How real are real numbers?

We discuss mathematical and physical arguments against continuity and in favor of discreteness, with particular emphasis on the ideas of Émile Borel (1871-1956).

Solving Leontief Input-Output Model with Trapezoidal Fuzzy Numbers and Gauss-Seidel Algorithm

In this work a fuzzy linear system is used to solve Leontief input-output model with fuzzy entries. For solving this model, we assume that the consumption matrix from di erent sectors of the economy and demand are known. These assumptions heavily depend on the information obtained from the industries. Hence uncertainties are involved in this information. The aim of this work is to model these uncertainties and to address them by fuzzy entries such as fuzzy numbers and LR-type fuzzy numbers (triangular and trapezoidal). Fuzzy linear system has been developed using fuzzy data and it is solved using Gauss-Seidel algorithm. Numerical examples show the e ciency of this algorithm. The famous example from Prof. Leontief, where he solved the production levels for U.S. economy in 1958, is also further analyzed.

A quantitative view on fuzzy numbers

Since its introduction, fuzzy set theory has become a useful tool in the mathematical modelling of problems in Operations Research and many other fields. The number of applications is growing continuously. In this thesis we investigate a special type of fuzzy set, namely fuzzy numbers. Fuzzy numbers (which will be considered in the thesis as possibility distributions) have been widely used in quantitative analysis in recent decades. In this work two measures of interactivity are defined for fuzzy numbers, the possibilistic correlation and correlation ratio. We focus on both the theoretical and practical applications of these new indices. The approach is based on the level-sets of the fuzzy numbers and on the concept of the joint distribution of marginal possibility distributions. The measures possess similar properties to the corresponding probabilistic correlation and correlation ratio. The connections to real life decision making problems are emphasized focusing on the financial applications. We extend the definitions of possibilistic mean value, variance, covariance and correlation to quasi fuzzy numbers and prove necessary and sufficient conditions for the finiteness of possibilistic mean value and variance. The connection between the concepts of probabilistic and possibilistic correlation is investigated using an exponential distribution. The use of fuzzy numbers in practical applications is demonstrated by the Fuzzy Pay-Off method. This model for real option valuation is based on findings from earlier real option valuation models. We illustrate the use of number of different types of fuzzy numbers and mean value concepts with the method and provide a real life application.

Numbers and Languages

The thesis presents results obtained during the authors PhD-studies. First systems of language equations of a simple form consisting of just two equations are proved to be computationally universal. These are systems over unary alphabet, that are seen as systems of equations over natural numbers. The systems contain only an equation X+A=B and an equation X+X+C=X+X+D, where A, B, C and D are eventually periodic constants. It is proved that for every recursive set S there exists natural numbers p and d, and eventually periodic sets A, B, C and D such that a number n is in S if and only if np+d is in the unique solution of the abovementioned system of two equations, so all recursive sets can be represented in an encoded form. It is also proved that all recursive sets cannot be represented as they are, so the encoding is really needed. Furthermore, it is proved that the family of languages generated by Boolean grammars is closed under injective gsm-mappings and inverse gsm-mappings. The arguments apply also for the families of unambiguous Boolean languages, conjunctive languages and unambiguous languages. Finally, characterizations for morphisims preserving subfamilies of context-free languages are presented. It is shown that the families of deterministic and LL context-free languages are closed under codes if and only if they are of bounded deciphering delay. These families are also closed under non-codes, if they map every letter into a submonoid generated by a single word. The family of unambiguous context-free languages is closed under all codes and under the same non-codes as the families of deterministic and LL context-free languages.

