Box Dimension Research Articles

Set pair analysis and system dynamics coupling approach for structure simulation and variation trend evaluation of water resources spatial equilibrium system

AbstractThe implement of water resources spatial equilibrium (WRSE) schemes is fundamental task of integrated water resources management in China, in which, the evaluation and simulation analysis of WRSE system is of great concern for understanding the overall variation and feedback characteristics of WRSE system. Therefore, we utilized the ordered degree, entropy and connection number coupling model to evaluate the variation of WRSE system, and also employed system dynamics (SD) and scenario simulation integrated method to reveal the feedback characteristics between different equilibrium variables and subsystems, and thus the set pair analysis‐SD based approach for structure simulation and variation trend evaluation of WRSE system was constructed. The application results in Anhui province, China demonstrated that, the overall variation of provincial spatial equilibrium situation of WRSE system presented obvious improving trend, 2009–2019, the index of ordered degree and connection number entropy in Hefei, increased from the minimum of 0.6434 (Grade 3, unequilibrium) to maximum of 0.9985 (Grade 1, equilibrium). Moreover, the future variation of WRSE system will display stable improving trend during 2020 to 2029, in which, annual water resources availability and water resources utilization efficiency will have significant influence on WRSE system. And the research findings can be favorable to formulate water resources development and utilization strategies.

A Fractal Study on Random Distribution of Recycled Concrete and Its Influence on Failure Characteristics

In order to quantitatively describe the influence of aggregate distribution on crack development and peak stress of recycled aggregate concrete, a multifractal spectrum theory was proposed to quantitatively characterize aggregate distribution in specimens. A mesomechanical model of reclaimed aggregate concrete mixed with natural aggregate and artificial aggregate was constructed. Numerical simulation tests were conducted on the uniaxial compression mechanical behavior of 25 groups of sample models with the same proportion and different aggregate distribution forms. Based on the box dimension theory, the multiple fractal spectrum method was used to quantitatively characterize the aggregate distribution form, and the key factors affecting cracks were explored based on the gray correlation degree. The research results show that the aggregate distribution in recycled aggregate concrete has multifractal characteristics. The multifractal spectrum was used to effectively characterize the aggregate distribution pattern, which can enlarge local details and provide new ideas for the quantitative analysis of the damage mode of recycled concrete. Secondly, by establishing a statistical model of the correlation between the multifractal spectrum width of the aggregate distribution pattern and the crack distribution box dimension, it was found that there was a positive correlation between the two, that is, the greater the multifractal spectrum width of the aggregate distribution pattern, the greater the crack box dimension, and the more complex the crack distribution. The complexity of aggregate distribution is closely related to the irregularity and complexity of mesoscopic failure crack propagation in recycled concrete specimens. In addition, gray correlation theory was applied to analyze the key factors affecting the formation of cracks in the specimens. The results showed that aggregate distribution had a first-order correlation with crack formation, and changes in aggregate distribution were an important factor affecting the performance of recycled concrete. Secondly, the poor mechanical properties of NAITZ led to obvious material damage, while NCA and MZ had a significant impact on the skeleton effect in the stress–strain process due to their large areas. This study deepens people’s understanding of the damage characteristics and cracking failure modes of recycled concrete. The study verifies the feasibility of the application of recycled aggregates and provides a valuable reference for engineering practice.

Thermal and hydrodynamic effects in variable geometry nanofluid transport with Thermo-Responsive liquid Composites: Dynamics of entropy generation

In this communication, the authors focused on energy loss during the flow of hybrid nanofluid in expanding/contracting channels. The goal is to determine how, in real-world applications, hybrid nanofluids can maximize energy efficiency and reduce entropy production, hence assisting in the development of more effective and sustainable thermal management systems. It is well documented that heat transfer is enhanced due to the presence of nanoparticles in a base fluid and hence decreases energy loss in the system. The second law of thermodynamics defines that heat transfer is not ideal; hence, entropy in a system always rises. Suitable measures can be taken to minimize energy loss. One method is to use a nanofluid, if multiple nanosized particles are used; it is named a hybrid nanofluid. In this communication, a comparative analysis of simple and hybrid nanofluids is provided. A mathematical model outlining the dynamics of the flow is provided. The upper plate acts as a porous plate that is contracting/expanding and through which coolant hybrid nanofluids enter the channel. The lower plate remains stationary and is heated externally. The equations governing the flow are converted into ordinary differential equations by employing the similarity transformation. These ODEs are then solved analytically to get the series solution by using HAM along with the given boundary conditions. The entropy equation is modelled using the Clausius Duhem inequality. Copper and silver nanoparticles are combined with water. The impacts of different dimensionless parameters on stream function, velocity profile, Nusselt number, entropy, and Bejan number are discussed, and their results are shown graphically.

