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Designers have been fascinated by exploring new geometries made by high-performance structures. In more specific terms, biological systems have always been proven to be characterised by sophisticated structures with adapting properties to nature challenges. Insightful analyses have shown how these natural structures are dominated by characteristics such as high energy absorption and elevated strength-weight proportion. Fractal geometries are examples of bio-inspired mathematical objects whose complex 3D structures can be obtained only by advanced manufacturing systems, such as additive manufacturing (AM). This study investigates the feasibility and energy absorption properties of a novel fractal structure based on a 3D Greek cross (3D-CFS). The structure was designed with different volume fractions and produced by powder bed fusion (PBF) AM processes in polyamide (PA12) and thermoplastic polyurethane (TPU). The 3D-CFS properties are investigated under quasi-static and dynamic compression tests. The analysis revealed that for certain geometrical parameters, the manufacturing of the structures is constrained by the sintered powder entrapped in the structure. However, in the case of powder-free structures, the results showed a high impact resistance and cushioning capability. Overall, in terms of specific energy absorption (SEA), the TPU structures showed values between 2.5 and 3.5 kJ/kg, while PA12 ones are between 7.5 and 17.4 kJ/kg, making the 3D-CFS structure compatible with personal protective equipment (PPE) applications. Compared to the literature data on cellular structures made by AM, 3D-CFS performs considerably better. Also, PA12 3D-CFS is better, with a SEA value up to 170% higher than that of a typical material employed for head PPE (e.g. EPS-60 SEA equal to 2.76 kJ/kg). In contrast, TPU 3D-CFS looks more promising in the case of multiple impact conditions. [ABSTRACT FROM AUTHOR]

The growing demand for space-efficient antennas compatible with portable electronic gadgets inspired the integration of recursively iterated fractal geometries (characterized by self-similarity, space-filling, and multiband/wideband capabilities) in antenna designs. Therefore, this article conducts an extensive survey on fractal-based single-port and multi-port patch antenna designs with multiband and ultrawideband characteristics for their implementation in 5G/IoT (Internet of Things) devices. The survey begins with a basic overview of fractal geometries and the iterated function system (IFS) technique employed for their generation. Further, it highlights the limitation of multipath fading prevalent in single-port antenna arrays that can be overcome by adopting multiple-input multiple-output (MIMO) technology. The MIMO antenna systems are vital for 5G networks to enhance data transmission rate, network capacity, and system reliability. Apart from these admirable attributes, the closely packed antenna elements in the MIMO configuration result in a severe mutual coupling. To address this limitation, various isolation enhancement techniques developed by distinguished researchers are thoroughly discussed in this article, detailing their merits and demerits. At last, this article portrays diverse band-notch structures integrated into the antenna designs to eradicate the existing interfering narrow bands in the ultrawideband (UWB) spectrum. The underlying reason for conducting this survey is to aid antenna designers and academicians with a thorough knowledge of distinct fractal geometries, various isolation improvement approaches, and band-notch techniques on a single platform, desired for designing 5G/IoT-based antenna systems. [ABSTRACT FROM AUTHOR]

Mandelbrot set, which was provided as a highlight in fractal and chaos, is studied by many researchers. With the extension of Mandelbrot set to generalized M set with different kinds of exponent k (k − M set), properties are hard to understand when k is a complex number. In this paper, fractal property of generalized M set with complex exponent z is studied. First, a relation is constructed between generalized M set with complex and real exponent. Then, distribution of z − M set on complex plane is researched. Meanwhile, symmetry of generalized M set is proved. Finally, graphics, generated by escape time algorithm, are the validated results of this paper. [ABSTRACT FROM AUTHOR]

Given that wavelet transform and fractal theory reveal the self-similarity characteristics of objects from macro to micro levels, this study proposes a wavelet fractal dimension (WFD) to extract the fractal dimension feature of the wear state of a deep hole drill bit by using binary wavelet function as the scale. Weierstrass–Mandelbrot fractal functions with different theoretical fractal dimensions are introduced to evaluate the accuracy of WFD. Four methods for defining fractal dimensions are applied to estimate the fractal dimension of the current signal from the spindle motor in deep hole machining processing. Then, the variation law of the estimated value of the fractal dimensions with drill wear is investigated. Results show that the estimated value of WFD presents the smallest error compared with the theoretical value. Moreover, compared with other methods, the WFD of the current signal provides the strongest correlation with drill bit wear, which offers accurate characteristics for the monitoring of tool wear state. [ABSTRACT FROM AUTHOR]

