The core of the thesis is the realization of three lessons of mathematics conducted in accordance with the CLIL method, which integrates the teaching a non-linguistic subject with foreign language teaching. The topic of the lessons was non-finite geometric series and the chosen foreign language was German. The first part of the thesis introduces key definitions and theorems concerning sequences and geometric series. Comparisons are drawn between approaches of the Czech Republic and two German-speaking countries, Austria and Germany, in relationship to the teaching non-finite geometric series. Furthermore, available teaching materials of the selected countries are compared and applied visualized problems which appear in them are analysed. In the second part, the CLIL teaching method is presented together with the methodology according to which the lessons were prepared, realized and subsequently assessed. To conclude, the thesis presents a detailed analysis of the preparation and progress of the lessons, including the reflection. The appendix comprises of the utilized teaching materials as well as a range of the solved problems.

This work investigates the self-organizing representation of temporal data in prototype-based neural networks. Extensions of the supervised learning vector quantization (LVQ) and the unsupervised self-organizing map (SOM) are considered in detail. The principle of Hebbian learning through prototypes yields compact data models that can be easily interpreted by similarity reasoning. In order to obtain a robust prototype dynamic, LVQ is extended by neighborhood cooperation between neurons to prevent a strong dependence on the initial prototype locations. Additionally, implementations of more general, adaptive metrics are studied with a particular focus on the built-in detection of data attributes involved for a given classifcation task. For unsupervised sequence processing, two modifcations of SOM are pursued: the SOM for structured data (SOMSD) realizing an efficient back-reference to the previous best matching neuron in a triangular low-dimensional neural lattice, and the merge SOM (MSOM) expressing the temporal context as a fractal combination of the previously most active neuron and its context. The first SOMSD extension tackles data dimension reduction and planar visualization, the second MSOM is designed for obtaining higher quantization accuracy. The supplied experiments underline the data modeling quality of the presented methods.

We study the dynamics of free test particles in a field of Schwarzschild black hole surrounded by an external exact thin axisymmetric solutions of Einstein's equations. Specifically, we use the Bach-Weyl ring and two member of the inverted Morgan-Morgan family of solutions as the additional sources. The fractal basin boundary and other meth- ods are used to detect and quantify chaos in time-like geodesic motion of the particles, primarily by computing box-counting dimension of said basin boundary. Our results mainly consist of the dependence of the chaoticity of these systems on mass and radius of the additional source as well as conserved energy and angular momentum of the test particles. We compare our results to literature and expand on them. 1

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The role of intrinsic hydrodynamic instability of the premixed flame (known as Landau-Darrieus instability) in various flame phenomena is studied by means of direct numerical simulations of the complete system of hydrodynamic equations. Rigorous study of flame dynamics and effect of Landau-Darrieus instability is essential for all premixed combustion problems where multidimensional effects cannot be disregarded. The present thesis consists of three parts. The first part deals with the fundamental problem of curved stationary flames propagation in tubes of different widths. It is shown that only simple "single-hump" slanted stationary flames are possible in wide tubes, and "multi-hump" flames in a laminar flow are possible in wide tubes only as a non-stationary mode of flame propagation. The stability limits of curved stationary flames in wider tubes are obtained, together with the dependence of the velocity of the stationary flame on the tube width. The flame dynamics in wider tubes is shown to be governed by a large-scale stability mechanism resulting in a highly slanted flame front. The second part of the thesis is dedicated to studies of acceleration and fractal structure of outward freely propagating flames. It is shown that in direct numerical simulation the development of Landau-Darrieus instability results in the formation of fractal-like flame front structure. The fractal excess for radially expanding flames in cylindrical geometry is evaluated. Two-dimensional simulation of radially expanding flames in cylindrical geometry displays a radial growth with 1.25 power law temporal behavior after some transient time. It is shown that the fractal excess for 2D geometry obtained in the numerical simulation is in good agreement with theoretical predictions. The difference in fractal dimension between 2D cylidrical and three-dimensional spherical radially expanding flames is outlined. Extrapolation of the obtained results for the case of spherical expanding flames gives a radial growth power law that is consistent with temporal behavior obtained in the survey of experimental data. The last part of the thesis concerns the role of Landau-Darrieus instability in the transition from deflagration to detonation. It is found that in sufficiently wide channels Landau-Darrieus instability may invoke nucleation of hot spots within the folds of the developing wrinkled flame, triggering an abrupt transition from deflagrative to detonative combustion. It is found that the mechanism of the transition is the temperature increase due to the influx of heat from the folded reaction zone, followed by autoignition. The transition occurs when the pressure elevation at the accelerating reaction front becomes high enough to produce a shock capable of supporting detonation. / QC 20101119