Entropy generation in radiative motion of tangent hyperbolic nanofluid in the presence of gyrotactic microorganisms and activation energy

In this work, entropy generation is optimized through the application of the second law of thermodynamics. The slip mechanisms, Brownian diffusions, and thermophoresis are elaborated using the tangent hyperbolic nanomaterial model. Magnetohydrodynamic (MHD) fluid is taken into consideration. To characterize the impact of activation energy, a unique model involving the binary chemical reaction is deployed. The effects of mixed convection that is nonlinear in nature, bioconvection, and Joule effect are all taken into consideration. The key partial differential equations (PDEs) are reduced into ordinary differential equations (ODEs) by utilizing appropriate similarity transformations and then solved numerically with the help of a built-in ‘bvp4c’ technique of MATLAB software. Varied flow parameters’ impacts on the nanoparticle volume concentration, entropy number, microorganism concentration, temperature, and velocity fields are analyzed using graphs. Various flow variables are taken into consideration to calculate the total rate of entropy generation. The obtained results show that concentration irreversibility, Joule effect irreversibility, viscous dissipation, and heat irreversibility all influence the entropy. The numerical outcomes were observed by fixing the physical parameters as 0.1<α<4.0, 0.1<M<1.2, 0.1<Nr<2.2, 0.1<Le<2.2, 0.1<Nb<0.4, 0.1<Nt<1.0, 2.0<⁡Pr⁡<5.0, and 0.1<Lb<2.0, as well as their impact on the momentum, thermal, concentration, and microorganism density profiles. From results, an increasing estimate of the variable representing chemical reaction indicates a decline in the concentration. The higher the chemical reaction variable, Hartmann number, and Weissenberg number, the higher the entropy number, while the Bejan number has a contrary behavior. Subsequently, all the outcomes are plotted in graphs and discussed in detail, when subjected to the involving physical quantities.

Performance evaluation of shot-blasted heat exchangers with MWCNT and activated carbon nanofluids: assessing entropy, exergy, sustainability index, Grashof, Rayleigh, and Richardson numbers for solar thermal applications

Performance evaluation of shot-blasted heat exchangers with MWCNT and activated carbon nanofluids: assessing entropy, exergy, sustainability index, Grashof, Rayleigh, and Richardson numbers for solar thermal applications

Fractal analysis of urban growth in complex systems

A complex network consists of number of elements which may interact with each other to form a complex system. The fractal feature is one of the most important characteristics in complex networks. This study examines the fractal analysis of Madaba City Centre as a complex system through the period to 1953-2022. In order to reveal the fractal characteristics of the study area box-counting (Db) and information (Di) dimensions were calculated using Benoit for five satellite images for years 1953, 1981, 1992, 2000, and 2022. Results showed that Madaba road networks have fractal characteristics for the study period, and the calculated fractal dimensions are between 1 and 2. Db values for years 1953, 1981, 1992, 2000, and 2022 are 1.38, 1.51, 1.55, 1.58, and 1.65, while Di values are 1.37, 1.52, 1.57, 1.60, and 1.67 respectively. The difference between Db and Di values for the same year was small, indicating the similarity between the two methods. Increasing the complexity of the system components and dynamic activities are other indicators of its growth, and there is a significant positive relationship between the fractal dimension value and the complexity level of the city in terms of population growth and area expansion; which increase the importance of fractal theory in studying the growth of the complex system like cities.

Quantitative recurrence problem on some Bedford-McMullen carpets

In this paper, we study the Hausdorff dimension of the quantitative recurrent set of the canonical endomorphism on the Bedford–McMullen carpets whose Hausdorff dimension and box dimension are equal.

The Application of Computed Tomography to Study the Soil Porosity of Mountain Red Earth