The experimental measurements of ${2D}$ 2 D micro/nanolayered dimples' dimensions (both geometry and pattern) on the published tensile fractographs of a series of austempered high-strength low-carbon bainitic steel are carried out and interpreted with the corresponding initial microstructural features and tensile mechanical responses as a function of austempering temperature. [ABSTRACT FROM AUTHOR]

We consider a random field ϕ (r) in d dimensions which is largely concentrated around small ‘hotspots’, with ‘weights’, w i . These weights may have a very broad distribution, such that their mean does not exist, or is dominated by unusually large values, thus not being a useful estimate. In such cases, the median W ¯ of the total weight W in a region of size R is an informative characterisation of the weights. We define the function F by ln W ¯ = F (ln R) . If F ′ (x) > d , the distribution of hotspots is dominated by the largest weights. In the case where F ′ (x) - d approaches a constant positive value when R → ∞ , the hotspots distribution has a type of scale-invariance which is different from that of fractal sets, and which we term ultradimensional. The form of the function F(x) is determined for a model of diffusion in a random potential. [ABSTRACT FROM AUTHOR]

The iterated function system (IFS) is important in different fields like image compression. An important feature of such systems is that they can be used to generate fractals. Yet, for the obtained fractals, it is diffcult to locally control them to generate new ones with desired structures at specific places. In this paper, we gave an attempt to solve this problem based on a nonuniform multiple function system. For this, we first analyzed the multiple function systems needed in the generation of the final desired fractals. Based on such analysis, the final fractals with desired structures at specific places can be generated using the nonuniform multiple function system. Moreover, these two procedures were summarized into two algorithms for convenience. Examples were also given to illustrate the performance of the nonuniform multiple function system and the two algorithms in this paper. [ABSTRACT FROM AUTHOR]

The utilization of microchannel heat sinks stands as one of the most reliable solutions for dissipating heat generated in electronic chips. In this numerical study, a fractal microchannel heat sink employing three nanofluids Cu-water, Al2O3-water, and TiO2-water with variable volume fractions of 2 and 4 percent as the cooling fluid within the microchannels was investigated. The fluid flow inside the microchannels was analyzed from both hydrodynamic and thermal perspectives. The parameters such as pump power, Nusselt number, and performance evaluation criterion (PEC) were studied. Results demonstrate that heat transfer increases with an increase in the flow rate and volume fraction of nanoparticles. The maximum temperature reduction for the Cu-water nanofluid at an inlet flow rate of 200 ml/min and a volume fraction of 4% is 2.41%, the highest among the investigated nanofluids. However, this nanofluid also exhibits the highest pressure drop, reaching 25% at a 4% volume fraction. The PEC number analysis reveals an overall performance increase for all three microchannels. The Cuwater nanofluid exhibits the best comprehensive performance, providing an 8% overall enhancement, followed by Al2O3-water and TiO2-water nanofluids, which increase the system performance by 5% and 4%, respectively. Furthermore, the study introduced fins and cavities to the microchannel branches to enhance heat transfer and overall performance. Results indicate an increase in heat transfer for both modified geometries. The microchannel with fins exhibits a 3.5% lower maximum temperature compared to the original geometry at an inlet flow rate of 200 ml/min, while the microchannel with cavities showed a 1% reduction. However, the microchannel with fins experiences a 400% higher pressure drop than the initial geometry, while the microchannel with cavities has a 4% increase. PEC number analysis demonstrated that the microchannel with cavities improves system performance by 8%, whereas the microchannel with fins reduced system performance by 4%. [ABSTRACT FROM AUTHOR]

This paper proposes a lossless compression and encryption algorithm for sequence images based on adaptive inter-frames coding. This method can use the correlation in the time dimension to reduce redundant information. To increase the complexity of chaotic systems, this paper proposes a novel two-dimensional coupled and transformed Chebyshev cubic map (2D-CTCCM). Compared with existing chaotic systems, 2D-CTCCM exhibits better randomness and complexity. Moreover, this paper employs the Chinese remainder theorem in the process of lossless compression to obtain better compression performance. We extend the fractal sorting matrix to multi-dimensional space and apply it to the process of permutation. This paper proposes an improved semi-tensor product (STP) diffusion method to solve the problem that existing STP diffusion methods cannot resist chosen-plaintext attacks. Experimental results show that the performance of our algorithm is better than other lossless compression algorithms. It has strong key sensitivity and plaintext sensitivity and can resist brute-force attacks, statistical attacks, known-plaintext and chosen-plaintext attacks. [ABSTRACT FROM AUTHOR]