We introduce the notion of the modulus of fractality and consider the problem of approximation of functions with a restriction on the modulus of fractality by partial sums of trigonometric Fourier series (Fourier sums). The upper estimate of the difference between the function and the corresponding Fourier sum in terms of the modulus of continuity and the modulus of fractality is given. Examples of functions from the considered classes with trigonometric Fourier series diverging at some point are constructed. / Вводится понятие модуля фрактальности и рассматривается задача приближения функций с ограничением на модуль фрактальности частичными суммами тригонометрических рядов Фурье (суммами Фурье). Приведена оценка сверху модуля разности функции и соответствующей суммы Фурье, выраженная в терминах модуля непрерывности и модуля фрактальности. Построены примеры функций из рассматриваемых классов с расходящимся в некоторой точке тригонометрическим рядом Фурье.

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Nanoparticles are used in many different applications because of their small size and unique properties. The usage is increasing rapidly, which will increase the nanoparticle exposure to the environment. Up till now, environmental behavior and ecotoxicology of nanoparticles have only been studied to a certain extent and because of the increasing usage, research should focus more on nanoparticle behavior and ecotoxicology. An effective way of studying nanoparticles in aqueous environments is to use mathematical models. In this study, the In vitro Sedimentation, Diffusion, and Dosimetry (ISDD) model was investigated and applied to copper, manganese, and zinc oxide nanoparticles to determine their sedimentation velocity in 1 mM NaClO4(aq).   The results show that the simulated sedimentation of nanoparticles in solution, i.e. the output from the ISDD model, can vary a lot depending on some of the input parameters in the model. The fact that some of these parameters have to be estimated increases the uncertainty of the ISDD model, although it is possible to yield results in great agreement with experimentally determined sedimentation velocities for the studied systems. The simulation results could always be explained by the theory behind it, which increases the reliability of the ISDD model.   The possibility of measuring the effective density of nanoparticle agglomerates using the volumetric centrifugation method was also investigated. This method makes it possible to avoid estimating the fractal dimension, an input parameter with great uncertainty in the ISDD model. The results look promising, although further investigation is needed.    The ISDD model seems to be a promising model for future simulation work. The model should be investigated further in order to minimize the uncertainties due to estimations. The possibility to predict nanoparticle sedimentation using a mathematical model will save a lot of time and money, and it can be a helpful tool in the extensive work of identifying the behavior of nanoparticles in aqueous environments.

Yes / The most recent face recognition systems are mainly dependent on feature representations obtained using either local handcrafted-descriptors, such as local binary patterns (LBP), or use a deep learning approach, such as deep belief network (DBN). However, the former usually suffers from the wide variations in face images, while the latter usually discards the local facial features, which are proven to be important for face recognition. In this paper, a novel framework based on merging the advantages of the local handcrafted feature descriptors with the DBN is proposed to address the face recognition problem in unconstrained conditions. Firstly, a novel multimodal local feature extraction approach based on merging the advantages of the Curvelet transform with Fractal dimension is proposed and termed the Curvelet–Fractal approach. The main motivation of this approach is that theCurvelet transform, a newanisotropic and multidirectional transform, can efficiently represent themain structure of the face (e.g., edges and curves), while the Fractal dimension is one of the most powerful texture descriptors for face images. Secondly, a novel framework is proposed, termed the multimodal deep face recognition (MDFR)framework, to add feature representations by training aDBNon top of the local feature representations instead of the pixel intensity representations. We demonstrate that representations acquired by the proposed MDFR framework are complementary to those acquired by the Curvelet–Fractal approach. Finally, the performance of the proposed approaches has been evaluated by conducting a number of extensive experiments on four large-scale face datasets: the SDUMLA-HMT, FERET, CAS-PEAL-R1, and LFW databases. The results obtained from the proposed approaches outperform other state-of-the-art of approaches (e.g., LBP, DBN, WPCA) by achieving new state-of-the-art results on all the employed datasets.