Mountain red soil, as a special type of soil in the South, has received widespread attention for its soil erosion problems. Its pore structure restricts water infiltration, thereby affecting the occurrence and development of soil erosion. In order to systematically obtain the distribution characteristics of the pore structure within the surface mountain red soil, this paper uses non-destructive CT detection technology to scan the soil column samples taken from the typical mountain red soil distribution area in Chenggong District, Kunming City, Yunnan Province. Image processing technology is applied to CT slices, and ImageJ (1.46r) software is used to obtain the distribution characteristics of pores within the soil column, including pore sizes and the number of pores at each depth, the proportion of pore area, roundness, and box-counting dimension. The results show that with the increase in depth, the proportion of pore area decreases linearly from the maximum value of 52.25% at the top to the minimum value of 2.02% at the bottom; the roundness of pores fluctuates between 0.8 and 0.9, overall increasing; the total number of pores generally first increases then decreases, and small pores are predominant, with the least number of large pores in the topsoil layer; the box-counting dimension shows a gradual linear decrease, with a maximum value of 1.7980 and a minimum value of 0.9878. The number of pores affects both roundness and the box-counting dimension, and the proportion of pore area also affects the box-counting dimension. There is a negative correlation between roundness and the box-counting dimension. The 3D visualization reconstruction of pores shows that most are interconnected, with the pore size significantly reducing with increasing depth. The quantitative analysis of parameters and 3D visualization reveal, to some extent, the impact of pore structure on the occurrence and development of soil erosion in mountain red soil. These research findings form the foundation for studying soil erosion in this region and provide a basis for systematically understanding its processes and mechanisms.

Single-clan settlements and multiple-clan settlements: a case study based on the evolution of spatial fractals in four traditional villages in the Xianggan region of China

ABSTRACT Compared with those in other Chinese provinces, the villages in Hunan and Jiangxi are characterized by complex clan networks. Our purpose was to elucidate the complexity and hierarchical changes in the evolution of clan-organized settlement patterns and the spatial fractal structure of traditional villages. Box-counting dimension analysis, which is based on fractal theory, was used to evaluate the evolution of four villages in Hunan and Jiangxi, China. Our findings indicated that (1) both single-clan and multiclan villages exhibit a spatial fractal pattern; (2) the fractal dimension of individual buildings is greater than that of building groups and the village as a whole; and (3) the self-similarity fractal dimension is greater for single-clan villages than for multiclan villages. These findings establish a connection between the restoration needs of traditional villages and the potential application of the self-similarity principle. They support a hierarchical approach to conservation, beginning with individual architectural units to preserve the villages’ original authenticity. Moreover, the observed fractal differentiation revealed the fundamental clan-cultural logic underlying traditional village spaces. This logic elucidates the potential of leveraging each village’s unique clan culture to counteract the homogenization of village space development, thereby revitalizing the grassroots dynamics of village spatial development.

On a class of fractal sets with different upper and lower box dimensions

On a class of fractal sets with different upper and lower box dimensions

Irreversibility analysis in an electro‐osmotically driven flow using ternary hybrid nanofluids in a microchannel with a porous material

AbstractFlow enhancement is one of the most significant challenges in microfluidics with extremely low permeability. Based on this, electrokinetics remediation for the double‐layer flow of hybrid ternary nanofluid is proposed based on the transport of ions under constant pumping pressure. The entropy generation volumetric rate relation is also modeled. The nonlinear system of equations is formulated, solved, and validated numerically by the collocation method and shooting Runge–Kutta method. Results are shown graphically to explore the impacts of governing parameters, such as the Darcy parameter, viscosity index, electrokinetic, and Joule heating effects, on the velocity, temperature, entropy, and Bejan number profiles. The flow and heat transmission in microchannels may be significantly changed and controlled by the electric double layer. The findings show that as the electrokinetic parameter's magnitude increases, the flow is slowed down, and thermal dispersion is impeded by nanoparticle collisions, which lowers the velocity field and heat transfer profile.

Fractal dimensions for iterated graph systems

Building upon Li & Britz (Li NZ, Britz T. 2024 On the scale-freeness of random colored substitution networks. Proc. Amer. Math. Soc . 152 , 1377–1389 (doi: 10.1090/proc/16604 )), this study aims to introduce fractal geometry into graph theory and to establish a potential theoretical foundation for complex networks. Specifically, we employ the method of substitution to create and explore fractal-like graphs, termed iterated graph systems (IGS) for the first time. While the concept of substitution is commonplace in fractal geometry and dynamical systems, its analysis in the context of graph theory remains a nascent field. By delving into the properties of these systems, including distance and diameter, we derive two primary outcomes. Firstly, within the deterministic IGS, we establish that the Minkowski dimension and Hausdorff dimension align through explicit formulae. Secondly, in the case of random IGS, we demonstrate that almost every Gromov–Hausdorff scaling limit exhibits identical Minkowski and Hausdorff dimensions analytically by their Lyapunov exponents. The exploration of IGS holds the potential to unveil novel directions. These findings not only, mathematically, contribute to our understanding of the interplay between fractals and graphs, but also, physically, suggest promising avenues for applications for complex networks.