Objective: Familial Mediterranean fever (FMF) is an inflammatory disease and chronic inflammation may affect bone turnover and metabolism. This study aimed to compare the morphological, fractal, and textural features of the mandibular bone in FMF patients with healthy controls on panoramic radiographs. Methods: Fifty patients with FMF and, age- and sex-matched 50 healthy controls were included in the study. Morphological evaluation of the mandibular cortex on digital panoramic images of a total of 100 individuals was performed using the mandibular cortical index (MCI). For fractal dimension (FD) and texture analysis of trabecular bone, regions of interest with a size of 50x50 pixels were selected from the trabecular bone region between the roots of the second premolar and first molar teeth. The boxcounting method was applied to calculate the FD. Since the pixel gray-scale levels of these regions showed different distributions, pre-processing was performed with histogram equalization for texture analysis. First-order and gray-level co-occurrence matrixbased second-order features of panoramic images were calculated and their textural characterizations were obtained. Results: The MCI values of the mandibular cortex did not significantly differ between the case and control groups (p>0.05). FD values for the trabecular bone were 1.43 in the case group and 1.44 in the control group, and there was no significant difference between them (p>0.05). First and second-order textural features of trabecular bone did not differ statistically significantly between the case and control groups (p>0.05). Conclusion: Morphological, fractal, and textural features of the mandibular bone did not differ on panoramic radiographs between FMF patients and healthy controls. [ABSTRACT FROM AUTHOR]

This paper investigates a type of iterated implicit function systems composed of equations F n (x , y) = c , where F n (x , y) is a continuous function, and c is a constant. The existence of attractors of iterated implicit function systems is proved based on different equation conditions, including the equation F n (x , y) = c containing the implicit function or being α n -contractive about y. Meanwhile, we give definitions of implicit convergence of functions and monotone sequence of iterated implicit function systems. Finally, some properties of attractors of iterated implicit function systems are elucidated. [ABSTRACT FROM AUTHOR]

AI-driven mineral prospectivity mapping (MPM) is a valid and increasingly accepted tool for delineating the targets of mineral exploration, but it suffers from noisy and unrepresentative input features. In this study, a set of fractal and multifractal methods, including box-counting calculation, concentration–area fractal modeling, and multifractal analyses, were employed to excavate the underlying nonlinear mineralization-related information from geological features. Based on these methods, multiple feature selection criteria, namely prediction–area plot, K-means clustering, information gain, chi-square, and the Pearson correlation coefficient, were jointly applied to rank the relative importance of ore-related features and their fractal representations, so as to choose the optimal input feature dataset readily used for training predictive AI models. The results indicate that fault density, the multifractal spectrum width (∆α) of the Yanshanian intrusions, information dimension (D1) of magnetic anomalies, correlation dimension (D2) of iron-oxide alteration, and the D2 of argillic alteration serve as the most effective predictor features representative of the corresponding ore-controlling elements. The comparative results of the model assessment suggest that all the AI models trained by the fractal datasets outperform their counterparts trained by raw datasets, demonstrating a significant improvement in the predictive capability of fractal-trained AI models in terms of both classification accuracy and predictive efficiency. A Shapley additive explanation was employed to trace the contributions of these features and to explain the modeling results, which imply that fractal representations provide more discriminative and definitive feature values that enhance the cognitive capability of AI models trained by these data, thereby improving their predictive performance, especially for those indirect predictor features that show subtle correlations with mineralization in the raw dataset. In addition, fractal-trained models can benefit practical mineral exploration by outputting low-risk exploration targets that achieve higher capturing efficiency and by providing new mineralization clues extracted from remote sensing data. This study demonstrates that the fractal representations of geological features filtered by multi-criteria feature selection can provide a feasible and promising means of improving the predictive capability of AI-driven MPM. [ABSTRACT FROM AUTHOR]

