Search results for: Haus-Dorff dimension

Authors: Kairat T. Mynbaev, Elena N. Lomakina

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We consider a Hardy-type operator generated by a family of open subsets of a Hausdorff topological space. The family is indexed with non-negative real numbers and is totally ordered. For this operator, we obtain two-sided bounds of its norm, a compactness criterion, and bounds for its approximation numbers. Previously, bounds for its approximation numbers have been established only in the one-dimensional case, while we do not impose any restrictions on the dimension of the Hausdorff space. The bounds for the norm and conditions for compactness earlier have been found using different methods by G. Sinnamon and K. Mynbaev. Our approach is different in that we use domain partitions for all problems under consideration.

Keywords: approximation numbers, boundedness and compactness, multidimensional Hardy operator, Hausdorff topological space

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Authors: Harsha Gopalakrishnan, Srijanani Anurag Prasad

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Quadrilateral labyrinth fractals are a new type of fractals that are introduced in this paper. They belong to a unique class of fractals on any plane quadrilateral. The previously researched labyrinth fractals on the unit square and triangle inspire this form of fractal. This work describes how to construct a quadrilateral labyrinth fractal and looks at the circumstances in which it can be understood as the attractor of an iterated function system. Furthermore, some of its topological properties and the Hausdorff and box-counting dimensions of the quadrilateral labyrinth fractals are studied.

Keywords: fractals, labyrinth fractals, dendrites, iterated function system, Haus-Dorff dimension, box-counting dimension, non-self similar, non-self affine, connected, path connected

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Authors: S. Shankar Bharathi

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Inspection of surface defects on metallic components has always been challenging due to its specular property. Occurrences of defects such as scratches, rust, pitting are very common in metallic surfaces during the manufacturing process. These defects if unchecked can hamper the performance and reduce the life time of such component. Many of the conventional image processing algorithms in detecting the surface defects generally involve segmentation techniques, based on thresholding, edge detection, watershed segmentation and textural segmentation. They later employ other suitable algorithms based on morphology, region growing, shape analysis, neural networks for classification purpose. In this paper the work has been focused only towards detecting scratches. Global and other thresholding techniques were used to extract the defects, but it proved to be inaccurate in extracting the defects alone. However, this paper does not focus on comparison of different segmentation techniques, but rather describes a novel approach towards segmentation combined with hausdorff dilation distance. The proposed algorithm is based on the distribution of the intensity levels, that is, whether a certain gray level is concentrated or evenly distributed. The algorithm is based on extraction of such concentrated pixels. Defective images showed higher level of concentration of some gray level, whereas in non-defective image, there seemed to be no concentration, but were evenly distributed. This formed the basis in detecting the defects in the proposed algorithm. Hausdorff dilation distance based on mathematical morphology was used to strengthen the segmentation of the defects.

Keywords: metallic surface, scratches, segmentation, hausdorff dilation distance, machine vision

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Authors: Siddharth Rana

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As we know so far, there are 3 dimensions that we are capable of interpreting and perceiving, and there is a 4th dimension, called time, about which we don’t know much yet. We, as humans, live in the 4th dimension, not the 3rd. We travel 3 dimensionally but cannot yet travel 4 dimensionally; perhaps if we could, then visiting the past and the future would be like climbing a mountain or going down a road. So far, we humans are not even capable of imagining any higher dimensions than the three dimensions in which we can travel. We are the beings of the 4th dimension; we are the beings of time; that is why we can travel 3 dimensionally; however, if, say, there were beings of the 5th dimension, then they would easily be able to travel 4 dimensionally, i.e., they could travel in the 4th dimension as well. Beings of the 5th dimension can easily time travel. However, beings of the 4th dimension, like us, cannot time travel because we live in a 4-D world, traveling 3 dimensionally. That means to ever do time travel, we just need to go to a higher dimension and not only perceive it but also be able to travel in it. However, traveling to the past is not very possible, unlike traveling to the future. Even if traveling to the past were possible, it would be very unlikely that an event in the past would be changed. In this paper, some approaches are provided to define time, our movement in time to the future, some aspects of time travel using dimensions, and how we can perceive a higher dimension.