Clinical evaluation of enalapril maleate and furosemide usage in dogs with degenerative myxomatous mitral valve, CHF functional class Ib

Degenerative myxomatous mitral valve (DMMV) is a heart disease of high incidence in small animal clinical medicine, affecting mainly older dogs and small breeds. Thus, a scientific investigation was performed in order to evaluate the clinical use of the medicines furosemide and enalapril maleate in dogs with this disease in CHF functional class Ib before and after the treatment was established. For this purpose 16 dogs with the given valve disease were used, separated into two groups: the first received furosemide (n=8) and the second received enalapril maleate (n=8) throughout 56 days. The dogs were evaluated in four stages (T0, T14, T28 and T56 day) in relation to clinical signs, hematological, biochemical and serum assessment, which included serum angiotensin converting enzyme (ACE) and aldosterone, as well as radiography, electrocardiography, Doppler-echocardiography and blood pressure. The results regarding the clinical, hematological and serum chemistry evaluations revealed no significant changes in both groups, but significant reductions in the values of ACE and aldosterone in the group receiving enalapril maleate were verified. The radiographic examination revealed reductions of VHS values and variable Pms wave of the electrocardiogram in both groups, but no changes in blood pressure values were identified. The echocardiogram showed a significant decrease of the variables LVDd/s in the studied groups and the FS% in animals that received only enalapril. Therefore, analysis of results showed that monotherapy based on enalapril maleate showed better efficiency of symptoms control in patients with CHF functional class Ib.

Non-Linear Unsteady Aerodynamic Response Approximation Using Multi-Layer Functionals

Non-linear functional representation of the aerodynamic response provides a convenient mathematical model for motion-induced unsteady transonic aerodynamic loads response, that accounts for both complex non-linearities and time-history effects. A recent development, based on functional approximation theory, has established a novel functional form; namely, the multi-layer functional. For a large class of non-linear dynamic systems, such multi-layer functional representations can be realised via finite impulse response (FIR) neural networks. Identification of an appropriate FIR neural network model is facilitated by means of a supervised training process in which a limited sample of system input-output data sets is presented to the temporal neural network. The present work describes a procedure for the systematic identification of parameterised neural network models of motion-induced unsteady transonic aerodynamic loads response. The training process is based on a conventional genetic algorithm to optimise the network architecture, combined with a simplified random search algorithm to update weight and bias values. Application of the scheme to representative transonic aerodynamic loads response data for a bidimensional airfoil executing finite-amplitude motion in transonic flow is used to demonstrate the feasibility of the approach. The approach is shown to furnish a satisfactory generalisation property to different motion histories over a range of Mach numbers in the transonic regime.

Composite artistry in the Book of Numbers : a study in biblical narrative conventions

The present thesis discusses the coherence or lack of coherence in the book of Numbers, with special regard to its narrative features. The fragmented nature of Numbers is a well-known problem in research on the book, affecting how we approach and interpret it, but to date there has not been any thorough investigation of the narrative features of the work and how they might contribute to the coherence or the lack of coherence in the book. The discussion is pursued in light of narrative theory, and especially in connection to three parameters that are typically understood to be invoked in the interpretation of narratives: 1) a narrative paradigm, or ‘story,’ meaning events related to each other temporally, causally, and thematically, in a plot with a beginning, middle, and end; 2) discourse, being the expression plane of a narrative, or the devices that an author has at hand in constructing a narrative; 3) the situation or languagegame of the narrative, prototypical examples being factual reports, which seeks to depict a state of affairs, and storytelling narratives, driven by a demand for tellability. In view of these parameters the present thesis argues that it is reasonable to form four groups to describe the narrative material of Numbers: genuine narratives (e.g. Num 12), independent narrative sequences (e.g. Num 5:1-4), instrumental scenes and situations (e.g. Num 27:1-5), and narrative fragments (e.g. Num 18:1). These groups are mixed throughout with non-narrative materials. Seen together, however, the narrative features of these groups can be understood to create an attenuated narrative sequence from beginning to end in Numbers, where one thing happens after another. This sequence, termed the ‘larger story’ of Numbers, concerns the wandering of Israel from Sinai to Moab. Furthermore, the larger story has a fragmented plot. The end-point is fixed on the promised land, Israel prepares for the wandering towards it (Num 1-10), rebels against wandering and the promise and is sent back into the wilderness (Num 13-14), returns again after forty years (Num 21ff.), and prepares for conquering the land (Num 22-36). Finally, themes of the promised land, generational succession, and obedience-disobedience, operate in this larger story. Purity is also a significant theme in the book, albeit not connected to plot in the larger story. All in all, sequence, plot, and theme in the larger story of Numbers can be understood to bring some coherence to the book. However, neither aspect entirely subsumes the whole book, and the four groups of narrative materials can also be understood to underscore the incoherence of the work in differentiating its variegated narrative contents. Numbers should therefore be described as an anthology of different materials that are loosely connected through its narrative features in the larger story, with the aim of informing Israelite identity by depicting a certain period in the early history of the people.

