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The purpose of this paper is to test the capability to properly analyze the electrical circuits of a novel constitutive relation of capacitor.

For ceteris paribus, the constitutive relations of the resistor and inductor have been reformulated by following the novel constitutive relation of capacitor. The responses of RL, RC, LC and RLC circuits defined on the fractal set described by these definitions have been derived by means of the fractal calculus and fractal Laplace transformation. A comparative Hamiltonian formalism-based analysis has been performed where the circuits described by the conventional and the formerly proposed revisited constitutive relations have also been considered.

This study has found that the novel constitutive relations give unreasonable results unlike the conventional ones. Like such previous revisited constitutive relations, an odd Hamiltonian has been obtained. On the other hand, the conventional constitutive relations give a reasonable Hamiltonian.

To the best of the author’s knowledge, for the first time, the analysis of fractal set defined electrical circuits by means of unconventional constitutive relations has been performed where the deficiency of the tested capacitive constitutive relation has been pointed out.

The purpose of this study is to originally present noise analysis of electrical circuits defined on fractal set.

The fractal integrodifferential equations of resistor-inductor, resistor-capacitor, inductor-capacitor and resistor-inductor-capacitor circuits subjected to zero mean additive white Gaussian noise defined on fractal set have been formulated. The fractal time component has also been considered. The closed form expressions for crucial stochastic parameters of circuit responses have been derived from these equations. Numerical simulations of power spectral densities based on the derived autocorrelation functions have been performed. A comparison with those without fractal time component has been made.

We have found that the Hausdorff dimension of the middle b Cantor set strongly affects the power spectral densities; thus, the average powers of noise induced circuit responses and the inclusion of fractal time component causes significantly different analysis results besides the physical measurability of electrical quantities.

For the first time, the noise analysis of electrical circuit on fractal set has been performed. This is also the very first time that the fractal time component has been included in the fractal calculus-based circuit analysis.

The purpose of this paper is to propose a novel nonlocal fractal calculus scheme dedicated to the analysis of fractal electrical circuit, namely, the generalized nonlocal fractal calculus.

For being generalized, an arbitrary kernel function has been adopted. The condition on order has been derived so that it is not related to the γ-dimension of the fractal set. The fractal Laplace transforms of our operators have been derived.

Unlike the traditional power law kernel-based nonlocal fractal calculus operators, ours are generalized, consistent with the local fractal derivative and use higher degree of freedom. As intended, the proposed nonlocal fractal calculus is applicable to any kind of fractal electrical circuit. Thus, it has been found to be a more efficient tool for the fractal electrical circuit analysis than any previous fractal set dedicated calculus scheme.

A fractal calculus scheme that is more efficient for the fractal electrical circuit analysis than any previous ones has been proposed in this work.

Many cities of various types are distributed in the large area of mountainous regions in China. In these cities, there are acute contradictions between man and earth. Considering that the space growth mode of mountainous cities is widely different from that of flatland cities, the fractal method was adopted in the research aimed at demarcating the urban growth boundary of mountainous cities. The fractal features of the investigated mountainous cities in space were figured out via inference from their function, dimension, region, grade, and environment, and the fractal mode and conceptual framework of urban growth boundary of Qin-Ba mountainous region were constructed according to some concepts and methods such as fractal dimension, fractal network, and fractal order. In the research, the traditional urban growth boundary form-was decomposed into scattered points (point form), paths (linear form), and patches (plane form) to form the fractal theory units for the research of urban growth boundary, and the leading idea, procedure, and control method for “fractal demarcation of urban growth boundary” were established to provide strategies for demarcation of urban space growth boundary of Qin-Ba mountainous region.

Neuroscience is providing new tools to potentially improve diagnosis and classification of autism spectrum disorder (ASD) based on biomarkers. The purpose of this paper, is to describe certain applications of fractal analysis, a tool used to measure information complexity observed within electroencephalograph (EEG) signals and neurogenetic code. It is argued here that a better method of diagnosis of ASD may exist based on these new tools.

Selective review of literature focused on the diagnosis of ASD and recent technological advances in scientific approaches to diagnosis of ASD. It is argued that higher levels of complex, coherent data are inversely related to pathology; in biological systems, lower complexity EEG during specific tasks may reveal pathology.

Clinicians and researchers are exploring new ways to describe mental illness based on biomarkers to improve reliability and validity of diagnostic methods. Specific application of chaos theory in the form of fractal analysis shows promise as one possible method.

This is a conceptual paper addressing the advantages of employing fractal analysis of EEG and genomics for the diagnosis of ASD.

Frank Lloyd Wright's famous house Fallingwater has been the subject of enduring scholarly debate centred on the allegedly clear parallels between its form and that of its surrounding natural setting. Despite these claims being repeated many times, no quantitative approach has ever been used to test this argument. In response, this paper uses a quantitative method, fractal analysis, to measure the relationship between the architecture of Fallingwater and of its natural surroundings.

Using fractal dimension analysis, a computational method that mathematically measures the characteristic visual complexity of an object, this paper mathematically measures and tests the similarity between the visual properties of Fallingwater and its natural setting. Twenty analogues of the natural surroundings of Fallingwater are measured and the results compared to those developed for the properties of eight views of the house.

Although individual results suggest various levels of visual similarity or difference, the complete set of results do not support the claim that the form of Frank Lloyd Wright's Fallingwater exhibits clear visual similarities to the surrounding landscape.

In addition to testing a prominent theory about Wright's building for the first time, the paper demonstrates a rare application of fractal analysis to interpreting relations between architecture and nature.