The importance of the effect of land use changes on watersheds has been widely acknowledged. Several studies have evaluated this effect through various approaches including non-stationary analysis, hydrological simulation and the observation of paired watersheds. The present study aims to describe the effect of land use changes on the hydrological response of watersheds considering the variation of the hydraulic properties of soil, which are related to the soil type and vegetal cover. This investigation was conducted in the watershed of Combeima River, Colombia, South America. By using distributed hydrological modelling, the effect of historical land use changes - including forest, crops and grasslands - on the magnitude of peak flows and mean annual runoff volumes was described. The analysis was carried out by relating land use changes to the hydraulic properties of soil, namely, the soil water content in the root zone or static storage (Hu) and the saturated hydraulic conductivity (Ks). Variation of the Hu and Ks values with respect to each soil type allowed quantifying the effect of changes in vegetal covers on the peak flows of flood events in Combeima River. Results of the analysis indicate that low Hu and Ks values are associated with land covers such as grasslands, which are characterized by having low infiltration, while high Hu and Ks values are more characteristic of forests. It was also identified that a decrease in the watershed infiltration capacity results in an increase in the magnitude of peak flows, while an increase in the infiltration capacity and soil water retention contributes to the attenuation of peak flows. Land use changes have been demonstrated to be a source of non-stationarity in the flow series, which can be identified through changes, positive or negative, in the time series trend. The hypothesis of the joint application of scale theory was tested in this study, showing that the invariance properties of the soil hydraulic properties are related to the flood regime and mean annual runoff volumes. The analysis focused mainly on two parameters: the static storage Hu and the saturated hydraulic conductivity Ks; therefore, this study did not attempt to explain the problem of non-stationarity, but rather to introduce the scalability properties of the soil hydraulic properties to predict flows, as a hydrological response to scenarios of land use change. Scenarios of spatial variation of land uses with respect to soil hydraulic properties were set up to assess the effect of those changes on the scalability properties of Hu and Ks and peak flows. Likewise, tests were conducted to evaluate the potential effects of the homogeneous distribution of precipitation on the scalability of the soil hydraulic properties during flood events. Properties of scale invariance were evaluated for the parameters of two probability distribution functions: GEV and Gumbel, for scenarios of land use change, considering the relationship between Hu and Ks and the magnitude of the flood quantiles. A similar analysis was carried out for the regime of mean annual runoff volumes through the application of the LogNormal distribution. The effect of land use changes on the non-stationarity of Combeima River flow series was evaluated using linear and non-linear stationary analysis, whose results verified the convenience of introducing the non-stationarity hypothesis in the frequency analysis of peak flows. Results of this study indicate that the incorporation of fractal theory to relate the hydraulic properties of soil and flow behavior in a watershed has potential practical applications in engineering and watershed management, given its simplicity as a power relation and usefulness to estimate the effects of land use changes on the flood regime. / Se ha reconocido la importancia de conocer el efecto de los cambios de usos del suelo sobre el régimen de caudales en cuencas hidrográficas. En este sentido, se han desarrollado investigaciones para evaluar dicho efecto desde diferentes enfoques como el análisis no estacionario, la simulación hidrológica y la observación de cuencas pareadas, entre otros. De manera que esta investigación contribuye a describir el efecto de cambios de uso del suelo sobre la respuesta hidrológica de las cuencas, considerando la variación propiedades hidráulicas de los suelos, las cuales se relacionan con el tipo de suelo y cobertura vegetal. Esta investigación se desarrolló en la cuenca del Río Combeima en Colombia-Suramérica, donde a partir de la modelación hidrológica distribuida, se describe el efecto de cambios históricos de usos del suelo como bosques, cultivos y pastizales, sobre la magnitud de los caudales máximos y volúmenes medios anuales de escorrentía. Para el desarrollo de este análisis, se relacionaron los cambios en el uso del suelo con las propiedades hidráulicas del suelo, específicamente, el contenido de agua en el suelo en zona de raíces o almacenamiento estático Hu y la conductividad hidráulica saturada Ks. La variación de los valores de Hu y Ks relacionados con cada uso del suelo, condujo a cuantificar el efecto de los cambios en las coberturas vegetales sobre los caudales pico en el régimen de crecidas del Río Combeima. Los resultados obtenidos, sugieren que valores bajos de Hu y Ks, se asocian con los cambios de uso del suelo y a su vez, influyen en la magnitud de los eventos de crecidas. En este contexto, esta investigación no se desarrolló en torno a explicar el