Keywords: time, dimensions, String theory, relativity

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Authors: S. Sushma, S. Balasubramanian, K. C. Latha, R. Sridhar

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Structural texture measures are used to address the aspect of breast cancer risk assessment in screening mammograms. The current study investigates whether texture properties characterized by local Fractal Dimension (FD) and lacunarity contribute to assess breast cancer risk. Fractal Dimension represents the complexity while the lacunarity characterize the gap of a fractal dimension. In this paper, we present our result confirming that the lacunarity value resulted in algorithm using mammogram images states that level of lacunarity will be low when the Fractal Dimension value will be high.

Keywords: breast cancer, fractal dimension, image analysis, lacunarity, mammogram

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Authors: Kaoutar Lamrini Uahabi, Mohamed Atounti

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In the present work, we consider one category of curves denoted by L(p, k, r, n). These curves are continuous arcs which are trajectories of roots of the trinomial equation zn = αzk + (1 − α), where z is a complex number, n and k are two integers such that 1 ≤ k ≤ n − 1 and α is a real parameter greater than 1. Denoting by L the union of all trinomial curves L(p, k, r, n) and using the box counting dimension as fractal dimension, we will prove that the dimension of L is equal to 3/2.

Keywords: feasible angles, fractal dimension, Minkowski sausage, trinomial curves, trinomial equation

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Authors: Zerroug Abdelhamid, Danielle Chassoux

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Various models are given to simulate homogeneous or heterogeneous cancerous tumors and extract in each case the boundary. The fractal dimension is then estimated by least squares method and compared to some previous methods.

Keywords: simulation, cancerous tumor, Markov fields, fractal dimension, extraction, recovering

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Authors: Li Hung-Hui, Chen Chi-Chieh, Yang Zon-Yee

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This study aims to explore the impact energy absorption in the fragmented processes of rock samples during the split-Hopkinson-pressure-bar tests. Three kinds of rock samples including granite, marble and sandstone were tested. The impact energy absorptions were calculated according to the incident, reflected and transmitted strain wave histories measured by a oscilloscope. The degree of fragment rocks after tests was quantified by the box dimension of the fractal theory. The box dimension of rock fragments was obtained from the particle size distribution curve by the sieve analysis. The results can be concluded that: (1) the degree of rock fragments after tests can be well described by the value of box dimension; (2) with the impact energy absorption increasing, the degrees of rock fragments are varied from the very large fragments to very small fragments, and the corresponding box dimension varies from 2.9 to 1.2.

Keywords: SHPB test, energy absorption, rock fragments, impact loading, box dimension

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Authors: Hemant Kumar Pathak

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In 1994, Matthews (S.G. Matthews, Partial metric topology, in: Proc. 8th Summer Conference on General Topology and Applications, in: Ann. New York Acad. Sci., vol. 728, 1994, pp. 183-197) introduced the concept of a partial metric as a part of the study of denotational semantics of data flow networks. He gave a modified version of the Banach contraction principle, more suitable in this context. In fact, (complete) partial metric spaces constitute a suitable framework to model several distinguished examples of the theory of computation and also to model metric spaces via domain theory. In this paper, we introduce the concept of almost partial Hausdorff metric. We prove a fixed point theorem for multi-valued mappings on partial metric space using the concept of almost partial Hausdorff metric and prove an analogous to the well-known Nadler’s fixed point theorem. In the sequel, we derive a homotopy result as an application of our main result.

Keywords: fixed point, partial metric space, homotopy, physical sciences

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Authors: M. Hussain, Aqsa Farooq

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Let G = (V,E) be a connected graph and distance between any two vertices a and b in G is a−b geodesic and is denoted by d(a, b). A set of vertices W resolves a graph G if each vertex is uniquely determined by its vector of distances to the vertices in W. A metric dimension of G is the minimum cardinality of a resolving set of G. In this paper line graph of honeycomb network has been derived and then we calculated the metric dimension on line graph of honeycomb network.

