Search Results (32)

The model explicitly incorporates boundary conditions that account for the complex interplay between sections experiencing varying degrees of reduction. This interaction significantly influences the overall deformation behavior and force loading. The control effect is associated with boundary conditions determined by the unevenness of the compression, which have certain quantitative and qualitative characteristics. These include additional loading, which is less than the main load, which implements the process of plastic deformation, and the ratio of control loads from the entrance and exit of the deformation site. According to this criterion, it follows from experimental data that the controlling effect on the plastic deformation site occurs with a ratio of additional and main loading in the range of 0.2–0.8. The next criterion is the coefficient of support, which determines the area of asymmetry of the force load and is in the range of 2.00–4.155. Furthermore, the criterion of the regulating force ratio at the boundaries of the deformation center forming a longitudinal plastic shear is within the limits of 2.2–2.5 forces and 1.3–1.4 moments of these forces. In this state, stresses and deformations of the plastic medium are able to realize the effects of plastic shaping. The force effect reduces with an increase in the unevenness of the deformation. This is due to a change in height of the longitudinal interaction of the disparate sections of the strip. There is an appearance of a new quality of loading—longitudinal plastic shear along the deformation site. The unbalanced additional force action at the entrance of the deformation source is balanced by the force source of deformation, determined by the appearance of a functional shift in the model of the stress state of the metal. The developed theory, using the generalized method of an argument of functions of a complex variable, allows us to characterize the functional shift in the deformation site using invariant Cauchy–Riemann relations and Laplace differential equations. Furthermore, the model allows for the investigation of material properties such as the yield strength and strain hardening, influencing the size and characteristics of the identified limit state zone. Future research will focus on extending the model to incorporate more complex material behaviors, including viscoelastic effects, and to account for dynamic loading conditions, more accurately reflecting real-world milling processes. The detailed understanding gained from this model offers significant potential for optimizing mill roll designs and processes for enhanced efficiency and reduced energy consumption. Full article

The Sparrow Search Algorithm (SSA), proposed by Jiankai Xue in 2020, is a swarm intelligence optimization algorithm that has received extensive attention due to its powerful optimization-seeking ability and rapid convergence. However, similar to other swarm intelligence algorithms, the SSA has the problem of being prone to falling into local optimal solutions during the optimization process, which limits its application effectiveness. To overcome this limitation, this paper proposes a Modified Sparrow Search Algorithm (MSSA), which enhances the algorithm’s performance by integrating three optimization strategies. Specifically, the Latin Hypercube Sampling (LHS) method is employed to achieve a uniform distribution of the initial population, laying a solid foundation for global search. An adaptive weighting mechanism is introduced in the producer update phase to dynamically adjust the search step size, effectively reducing the risk of the algorithm falling into local optima in later iterations. Meanwhile, the cat mapping perturbation and Cauchy mutation operations are integrated to further enhance the algorithm’s global exploration ability and local development efficiency, accelerating the convergence process and improving the quality of the solutions. This study systematically validates the performance of the MSSA through multi-dimensional experiments. The MSSA demonstrates excellent optimization performance on 23 benchmark test functions and the CEC2019 standard test function set. Its application to three practical engineering problems, namely the design of welded beams, reducers, and cantilever beams, successfully verifies the effectiveness of the algorithm in real-world scenarios. By comparing it with deterministic algorithms such as DIRET and BIRMIN, and based on the five-dimensional test functions generated by the GKLS generator, the global optimization ability of the MSSA is thoroughly evaluated. In addition, the successful application of the MSSA to the problem of robot path planning further highlights its application advantages in complex practical scenarios. Experimental results show that, compared with the original SSA, the MSSA has achieved significant improvements in terms of convergence speed, optimization accuracy, and robustness, providing new ideas and methods for the research and practical application of swarm intelligence optimization algorithms. Full article

A numerical model to simulate the laser thermoforming process (LTF) is proposed. It is developed on the basis of the thermodynamically consistent theory of coupled thermo-viscoplasticity and is suitable for modeling the LTF for thin-walled metal structural elements. In the frame of this model, the problem statement consists of the Cauchy relation, equations of motion, and the energy balance equation, which is reduced to the heat conduction equation, along with mechanical and thermal boundary conditions, as well as initial conditions. To describe the behavior of the material, a generalized model of physically nonlinear temperature-dependent thermo-viscoplasticity is used. Spatial discretization of the axisymmetric problem of laser pulse loading of the disk is performed by the FEM. The unsteady LTF process of the deformed disk configuration is simulated. The final profile of the disk is obtained as a result of a thermally induced residual stress–strain state caused by the rapid heating and subsequent gradual cooling of the material under the laser-irradiated area. Full article