Fractional derivative of Hermite fractal splines on the fractional-order delayed neural networks synchronization

The purpose of this research is twofold. First, the master–slave synchronization of fractional-order neural networks is explored with time delays using aperiodic intermittent control. Then we present a sufficient condition for master–slave synchronization of delayed fractional-order neural networks via average-width intermittent control technique. A numerical simulation is used to demonstrate the efficacy of the derived results. Second, a novel investigation of the Caputo-fractional derivative of Hermite fractal splines is accomplished. Moreover, its box counting dimension is estimated and related with the Caputo-fractional order. Additionally, we propose an image encryption algorithm utilizing the semi-tensor product (STP). The efficiency of the algorithm is evaluated through the application of statistical measures.

Spectral theory for fractal pseudodifferential operators

The paper deals with the distribution of eigenvalues of the compact fractal pseudodifferential operator Tτμ\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$T^\\mu _\ au $$\\end{document}, (Tτμf)(x)=∫Rne-ixξτ(x,ξ)(fμ)∨(ξ)dξ,x∈Rn,\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$\\begin{aligned} \\big ( T^\\mu _\ au f\\big )(x) = \\int _{{{\\mathbb {R}}}^n} e^{-ix\\xi } \\, \ au (x,\\xi ) \\, \\big ( f\\mu \\big )^\\vee (\\xi ) \\, {\\mathrm d}\\xi , \\qquad x\\in {{\\mathbb {R}}}^n, \\end{aligned}$$\\end{document}in suitable special Besov spaces Bps(Rn)=Bp,ps(Rn)\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$B^s_p ({{\\mathbb {R}}}^n) = B^s_{p,p} ({{\\mathbb {R}}}^n)$$\\end{document}, s>0\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$s>0$$\\end{document}, 1<p<∞\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$1<p<\\infty $$\\end{document}. Here τ(x,ξ)\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$\ au (x,\\xi )$$\\end{document} are the symbols of (smooth) pseudodifferential operators belonging to appropriate Hörmander classes Ψ1,δσ(Rn)\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$\\Psi ^\\sigma _{1, \\delta } ({{\\mathbb {R}}}^n)$$\\end{document}, σ<0\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$\\sigma <0$$\\end{document}, 0≤δ≤1\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$0 \\le \\delta \\le 1$$\\end{document} (including the exotic case δ=1\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$\\delta =1$$\\end{document}) whereas μ\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$\\mu $$\\end{document} is the Hausdorff measure of a compact d–set Γ\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$\\Gamma $$\\end{document} in Rn\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$${{\\mathbb {R}}}^n$$\\end{document}, 0<d<n\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$0<d<n$$\\end{document}. This extends previous assertions for the positive-definite selfadjoint fractal differential operator (id-Δ)σ/2μ\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$(\ extrm{id}- \\Delta )^{\\sigma /2} \\mu $$\\end{document} based on Hilbert space arguments in the context of suitable Sobolev spaces Hs(Rn)=B2s(Rn)\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$H^s ({{\\mathbb {R}}}^n) = B^s_2 ({{\\mathbb {R}}}^n)$$\\end{document}. We collect the outcome in the Main Theorem below. Proofs are based on estimates for the entropy numbers of the compact trace operator trμ:Bps(Rn)↪Lp(Γ,μ),s>0,1<p<∞.\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$\\begin{aligned} \ extrm{tr}\\,_\\mu : \\quad B^s_p ({{\\mathbb {R}}}^n) \\hookrightarrow L_p (\\Gamma , \\mu ), \\quad s>0, \\quad 1<p<\\infty . \\end{aligned}$$\\end{document}We add at the end of the paper a few personal reminiscences illuminating the role of Pietsch in connection with the creation of approximation numbers and entropy numbers.

On Microplasticity-induced Fatigue Fracture and its Relation to Entropy

Abstract The study delves into the intricate effects of microplasticity on fracture formation in testing specimens under axial cyclic loading. The primary aim is to pinpoint the juncture at which microplasticity becomes discernible across the stress cycle. Fatigue tests are conducted on varied specimens until failure using a fatigue testing machine, while recording parameters such as frequency, stress amplitude, applied power, and tensile strain. The investigation seeks to ascertain whether cracks must attain a specific size before manifesting these subtle alterations. A conjectured relationship is proposed between the number of cycles and entropy throughout the process. Additionally, a hypothesis is posited suggesting that microplasticity emerges only once the crack surpasses a certain threshold, such as grain size. This research provides insights into material fracture mechanisms and their implications for product durability and safety. Such discernments into the product life cycle under analogous conditions hold promise for delineating operational limits.