Keywords: Resolving set, Metric dimension, Honeycomb network, Line graph

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Authors: Jiradeach Kalayaruan, Tosawat Seetawan

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This paper studied the energy of the nature systems by looking at the overall image throughout the universe. The energy of the nature systems was developed from the Einstein’s energy equation. The researcher used the new ideas called even 2n and odd 3n light dimension energy states systems, which were developed from Einstein’s relativity energy theory equation. In this study, the major methodology the researchers used was the basic principle ideas or beliefs of some religions such as Buddhism, Christianity, Hinduism, Islam, or Tao in order to get new discoveries. The basic beliefs of each religion - Nivara, God, Ether, Atman, and Tao respectively, were great influential ideas on the researchers to use them greatly in the study to form new ideas from philosophy. Since the philosophy of each religion was alive with deep insight of the physical nature relative energy, it connected the basic beliefs to light dimension energy states systems. Unfortunately, Einstein’s original relative energy equation showed only even 2n light dimension energy states systems (if n = 1,…,∞). But in advance ideas, the researchers multiplied light dimension energy by Einstein’s original relative energy equation and get new idea of theoritical physics in odd 3n light dimension energy states systems (if n = 1,…,∞). Because from basic principle ideas or beliefs of some religions philosophy of each religion, you had to add the media light dimension energy into Einstein’s original relative energy equation. Consequently, the simple meaning picture in deep insight showed that you could touch light dimension energy of Nivara, God, Ether, Atman, and Tao by light dimension energy. Since light dimension energy was transferred by Nivara, God, Ether, Atman and Tao, the researchers got the new equation of odd 3n light dimension energy states systems. Moreover, the researchers expected to be able to solve overview problems of all light dimension energy in all nature relative energy, which are developed from Eistein’s relative energy equation.The finding of the study was called 'super nature relative energy' ( in odd 3n light dimension energy states systems (if n = 1,…,∞)). From the new ideas above you could do the summation of even 2n and odd 3n light dimension energy states systems in all of nature light dimension energy states systems. In the future time, the researchers will expect the new idea to be used in insight theoretical physics, which is very useful to the development of quantum mechanics, all engineering, medical profession, transportation, communication, scientific inventions, and technology, etc.

Keywords: 2n light dimension energy states systems effect, Ether, even 2n light dimension energy states systems, nature relativity, Nivara, odd 3n light dimension energy states systems, perturbation points energy, relax point energy states systems, stress perturbation energy states systems effect, super relative energy

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Authors: Manish Kumar Thakur, Subrata Kumar Ghosh

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Various types of particles found in lubricant may be characterized by their fractal dimension. Some of the available methods are: yard-stick method or structured walk method, box-counting method. This paper presents a review of the developments and progress in fractal dimension computing methods as applied to characteristics the surface of wear particles. An overview of these methods, their implementation, their advantages and their limits is also present here. It has been accepted that wear particles contain major information about wear and friction of materials. Morphological analysis of wear particles from a lubricant is a very effective way for machine condition monitoring. Fractal dimension methods are used to characterize the morphology of the found particles. It is very useful in the analysis of complexity of irregular substance. The aim of this review is to bring together the fractal methods applicable for wear particles.

Keywords: fractal dimension, morphological analysis, wear, wear particles

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Authors: Rhea Kapoor

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Fractal dimension provides a way to characterize non-geometric shapes like those found in nature. The purpose of this research is to estimate Minkowski fractal dimension of human lung images for early detection of lung cancer. Lung cancer is the leading cause of death among all types of cancer and an early histopathological analysis will help reduce deaths primarily due to late diagnosis. A Python application program, PathoPy2.0, was developed for analyzing medical images in pixelated format and estimating Minkowski fractal dimension using a new box-counting algorithm that allows windowing of images for more accurate calculation in the suspected areas of cancerous growth. Benchmark geometric fractals were used to validate the accuracy of the program and changes in fractal dimension of lung images to indicate the presence of issues in the lung. The accuracy of the program for the benchmark examples was between 93-99% of known values of the fractal dimensions. Fractal dimension values were then calculated for lung images, from National Cancer Institute, taken over time to correctly detect the presence of cancerous growth. For example, as the fractal dimension for a given lung increased from 1.19 to 1.27 due to cancerous growth, it represents a significant change in fractal dimension which lies between 1 and 2 for 2-D images. Based on the results obtained on many lung test cases, it was concluded that fractal dimension of human lungs can be used to diagnose lung cancer early. The ideas behind PathoPy2.0 can also be applied to study patterns in the electrical activity of the human brain and DNA matching.