Spontaneous Focusing on Quantitative Relations and the Development of Rational Number Conceptual Knowledge

The aim of the present set of studies was to explore primary school children’s Spontaneous Focusing On quantitative Relations (SFOR) and its role in the development of rational number conceptual knowledge. The specific goals were to determine if it was possible to identify a spontaneous quantitative focusing tendency that indexes children’s tendency to recognize and utilize quantitative relations in non-explicitly mathematical situations and to determine if this tendency has an impact on the development of rational number conceptual knowledge in late primary school. To this end, we report on six original empirical studies that measure SFOR in children ages five to thirteen years and the development of rational number conceptual knowledge in ten- to thirteen-year-olds. SFOR measures were developed to determine if there are substantial differences in SFOR that are not explained by the ability to use quantitative relations. A measure of children’s conceptual knowledge of the magnitude representations of rational numbers and the density of rational numbers is utilized to capture the process of conceptual change with rational numbers in late primary school students. Finally, SFOR tendency was examined in relation to the development of rational number conceptual knowledge in these students. Study I concerned the first attempts to measure individual differences in children’s spontaneous recognition and use of quantitative relations in 86 Finnish children from the ages of five to seven years. Results revealed that there were substantial inter-individual differences in the spontaneous recognition and use of quantitative relations in these tasks. This was particularly true for the oldest group of participants, who were in grade one (roughly seven years old). However, the study did not control for ability to solve the tasks using quantitative relations, so it was not clear if these differences were due to ability or SFOR. Study II more deeply investigated the nature of the two tasks reported in Study I, through the use of a stimulated-recall procedure examining children’s verbalizations of how they interpreted the tasks. Results reveal that participants were able to verbalize reasoning about their quantitative relational responses, but not their responses based on exact number. Furthermore, participants’ non-mathematical responses revealed a variety of other aspects, beyond quantitative relations and exact number, which participants focused on in completing the tasks. These results suggest that exact number may be more easily perceived than quantitative relations. As well, these tasks were revealed to contain both mathematical and non-mathematical aspects which were interpreted by the participants as relevant. Study III investigated individual differences in SFOR 84 children, ages five to nine, from the US and is the first to report on the connection between SFOR and other mathematical abilities. The cross-sectional data revealed that there were individual differences in SFOR. Importantly, these differences were not entirely explained by the ability to solve the tasks using quantitative relations, suggesting that SFOR is partially independent from the ability to use quantitative relations. In other words, the lack of use of quantitative relations on the SFOR tasks was not solely due to participants being unable to solve the tasks using quantitative relations, but due to a lack of the spontaneous attention to the quantitative relations in the tasks. Furthermore, SFOR tendency was found to be related to arithmetic fluency among these participants. This is the first evidence to suggest that SFOR may be a partially distinct aspect of children’s existing mathematical competences. Study IV presented a follow-up study of the first graders who participated in Studies I and II, examining SFOR tendency as a predictor of their conceptual knowledge of fraction magnitudes in fourth grade. Results revealed that first graders’ SFOR tendency was a unique predictor of fraction conceptual knowledge in fourth grade, even after controlling for general mathematical skills. These results are the first to suggest that SFOR tendency may play a role in the development of rational number conceptual knowledge. Study V presents a longitudinal study of the development of 263 Finnish students’ rational number conceptual knowledge over a one year period. During this time participants completed a measure of conceptual knowledge of the magnitude representations and the density of rational numbers at three time points. First, a Latent Profile Analysis indicated that a four-class model, differentiating between those participants with high magnitude comparison and density knowledge, was the most appropriate. A Latent Transition Analysis reveal that few students display sustained conceptual change with density concepts, though conceptual change with magnitude representations is present in this group. Overall, this study indicated that there were severe deficiencies in conceptual knowledge of rational numbers, especially concepts of density. The longitudinal Study VI presented a synthesis of the previous studies in order to specifically detail the role of SFOR tendency in the development of rational number conceptual knowledge. Thus, the same participants from Study V completed a measure of SFOR, along with the rational number test, including a fourth time point. Results reveal that SFOR tendency was a predictor of rational number conceptual knowledge after two school years, even after taking into consideration prior rational number knowledge (through the use of residualized SFOR scores), arithmetic fluency, and non-verbal intelligence. Furthermore, those participants with higher-than-expected SFOR scores improved significantly more on magnitude representation and density concepts over the four time points. These results indicate that SFOR tendency is a strong predictor of rational number conceptual development in late primary school children. The results of the six studies reveal that within children’s existing mathematical competences there can be identified a spontaneous quantitative focusing tendency named spontaneous focusing on quantitative relations. Furthermore, this tendency is found to play a role in the development of rational number conceptual knowledge in primary school children. Results suggest that conceptual change with the magnitude representations and density of rational numbers is rare among this group of students. However, those children who are more likely to notice and use quantitative relations in situations that are not explicitly mathematical seem to have an advantage in the development of rational number conceptual knowledge. It may be that these students gain quantitative more and qualitatively better self-initiated deliberate practice with quantitative relations in everyday situations due to an increased SFOR tendency. This suggests that it may be important to promote this type of mathematical activity in teaching rational numbers. Furthermore, these results suggest that there may be a series of spontaneous quantitative focusing tendencies that have an impact on mathematical development throughout the learning trajectory.