In this paper, the possibility of using monofractal and multifractal analysis of acoustic signals of pipelines to detect leaks is considered. An experimental stand has been created to study the fractal characteristics of acoustic signals of pipelines with "slit" type defects. During the experiments, defects of the "slit" type pipeline with dimensions of 2 mm, 8 mm, and 20 mm were modeled. Detrended fluctuation analysis (DFA) and the multifractal detrended fluctuation analysis (MF-DFA) were used. As a result of the experimental studies, it was found that the occurrence of leakage leads to the occurrence of anticorrelated vibrations in a pipeline with multifractal properties. The analyses of acoustic signals by DFA and MF-DFA methods make it possible to reliably determine the leakage. The Hurst exponent and the width of the multifractal spectrum can serve as indicators of the occurrence of leaks in pipelines. [ABSTRACT FROM AUTHOR]

Most geophysical and geochemical data are commonly acknowledged to exhibit fractal and multifractal properties, but the fractal characteristics of polarizability have received limited attention from the literature. The present study demonstrates that the polarizability data of the graphite deposits have fractal characteristics and introduces the fractal method for its quantitative analysis to indicate and predict the properties of graphite deposits. The results show that the concentration-area (C-A) method is superior to classical interpolation in anomaly extraction but inferior to the spectrum-area (S-A) method in the coverage region. Because the type of graphite ore is sedimentary-metamorphic in this area, the graphite ore-bodies can be regarded as a special stratum, which is different from most metal deposits, and the anomaly of graphite ore are shown in the background mode of the S-A method. The high values of the background mode effectively indicate the potential areas where the graphite-bearing strata occur, while observing a decrease in the power-law exponent (β) of the background mode as the width of ore-bodies increases. The validity of this conclusion was confirmed based on the vertical profiles of the predicted area, and the uncharted ore vein was thereby identified. Furthermore, it was found that the anomaly mode can serve as a grade indicator of graphite ore rather than delineating the fault. By integrating the background and anomaly modes of the S-A method, we can quantitatively predict and effectively identify high-grade targets from sedimentary deposits containing minerals in future exploration. [ABSTRACT FROM AUTHOR]

The fractal structure of porous carbon material doped with manganese before and after laser irradiation was investigated by the method of small-angle X-ray scattering. The type of fractal aggregate and the value of its fractal dimension D, which is 1.4–1.5 for non-irradiated samples of the first level of fractal aggregation and 2.7 for irradiated samples of the second level of fractal aggregation, were determined. [ABSTRACT FROM AUTHOR]

We study the group TA of rearrangements of the airplane limit space introduced by Belk and Forrest (2019). We prove that TA is generated by a copy of Thompson's group F and a copy of Thompson's group T, hence it is finitely generated. Then we study the commutator subgroup [TA; TA], proving that the abelianization of TA is isomorphic to Z and that [TA; TA] is simple, finitely generated and acts 2-transitively on the so-called components of the airplane limit space. Moreover, we show that TA is contained in T and contains a natural copy of the basilica rearrangement group TB studied by Belk and Forrest (2015). [ABSTRACT FROM AUTHOR]

Scale invariance, which refers to the preservation of geometric properties regardless of observation scale, is a prevalent phenomenon in ecological systems. This concept is closely associated with fractals, and river networks serve as prime examples of fractal systems. Quantifying river network complexity is crucial for unveiling the role of river fractals in riverine ecological dynamics, and researchers have used a metric of "branching probability" to do so. Previous studies showed that this metric reflects the fractal nature of river networks. However, a recent article by Carraro and Altermatt (2022) contradicted this classical observation and concluded that branching probability is "scale dependent." I dispute this claim and argue that their major conclusion is derived merely from their misconception of scale invariance. Their analysis in the original article (fig. 3a) provided evidence that branching probability is scale‐invariant (i.e., branching probability exhibits a power‐law scaling), although the authors erroneously interpreted this result as a sign of scale dependence. In this article, I re‐introduce the definition of scale invariance and show that branching probability meets this definition. This provided an opportunity to address the divergent use of "scale invariance" and "scaling" between fractal theory and ecology. [ABSTRACT FROM AUTHOR]