Keywords: fractals, histopathological analysis, image processing, lung cancer, Minkowski dimension

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Authors: Lana Horvat Dmitrović

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The main purpose of this paper is to study the box dimension as fractal property of bifurcations of discrete dynamical systems in higher dimensions. The paper contains the fractal analysis of the orbits near the hyperbolic and non-hyperbolic fixed points in discrete dynamical systems. It is already known that in one-dimensional case the orbit near the hyperbolic fixed point has the box dimension equal to zero. On the other hand, the orbit near the non-hyperbolic fixed point has strictly positive box dimension which is connected to the non-degeneracy condition of certain bifurcation. One of the main results in this paper is the generalisation of results about box dimension near the hyperbolic and non-hyperbolic fixed points to higher dimensions. In the process of determining box dimension, the restriction of systems to stable, unstable and center manifolds, Lipschitz property of box dimension and the notion of projective box dimension are used. The analysis of the bifurcations in higher dimensions with one multiplier on the unit circle is done by using the normal forms on one-dimensional center manifolds. This specific change in box dimension of an orbit at the moment of bifurcation has already been explored for some bifurcations in one and two dimensions. It was shown that specific values of box dimension are connected to appropriate bifurcations such as fold, flip, cusp or Neimark-Sacker bifurcation. This paper further explores this connection of box dimension as fractal property to some specific bifurcations in higher dimensions, such as fold-flip and flip-Neimark-Sacker. Furthermore, the application of the results to the unit time map of continuous dynamical system near hyperbolic and non-hyperbolic singularities is presented. In that way, box dimensions which are specific for certain bifurcations of continuous systems can be obtained. The approach to bifurcation analysis by using the box dimension as specific fractal property of orbits can lead to better understanding of bifurcation phenomenon. It could also be useful in detecting the existence or nonexistence of bifurcations of discrete and continuous dynamical systems.

Keywords: bifurcation, box dimension, invariant manifold, orbit near fixed point

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Authors: O. Boussoufi, K. Lamrini Uahabi, M. Atounti

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The main purpose of this paper is to calculate the fractal dimension of some Julia Sets and Mandelbrot Set in the Misiurewicz Points. Using Matlab to generate the Julia Sets images that match the Misiurewicz points and using a Fractal software, we were able to find different measures that characterize those fractals in textures and other features. We are actually focusing on fractal dimension and the error calculated by the software. When executing the given equation of regression or the log-log slope of image a Box Counting method is applied to the entire image, and chosen settings are available in a FracLAc Program. Finally, a comparison is done for each image corresponding to the area (boundary) where Misiurewicz Point is located.

Keywords: box counting, FracLac, fractal dimension, Julia Sets, Mandelbrot Set, Misiurewicz Points

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Authors: Saeedeh Shahbazkhany

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Cancer is a terrible disease that, if not diagnosed early, therapy can be difficult while it is easily medicable if it is diagnosed in early stages. So it is very important for cancer diagnosis that medical procedures are performed. In this paper we introduce a new method. In this method, we only need pictures of healthy cells and cancer cells. In fact, where we suspect cancer, we take a picture of cells or tissue in that area, and then take some pictures of the surrounding tissues. Then, fractal dimension of images are calculated and compared. Cancer can be easily detected by comparing the fractal dimension of images. In this method, we use Matlab software.

Keywords: Matlab software, fractal dimension, cancer, surrounding tissues, cells or tissue, new method

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Authors: Byeongcheol Kang, Junyi Kim, Hyungsik Jung, Hyungjun Yang, Jaewoo An, Jonggeun Choe