This paper aims to propose a semi-analytical model to investigate the elastic-plastic contact between fractal rough surfaces. Parametric studies have been performed to analyze the dependencies between the contact properties and the scale-independent fractal parameters.

A modified two-variable Weierstrass-Mandelbrot function has been used to build the geometrical model of rough surfaces. The computation program was developed using software MATLAB R2015a. The results have been qualitatively validated by the existing theoretical and experimental results in the literature.

In most cases, a nonlinear relation between the load and the displacement of the rigid plane is found. Only under the condition of larger loads, an approximate linear relation can be seen for great D and small G values. (D: fractal dimension and G: fractal roughness).

The contact model of the cylindrical joints (conformal contact) with radial clearance is constructed by using the fractal theory and the Kogut-Etsion elastic-plastic contact model, which includes purely elastic, elastic-plastic and fully plastic contacts. The present method can generate a more reliable calculation result as compared with the Hertz contact model and a higher calculation efficiency as compared with the finite element method for the conformal contact problem.

The purpose of the paper is to explore coherence across key disciplines of knowledge management (KM) for a general model as a way to address performance dissatisfaction in the field.

Research employed an evidence‐based meta‐analysis (287 aspects of literature), triangulated through an exploratory survey (91 global respondents), to gather data on the drivers for KM. The paper attempts to demonstrate self‐similarity across six key KM disciplines using fractal theory as a data analysis tool.

Appear to demonstrate self‐affinity between key disciplines in the field of KM. This provides a strong signpost for future research in the field when attempting to address practitioner dissatisfaction in performance.

The paper cannot determine importance, or value of the factors discussed. The meta‐analysis allows us to determine the existence of the identified functions and enablers. Limited representation of literature from outside the Northern Hemisphere will not allow for an assertion as to validity outside of this area. Findings could not determine whether factors were stable through time. While outliers in the data provide signposts for further research, it could be attributed to situated variance.

This paper could influence future research and practice through support for the development of general models for the field. It signposts affinity between disciplines, which could direct theorists and practitioners to explore solutions outside of their situated discipline through a shared understanding.

The fractal theory data analysis approach appears to be unusual if not unique in the field of KM. The evidence‐based meta‐analysis provides depth and rigour with the results triangulated against an exploratory survey, which offers a richness of findings that speaks directly to the needs of the field.

This paper aims to present the results of the comparison between different approaches to the prediction of electricity prices. It is well-known that the properties of the data generation process may prefer some modeling methods over the others. The data having an origin in social or market processes are characterized by unexpectedly wide realization space resulting in the existence of the long tails in the probabilistic density function. These data may not be easy in time series prediction using standard approaches based on the normal distribution assumptions. The electricity prices on the deregulated market fall into this category.

The paper presents alternative approaches, i.e. memory-based prediction and fractal approach compared with established nonlinear method of neural networks. The appropriate interpretation of results is supported with the statistical data analysis and data conditioning. These algorithms have been applied to the problem of the energy price prediction on the deregulated electricity market with data from Polish and Austrian energy stock exchanges.

The first outcome of the analysis is that there are several situations in the task of time series prediction, when standard modeling approach based on the assumption that each change is independent of the last following random Gaussian bell pattern may not be a true. In this paper, such a case was considered: price data from energy markets. Electricity prices data are biased by the human nature. It is shown that more relevant for data properties was Cauchy probabilistic distribution. Results have shown that alternative approaches may be used and prediction for both data memory-based approach resulted in the best performance.

“Personalization” of the model is crucial aspect in the whole methodology. All available knowledge should be used on the forecasted phenomenon and incorporate it into the model. In case of the memory-based modeling, it is a specific design of the history searching routine that uses the understanding of the process features. Importance should shift toward methodology structure design and algorithm customization and then to parameter estimation. Such modeling approach may be more descriptive for the user enabling understanding of the process and further iterative improvement in a continuous striving for perfection.

Memory-based modeling can be practically applied. These models have large potential that is worth to be exploited. One disadvantage of this modeling approach is large calculation effort connected with a need of constant evaluation of large data sets. It was shown that a graphics processing unit (GPU) approach through parallel calculation on the graphical cards can improve it dramatically.

The modeling of the electricity prices has big impact of the daily operation of the electricity traders and distributors. From one side, appropriate modeling can improve performance mitigating risks associated with the process. Thus, the end users should receive higher quality of services ultimately with lower prices and minimized risk of the energy loss incidents.

The use of the alternative approaches, such as memory-based reasoning or fractals, is very rare in the field of the electricity price forecasting. Thus, it gives a new impact for further research enabling development of better solutions incorporating all available process knowledge and customized hybrid algorithms.

The purpose of this paper is to study the tribological effect of zinc borate ultrafine powder (ZBUP) oil additive on the running-in quality.

The running-in quality was assessed by friction coefficient and surface topography. Fractal parameters including fractal dimension, the width of multifractal, the multifractal difference, multifractal parameters, phase trajectory and correlation dimension were used to extract the nonlinear characteristics of surface topography and friction coefficient.

When the ZBUP additive was added, the convergence degree of the phase trajectory and the stability of the running in were higher than that of base oil. It indicates that the ZBUP additive can improve the running-in quality of sliding bearing. Besides, the ZBUP additive can shorten the running-in time. A boundary protective film, which has good friction-reducing and anti-wear effects, was generated on the surface when the ZBUP additive was added.

The results have a great significance to improve the running-in quality and prolong the service life of the sliding bearing.