Due to the recent expansion in the generations of the communications systems, it is utmost priority to transmit a large amount of data over a wideband frequency spectrum. For this single ultra-wideband (UWB) antennas are the prime choice as compared to the multiple narrow band antennas. A modified pentagonal fractal patch antenna with a modified ground plane covering ultra-wideband has been proposed. The antenna has a compact size of 25 mm × 25 mm × 1.6 mm with peak gain of 2.2 dB. The UWB coverage of the design is achieved by implementing modified co-planar ground, modified fractal geometry and coplanar feed. The proposed design possesses the significant resonance and radiation performance with very compact size on low-cost substrate while covering the whole UWB. Finally, the simulated resonating and radiation characteristics have been validated with the measured characteristics of the fabricated prototype and the results are quite promising. [ABSTRACT FROM AUTHOR]

The simulation and characterisation of randomly rough surfaces is an important topic in surface science, tribology, geo- and planetary sciences, image analysis and optics. Extensions to general random processes with two continuous variables are straightforward. Several surface generation algorithms are available, and preference for one or another method often depends on the specific scientific field. The same holds for the methods to estimate the fractal dimension D. This work analyses six algorithms for the determination of D as a function of the size of the domain, variance, and the input value for D, using surfaces generated by Fourier filtering techniques and the random midpoint displacement algorithm. Several of the methods to determine fractal dimension are needlessly complex and severely biased, whereas simple and computationally efficient methods produce better results. A fine-tuned analysis of the power spectral density is very precise and shows how the different surface generation algorithms deviate from ideal fractal behaviour. For large datasets defined on equidistant two-dimensional grids, it is clearly the most sensitive and precise method to determine fractal dimension. [ABSTRACT FROM AUTHOR]

In this paper, a Newton-type iterative scheme for solving nonlinear systems is designed. In the process of proving the convergence order, we use the higher derivatives of the function and show that the convergence order of this iterative method is six. In order to avoid the influence of the existence of higher derivatives on the proof of convergence, we mainly discuss the convergence of this iterative method under weak conditions. In Banach space, the local convergence of the iterative scheme is established by using the ω -continuity condition of the first-order Fréchet derivative, and the application range of the iterative method is extended. In addition, we also give the radius of a convergence sphere and the uniqueness of its solution. Finally, the superiority of the new iterative method is illustrated by drawing attractive basins and comparing them with the average iterative times of other same-order iterative methods. Additionally, we utilize this iterative method to solve both nonlinear systems and nonlinear matrix sign functions. The applicability of this study is demonstrated by solving practical chemical problems. [ABSTRACT FROM AUTHOR]

The restorative and mental state enhancing effects of brief mindfulness-based interventions (MBIs) and restorative environments such as nature has been supported in the research literature. However, regular adoption of these practices is limited by practical constraints and motivational barriers. The current study addressed these challenges by introducing two novel approaches which utilise the immersive and interactive qualities of virtual reality (VR). This included an interactive MBI and an abstract restorative environment using fractal-like imagery. These approaches were explored using a comparative evaluation of two short (6 min) VR interventions: Passive VR (applying principles from restorative interventions) and Interactive VR (implementing a focused attention form of mindfulness meditation). A mixed methods approach revealed increased state mindfulness, reduced mental fatigue, and enhanced aspects of mood (calm/relaxation, anxiety) consistently between conditions. Between group differences revealed additional benefits for cognition (focus), mood (happiness and sadness), and motivational value with the interactive intervention. The abstract environment, used in both interventions, maintained comparable levels of perceived restoration with a nature VR control condition. The results provide preliminary evidence supporting the use of interactive approaches for mindfulness interventions and abstract versions of restorative environments. [ABSTRACT FROM AUTHOR]

We develop the local convergence of the six order Contraharmonic-mean Newton's method (CHN) to solve Banach space valued equations. Our analysis approach is two fold: The first way uses Taylor's series and derivatives of higher orders. The second one uses only the first derivatives. We examine the theoretical results by solving a boundary value problem also using the examples relating the proposed method with other's methods such as Newton's, Kou's and Jarratt's to show that the proposed method performs better. The conjugate maps for second-degree polynomial are verified. We also calculate the fixed points (extraneous). The article is completed with the study of basins of attraction, which support and further validate the theoretical and numerical results. [ABSTRACT FROM AUTHOR]