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It is important to figure out reservoir properties for better production management. Due to the limited information, there are geological uncertainties on very heterogeneous or channel reservoir. One of the solutions is to generate multiple equi-probable realizations using geostatistical methods. However, some models have wrong properties, which need to be excluded for simulation efficiency and reliability. We propose a novel method of model selection scheme, based on distance-based clustering for reliable application of production optimization algorithm. Distance is defined as a degree of dissimilarity between the data. We calculate Hausdorff distance to classify the models based on their similarity. Hausdorff distance is useful for shape matching of the reservoir models. We use multi-dimensional scaling (MDS) to describe the models on two dimensional space and group them by K-means clustering. Rather than simulating all models, we choose one representative model from each cluster and find out the best model, which has the similar production rates with the true values. From the process, we can select good reservoir models near the best model with high confidence. We make 100 channel reservoir models using single normal equation simulation (SNESIM). Since oil and gas prefer to flow through the sand facies, it is critical to characterize pattern and connectivity of the channels in the reservoir. After calculating Hausdorff distances and projecting the models by MDS, we can see that the models assemble depending on their channel patterns. These channel distributions affect operation controls of each production well so that the model selection scheme improves management optimization process. We use one of useful global search algorithms, particle swarm optimization (PSO), for our production optimization. PSO is good to find global optimum of objective function, but it takes too much time due to its usage of many particles and iterations. In addition, if we use multiple reservoir models, the simulation time for PSO will be soared. By using the proposed method, we can select good and reliable models that already matches production data. Considering geological uncertainty of the reservoir, we can get well-optimized production controls for maximum net present value. The proposed method shows one of novel solutions to select good cases among the various probabilities. The model selection schemes can be applied to not only production optimization but also history matching or other ensemble-based methods for efficient simulations.

Keywords: distance-based clustering, geological uncertainty, particle swarm optimization (PSO), production optimization

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Authors: Razieh Khalafi

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Myocardial infarction (MI) or acute myocardial infarction (AMI), commonly known as a heart attack, occurs when blood flow stops to part of the heart causing damage to the heart muscle. An ECG can often show evidence of a previous heart attack or one that's in progress. The patterns on the ECG may indicate which part of your heart has been damaged, as well as the extent of the damage. In chaos theory, the correlation dimension is a measure of the dimensionality of the space occupied by a set of random points, often referred to as a type of fractal dimension. In this research by considering ECG signal as a random walk we work on forecasting the oncoming heart attack by analyzing the ECG signals using the correlation dimension. In order to test the model a set of ECG signals for patients before and after heart attack was used and the strength of model for forecasting the behavior of these signals were checked. Results shows this methodology can forecast the ECG and accordingly heart attack with high accuracy.

Keywords: heart attack, ECG, random walk, correlation dimension, forecasting

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Authors: Razi Khalafi

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Myocardial Infarction (MI) or acute Myocardial Infarction (AMI), commonly known as a heart attack, occurs when blood flow stops to part of the heart causing damage to the heart muscle. An ECG can often show evidence of a previous heart attack or one that's in progress. The patterns on the ECG may indicate which part of your heart has been damaged, as well as the extent of the damage. In chaos theory, the correlation dimension is a measure of the dimensionality of the space occupied by a set of random points, often referred to as a type of fractal dimension. In this research by considering ECG signal as a random walk we work on forecasting the oncoming heart attack by analysing the ECG signals using the correlation dimension. In order to test the model a set of ECG signals for patients before and after heart attack was used and the strength of model for forecasting the behaviour of these signals were checked. Results show this methodology can forecast the ECG and accordingly heart attack with high accuracy.

Keywords: heart attack, ECG, random walk, correlation dimension, forecasting

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Authors: Amir Hajian, Sepehr Damavandinejadmonfared

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In this paper the issue of dimensionality reduction is investigated in finger vein recognition systems using kernel Principal Component Analysis (KPCA). One aspect of KPCA is to find the most appropriate kernel function on finger vein recognition as there are several kernel functions which can be used within PCA-based algorithms. In this paper, however, another side of PCA-based algorithms -particularly KPCA- is investigated. The aspect of dimension of feature vector in PCA-based algorithms is of importance especially when it comes to the real-world applications and usage of such algorithms. It means that a fixed dimension of feature vector has to be set to reduce the dimension of the input and output data and extract the features from them. Then a classifier is performed to classify the data and make the final decision. We analyze KPCA (Polynomial, Gaussian, and Laplacian) in details in this paper and investigate the optimal feature extraction dimension in finger vein recognition using KPCA.