problema de la no estacionariedad, sino que propone introducir las propiedades de escalabilidad de las propiedades hidráulicas del suelo para predecir caudales como respuesta hidrológica en escenarios de cambios de uso del suelo. Para lograrlo, se realizaron simulaciones en una cuenca hipotética basada en la información de la cuenca del Río Combeima, en donde se plantearon escenarios de variación espacial de los usos del suelo en relación con las propiedades hidráulicas, para evaluar su efecto sobre las propiedades de escalabilidad de los parámetros Hu y Ks en relación con los caudales máximos. Por otra parte, se evaluaron las propiedades de invarianza en escala, de los parámetros de las funciones de distribución de probabilidad: GEV y Gumbel, en escenarios de cambios de uso del suelo, considerando la relación entre los parámetros Hu y Ks, y la magnitud de los cuantiles de crecidas. Adicionalmente, se realizó un análisis similar para el régimen de volúmenes anuales medios de escorrentía, mediante la aplicación de la función LogNormal. El efecto de los cambios de uso del suelo sobre la no estacionariedad de las series de caudales en la cuenca del Combeima se evaluó mediante un análisis no estacionario lineal y no lineal, cuyos resultados permitieron identificar la conveniencia de introducir la hipótesis de no estacionariedad en el análisis de frecuencia de caudales máximos. Los resultados obtenidos, indican que la incorporación de la teoría fractal en la relación entre las propiedades hidráulicas del suelo y el comportamiento de los caudales en cuencas hidrográficas, tiene potenciales aplicaciones prácticas en la ingeniería y la planificación de cuencas, dada su sencillez, ya que se expresa como una relación de potencia, útil para realizar estimaciones de los efectos de los cambios en los usos del suelo sobre el régimen de caudales. / S'ha reconegut l'importancia de coneixer l'efecte dels canvis d'usos del sol sobre el regim de cabals en conques hidrografiques. En este sentit, s'han desenrollat investigacions per a evaluar dit efecte des de diferents enfocaments com l'analisis no estacionari, la simulacio hidrologica i l'observacio de conques PAREADAS, entre atres. De manera que esta investigacio contribuix a descriure l'efecte de canvis d'us del sol sobre la resposta hidrologica de les conques, considerant la variacio propietats hidrauliques dels sols, les quals se relacionen en el tipo de sol i cobertura vegetal. Esta investigacio se desenrollà en la conca del Riu COMBEIMA en COLOMBIA-SURAMÉRICA, a on a partir de la MODELACIÓN hidrologica distribuida, se descriu l'efecte de canvis historics d'usos del sol com boscs, conreus i PASTIZALES, sobre la magnitut dels cabals maxims i VOLÚMENES mijos anuals d'ESCORRENTÍA. Per a el desenroll d'este analisis, se relacionaren els canvis en l'us del sol en les propietats hidrauliques del sol, especificament, el contingut d'aigua en el sol en zona d'arraïls o almagasenament estatic HU i la conductivitat hidraulica saturada KS. La variacio dels valors d'HU i KS relacionats en cada us del sol, condui a CUANTIFICAR l'efecte dels canvis en les cobertures vegetals sobre els cabals bec en el regim de creixcudes del Riu COMBEIMA. Els resultats obtinguts, sugerixen que valors baixos d'HU i KS, s'associen en els canvis d'us del sol i a la seua volta, influixen en la magnitut dels events de creixcudes. En este context, esta investigacio no se desenrollà en torn a explicar el problema de la no ESTACIONARIEDAD, sino que propon introduir les propietats d'ESCALABILIDAD de les propietats hidrauliques del sol per a PREDECIR cabals com resposta hidrologica en escenaris de canvis d'us del sol. Per a conseguir-ho, se realisaren simulacions en una conca hipotetica basada en l'informacio de la conca del Riu COMBEIMA, a on se plantejaren escenaris de variacio ESPACIAL dels usos del sol en relacio en les propietats hidrauliques, per a evaluar el seu efecte sobre les propietats d'ESCALABILIDAD dels parametros HU i KS en relacio en els cabals maxims. Per atra part, s'evaluaren les propietats d'INVARIANZA en escala, dels parametros de les funcions de distribucio de provabilitat: GEV i GUMBEL, en escenaris de canvis d'us del sol, considerant la relacio entre els parametros HU i KS, i la magnitut dels CUANTILES de creixcudes. Adicionalment, se realisà un analisis similar per al regim de VOLÚMENES anuals mijos d'ESCORRENTÍA, mediant l'aplicacio de la funcio LOGNORMAL. L'efecte dels canvis d'us del sol sobre la no ESTACIONARIEDAD de les series de cabals en la conca del COMBEIMA s'evaluà mediant un analisis no estacionari llinial i no llinial, CUYOS resultats permeteren identificar la cominencia d'introduir l'HIPÓTESIS de no ESTACIONARIEDAD en l'analisis de freqüencia de cabals maxims. Els resultats obtinguts, indiquen que l'incorporacio de la teoria FRACTAL en la relacio entre les propietats hidrauliques del sol i el comportament dels cabals en conques hidrografiques, te potencials aplicacions practiques en l'ingenieria i la PLANIFICACIÓN de conques, donada la seua senzillea, ya que s'expressa com una relacio de potencia, util per a realisar valoracions dels efectes dels canvis en els usos del sol sobre el regim de cabals. / Peña Rojas, LE. (2017). ESCALAMIENTO DE PROPIEDADES HIDRÁULICAS DEL SUELO EN EL RÉGIMEN DE CRECIDAS A ESCALA DE CUENCA. APLICACIÓN EN LA CUENCA DEL RÍO COMBEIMA (SURAMÉRICA) [Tesis doctoral]. Universitat Politècnica de València. https://doi.org/10.4995/Thesis/10251/90390