A sriyantra/srichakra-shaped wideband fractal-based monopole antenna is designed and substrate material analysis is performed to determine its ability to meet the needs of S-, C-, X-, and Ku-band communication applications. The proposed model design is inspired by sriyantra, which is believed to be a source of energy to the universe according to Indian mythology. This work is focused on the integration of fractal geometry with sriyantra/srichakra for providing a linkage between philosophical belief and a modern communication system with experimental validation. The designed antenna performance characteristics are analysed on various substrates of rigid, flexible, and textile materials to identify the suitable model as per the requirements of specified applications. The proposed model provides 17.7 GHz bandwidth, a peak realized gain of 8.66 dB, and peak efficiency of 95% with RT/duroid 5880 substrate material. The design with polyimide for the proposed structure provides bandwidth of 14.8 GHz, peak gain of 6.18 dB, and peak efficiency of 90%. The same design was implemented on the fabric substrate material of bed sheet cotton, achieving bandwidth of 12.5 GHz, peak gain of 6.39 GHz, and peak efficiency of 92%. The proposed srichakra structure of the fractal monopole antenna on three substrate materials provides wide bandwidth with considerable gain and efficiency in S-, C-, X-, and Ku-band communication applications. The experimental validation provides a good correlation with the simulation results obtained from the CST (computer simulation technology) tool for applicability in communication systems. [ABSTRACT FROM AUTHOR]

Drone based surveillance and communication systems are playing a vital role in modern days for both military and civilian applications. Antennas with low profile, smaller size, and light weight are essential for the realization of these systems. A novel fractal-inspired hybrid microstrip patch antenna realized with Sierpinski gasket fractal slots cut in the radiating patch along with corresponding ground structure simultaneously defected with Sierpinski carpet fractal slots is reported for the first time. The antenna resonates at 2.4 GHz with a measured return loss of 17 dB, gain of 7 dB and measured 3 dB beamwidth is of the order of 70°. The current approach leads to the size reduction of the antenna to the extent of 55 % in comparison to standard radiating patch antenna resonating at the same frequency. The fractal-inspired hybrid microstrip patch antenna is a promising candidate for drone-based surveillance and communication applications owing to its miniaturization and good directional radiation properties. [ABSTRACT FROM AUTHOR]

Objective: Familial Mediterranean fever (FMF) is an inflammatory disease and chronic inflammation may affect bone turnover and metabolism. This study aimed to compare the morphological, fractal, and textural features of the mandibular bone in FMF patients with healthy controls on panoramic radiographs. Methods: Fifty patients with FMF and, age- and sex-matched 50 healthy controls were included in the study. Morphological evaluation of the mandibular cortex on digital panoramic images of a total of 100 individuals was performed using the mandibular cortical index (MCI). For fractal dimension (FD) and texture analysis of trabecular bone, regions of interest with a size of 50x50 pixels were selected from the trabecular bone region between the roots of the second premolar and first molar teeth. The boxcounting method was applied to calculate the FD. Since the pixel gray-scale levels of these regions showed different distributions, pre-processing was performed with histogram equalization for texture analysis. First-order and gray-level co-occurrence matrix-based second-order features of panoramic images were calculated and their textural characterizations were obtained. Results: The MCI values of the mandibular cortex did not significantly differ between the case and control groups (p>0.05). FD values for the trabecular bone were 1.43 in the case group and 1.44 in the control group, and there was no significant difference between them (p>0.05). First and second-order textural features of trabecular bone did not differ statistically significantly between the case and control groups (p>0.05). Conclusion: Morphological, fractal, and textural features of the mandibular bone did not differ on panoramic radiographs between FMF patients and healthy controls.

The study is devoted to the consideration of the terms, which are the most frequently used and significant for the formation of meaning in linguistics. The relevance of the study is, on the one hand, determined by the variety of approaches to their definition and interpretation, and, on the other hand, by the necessity to specify them to facilitate academic communication and linguistic analysis. The purpose of this work is to consider a number of such concepts and substantiate our approach to them and their interpretation. The study uses both general theoretical and linguistic research methods. Particular attention is paid to phenomenological analysis while considering the terms themselves, as well as semantic, categorical-constitutive, positional and pragmatic analysis while studying empirical material. There are considered the concepts of text, discourse, dicteme as a text unit, language personality of an author, or a narrator and a reader/listener. The article analyzes differences between the text and discourse concepts. The work substantiates heuristic potential of a dicteme as a minimum text unit. The dicteme is studied both - from elementary and holistic approaches, as a fractal that forms the space of the whole text according to synergistic laws. The study emphasizes the ideological role of a linguistic personality both at the stages of creation and consumption of a text. There is carried out a linguistic analysis of an English literary text in order to identify denotative and conceptual information in its ideological and aesthetic manifestation in it. The study highlights the role of strong positions of text in the transfer of conceptual information and considers the function of influence in an artistic and media works, which, in the first case, is mainly emotive in nature, and, in the second, manipulative. It underlines the interdependence of the conceptual priorities of the creator and consumer of a media text.