Keywords: biometrics, finger vein recognition, principal component analysis (PCA), kernel principal component analysis (KPCA)

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Authors: Kyung-Ja Cho, Sun Jin Park

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This study examined what effective dimension affects facial attractiveness. Two orthogonal dimensions, sharp-soft and babyish-mature, were used to rate the levels of facial attractiveness in 20’s women. This research also investigated the sex difference on the effect of effective dimension of face on attractiveness. The test subjects composed of 15 males and 18 females. They looked 330 photos of women in 20s. Then they rated the levels of the effective dimensions of faces with sharp-soft and babyish-mature, and the attraction with charmless-charming. The respond forms were Likert scales, the answer was scored from 1 to 9. As a result of multiple regression analysis, the subject reported the milder and younger appearance as more attractive. Both male and female subjects showed the same evaluation. This result means that two effective dimensions have the effect on estimating attractiveness.

Keywords: affective dimension of faces, facial attractiveness, sharp-soft, babyish-mature

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Authors: Mitra Saberi, Saeideh Fakhari, Amir Karam, Ali Ahmadabadi

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Geomorphology is the scientific study of the characteristics of form and shape of the Earth's surface. The existence of types of landforms and their variation is mainly controlled by changes in the shape and position of land and topography. In fact, the interest and application of fractal issues in geomorphology is due to the fact that many geomorphic landforms have fractal structures and their formation and transformation can be explained by mathematical relations. The purpose of this study is to identify and analyze the fractal behavior of landforms of macro geomorphologic regions of Iran, as well as studying and analyzing topographic and landform characteristics based on fractal relationships. In this study, using the Iranian digital elevation model in the form of slopes, coefficients of deposition and alluvial fan, the fractal dimensions of the curves were calculated through the box counting method. The morphometric characteristics of the landforms and their fractal dimension were then calculated for 4criteria (height, slope, profile curvature and planimetric curvature) and indices (maximum, Average, standard deviation) using ArcMap software separately. After investigating their correlation with fractal dimension, two-way regression analysis was performed and the relationship between fractal dimension and morphometric characteristics of landforms was investigated. The results show that the fractal dimension in different pixels size of 30, 90 and 200m, topographic curves of different landform units of Iran including mountain, hill, plateau, plain of Iran, from1.06in alluvial fans to1.17in The mountains are different. Generally, for all pixels of different sizes, the fractal dimension is reduced from mountain to plain. The fractal dimension with the slope criterion and the standard deviation index has the highest correlation coefficient, with the curvature of the profile and the mean index has the lowest correlation coefficient, and as the pixels become larger, the correlation coefficient between the indices and the fractal dimension decreases.

Keywords: box counting method, fractal dimension, geomorphology, Iran, landform

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Authors: Sadegh Marzban, Mohamad Sobhan Sheikh Andalibi, Farnaz Ghassemi, Farzad Towhidkhah

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Parkinson's disease (PD), which is characterized by the tremor at rest, rigidity, akinesia or bradykinesia and postural instability, affects the quality of life of involved individuals. The concept of a fractal is most often associated with irregular geometric objects that display self-similarity. Fractal dimension (FD) can be used to quantify the complexity and the self-similarity of an object such as tremor. In this work, we are aimed to propose a new method for evaluating hyperkinetic movements such as tremor, by using the FD and other correlated parameters in patients who are suffered from PD. In this study, we used 'the tremor data of Physionet'. The database consists of fourteen participants, diagnosed with PD including six patients with high amplitude tremor and eight patients with low amplitude. We tried to extract features from data, which can distinguish between patients before and after medication. We have selected fractal dimensions, including correlation dimension, box dimension, and information dimension. Lilliefors test has been used for normality test. Paired t-test or Wilcoxon signed rank test were also done to find differences between patients before and after medication, depending on whether the normality is detected or not. In addition, two-way ANOVA was used to investigate the possible association between the therapeutic effects and features extracted from the tremor. Just one of the extracted features showed significant differences between patients before and after medication. According to the results, correlation dimension was significantly different before and after the patient's medication (p=0.009). Also, two-way ANOVA demonstrates significant differences just in medication effect (p=0.033), and no significant differences were found between subject's differences (p=0.34) and interaction (p=0.97). The most striking result emerged from the data is that correlation dimension could quantify medication treatment based on tremor. This study has provided a technique to evaluate a non-linear measure for quantifying medication, nominally the correlation dimension. Furthermore, this study supports the idea that fractal dimension analysis yields additional information compared with conventional spectral measures in the detection of poor prognosis patients.

