The heat content of a domain D of &Ropf;^d is defined as</sp> < p >E(s) = &int;_D u(s,x)dx, where u is the solution to the heat equation with zero initial condition and unit Dirichlet boundary condition. This thesis studies the behaviour of E(s) for small s with a particular emphasis on the case where $D$ is a planar domain whose boundary is a random Koch curve. When &part;D is spatially homogeneous, we show that we can recover the upper and lower Minkowski dimensions of &part;D from E(s). Furthermore, in some cases where the Minkowski dimension does exist, finer fluctuations can be recovered and the heat content is controlled by s^&alpha; exp{f (log(1/s)} for small s, for some positive &alpha; and some regularly varying function f. When &part;D is statistically self-similar, the heat content asymptotics are studied using a law of large numbers for the general branching process, and we show that the Minkowski dimension and content of &part;D exist and can be recovered from E(s). More precisely the heat content has an almost sure expansion E(s) = c₁ s^&alpha; N_&infin; + o(s^&alpha;), a.s. for small s, for some positive c₁ and &alpha; and a positive random variable N_&infin; with unit expectation. To study the fluctuations around these asymptotics, we prove a central limit theorem for the general branching process. The proof follows a standard Taylor expansion argument and relies on the independence built into the general branching process. The limiting distribution established here is reminiscent of those arising in central limit theorems for martingales. When &part;D is a statistically self-similar Cantor subset of &Ropf;, we discuss examples where we have and fail to have a central limit theorem for the heat content. We conclude with an open question about the fluctuations of the heat content when &part;D is a statistically self-similar Koch curve.

Basic idea of fractal simplex algorithm is based in the theory of matrix counting and knowledge of matrix representation of simplex tabuleao from revised simplex method. My desire is to explain theoretical basics on which this algorithm works and provide solution in language Visual Basic for Applications in application MS Excel 2007. Main benefit I see in the fact, that algorithm can solved specific class of mathematical problems in a way of exactness counting whithout necessity of using decimal numbers.

The mission of the Technology Transfer Programme Office is to increase impact on a society by transferring technologies developed by the European Space Agency. Method and Apparatus for compressing time series is a patented compression algorithm designed to be efficient as its purpose is to run on deep space probes or satellites. The algorithm is inspired by a method for fractal terrain generation, namely the midpoint displacement algorithm. This work introduces fractals, their application and modifying the patented algorithm, in order to achieve greater compression. The modification lies in modifying the displacement mechanism. The modified algorithm is capable of reducing data up to 25 %, compared to the patented algorithm. The modification made the algorithm less efficient. In large-scale test, performed on Rosetta spacecraft telemetry, the modified algorithm achieved around 5 % higher compression.

Redes neurais caracterizadas por cadeias de osciladores acoplados são um dentre vários tipos de redes que possuem propriedades peculiares relacionadas com a sua estrutura topológica. A dinâmica que descreve o comportamento dessas redes é modelada por sistemas de equações diferenciais, nos quais cada neurônio (nó) é considerado como um oscilador. Estudos realizados em redes desse tipo, em tarefas de reconhecimento de padrões estáveis gerados aleatoriamente, têm apresentado resultados computacionais satisfatórios. Esta tese propôs um desenvolvimento teórico e computacional que forneceu um algoritmo, para o estudo do desempenho de redes neurais em forma de osciladores de Ciclo-Limite de Stuart-Landau, no reconhecimento de figuras fractais. Neste trabalho apresentaremos contextos reais em que podemos encontrar características deste tipo de redes e motivações. Em seguida, serão expostos conceitos de redes de Hopfield, reconhecimento de padrões, teorias dos fractais e dos osciladores de Ciclo-Limite de Stuart-Landau; tais conceitos, por sua vez, serviram como ferramentas principais para o algoritmo construído que será explicado posteriormente. Antes de apresentá-lo, será exposta a maneira como a dinâmica desses osciladores pode se tornar caótica, por meio de simulações computacionais alterando numericamente variáveis intrínsecas, como tempos de disparos entre neurônios, ou quantidades destes no sistema. Estas descobertas serviram como confirmações para elaborar e compor do algoritmo, bem como orientaram as simulações de reconhecimento de figuras fractais. Por fim, será apresentada a conclusão dos resultados encontrados. / Neural networks characterized by chains of coupled oscillators are one of several types of networks which have peculiar properties related with their topological structure. The dynamics that describes the behavior of these networks is modeled by systems of differential equations, of which each neuron (node) is considered as an oscillator. Studies on such networks, in tasks of recognizing randomly generated stable patterns, have presented satisfactory computational results. This thesis proposed a theoretical and computational development that provided an algorithm for the study of the performance of neural networks in the form of Cycle-Limit oscillators of Stuart-Landau, in the recognition of fractals. In this work we will present real contexts in which we can find characteristics of this type of networks and motivations. Next, concepts of Hopfield networks, pattern recognition, fractals theories and the Stuart-Landau Cycle-Limit oscillators will be presented; these concepts, in turn, served as the main tools for the algorithm constructed that will be explained later. Before presenting it, it will be exposed how the dynamics of these oscillators can become chaotic, through computer simulations numerically altering intrinsic variables, such as firing times between neurons, or quantities of these in the system. These findings served as confirmations for elaborating and composing the algorithm, as well as guiding the simulations of the recognition of fractals. Finally, the results will be presented.

