Medición de la dimensión fractal de la microestructura de aceros

Tesis (Maestría en Ciencias de la Ingeniería Mecánica, con especialidad en Materiales). U. A. N. L.

Geometría fractal de las fronteras de grano del acero AISI 304 sometido a deformación por Víctor Miguel Trejo Ramón

Tesis (Maestría en Ciencias de la Ingeniería Mecánica con Especialidad en Materiales) U.A.N.L.

Caracterización fractal en fronteras de grano de materiales cristalinos utilizando microscopía electrónica por Jesús Garza Paz

Tesis (Maestría en Ciencias de la Ingeniería Mecánica con Especialidad en Materiales) U.A.N.L.

Estudio de microestructuras dendríticas mediante análisis fractal

Tesis (Maestría en Ciencias de la Ingeniería Mecánica con Especialidad en Materiales) U.A.N.L.

Applications of Fractal Based Structures in Radar Cross Section Reduction

This thesis presents the Radar Cross Section measurements of different geometric structures such as flat plate,cylinder, corner reflector and circular cone loaded with fractal based metallo dielectric structures.Use of different fractal geometris,metallizations of different shapes as well as the frequency tanability is investigated for TE and TM polarization of the incident electromagnetic field.Application of fractal based metallo-dielectric structures results in RCS reduction over a wide range of frequency bands.RCS enhancement of dihedral corner is observed at certain acute and obtuse corner angles.The experimental results are validated using electromagnetic simulation softwares.

Scattering Behaviour of fractal based metallo-dielectric structures

The scattering behaviour of fractal based metallodielectric structures loaded over metallic targets of different shapes such as flat plate, cylinder and dihedral corner reflector are investigated for both TE and TM polarizations of the incident wave. Out of the various fractal structures studied,square Sierpinski carpet structure is found to give backscattering reduction for an appreciable range of frequencies. The frequency of minimum backscattering depends on the geometry of the structure as well as on the thickness of the substrate. This structure when loaded over a dihedral corner reflector is showing an enhancement in RCS for corner angles other than 90◦.

Radar cross-section enhancement of dihedral corner reflector using fractal-based metallo-dielectric structures

Effective use of fractal-based metallo-dielectric structures for enhancing the radar cross-section (RCS) of dihedral corner reflectors is reported. RCS enhancement of about 30 dBsm is obtained for corner reflectors with corner angles other than 90deg. This may find application in remote sensing and synthetic aperture radar.

Fractal based techniques for classification of mammograms and identification of microcalcifications

After skin cancer, breast cancer accounts for the second greatest number of cancer diagnoses in women. Currently the etiologies of breast cancer are unknown, and there is no generally accepted therapy for preventing it. Therefore, the best way to improve the prognosis for breast cancer is early detection and treatment. Computer aided detection systems (CAD) for detecting masses or micro-calcifications in mammograms have already been used and proven to be a potentially powerful tool , so the radiologists are attracted by the effectiveness of clinical application of CAD systems. Fractal geometry is well suited for describing the complex physiological structures that defy the traditional Euclidean geometry, which is based on smooth shapes. The major contribution of this research include the development of • A new fractal feature to accurately classify mammograms into normal and normal (i)With masses (benign or malignant) (ii) with microcalcifications (benign or malignant) • A novel fast fractal modeling method to identify the presence of microcalcifications by fractal modeling of mammograms and then subtracting the modeled image from the original mammogram. The performances of these methods were evaluated using different standard statistical analysis methods. The results obtained indicate that the developed methods are highly beneficial for assisting radiologists in making diagnostic decisions. The mammograms for the study were obtained from the two online databases namely, MIAS (Mammographic Image Analysis Society) and DDSM (Digital Database for Screening Mammography.

A Novel Planar Fractal Antenna with CPW-Feed for Multiband Applications

In this paper, a multiband antenna using a novel fractal design is presented. The antenna structure is formed by inscribing a hexagonal slot within a circle. This base structure is then scaled and arranged within the hexagon along its sides without touching the outer structure. The proposed CPW fed, low profile antenna offers good performance in the 1.65 – 2.59 GHz, 4.16 – 4.52 GHz and 5.54 – 6.42 GHz bands and is suitable for GSM 1800/1900, Bluetooth, IMT advanced systems and upper WLAN applications. The antenna has been fabricated on a substrate of height 1.6 mm and εr = 4.4 and simulation and experimental results are found to be in good agreement

Fast Fractal Coding Method for the Detection of Microcalcification in Mammograms

The presence of microcalcifications in mammograms can be considered as an early indication of breast cancer. A fastfractal block coding method to model the mammograms fordetecting the presence of microcalcifications is presented in this paper. The conventional fractal image coding method takes enormous amount of time during the fractal block encoding.procedure. In the proposed method, the image is divided intoshade and non shade blocks based on the dynamic range, andonly non shade blocks are encoded using the fractal encodingtechnique. Since the number of image blocks is considerablyreduced in the matching domain search pool, a saving of97.996% of the encoding time is obtained as compared to theconventional fractal coding method, for modeling mammograms.The above developed mammograms are used for detectingmicrocalcifications and a diagnostic efficiency of 85.7% isobtained for the 28 mammograms used.

A New Fast Fractal Modeling Approach for the Detection of Microcalcifications in Mammograms

In this paper, a novel fast method for modeling mammograms by deterministic fractal coding approach to detect the presence of microcalcifications, which are early signs of breast cancer, is presented. The modeled mammogram obtained using fractal encoding method is visually similar to the original image containing microcalcifications, and therefore, when it is taken out from the original mammogram, the presence of microcalcifications can be enhanced. The limitation of fractal image modeling is the tremendous time required for encoding. In the present work, instead of searching for a matching domain in the entire domain pool of the image, three methods based on mean and variance, dynamic range of the image blocks, and mass center features are used. This reduced the encoding time by a factor of 3, 89, and 13, respectively, in the three methods with respect to the conventional fractal image coding method with quad tree partitioning. The mammograms obtained from The Mammographic Image Analysis Society database (ground truth available) gave a total detection score of 87.6%, 87.6%, 90.5%, and 87.6%, for the conventional and the proposed three methods, respectively.

Construction of fractal interpolation surfaces on rectangular grids

We present a general method of generating continuous fractal interpolation surfaces by iterated function systems on an arbitrary data set over rectangular grids and estimate their Box-counting dimension.

Construction of recurrent fractal interpolation surfaces(RFISs) on rectangular grids

A recurrent iterated function system (RIFS) is a genaralization of an IFS and provides nonself-affine fractal sets which are closer to natural objects. In general, it's attractor is not a continuous surface in R3. A recurrent fractal interpolation surface (RFIS) is an attractor of RIFS which is a graph of bivariate continuous interpolation function. We introduce a general method of generating recurrent interpolation surface which are at- tractors of RIFSs about any data set on a grid.

Actividades de geometría fractal en el aula de secundaria (II).

Análisis en torno al concepto de fractal. Se exponen diferentes formas de generar fractales y algunas de sus aplicaciones.

Actividades de geometría fractal en el aula de secundaria (I).

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