The aim of the study is to establish the most appropriate business strategy for Piksel Indonesia which is a creative company focusing on technology and fashion designs, resulting from the batik ...consumption preferences while planning to use batik products. Data from 338 respondents were randomly collected from several cities in Indonesia. The first section deals with the demographic background of the respondents, and the remaining of the questions deal with the respondents’ impulse towards batik products. The survey results show differences in previous studies. The first difference is the source of information about batik products obtained by the customer. Secondly, the study by the researchers builds on the consumer’s tastes about the batik style and the results are 54.6 percent. Integrated cost leadership/differentiation is Piksel Indonesia’s best business strategy. For Batik Fractal, their batik products brand, low cost was achieved by employing their vendor to produce the product from the minimum overhead. The production flow begins with the order of the customer that the pattern, colour, material and size chart have been determined. JBatik, which is a parametric software to make a new and distinguish batik pattern established by Piksel Indonesia, has no direct competitors at present. As with Batik Fractal, integrated cost management/differentiation strategy is the best strategy.
The conventional mathematical methods are based on characteristic length, while urban form has no characteristic length in many aspects. Urban area is a scale-dependence measure, which indicates the ...scale-free distribution of urban patterns. Thus, the urban description based on characteristic lengths should be replaced by urban characterization based on scaling. Fractal geometry is one powerful tool for the scaling analysis of cities. Fractal parameters can be defined by entropy and correlation functions. However, the question of how to understand city fractals is still pending. By means of logic deduction and ideas from fractal theory, this paper is devoted to discussing fractals and fractal dimensions of urban landscape. The main points of this work are as follows. Firstly, urban form can be treated as pre-fractals rather than real fractals, and fractal properties of cities are only valid within certain scaling ranges. Secondly, the topological dimension of city fractals based on the urban area is 0; thus, the minimum fractal dimension value of fractal cities is equal to or greater than 0. Thirdly, the fractal dimension of urban form is used to substitute the urban area, and it is better to define city fractals in a two-dimensional embedding space; thus, the maximum fractal dimension value of urban form is 2. A conclusion can be reached that urban form can be explored as fractals within certain ranges of scales and fractal geometry can be applied to the spatial analysis of the scale-free aspects of urban morphology.
The coronavirus disease 2019 (COVID-19) pandemic has fatalized 216 countries across the world and has claimed the lives of millions of people globally. Researches are being carried out worldwide by ...scientists to understand the nature of this catastrophic virus and find a potential vaccine for it. The most possible efforts have been taken to present this paper as a form of contribution to the understanding of this lethal virus in the first and second wave. This paper presents a unique technique for the methodical comparison of disastrous virus dissemination in two waves amid five most infested countries and the death rate of the virus in order to attain a clear view on the behaviour of the spread of the disease. For this study, the data set of the number of deaths per day and the number of infected cases per day of the most affected countries, the USA, Brazil, Russia, India, and the UK, have been considered in the first and second waves. The correlation fractal dimension has been estimated for the prescribed data sets of COVID-19, and the rate of death has been compared based on the correlation fractal dimension estimate curve. The statistical tool, analysis of variance, has also been used to support the performance of the proposed method. Further, the prediction of the daily death rate has been demonstrated through the autoregressive moving average model. In addition, this study also emphasis a feasible reconstruction of the death rate based on the fractal interpolation function. Subsequently, the normal probability plot is portrayed for the original data and the predicted data, derived through the fractal interpolation function to estimate the accuracy of the prediction. Finally, this paper neatly summarized with the comparison and prediction of epidemic curve of the first and second waves of COVID-19 pandemic to visualize the transmission rate in the both times.
Dam concrete suffers from serious abrasion damages in southwestern China, the abrasion resistance of concrete is therefore one of the most important factors determining the reliability even the ...safety of the dams. In the present work, the effects of fly and/or silica fume on the mechanical properties, drying shrinkage, as well the cracking and abrasion resistance of concrete were investigated, then the pore structures of concrete added with fly ash and silica fume and the pore surface fractal dimensions (
D
s
) were determined by the mercury intrusion porosimetry (MIP) method and a fractal model, respectively. Finally, the relationships between the abrasion resistance of concrete and the porosity as well as the
D
s
were revealed and discussed. The results indicate that silica fume significantly increases the drying shrinkage especially at early age, while the incorporation of fly ash and silica fume together can decrease the early plastic shrinkage-induced cracking risk and the final shrinkage to some degrees. Besides, the utilization of 5
wt.% silica fume and 20
wt.% fly ash together increases the abrasion resistance and mechanical property by about 4–9% at various ages. In addition, the compressive strength and the abrasion resistance of concrete are linearly correlated with the concrete porosity and the
D
s
. Both the fly ash and silica fume could decrease the porosity of concrete and increase the
D
s
, therefore the concrete containing fly ash and silica fume have desired mechanical property and abrasion resistance. Moreover,
D
s
has a more profound effect on the abrasion resistance of concrete than the concrete porosity. The addition of 5
wt.% silica fume and 20
wt.% fly ash together is suitable for the concretes used for wearing surfaces in terms of mechanical property, cracking and abrasion resistance.