Load carriage experiments are typically performed from a linear perspective that assumes that movement variability is equivalent to error or noise in the neuromuscular system. A complimentary, nonlinear perspective that treats variability as the object of study has generated important results in movement science outside load carriage settings. To date, no systematic review has yet been conducted to understand how load carriage dynamics change from a nonlinear perspective. The goal of this systematic review is to fill that need. Relevant literature was extracted and reviewed for general trends involving nonlinear perspectives on load carriage. Nonlinear analyses that were used in the reviewed studies included sample, multiscale, and approximate entropy; the Lyapunov exponent; fractal analysis; and relative phase. In general, nonlinear tools successfully distinguish between unloaded and loaded conditions in standing and walking, although not in a consistent manner. The Lyapunov exponent and entropy were the most used nonlinear methods. Two noteworthy findings are that entropy in quiet standing studies tends to decrease, whereas the Lyapunov exponent in walking studies tends to increase, both due to added load. Thus, nonlinear analyses reveal altered load carriage dynamics, demonstrating promise in applying a nonlinear perspective to load carriage while also underscoring the need for more research. [ABSTRACT FROM AUTHOR]

To explore the dynamic mechanical response of layered rocks under different impact pressures, dynamic impact experiments were performed on five sets of layered rock-like specimens at different dips with a splitting Hopkinson compression bar. The effects of impact pressure on the compressive properties of layered rocks are researched. The fracture patterns are also discussed regarding fragmentation morphology, fractal characteristics, and energy dissipation. The findings suggest that the dynamic compressive strength shows the "U" shape variation with the dip angle θ, firstly declining and then enlarging. The dynamic compressive strength grows with increased impact pressure at different dip angles. The dynamic compressive strength of the layered rock at different dip angles increased the fastest with the change of impact pressure from 0.2 MPa to 0.3 MPa. The fractal dimension D tends to enlarge with increasing impact load. There is a highly linear relationship between them. The D of the sample fragments increases slower as the θ increases. In general, the absorbed energy declines first and then enlarges. With the higher impact pressure, the percentage of the total absorbed energy increases for each θ, besides the energy gains. The broken effect of a high dip angle specimen is better when crushing rock at low impact pressure. And when that is high, it is easy to cut the surrounding rock vertically or parallel to the layer direction. [ABSTRACT FROM AUTHOR]

The paper introduces a fractal geometry utilizing an Octagonal Split Ring Resonator (SRR) hybrid DRA as its basis. The primary antenna consists of a conventional Octagonal patch, which is then scaled down by 0.5 in the first iteration and further by 0.25 in the second and then the DRA is utilized to enhance its performance. Remarkably compact at 6 × 6.2 cm, the antenna demonstrates effectiveness across frequencies of 5.1, 6.8, and 7.2 GHz notably; it maintains a gain above 3.3 dBi and directivity above 4.1 dBi in all operational bands. Analysis employing surface current and return loss substantiates the impact of the fractal design with DR. These simulations and measured results affirm the proposed antenna's suitability for robust C band wireless applications, offering promising performance in antenna parameters.

We develop the local convergence of the six order Contraharmonic-mean Newton’s method (CHN) to solve Banach space valued equations. Our analysis approach is two fold: The first way uses Taylor’s series and derivatives of higher orders. The second one uses only the first derivatives. We examine the theoretical results by solving a boundary value problem also using the examples relating the proposed method with other’s methods such as Newton’s, Kou’s and Jarratt’s to show that the proposed method performs better. The conjugate maps for second-degree polynomial are verified. We also calculate the fixed points (extraneous). The article is completed with the study of basins of attraction, which support and further validate the theoretical and numerical results.

Abstract The integration of biology, computer science, and statistics has given rise to the interdisciplinary field of bioinformatics, which aims to decode biological intricacies. It produces extensive and diverse features, presenting an enormous challenge in classifying bioinformatic problems. Therefore, an intelligent bioinformatics classification system must select the most relevant features to enhance machine learning performance. This paper proposes a feature selection model based on the fractal concept to improve the performance of intelligent systems in classifying high-dimensional biological problems. The proposed fractal feature selection (FFS) model divides features into blocks, measures the similarity between blocks using root mean square error (RMSE), and determines the importance of features based on low RMSE. The proposed FFS is tested and evaluated over ten high-dimensional bioinformatics datasets. The experiment results showed that the model significantly improved machine learning accuracy. The average accuracy rate was 79% with full features in machine learning algorithms, while FFS delivered promising results with an accuracy rate of 94%.

