HILBERT BETWEEN THE FORMAL AND THE INFORMAL SIDE OF MATHEMATICS

Abstract: In this article we analyze the key concept of Hilbert's axiomatic method, namely that of axiom. We will find two different concepts: the first one from the period of Hilbert's foundation of geometry and the second one at the time of the development of his proof theory. Both conceptions are linked to two different notions of intuition and show how Hilbert's ideas are far from a purely formalist conception of mathematics. The principal thesis of this article is that one of the main problems that Hilbert encountered in his foundational studies consisted in securing a link between formalization and intuition. We will also analyze a related problem, that we will call "Frege's Problem", form the time of the foundation of geometry and investigate the role of the Axiom of Completeness in its solution.

Some advances in mathematical models for preference relations

Preference relations, and their modeling, have played a crucial role in both social sciences and applied mathematics. A special category of preference relations is represented by cardinal preference relations, which are nothing other than relations which can also take into account the degree of relation. Preference relations play a pivotal role in most of multi criteria decision making methods and in the operational research. This thesis aims at showing some recent advances in their methodology. Actually, there are a number of open issues in this field and the contributions presented in this thesis can be grouped accordingly. The first issue regards the estimation of a weight vector given a preference relation. A new and efficient algorithm for estimating the priority vector of a reciprocal relation, i.e. a special type of preference relation, is going to be presented. The same section contains the proof that twenty methods already proposed in literature lead to unsatisfactory results as they employ a conflicting constraint in their optimization model. The second area of interest concerns consistency evaluation and it is possibly the kernel of the thesis. This thesis contains the proofs that some indices are equivalent and that therefore, some seemingly different formulae, end up leading to the very same result. Moreover, some numerical simulations are presented. The section ends with some consideration of a new method for fairly evaluating consistency. The third matter regards incomplete relations and how to estimate missing comparisons. This section reports a numerical study of the methods already proposed in literature and analyzes their behavior in different situations. The fourth, and last, topic, proposes a way to deal with group decision making by means of connecting preference relations with social network analysis.

Using data mining to identify factors that influence the degree of leg injuries in broilers

Locomotor problems prevent the bird to move freely, jeopardizing the welfare and productivity, besides generating injuries on the legs of chickens. The objective of this study was to evaluate the influence of age, use of vitamin D, the asymmetry of limbs and gait score, the degree of leg injuries in broilers, using data mining. The analysis was performed on a data set obtained from a field experiment in which it was used two groups of birds with 30 birds each, a control group and one treated with vitamin D. It was evaluated the gait score, the asymmetry between the right and left toes, and the degree of leg injuries. The Weka ® software was used in data mining. In particular, C4.5 algorithm (also known as J48 in Weka environment) was used for the generation of a decision tree. The results showed that age is the factor that most influences the degree of leg injuries and that the data from assessments of gait score were not reliable to estimate leg weakness in broilers.

Determination of total accumulated rainfall, global radiation, evapotranspiration and degree-days originated from the ECMWF model to sugar cane crop

The climate variability between the growth and harvesting of sugar cane is very important because it directly affects yield. The MODIS sensor has characteristics like spatial and temporal resolution that can be applied to monitoring of vegetative vigor variability in the land surface and then, temporal profiles generation. Agro meteorological data from ECMWF model are free and easy to access and have a good representation of reality. In this study, we used the period between sugar cane growth and harvest in the state of Sao Paulo, Brazil, from temporal profiles selecting of NDVI behavior. For each period the precipitation, evapotranspiration, global radiation, length (days) and degree-days were accumulated. The periods were presented in a map format on MODIS spatial resolution of 250 meters. The results showed the spatial variability of climate variables and the relationship to the reality presented by official data.

Self-Assessement Report for International Accreditation - Bachelor's and Master's degree programmes in Energy Technology

Self-Assessment Report was made for the accreditation of degree programmes in Energy Technology. The report includes the following items: the content,concept and implementation of of the degree programmes, the resources, the quality management and further development of the degree programmes.

Self-Assessment Report for International Accreditation – Bachelor’s and Master’s degree programmes in Industrial Management

Self-assessment report for accreditation of the Bachelor's and Master's degree programs in Industrial Management.

Self assessment report for international accreditation - Bachelor's and Master's degree programmes in Mechanical Engineering

Itsearviointiraportissa kuvataan Lappeenrannan teknillisen yliopiston konetekniikan kandidaatin ja diplomi-insinöörin tutkinto-ohjelmat opetussuunnitelman 2011-2012 mukaisesti. Itsearviointiraportti on tuotettu saksalaisen ASIIN-akkreditointiorganisaation raportointimallin mukaisesti.

Self-Assessment Report for International Accreditation - Bachelor’s and Master’s degree programmes in Environmental Technology

Ympäristötekniikan kandidaatin ja diplomi-insinöörin tutkinto-ohjelmien itsearviointiraportissa käsitellään tutkinto-ohjelmien osaamistavoitteita ja niiden saavuttamista. Raportissa käydään läpi myös käytössä olevat resurssit sekä tutkinto-ohjelmiin liittyviä tunnuslukuja. Itsearviointi on toteutettu kansainvälisen akkreditointijärjestön kriteerien mukaisesti (ASIIN ja EUR-ACE).