Keywords: correlation dimension, non-linear measure, Parkinson’s disease, tremor

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Authors: Nkiru I. Ibeakuzie, Paul D. J. Watson, John F. Pescatore

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In roadway construction, the cost of soil-cement stabilization per unit area is significantly influenced by the binder content, hence the need to optimise cement usage. This research work will characterize the influence of soil fractal geometry on properties of cement-stabilized soil, and strive to determine a correlation between mechanical proprieties of cement-stabilized soil and the mass fractal dimension Dₘ indicated by particle size distribution (PSD) of aggregate mixtures. Since strength development in cemented soil relies not only on cement content but also on soil PSD, this study will investigate the possibility of reducing cement content by changing the PSD of soil, without compromising on strength, reduced permeability, and compressibility. A series of soil aggregate mixes will be prepared in the laboratory. The mass fractal dimension Dₘ of each mix will be determined from sieve analysis data prior to stabilization with cement. Stabilized soil samples will be tested for strength, permeability, and compressibility.

Keywords: fractal dimension, particle size distribution, cement stabilization, cement content

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Authors: I. Arockiarani

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The focus of the paper is to furnish the entropy measure for a neutrosophic set and neutrosophic soft set which is a measure of uncertainty and it permeates discourse and system. Various characterization of entropy measures are derived. Further we exemplify this concept by applying entropy in various real time decision making problems.

Keywords: entropy measure, Hausdorff distance, neutrosophic set, soft set

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Authors: Abraham Terán Salcedo, Didier Samayoa Ochoa

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This work presents a numerical implementation of a method for estimating the box-counting dimension of self-avoiding curves on a planar space, fractal objects captured on digital images; this method is named fractioning estimator. Classical methods of digital image processing, such as noise filtering, contrast manipulation, and thresholding, among others, are used in order to obtain binary images that are suitable for performing the necessary computations of the fractioning estimator. A user interface is developed for performing the image processing operations and testing the fractioning estimator on different captured images of real-life fractal objects. To analyze the results, the estimations obtained through the fractioning estimator are compared to the results obtained through other methods that are already implemented on different available software for computing and estimating the box-counting dimension.

Keywords: box-counting, digital image processing, fractal dimension, numerical method

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Authors: Hadi Farhadian, Homayoon Katibeh

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Groundwater inflow to the tunnels is one of the most important problems in tunneling operation. The objective of this study is the investigation of model dimension effects on tunnel inflow assessment in discontinuous rock masses using numerical modeling. In the numerical simulation, the model dimension has an important role in prediction of water inflow rate. When the model dimension is very small, due to low distance to the tunnel border, the model boundary conditions affect the estimated amount of groundwater flow into the tunnel and results show a very high inflow to tunnel. Hence, in this study, the two-dimensional universal distinct element code (UDEC) used and the impact of different model parameters, such as tunnel radius, joint spacing, horizontal and vertical model domain extent has been evaluated. Results show that the model domain extent is a function of the most significant parameters, which are tunnel radius and joint spacing.