In this paper, Al films were deposited on glass and steel substrates by using thermal evaporation technique. X-ray diffraction (XRD) analysis was used for structural characterization of Al thin films. It was found that the growth process mechanism of Al film on two substrates was different. The difference in the growth mechanism and microstructures affects the surface properties. Atomic force microscope (AFM) and field emission scanning electron microscope (FESEM) have been used to describe the surface morphology and fractal properties of Al films. The fractal properties obtained by autocorrelation function (ACF), height-height correlation function (H(r)) and Minkowski function are described and compared with each other. The results of 2D AFM images show that the Al film on the steel substrate has higher surface roughness, roughness exponent, and lateral correlation length compared to the glass substrate. However, the Al film on the glass substrate has a higher spatial complexity with a fractal dimension of Df = 2.88.

Fractals have been theoretically used to explain visual beauty from the urban scale to the context of architectural facades. How we perceive the visual beauty of architecture is likely dependent on subjectivity. However, the fractal is applicable for defining visual beauty and as a quantifiable method that provides objectivity for analysis. Previous research has used fractals, particularly in faca­des, to determine the beauty in complex geometry and quantify the complexity. However, the application of fractals in traditional architecture remains to be explored. Therefore, this article will discuss in detail how fractal is a suitable method to study the visual beauty of traditional architectural facades using fractal geometry and fractal dimension index. The case used to illustrate the imple­mentation is Kori Agung of Balinese traditional architecture, known for its grandeur and luxurious facade images. It embodies the visual beauty of its facade due to its textured, layered, and complex visual appearance.

Soft robotics, with their application in biomedical fields like flexible surgical tools and wearable exo-suits, have revolutionized biomedical practices. To adapt to different scales of application scenarios, our research emphasizes fractal-inspired soft robotics, leveraging the unique scalable and reconfigurable properties of fractal structures. This study focuses on the computational design and simulation of these robots. Traditional modeling methods, apt for rigid robotic arms, falter for soft materials due to their extensive flexibility. We introduced a deep learning strategy with physics-informed neural network for accurate soft robot dynamics modeling. Unlike existing networks optimized for rigid systems, our approach integrates elastic beam theory and deformation laws into Lagrangian Dynamics, making it ideal for simulating fractal soft robotic arms. Compared to conventional finite element simulations and learning approaches, our method shows superior effectiveness. We also conducted simple simulation experiments to show that fractal soft arm is potentially suitable for medical procedures (such as dilating passages) and proved that this fractal-designed soft robotic arm exhibits good portability and adaptability to various scenarios, making it a promising candidate for guiding the design of future surgical robots.

The objective of the image retargeting operator is to reduce the size of the image in a content-aware fashion. To strengthen the process of single operator-based image retargeting different hybrid sequences are being investigated. The visual quality of fractal images can be improved by utilizing efficient retargeting operators. In this paper, three frameworks are developed and combined to minimize the deficiencies of image retargeting operations. In framework-1, a seam diversion-based image retargeting technique is developed to overcome the drawbacks of the existing seam carving (SC) technique. In framework-2, the technique developed in framework-1 is combined with other retargeting operators to produce an efficient hybrid sequence of image retargeting operators. The objective of framework-2 is to overcome the limitation of single operator based image retargeting. In framework-3, an improved affine transformation function is developed that incorporates hybrid sequence of operator proposed in the framework-2. The main objective of framework-3 is to replace the scaling operator from the existing affine transformation. The structural similarity index measure (SSIM) metric is used to measure the performance of framework-1. The comparative analysis reveals that the performance of the retargeting technique proposed in framework-1 is 7% higher as compared to the existing SC technique. The superiority of framework-2 and 3 is analyzed using an optimization function in which Image Euclidian Distance (IMED) and Dominant Color Descriptor (DCD) techniques are incorporated. Finally, the performance analysis of framework-2 and 3 discloses their higher efficacy as compared to existing state-of-the-art. [ABSTRACT FROM AUTHOR]