civil, Cursos 2010-2011, 2011-2012 i 2012-2013

Exàmens resolts de Fonaments Matemàtics de l'Enginyeria II del Grau en Enginyeria Civil de la Universitat d'Alacant dels cursos 2010-2011, 2011-2012 i 2012-2013

Linguistic Systems and Knowledge of Reality

Linguistic systems are the human tools to understand reality. But is it possible to attain this reality? The reality that we perceive, is it just a fragmented reality of which we are part? In this paper the authors present is an attempt to address this question from an epistemological and philosophic linguistic point of view.

Modeling construction time in Spanish building projects

The literature states that project duration is affected by various scope factors. Using 168 building projects carried out in Spain, this paper uses the multiple regression analysis to develop a forecast model that allows estimating project duration of new builds. The proposed model uses project type, gross floor area (GFA), the cost/GFA relationship and number of floors as predictor variables. The research identified the logarithmic form of construction speed as the most appropriate response variable. GFA has greater influence than cost on project duration but both factors are necessary to achieve a forecast model with the highest accuracy. We developed an analysis to verify the stability of forecasted values and showed how a model with high values of fit and accuracy may display an anomalous behavior in the forecasted values. The sensitivity of the proposed forecast model was also analyzed versus the variability of construction costs.

Neutrosophic and Modal Components of Relations in Complex Systems

Semiotic components in the relations of complex systems depend on the Subject. There are two main semiotic components: Neutrosophic and Modal. Modal components are alethical and deontical. In this paper the authors applied the theory of Neutrosophy and Modal Logic to Deontical Impure Systems.

Linguistic Knowledge of Reality: A Metaphysical Impossibility?

Reality contains information (significant) that becomes significances in the mind of the observer. Language is the human instrument to understand reality. But is it possible to attain this reality? Is there an absolute reality, as certain philosophical schools tell us? The reality that we perceive, is it just a fragmented reality of which we are part? The work that the authors present is an attempt to address this question from an epistemological, linguistic and logical-mathematical point of view.

Data analysis using circular causality in networks

Complex systems in causal relationships are known to be circular rather than linear; this means that a particular result is not produced by a single cause, but rather that both positive and negative feedback processes are involved. However, although interpreting systemic interrelationships requires a language formed by circles, this has only been developed at the diagram level, and not from an axiomatic point of view. The first difficulty encountered when analysing any complex system is that usually the only data available relate to the various variables, so the first objective was to transform these data into cause-and-effect relationships. Once this initial step was taken, our discrete chaos theory could be applied by finding the causal circles that will form part of the system attractor and allow their behavior to be interpreted. As an application of the technique presented, we analyzed the system associated with the transcription factors of inflammatory diseases.

Difference schemes for numerical solutions of lagging models of heat conduction

Non-Fourier models of heat conduction are increasingly being considered in the modeling of microscale heat transfer in engineering and biomedical heat transfer problems. The dual-phase-lagging model, incorporating time lags in the heat flux and the temperature gradient, and some of its particular cases and approximations, result in heat conduction modeling equations in the form of delayed or hyperbolic partial differential equations. In this work, the application of difference schemes for the numerical solution of lagging models of heat conduction is considered. Numerical schemes for some DPL approximations are developed, characterizing their properties of convergence and stability. Examples of numerical computations are included.

Feedbacks between vegetation pattern and resource loss dramatically decrease ecosystem resilience and restoration potential in a simple dryland model

Conceptual frameworks of dryland degradation commonly include ecohydrological feedbacks between landscape spatial organization and resource loss, so that decreasing cover and size of vegetation patches result in higher water and soil losses, which lead to further vegetation loss. However, the impacts of these feedbacks on dryland dynamics in response to external stress have barely been tested. Using a spatially-explicit model, we represented feedbacks between vegetation pattern and landscape resource loss by establishing a negative dependence of plant establishment on the connectivity of runoff-source areas (e.g., bare soils). We assessed the impact of various feedback strengths on the response of dryland ecosystems to changing external conditions. In general, for a given external pressure, these connectivity-mediated feedbacks decrease vegetation cover at equilibrium, which indicates a decrease in ecosystem resistance. Along a gradient of gradual increase of environmental pressure (e.g., aridity), the connectivity-mediated feedbacks decrease the amount of pressure required to cause a critical shift to a degraded state (ecosystem resilience). If environmental conditions improve, these feedbacks increase the pressure release needed to achieve the ecosystem recovery (restoration potential). The impact of these feedbacks on dryland response to external stress is markedly non-linear, which relies on the non-linear negative relationship between bare-soil connectivity and vegetation cover. Modelling studies on dryland vegetation dynamics not accounting for the connectivity-mediated feedbacks studied here may overestimate the resistance, resilience and restoration potential of drylands in response to environmental and human pressures. Our results also suggest that changes in vegetation pattern and associated hydrological connectivity may be more informative early-warning indicators of dryland degradation than changes in vegetation cover.

Generation of representation models for complex systems using Lagrangian functions

In this article, a new methodology is presented to obtain representation models for a priori relation z = u(x1, x2, . . . ,xn) (1), with a known an experimental dataset zi; x1i ; x2i ; x3i ; . . . ; xni i=1;2;...;p· In this methodology, a potential energy is initially defined over each possible model for the relationship (1), what allows the application of the Lagrangian mechanics to the derived system. The solution of the Euler–Lagrange in this system allows obtaining the optimal solution according to the minimal action principle. The defined Lagrangian, corresponds to a continuous medium, where a n-dimensional finite elements model has been applied, so it is possible to get a solution for the problem solving a compatible and determined linear symmetric equation system. The computational implementation of the methodology has resulted in an improvement in the process of get representation models obtained and published previously by the authors.

Topological structures of complex belief systems

The concepts of substantive beliefs and derived beliefs are defined, a set of substantive beliefs S like open set and the neighborhood of an element substantive belief. A semantic operation of conjunction is defined with a structure of an Abelian group. Mathematical structures exist such as poset beliefs and join-semilattttice beliefs. A metric space of beliefs and the distance of belief depending on the believer are defined. The concepts of closed and opened ball are defined. S′ is defined as subgroup of the metric space of beliefs Σ and S′ is a totally limited set. The term s is defined (substantive belief) in terms of closing of S′. It is deduced that Σ is paracompact due to Stone's Theorem. The pseudometric space of beliefs is defined to show how the metric of the nonbelieving subject has a topological space like a nonmaterial abstract ideal space formed in the mind of the believing subject, fulfilling the conditions of Kuratowski axioms of closure. To establish patterns of materialization of beliefs we are going to consider that these have defined mathematical structures. This will allow us to understand better cultural processes of text, architecture, norms, and education that are forms or the materialization of an ideology. This materialization is the conversion by means of certain mathematical correspondences, of an abstract set whose elements are beliefs or ideas, in an impure set whose elements are material or energetic. Text is a materialization of ideology.