Keywords: water inflow, tunnel, discontinues rock, numerical simulation

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Authors: Abdelbaky Abouzeid

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The study aimed at determining the effect of using the active learning on achievement and attitudes toward studying the human rights course for the Bahrain Teachers College students and the extent to which any differences of statistical significance according to gender and section can exist. To achieve the objectives of the study, the researcher developed and implemented research tools such as academic achievement test and the scale of attitudes towards the study of the Human Rights Course. The scale of attitudes towards Human Rights was constructed of 40 items investigating four dimensions; the cognitive dimension, the behavioral dimension, the affective dimension, and course quality dimension. The researcher then applied some of the active learning strategies in teaching this course to all students of the first year of the Bahrain Teachers College (102 male and female students) after excluding two students who did not complete the course requirements. Students were divided into five groups. These strategies included interactive lecturing, presentations, role playing, group projects, simulation, brainstorming, concept maps and mind maps, reflection and think-pair-share. The course was introduced to students during the second semester of the academic year 2016-2017. The study findings revealed that the use of active learning strategies affected the achievement of students of Bahrain Teachers College in the Human Rights course. The results of the T-test showed statistically significant differences on the pre-test and post-test in favor of the post-test. No statistically significant differences in the achievement of students according to the section and gender were found. The results also indicated that the use of active learning strategies had a positive effect on students' attitudes towards the study of the Human Rights Course on all the scale’s items. The general average reached (4.26) and the percentage reached (85.19%). Regarding the effect of using active learning strategies on students’ attitudes towards all the four dimensions of the scale, the study concluded that the behavioral dimension came first; the quality of the course came second, the cognitive dimension came third and in the fourth place came the affective dimension. No statistically significant differences in the attitude towards studying the Human Rights Course for the students according to their sections or gender were found. Based on the findings of the study, the researchers suggested some recommendations that can contribute to the development of teaching Human Rights Course at the University of Bahrain.

Keywords: attitudes, academic achievement, human rights, behavioral dimension, cognitive dimension, affective dimension, quality of the course

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Authors: Phyo Wai Aung, Sysoev Oleg Evgenevich, Boris Necolavet Maryin

Abstract:

The article deals with theoretical problems of correlation of processes of microstructure changes of structural materials under cyclic loading and acoustic emission. The ways of the evolution of a microstructure under the influence of cyclic loading are shown depending on the structure of the initial crystal structure of the material. The spectra of the frequency characteristics of acoustic emission signals are experimentally obtained when testing titanium samples for cyclic loads. Changes in the fractal dimension of the acoustic emission signals in the selected frequency bands during the evolution of the microstructure of structural materials from the action of cyclic loads, as well as in the destruction of samples, are studied. The experimental samples were made of VT-20 structural material widely used in aircraft and rocket engineering. The article shows the striving of structural materials for synergistic stability and reduction of the fractal dimension of acoustic emission signals, in accordance with the degradation of the microstructure, which occurs as a result of fatigue processes from the action of low cycle loads. As a result of the research, the frequency range of acoustic emission signals of 100-270 kHz is determined, in which the fractal dimension of the signals, it is possible to most reliably predict the durability of structural materials.

Keywords: cyclic loadings, material structure changing, acoustic emission, fractal dimension

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Authors: Ali Albadri

Abstract:

The logistics equation has never been used or studied in scientific fields outside the field of ecology. It has never been used to understand the behavior of a dynamic system of mechanical machines, like an escalator. We have studied the compatibility of the logistic map against real measurements from an escalator. This study has proven that there is good compatibility between the logistics equation and the experimental measurements. It has discovered the potential of a relationship between the fractal dimension and the non-linearity parameter, R, in the logistics equation. The fractal dimension increases as the R parameter (non-linear parameter) increases. It implies that the fractal dimension increases as the phase of the life span of the machine move from the steady/stable phase to the periodic double phase to a chaotic phase. The fractal dimension and the parameter R can be used as a tool to verify and check the health of machines. We have come up with a theory that there are three areas of behaviors, which they can be classified during the life span of a machine, a steady/stable stage, a periodic double stage, and a chaotic stage. The level of attention to the machine differs depending on the stage that the machine is in. The rate of faults in a machine increases as the machine moves through these three stages. During the double period and the chaotic stages, the number of faults starts to increase and become less predictable. The rate of predictability improves as our monitoring of the changes in the fractal dimension and the parameter R improves. The principles and foundations of our theory in this work have and will have a profound impact on the design of systems, on the way of operation of systems, and on the maintenance schedules of the systems. The systems can be mechanical, electrical, or electronic. The discussed methodology in this paper will give businesses the chance to be more careful at the design stage and planning for maintenance to control costs. The findings in this paper can be implied and used to correlate the three stages of a mechanical system to more in-depth mechanical parameters like wear and fatigue life.

Keywords: logistcs map, bifurcation map, fractal dimension, logistics equation

Procedia PDF Downloads 79