Differential Equations on Fractals opens the door to understanding the recently developed area of analysis on fractals, focusing on the construction of a Laplacian on the Sierpinski gasket and ...related fractals. Written in a lively and informal style, with lots of intriguing exercises on all levels of difficulty, the book is accessible to advanced undergraduates, graduate students, and mathematicians who seek an understanding of analysis on fractals. Robert Strichartz takes the reader to the frontiers of research, starting with carefully motivated examples and constructions. One of the great accomplishments of geometric analysis in the nineteenth and twentieth centuries was the development of the theory of Laplacians on smooth manifolds. But what happens when the underlying space is rough? Fractals provide models of rough spaces that nevertheless have a strong structure, specifically self-similarity. Exploiting this structure, researchers in probability theory in the 1980s were able to prove the existence of Brownian motion, and therefore of a Laplacian, on certain fractals. An explicit analytic construction was provided in 1989 by Jun Kigami. Differential Equations on Fractals explains Kigami's construction, shows why it is natural and important, and unfolds many of the interesting consequences that have recently been discovered. This book can be used as a self-study guide for students interested in fractal analysis, or as a textbook for a special topics course.
This paper presents a novel fractal solution to investigate the permeability and the Kozeny-Carman (KC) constant of fibrous porous media made up of solid particles and porous fibers. The proposed ...model has been verified with satisfying agreements of the permeability and KC constant of fibrous porous media obtained by our model and those obtained by experimental data, analytical solution, and numerical simulation reported in literature. The results demonstrate that 1) an increase in particle diameter leads to an increase in the absolute permeability; 2) an increase in the tortuosity fractal dimension leads to an increase in the KC constant and decreases in the dimensionless permeability and absolute permeability; 3) an increase in the porosity results in increases in the dimensionless permeability and absolute permeability of the fibrous porous media; 4) increases in the fiber diameter yields an increase in the absolute permeability of fibrous porous media. The proposed fractal model explicitly relates the KC constant and the permeability to the microstructural parameters of the fibrous porous media, and consequently facilitating the understanding of the detailed physical mechanisms for fluids transport through fibrous porous media.
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•A novel fractal solution for permeability and KC constant is obtained.•The effects of micro-structural parameters on permeability are discussed.•Good agreement between the model predictions and experimental data are found.
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•The full-scale pore structure of coal before and after water intrusion was studied.•The minerals content of coal before and after water intrusion was analyzed.•The influence ...mechanism of water intrusion on the pore of coal was analyzed.
The formation water intruding into the coal seam through cross-layer seriously reduces the gas extraction efficiency. In this work, a series of experiments were carried out to investigate the influence of long-time pressure water on the mineral content and pore structure of coal. Results show that, the water intrusion makes a decrease in the types and contents of mineral in coal. Furthermore, full-scale pore size was analyzed by using low-temperature N2 adsorption and CO2 adsorption experiment, indicating that the macropore shows a different change trend before and after water intrusion. For TY and YZ sample, the macropore volume decreased by 18.56% and 0.98%, respectively. For QC sample, the macropore volume increased by 3.20%, while the micropore volume, mesopore volume and total volume of three samples increase in different extent, which are 16.67%–30.77%, 11.56%–17.59%, and 16.10%–125.00%, respectively. Then, the fractal dimension of coal before and after water intrusion was calculated by using FHH model, showing that the fractal dimension D1 decreases while the fractal dimension D2 increases after water intrusion because the water intrusion is able to create and expand pore of coal but it can reduce the roughness of the pore surface. Finally, the influence mechanism of water intrusion on the pore structure of coal is analyzed based on clay mineral collapse, mineral dissolution and coal swelling. The clay minerals in coal is a key factor impacting the pore structure during water intrusion process due to its poor water stability. In addition, the mineral dissolution and coal swelling also play the significant roles in pore structure. This work is significant for the gas control and prevention of coal mine in rich-water coal strata.
The intriguing properties of polycyclic structure known as benzenoid hydrocarbons, which are unsaturated and totally conjugated molecules with hexagonal rings, continue to entice researchers to ...investigate their chemical and physical molecular structure with reference to aromaticity. To correlate important molecular structural attributes such as enthalpy, melting, boiling point, and cyclicity, numerical descriptors or topological indices which have been used for decades, for variety of two and three dimensional chemical structures networks or graphs with vital physicochemical properties. To determine the degree‐based topological indices, in this study, the degrees of the chemical structure or graph of the molecule under examination are utilized. In molecular graph theory, M‐polynomial is a relatively recent approach for investigating chemical networks and structures. It shows numerical descriptors in algebraic form and highlights molecular properties as a polynomial function. In this study, we propose a polynomials presentation of two‐dimensional coronene fractal structures and compute numerous M‐polynomials, including the M‐polynomials of the first and second Zagreb indexes, as well as the Randic index.
Topological indices is an important tool to study chemical and computer networks. M‐polynomials is based on the topological indices and also the generalized version of topological descriptors. Study of two‐dimensional coronene fractal structures are carried in this work. These novel structures are discussed with the tool of M‐polynomials, mainly first and second Zagreb index, general Randic index‐based M‐polynomials are studied. Moreover, we studied these M‐polynomials for multiple coronene fractal structures, like zigzag hexagonal coronene fractals, armchair hexagonal coronene fractals, rectangular hexagonal coronene fractals.
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