In this thesis we propose several novel configurations of bandpass filters (BPFs) with two transmission zeros by using the fractal theory. By means of the fractal theory, the dimension of the proposed BPFs can be effectively reduced. Furthermore, the proposed BPFs can be easily fabricated by using multilayer structure based on low-temperature cofired ceramic (LTCC) technology. Under the condition of the same dielectric thickness and coupling coefficient, we compared the conventional square open-loop BPF with the proposed fractal ones. The results show that the reduction in the dimension of the proposed BPFs is evident. Specifically, the dimension of the proposed Koch¡¦s, Minkowski_1st, and Minkowski_2nd filters can be reduced by about 36.5%, 32%, and 51.5%, respectively. Finally, the simulation and measurement results are reported in this thesis.

Traditional Content-based image retrieval supports image searches based on color, texture and shape. However it is difficult and nonintuitive for most user to use those low level features to query images. And for most user they like search by keywords . For example , recently Google provide services in image search. Although it is named image search , but actually it is search by keywords ,not image-contents. For this reason MPEG-7 now support textual annotation standard which is MPEG-7 Multimedia Description Schemes (DSs) are metadata structures for describing and annotating audio-visual (AV) content. But manual annotation of image or video take time and expensive. we propose a system which could help us to make suitable auto-annotations.We extract the image factal features and use Diverse Density Algorithm for training models. In this way , user and system can interact in real-time . When trained models in database is growing, the system auto-annotation success rate is increasing.

Fractal image compression is based on the representation of an image by contractive transforms whose xed points are close to the original image. In the encoding of fractal image compression, most of the time is spent on nding the close match between a range block and a large pool of domain blocks. In this thesis, we use the intra-block variances distributions of domain blocks to reduce the searching space. For nding a close match we need only search the domain blocks whose maximal intra-block variance quadrants are the same as that of the range block in nding a close match. The experiment results show that our algorithm can reduce much encoding time with only slight loss of quality.

In this thesis, the study focuses on the antenna design for integrated passive devices. By using the substrate of piezoelectric material with high permittivity and introducing the fractal structures, the size reduction is obtained. Part of the research analyzes the influences of the surrounding environment on the antenna performances, including the effects of external formations, internal components, and interconnections. The results can provide the design rules for developing IPD antennas. The other part of the research emphasizes the design of IPD antenna itself, involving the investigations on the characteristics of substrate and fractals. The trade-off between compactness and radiation efficiency is pointed out, and then a design of modified ground plane is presented. When the modified design is placed on the system ground plane that exists in real system, the radiation efficiency can be improved significantly. Therefore, the concept of the compact IPD antenna is achieved.

In this work we used the profilogramms of surfaces, which were gained after the surface was processed (coarsened) with abrasive paper of 24, 36, 40, 60 and 100 numbers. We assessed fractal dimensions of all profilogramms and founded dependence of fractal dimension on abrasive paper number. We found that the more is the coarse of the surface the smaller is fractal dimension. As we didn’t want to do experiment which ask many resources – we modeled theoretically researched profilogramms–fractals, calculated and modeled dimensions of fractal profilogramms. We created programmable tools for theoretical research: the profilogramms-fractals models of adequate surfaces, also examined fractal dimensions of modeled profilogramms. With every profilogramm which has adequate fractal dimension we modeled the surface and calculated his area. We applied the linear regression model for logarithmic data and founded the interrelation between the area or the surface and fractal dimension.

"Fraktalai" is a program for creating and editing IFS and Flame Fractal parameters. Once a nice fractal has been found the parameters can be exported to IFS for use with my Iterated Function Systems coloring algorithm. The IFS files that it creates can also be viewed in other fractal programs. Iterated Function Systems is used in image compression. It also becomes very popular as a way of producing fractal images. "Fraktalai" only makes a distinction between Iterated Function Systems and Flame Fractals when loading and saving parameters. The algorithm that generates random fractals is designed to create reasonably interesting parameters but it has no sense of beauty, so you will probably want to make some adjustments. The supplied gradients were created from image files using a special algorithm (you may have noticed the names of a few famous paintings). This sort of gradient looks very nice with Flame Fractals, and "Fraktalai" has the ability to create similar gradients from BMP or JPEG images.

In our research we analyse electrocardiograms (ECG). The aim of this research is to apply the fractal dimension computing method to electrocardiograms, i.e. to create an algorithm, due to which it would be possible to get a few parameters describing ECG. Then, to check, whether the created the mathematical model for computing fractal dimension classify the possessed data. According to Hausdorf “capacity dimension” we compute and analyze “capacity coefficient”. The research of the plane “capacity coefficient” was carried out in this work (it is a fractal dimension, which was computed at the fixed dimension of the iterational window). The computing algorithm was made, with the help of which the ECG plane capacity coefficient was computed for 300 persons. When the initial information on the examined persons is known, the results are tried to be assessed from the mathematical, as well as medical, point of view.