Continued Compliance and Degree of Satisfaction in Nulligravida and Parous Women with Intrauterine Contraceptive Devices

Purpose To evaluate the compliance and degree of satisfaction of nulligravida (has not given birth) and parous (had already given birth) women who are using intrauterine devices (IUDs). Methods A cross-sectional cohort study was conducted comparing nulligravida and parous women who had had an IUD inserted between July 2009 and November 2011. A total of 84 nulligravida women and 73 parous women were included. Interviews were conducted with women who agreed to participate through telephone contact. Statistical analysis was performed with Student s t-test and Mann-Whitney test for numeric variables; Pearson s chi-square test to test associations; and, whenever pertinent, Fisher s exact test for categorical variables. A survival curve was constructed to estimate the likelihood of each woman continuing the use of the IUD. A significance level of 5% was established. Results When compared with parous women, nulligravida women had a higher education level (median: 12 vs. 10 years). No statistically significant differences were found between the nulligravida and parous women with respect to information on the use of the IUD, prior use of other contraceptive methods, the reason for having chosen the IUD as the current contraceptive method, reasons for discontinuing the use and adverse effects, compliance, and degree of satisfaction. The two groups did not show any difference in terms of continued use of the IUD (p = 0.4). Conclusion There was no difference in compliance or the degree of satisfaction or continued use of IUDs between nulligravida and parous women, suggesting that IUD use may be recommended for women who have never been pregnant.

Conceptions of mathematics teacher education : thoughts among teacher educators in Tanzania

This study addresses the question of teacher educators’ conceptions of mathematics teacher education (MTE) in teacher colleges in Tanzania, and their thoughts on how to further develop it. The tension between exponents of content as opposed to pedagogy has continued to cause challenging conceptual differences, which also influences what teacher educators conceive as desirable in the development of this domain. This tension is connected to the dissatisfaction of parents and teachers with the failure of school mathematics. From this point of view, the overall aim was to identify and describe teacher educators’ various conceptions of MTE. Inspired by the debate among teacher educators about what the balance should be between subject matter and pedagogical knowledge, it was important to look at the theoretical faces of MTE. The theoretical background involved the review of what is visible in MTE, what is yet to be known and the challenges within the practice. This task revealed meanings, perspectives in MTE, professional development and assessment. To do this, two questions were asked, to which no clear solutions satisfactorily existed. The questions to guide the investigation were, firstly, what are teacher educators’ conceptions of MTE, and secondly, what are teacher educators’ thoughts on the development of MTE? The two questions led to the choice of phenomenography as the methodological approach. Against the guiding questions, 27 mathematics teacher educators were interviewed in relation to the first question, while 32 responded to an open-ended questionnaire regarding question two. The interview statements as well as the questionnaire responses were coded and analysed (classified). The process of classification generated patterns of qualitatively different ways of seeing MTE. The results indicate that MTE is conceived as a process of learning through investigation, fostering inspiration, an approach to learning with an emphasis on problem solving, and a focus on pedagogical knowledge and skills in the process of teaching and learning. In addition, the teaching and learning of mathematics is seen as subject didactics with a focus on subject matter and as an organized integration of subject matter, pedagogical knowledge and some school practice; and also as academic content knowledge in which assessment is inherent. The respondents also saw the need to build learner-educator relationships. Finally, they emphasized taking advantage of teacher educators’ neighbourhood learning groups, networking and collaboration as sustainable knowledge and skills sharing strategies in professional development. Regarding desirable development, teacher educators’ thoughts emphasised enhancing pedagogical knowledge and subject matter, and to be determined by them as opposed to conventional top-down seminars and workshops. This study has revealed various conceptions and thoughts about MTE based on teacher educators´ diverse history of professional development in mathematics. It has been reasonably substantiated that some teacher educators teach school mathematics in the name of MTE, hardly distinguishing between the role and purpose of the two in developing a mathematics teacher. What teacher educators conceive as MTE and what they do regarding the education of teachers of mathematics revealed variations in terms of seeing the phenomenon of interest. Within limits, desirable thoughts shed light on solutions to phobias, and in the same way low self-esteem and stigmatization call for the building of teacher educator-student teacher relationships.

Self-assessment report for international accreditation - Bachelor's and Master's degree programmes in Information Technology

Lappeenrannan teknillisen yliopiston Tietotekniikan kandidaatin ja maisterin tutkinto-ohjelmien itsearviointi toteutettiin v. 2012 kansainvälistä akkreditointia varten. Itsearviointiraportissa kuvataan tutkinto-ohjelmien tavoitteet, toteutus ja arviointimenettelyt sekä tulokset.

Chaos in a Two-Degree of Freedom Duffing Oscillator

High dimensional dynamical systems has intricate behavior either on temporal or on spatial evolution properties. Nevertheless, most of the work on chaotic dynamics has been concentrated on temporal behavior of low-dimensional systems. This contribution is concerned with the chaotic response of a two-degree of freedom Duffing oscillator. Since the equations of motion are associated with a five-dimensional system, the analysis is performed by considering two Duffing oscillators, both with single-degree of freedom, coupled by a spring-dashpot system. With this assumption, it is possible to analyze the transmissibility of motion between the two oscillators.

Best Practices of International Double Master's Degree Programmes: Comparative Study on Finnish and Russian Universities

The purpose of this report is to disseminate the best practices of double degree programmes’ organization, implementation and development between Russian and European universities. The findings reveal good developments in the field of double degree cooperation between Russian and European universities and a high motivation from both parties. The report depicts different models of building a joint curriculum and organizing academic mobility. Foreign language skills improvement for students and university staff, involvement of international companies, and joint strategy and actions in marketing and quality assurance are some redevelopments points recommended in the report.