Исследование распределения контроля и метрик разнообразия в децентрализованных автономных организациях

This study empirically investigates the distribution of control and diversity in decentralized autonomous organizations (DAOs) on the Ethereum blockchain. It uses a number of measures-the Nakamoto coefficient, Gini coefficient, Her-findahl-Hirschman index, Theil index, Shannon entropy, and Simpson diversity index-to assess decentralization and fairness in the distribution of control tokens. The analysis reveals a complex landscape in which some DAOs exhibit decentralization with diversity in the distribution of control, while others exhibit significant concentration of power and inequality in the distribution of power. A key observation is the coexistence of a broad distribution of control among EOA addresses with significant inequality in the ownership of control tokens. This indicates that a broad distribution of control does not always correlate with a fair distribution of management tokens. The study also highlights the possibil-ity of delegation mechanisms that may lead to a more equitable distribution of power compared to direct representa-tion. This study provides insight into the governance dynamics of DAOs by demonstrating the complex multi-level bal-ance between decentralization and centralization in a decentralized technology infrastructure.

Study on the tensile properties of a novel modular splicing joint

The interconnection among module elements within a modular structure assumes a pivotal role in upholding structural integrity and stability. To address the challenges posed by existing inter-module connection joints, which necessitate operational space and may compromise the integrity of the module unit while impeding assembly efficiency, an innovative modular steel structure splicing joint is proposed. Through adjustments to the dimensions of the connection box and fastener components, four distinct spliced joints were established for axial tensile analysis. The subsequent evaluation included an examination of axial tensile capacity, strain distribution, and failure modes at critical points across various joints, providing insights into their tensile effectiveness. To comprehensively explore the influence of size parameters on tensile performance, a corresponding numerical model was developed for parametric analysis. Results indicate that tensile failure modes entail the extrication of the lower-end plate from the upper module column connection box and the cylindrical radius of the fastener. Notably, the protrusion radius of the fastener (R2), markedly influences the tensile bearing capacity of the spliced joints, with precedence over the lower end plate thickness (d0), cylinder radius (R1), sliding block thickness (d1), and limiting plate thickness (d2). The joint obviates the need for external operations to interlink module units, thereby augmenting the installation efficiency of the modular structure and mitigating complexities in design and the enigmatic transmission of forces within the self-locking joint.

Agricultural Data Analysis using Machine Learning: A Study on Dry Bean Classification

The classification of Dry Beans using various techniques such as Support Vector Machine (SVM) classification, K-means clustering, Decision Trees and Random Forest (RF) classification using an ipython notebook. To refine the model, performance matrix graphs of Cross entropy vs Epoch number, True value vs Predictive value and Accuracy vs Epoch. This analysis is often used in agricultural practices for improved crop management, increasing yield, resource optimization, enhancing sustainability etc.

Optimizing Object Detection Algorithms for Congenital Heart Diseases in Echocardiography: Exploring Bounding Box Sizes and Data Augmentation Techniques.

Congenital heart diseases (CHDs), particularly atrial and ventricular septal defects, pose significant health risks and common challenges in detection via echocardiography. Doctors often employ the cardiac structural information during the diagnostic process. However, prior CHD research has not determined the influence of including cardiac structural information during the labeling process and the application of data augmentation techniques. This study utilizes advanced artificial intelligence (AI)-driven object detection frameworks, specifically You Look Only Once (YOLO)v5, YOLOv7, and YOLOv9, to assess the impact of including cardiac structural information and data augmentation techniques on the identification of septal defects in echocardiographic images. The experimental results reveal that different labeling strategies substantially affect the performance of the detection models. Notably, adjustments in bounding box dimensions and the inclusion of cardiac structural details in the annotations are key factors influencing the accuracy of the model. The application of deep learning techniques in echocardiography enhances the precision of detecting septal heart defects. This study confirms that careful annotation of imaging data is crucial for optimizing the performance of object detection algorithms in medical imaging. These findings suggest potential pathways for refining AI applications in diagnostic cardiology studies.

Generation of Mandelbrot and Julia sets by using M-iteration process

In this manuscript, we introduce the M-iteration process for generating Mandelbrot and Julia sets. We establish an escape criterion for a polynomial of the form xk+1+c in the complex plane corresponding to the M-iteration process. Next, we present some graphical examples of Mandelbrot and Julia sets generated using the proven escape criterion and the escape-time algorithm. We also compare the images generated with the M, Mann, and Picard–Mann iterations. Moreover, we study the dependency between the iterations’ parameters and three numerical measures (the average escape time, non-escaping area index, and box-counting dimension) used in the literature. The results show that fractal images generated using the M-iteration are entirely different from those generated using the other two analysed iteration schemes. Moreover, the dependencies are highly non-linear and vary between the iterations.