Jännitettä nostavan hakkurin käyttö akkukäyttöisessä audiolaitteessa

Audiovahvistimet pohjautuvat yhä useammin D-luokan vahvistimiin niiden korkean hyötysuhteen takia. Tämä mahdollistaa pidemmän käyttöajan tai vastaavasti tehon lisäämisen kannettavissa audiolaitteissa. Kuitenkin, jotta akkukäyttöisestä audiolaitteesta saataisiin suurempaa tehoa, se vaatii yleensä korkeamman jännitteen kuin yksittäisen akun lähtöjännite on. Korkeampi jännite voidaan saavuttaa lisäämällä akkuja tai käyttämällä jännitettä nostavaa hakkuria. Hakkureissa syntyy kuitenkin kytkennästä johtuvaa värettä, mille D-luokan vahvistimet ovat alttiita. Tässä työssä tutkitaan boost- ja Čuk-hakkurin soveltuvuutta jännitteen nostoon akkukäyttöisessä audiolaitteessa. Käytännön sovelluksena toimii Porsas, josta halutaan saada 500 W teho. Työssä tutkitaan audiolaitteen asettamia ehtoja jännitelähteelle sekä hakkurien mitoittamista ehtojen mukaisesti. Työn tutkimustapana on kirjallisuustutkimus ja simulointi. Audiolaitteen jännitelähteeltä vaatima teho vaihtelee suuresti. Tämä tulee ottaa huomioon hakkurin komponenttien mitoituksessa. Lisäksi hakkurin lähtöjännitteen väre pyritään minimoimaan, koska sillä on suuri vaikutus vahvistimen toimintaan. Tulovirran väreen minimoinnilla on pidentävä vaikutus akun purkusykliin. Hakkurien laskennalliset komponenttien arvot sekä simuloinnit osoittavat, että hakkurit olisivat myös mahdollista tehdä käytännössä. Simulointien perusteella boost-hakkurin komponenttien arvot ovat pienempiä kuin Čuk-hakkurin. Boost-hakkurille löytyy myös valmiita ohjainpiirejä enemmän. Toisaalta Čuk-hakkurilla on mahdollista tehdä myös energiansäästötila. Hakkurien ohjaus ja jäähdytys vaatisivat jatkotutkimusta.

Local Features in Image and Video Processing - Object Class Matching and Video Shot Detection

The usage of digital content, such as video clips and images, has increased dramatically during the last decade. Local image features have been applied increasingly in various image and video retrieval applications. This thesis evaluates local features and applies them to image and video processing tasks. The results of the study show that 1) the performance of different local feature detector and descriptor methods vary significantly in object class matching, 2) local features can be applied in image alignment with superior results against the state-of-the-art, 3) the local feature based shot boundary detection method produces promising results, and 4) the local feature based hierarchical video summarization method shows promising new new research direction. In conclusion, this thesis presents the local features as a powerful tool in many applications and the imminent future work should concentrate on improving the quality of the local features.