Charles University, Faculty of Pharmacy in Hradec Králové Department of: Pharmaceutical technology Supervisor: doc. PharmDr. Zdeňka Šklubalová, Ph.D. Consultant: Ing. Hana Hurychová Student: Eliška Dostálová Title of Thesis: Study of bulk and consolidation properties of size fractions of anhydrous lactose The bulk and consolidation behaviour of pharmaceutical excipients belong to their important properties. Properties of five size fractions of anhydrous lactose having the particle size in the range of 1-400 µm were studied in this thesis. The measurement was carried out by using static and dynamic pharmacopoeial methods. The bulk density and the tapped density, the angle of repose were evaluated as well as the true density of particles by using the gas pycnometry. The mass flow rate through the orifice of a model conical hopper by the force of gravity was estimated for the individual size fractions. The discharge rate through the orifice having the diameter in a range of 0.6-1.5 cm was modelled with the Beverloo et al and Jones & Pilpel power regression equations; the precision of the flow rate prediction was about 3 %. The best bulk properties were detected for the particle size fraction 246 µm. The results of the evaluation of the consolidation dynamic during the tapping of powder bed permitted...

Králové doc. PharmDr. Zdeňka Šklubalová, Ph.D. Ing. Hana Hurychová, Ph.D. Monika Hnatková The objective of this diploma thesis was to evaluate the flow and consolidation behaviour of the size fractions of lactose for direct compression - Tabletose® 80 in a range of 80-400 μm obtained by sieving. The nonlinear influence of the particle size on the flow rate was detected; the fractions of Tablettose® 80 with the mean size of 245 and 346 µm showed the best flowability. The influence of the diameter of the hopper opening on the flow rate was modeled using the Beverloo and/or Jones & Pilpel flow equation; the latter described the results better. The assessment of volume changes by gravitational tapping allowed to observe dynamics of consolidation and to express porosity factor for the powder bed, which enabled an estimation of the angle of internal friction.

1 Abstract Charles University, Faculty of Pharmacy in Hradci Králové Department of: Department of Pharmaceutical Technology Supervisor: Doc. PharmDr. Zdeňka Šklubalová, Ph. D. Consultant PharmDr. Karel Palát, CSc., Mgr. Žofie Trpělková Student: Martina Litošová Title of Thesis: Homogenization of powder blends using a Turbula mixer. In this experimental work, the influencing of the homogeneity of the powder mixture of acetylsalicylic acid (ASA) and microcrystalline cellulose (Avicel PH102) due to the rotational speed of the mixing container in a range of 23−101 rpm, and the mixing time was studied using the Turbula shaker mixer. Within time interval 2-62 minutes, the content of ASA in samples was measured by near-infrared spectrometry. The expression of standard deviation was used to evaluate the homogeneity of samples. The best results were detected at a rotational speed of 34 rpm within time interval of 14−30 min.

Charles University, Faculty of Pharmacy in Hradci Králové Department of: Pharmaceutical technology Supervisor: doc. PharmDr. Zdeňka Šklubalová, Ph.D. Consultant: Mgr. Žofie Trpělková Student: Aneta Mrázková Title of Thesis: The study of influence of the measurement method on static angle of repose of free-flowable excipients. Good flow and consolidation properties of powders represent significant characteristics of pharmaceutical excipients They are important for manufacturing of powders into solid dosage forms. Flow behavior of 6 free flowing excipients was evaluated in this diploma thesis. The main target was a study of the influence of the masurement method and the orifice size of a conical hopper on static angle of repose (AOR). The automatic tester and the prototype for measuring AOR having orifice sizes in a range of 6-15 mm were used for the measurement. A significant difference between the results of these two methods (P <0.01) was observed. The decrease in AOR was detected when increased the orifice diameter, the effect was significant (P <0.01) only in automatic tester for two out of six measured powders. Surprisingly, the significant influence of the orifice size on AOR was registered for a sweetener Palatinose with protype equipment.

In this work, we propose the application fractal compression techniques to textured images segmentation, and use the transformation coefficients as features for segmentation. The result is improved by combining fractal dimension feature and the transformation coefficients from the original and its filter versions. Feature vectors are clustered together using K-mean algorithm with features pre-smoothing. The numbers of feature are minimized to reach the compromise result. In the integrated approach, we attempt to improve segmentation of texture images using our method. Background knowledge of image segmentation and image compression will be presented. Algorithms for fractal dimension calculation, K-means clustering, and fractal compression is given. Experimental results are included, and possible future work is mentioned.

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