This thesis introduces fractal interpolation functions, exposes advantages of fractal interpolation of real world objects and presents some newly developed procedures, associated with fractal interpolation process. The work briefly presents the context needed for introduction of fractal approach and relevant definitions. Also, the detailed description of fractal generating algorithms (deterministic, random iteration, “escape time”) as well as fractal classifications is presented. Since the research object is theoretical and practical aspects of fractal interpolation function analysis, special attention is paid to geometric fractals, obtained using systems of iterated functions (IFS). The notion of a fractal interpolation function is introduced in the work. The author shows that it is possible to generate fractal interpolation functions for various types of data. The generated functions are “close” (in the sense of Housdorf dimension) to the data under processing, i.e., it is possible to ensure that the fractal interpolation graph dimension were equal to the fractal dimension of experimental data (graph). The random iteration algorithm is used for the analysis of fractal interpolation functions, since it is relatively simple and fast enough. The author makes an attempt to analyze and solve the problem of choosing interpolation points (general case). A few approaches are proposed, namely the uniform distribution of interpolation points (for the interactive use) and collage. On... [to full text]

Canola protein isolate (CPI) has tremendous potential as a protein alternative to soy within the global protein ingredient market. The overall goal of this thesis was to compare and contrast the gelling mechanism of CPI with a commercial soy protein isolate (SPI) ingredient. Specifically, the gelation properties of CPI and SPI were evaluated as a function of protein concentration (5.0–9.0%), destabilizing agent [0.1 – 5.0 M urea; 0.1 and 1.0% 2-mercaptoethanol], ionic strength (0.1, 0.5 M NaCl) and pH (3.0, 5.0, 7.0, 9.0). The fractal properties of CPI were evaluated as a function of protein concentration (5.0 – 9.0%) and pH (3.0, 5.0, 7.0, 9.0). In the first study, the gelling properties of CPI and SPI as a function of concentration were evaluated, along with the nature of the interactions within their respective gel networks. Overall, the magnitude of the storage modulus (G') of the gel was found to increase with increasing concentration at pH 7.0, whereas the gelling temperature (Tgel) remained constant at ~88ºC. As the NaCl level was increased from 0.1 to 0.5 M, the zeta potential was found to be reduced from ~-20 to -4 mV, but with little effect on Tgel or network strength. In the presence of 2-mercaptoethanol, networks became weaker, indicating the importance of disulfide bridging within the CPI network. Disulfide bridging, electrostatics and hydrogen bonding are all thought to have a role in CPI gelation. In the case of SPI, the magnitude of the storage modulus (G') and Tgel were found to increase and decrease (~80ºC to 73ºC), respectively, with increasing urea concentration at pH 7.0. Increases in NaCl from 0.1 to 0.5 M reduced the zeta potential from ~-44 to -13 mV and caused a shift in Tgel from ~84ºC to 67ºC, and increased G'. No gels were formed in the presence of 2-mercaptoethanol. In the second study, the effect of pH on the gelling properties of CPI and SPI was evaluated. Surface charge (i.e., zeta potential) measurements as a function of pH found CPI to be positively (+18.6 mV), neutral and negatively (-32 mV) charged at pH 3.0, ~5.6 and 9.0, respectively. On the other hand, SPI was observed to be positively (+35.4 mV), neutral and negatively (-51 mV) charged at pH 3.0, 5.0 and 9.0, respectively. An increases in NaCl concentration from 0 M to 0.1 M resulted in a reduction in surface charge at all pHs for both CPI and SPI. Differential scanning calorimetry was performed to determine the thermal properties of CPI. The gelation temperature was found to be above the onset temperature for denaturation. For CPI, the onset of denaturation was found to occur at ~68ºC and then increased to ~78-79ºC at pH 7.0-9.0. With respect to rheological properties, SPI did not gel at pH 9.0, and G' declined as pH increased from 3.0 to 7.0. CPI did not gel at pH 3.0, however the network formed at pH 5.0 became stronger (higher G') as pH increased. The SPI gelling temperature at pH 3.0, 5.0 and 7.0 was observed to be ~85.6, ~46 and ~81ºC, respectively. SPI gels formed at pH 5.0 earlier due to increased protein aggregation near its isoelectric point (pI). The gelation temperature for CPI at pH 5.0 and 7.0 were similar (~88ºC), then declined at pH 9.0 (~82ºC). Network structure of CPI as a function of pH also was investigated using confocal scanning light microscopy (CSLM). As the pH became more alkaline from pH 7.0 to pH 9.0, there was a decrease in lacunarity (~0.41->~0.25). However, the fractal dimension was found to increase (from ~1.54 to ~1.82) showing that increasing the pH resulted in a more compacted CPI network. In summary, protein-protein aggregation induced either by increasing concentration or changing the pH resulted in network formation for both CPI and SPI, where both networks were thought to be stabilized by disulfide bridging and hydrogen bonding. SPI underwent protein aggregation earlier than CPI near its pI value, whereas CPI gels formed the strongest networks away from its pI under alkaline conditions. In all cases, CPI grew in diffusion-limited cluster-cluster aggregation to from the gel network.

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