The improvement of enclosure protection class of power electronics device

Tässä diplomityössä tutkittiin vaihtoehtoja tehoelektroniikkalaitteiden kotelointiluokan kehittämiseksi. Haasteena paremman suojauksen suunnittelussa on laitteiden tuottama suuri määrä lämpöä, joka vaatii tehokkaan jäähdytyksen. Työn tuloksena saatu prototyyppi IP33 luokkaa varten täyttää standardissa SFS-EN 60529+A1 asetetut vaatimukset kyseiselle kotelointiluokalle. Rakenteessa ja valmistettavuudessa havaittiin muutama ongelma, jotka ovat korjattavissa pienillä muutoksilla. Korkeampia suojausluokkia varten testattiin IP54-luokiteltujen filtterituulettimien vaikutusta laitteen jäähdytykseen. Testien perusteella jäähdytysteho on riittävä ja filtterituulettimet todettiin toimivaksi ratkaisuksi korkeammille suojausluokille. Työn perusteella voidaan todeta, että nykyiset laitteet voidaan muokata vastaamaan IP33 luokan vaatimuksia kohtuullisen pienillä muutoksilla. Tätä korkeammat suojausluokat vaatisivat niin suuria muutoksia designiin, että todennäköisesti täysin uuden laitteen suunnittelu olis kannattavin vaihtoehto.

Regulation of T cell response to leishmania antigens by determinants of histocompatibility leukocyte class I and II molecules

It has been shown that HLA class I molecules play a significant role in the regulation of the proliferation of T cells activated by mitogens and antigens. We evaluated the ability of mAb to a framework determinant of HLA class I molecules to regulate T cell proliferation and interferon gamma (IFN-g) production against leishmania, PPD, C. albicans and tetanus toxoid antigens in patients with tegumentary leishmaniasis and healthy subjects. The anti-major histocompatibility complex (MHC) mAb (W6/32) suppressed lymphocyte proliferation by 90% in cultures stimulated with aCD3, but the suppression was variable in cultures stimulated with leishmania antigen. This suppression ranged from 30-67% and was observed only in 5 of 11 patients. IFN-g production against leishmania antigen was also suppressed by anti-HLA class I mAb. In 3 patients IFN-g levels were suppressed by more than 60%, while in the other 2 cultures IFN-g levels were 36 and 10% lower than controls. The suppression by HLA class I mAb to the proliferative response in leishmaniasis patients and in healthy controls varied with the antigens and the patients or donors tested. To determine whether the suppression is directed at antigen presenting cells (APCs) or at the responding T cells, experiments with antigen-primed non-adherent cells, separately incubated with W6/32, were performed. Suppression of proliferation was only observed when the W6/32 mAb was added in the presence of T cells. These data provide evidence that a mAb directed at HLA class I framework determinants can suppress proliferation and cytokine secretion in response to several antigens.

Daily birth numbers in Passo Fundo, South Brazil, 1997-1999: trends and periodicities

Between October 6, 1997 and April 30, 1999, 5011 births (mean: 8.76 per day) were registered in the city of Passo Fundo, South Brazil. The sequence of 572 daily birth numbers was not random (iteration test). Neyman distribution (m = ¥) showed the best fit. Clusters of days with higher birth numbers alternated with days with low numbers of births. Periodogram analysis revealed a significant periodicity of 6.98 days. The cosinor regression, testing 10 a priori supposed period lengths, found significant seasonality peaking in August-September and significantly highest birth numbers on Thursdays. Among the lunar and solar rotation cycles, the tropic lunar cycle and its 4th harmonic were most pronounced, in agreement with results concerning natality in Germany obtained by Svante Arrhenius in the 19th century. These findings confirm Derer-Halberg's concept of multiseptans. In addition to cycling, a significantly increasing linear trend with a daily increase of 0.0045 births was encountered. This documents a growth of the population in agreement with national statistical data.