Transition matrices characterizing a certain totally discontinuous map of the interval

We study a totally discontinuous interval map defined in [0,1] which is associated to a deformation of the shift map on two symbols 0−1. We define a sequence of transition matrices which characterizes the effect of the interval map on a family of partitions of the interval [0,1]. Recursive algorithms that build the sequence of matrices and their left and right eigenvectors are deduced. Moreover, we compute the Artin zeta function for the interval map.

SEAMS SCHOOL FINAL REPORT

In this school, we introduced the basis of the mathematical analysis to study differential equations (ordinary and partial). One aim to prepare students and staff members for more concrete problems arising in mathematical modeling in engineering and biological processes. Theoretical and numerical lectures were given, with a presentation of free scientific computing software using Python. A website and a drive were created to facilitate exchanges between students, lecturers and organizers: The school was sponsored by CIMPA (Centre International de Mathématiques Pures et Appliquées) IMU (International Mathematical Union) ISP (International Science Programme) NUOL (National University of Laos) Erasmus Mundus ERDF – Picardie Region Beerlao ETL3G

Scaling laws and thermodynamic analysis for vascular branching of microvessels

When blood flows through small vessels, the two-phase nature of blood as a suspension of red cells (erythrocytes) in plasma cannot be neglected, and with decreasing vessel size, a homogeneous continuum model become less adequate in describing blood flow. Following the Haynes’ marginal zone theory, and viewing the flow as the result of concentric laminae of fluid moving axially, the present work provides models for fluid flow in dichotomous branching composed by larger and smaller vessels, respectively. Expressions for the branching sizes of parent and daughter vessels, that provides easier flow access, are obtained by means of a constrained optimization approach using the Lagrange multipliers. This study shows that when blood behaves as a Newtonian fluid, Hess – Murray law that states that the daughters-to-parent diameter ratio must equal to 2^(-1/3) is valid. However, when the nature of blood as a suspension becomes important, the expression for optimum branching diameters of vessels is dependent on the separation phase lengths. It is also shown that the same effect occurs for the relative lengths of daughters and parent vessels. For smaller vessels (e. g., arterioles and capillaries), it is found that the daughters-to-parent diameter ratio may varies from 0,741 to 0,849, and the daughters-to-parent length ratio varies from 0,260 to 2,42. For larger vessels (e. g., arteries), the daughters-to-parent diameter ratio and the daughters-to-parent length ratio range from 0,458 to 0,819, and from 0,100 to 6,27, respectively. In this paper, it is also demonstrated that the entropy generated when blood behaves as a single phase fluid (i. e., continuum viscous fluid) is greater than the entropy generated when the nature of blood as a suspension becomes important. Another important finding is that the manifestation of the particulate nature of blood in small vessels reduces entropy generation due to fluid friction, thereby maintaining the flow through dichotomous branching vessels at a relatively lower cost.

Analysis of Dyscalculia Evidences through Artificial Intelligence Systems

Dyscalculia is usually perceived of as a specific learning difficulty for mathematics or, more appropriately, arithmetic. Because definitions and diagnoses of dyscalculia are in their infancy and sometimes are contradictory. However, mathematical learning difficulties are certainly not in their infancy and are very prevalent and often devastating in their impact. Co-occurrence of learning disorders appears to be the rule rather than the exception. Co-occurrence is generally assumed to be a consequence of risk factors that are shared between disorders, for example, working memory. However, it should not be assumed that all dyslexics have problems with mathematics, although the percentage may be very high, or that all dyscalculics have problems with reading and writing. Because mathematics is very developmental, any insecurity or uncertainty in early topics will impact on later topics, hence to need to take intervention back to basics. However, it may be worked out in order to decrease its degree of severity. For example, disMAT, an app developed for android may help children to apply mathematical concepts, without much effort, that is turning in itself, a promising tool to dyscalculia treatment. Thus, this work will focus on the development of a Decision Support System to estimate children evidences of dyscalculia, based on data obtained on-the-fly with disMAT. The computational framework is built on top of a Logic Programming approach to Knowledge Representation and Reasoning, grounded on a Case-based approach to computing, that allows for the handling of incomplete, unknown, or even self-contradictory information.

Single diode model parameters analysis of photovoltaic cell

In this paper it is proposed to obtain enhanced and more efficient parameters model from generalized five parameters (single diode) model of PV cells. The paper also introduces, describes and implements a seven parameter model for photovoltaic cell (PV cell) which includes two internal parameters and five external parameters. To obtain the model the mathematical equations and an equivalent circuit consisting of a photo generated current source, a series resistor, a shunt resistor and a diode is used. The fundamental equation of PV cell is used to analyse and best fit the observation data. Especially bisection iteration method is used to obtain the expected result and to understand the deviation of changes in different parameters situation at various conditions respectively. The produced model can be used of measuring and understanding the actions of photovoltaic cells for certain changes and parameters extraction. The effect is also studied with I-V and P-V characteristics of PV cells though it is a challenge to optimize the output with real time simulation. The working procedure is also discussed and an experiment presented to get the closure and insight about the produced model and to decide upon the model validity. At the end, we observed that the result of the simulation is very close to the produced model.