The resolution of the unmanned aerial vehicle (UAV) path-planning problem frequently leverages optimization algorithms as a foundational approach. Among these, the recently proposed crayfish optimization algorithm (COA) has garnered significant attention as a promising and noteworthy alternative. Nevertheless, COA’s search efficiency tends to diminish in the later stages of the optimization process, making it prone to premature convergence into local optima. To address this limitation, an improved COA (ICOA) is proposed. To enhance the quality of the initial individuals and ensure greater population diversity, the improved algorithm utilizes chaotic mapping in conjunction with a stochastic inverse learning strategy to generate the initial population. This modification aims to broaden the exploration scope into higher-quality search regions, enhancing the algorithm’s resilience against local optima entrapment and significantly boosting its convergence effectiveness. Additionally, a nonlinear control parameter is incorporated to enhance the algorithm’s adaptivity. Simultaneously, a Cauchy variation strategy is applied to the population’s optimal individuals, strengthening the algorithm’s ability to overcome stagnation. ICOA’s performance is evaluated by employing the IEEE CEC2017 benchmark function for testing purposes. Comparison results reveal that ICOA outperforms other algorithms in terms of optimization efficacy, especially when applied to complex spatial configurations and real-world problem-solving scenarios. The proposed algorithm is ultimately employed in UAV path planning, with its performance tested across a range of terrain obstacle models. The findings confirm that ICOA excels in searching for paths that achieve safe obstacle avoidance and lower trajectory costs. Its search accuracy is notably superior to that of the comparative algorithms, underscoring its robustness and efficiency. ICOA ensures the balanced exploration and exploitation of the search space, which are particularly crucial for optimizing UAV path planning in environments with symmetrical and asymmetrical constraints. Full article

Using digital and non-digital card games to teach mathematics is a well-established didactic technique widely applied at different levels of education. Game-based learning strategies are also gaining ground in higher education, but the use of maths card games in university settings remains limited. Generation Z students are true digital natives, members of a hyper-cognitive generation with a learning profile different from any previous generation. In this paper, an original non-digital card game, Blue Yeti, is presented that supports determining the convergence property of improper integrals using the comparison theorems and the Cauchy–Maclaurin test, providing a motivational and effective way of acquiring knowledge for Gen Z students. This paper provides a comprehensive overview of the development process, rules, and gameplay mechanics of Blue Yeti, which was created as a key component of a multifunctional didactic framework. In addition, it presents findings from a two-year research study conducted among first-year bachelor’s students in computer science on the benefits of playing Blue Yeti. Quantitative studies were carried out with 63 first-year IT students using a quasi-experimental research design to measure the effectiveness of the game. A pre- and post-test design was used with the experimental group of 31 participants to evaluate the short-term effects of card game-based learning. A t-test for paired samples was used for hypothesis testing. To assess the medium-term impact, the results from the related midterm exam problems were statistically analysed, comparing the outcomes of the experimental group with those of the control group using the Mann–Whitney U-test. The results indicated that the experimental group outperformed the control group, achieving a mean score of 3.03 out of 6 on the designated midterm exam problems, compared to the control group’s mean score of 1.78. Additionally, student attitudes towards the game were measured using a mixed-method approach, which provided not only quantitative data but also qualitative information on student attitudes towards Blue Yeti, complementing the statistics on learning outcomes. The results of the study clearly support the effectiveness of the card game. Full article

This manuscript deals with a novel two-parameter stochastic distribution, obtained by transforming the Cauchy distribution, using generalized logistic mapping, into a unit interval. In this way, according to the well-known properties of the Cauchy distribution, a unit random variable with significantly accentuated values at the ends of the unit interval is obtained. Therefore, the proposed stochastic distribution, named the Cauchy–logistic unit distribution, represents a stochastic model that may be suitable for modeling phenomena and processes with emphasized extreme values. Key stochastic properties of the CLU distribution are examined, such as moments, entropy, modality, and symmetry conditions. In addition, a quantile-based parameter estimation procedure, an asymptotic analysis of the thus obtained estimators, and their Monte Carlo simulation study are conducted. Finally, the application of the proposed distribution in stochastic modeling of some real-world data with emphasized extreme values is provided. Full article

The primary objective of our study is to analyze how the nature of explanatory variables influences the values and behavior of impurity measures, including the Shannon, Rényi, Tsallis, Sharma–Mittal, Sharma–Taneja, and Kapur entropies. Our analysis aims to use these measures in the interactive learning of decision trees, particularly in the tie-breaking situations where an expert needs to make a decision. We simulate the values of explanatory variables from various probability distributions in order to consider a wide range of variability and properties. These probability distributions include the normal, Cauchy, uniform, exponential, and two beta distributions. This research assumes that the values of the binary responses are generated from the logistic regression model. All of the six mentioned probability distributions of the explanatory variables are presented in the same graphical format. The first two graphs depict histograms of the explanatory variables values and their corresponding probabilities generated by a particular model. The remaining graphs present distinct impurity measures with different parameters. In order to examine and discuss the behavior of the obtained results, we conduct a sensitivity analysis of the algorithms with regard to the entropy parameter values. We also demonstrate how certain explanatory variables affect the process of interactive tree learning. Full article

This paper presents a general analytical solution for the problem of locating points in planar regions with an arbitrary geometry at the boundary. The proposed methodology overcomes the traditional solutions used for polygonal regions. The method originated from the explicit evaluation of the contour integral using the Residue and Cauchy theorems, which then evolved toward a technique very similar to the winding number and, finally, simplified into a variant of ray-crossing approach slightly more informed and more universal than the classic approach, which had been used for decades. The very close relation of both techniques also emerges during the derivation of the solution. The resulting algorithm becomes simpler and potentially faster than the current state of the art for point locations in arbitrary polygons because it uses fewer operations. For polygonal regions, it is also applicable without further processing for special cases of degeneracy, and it is possible to use in fully integer arithmetic; it can also be vectorized for parallel computation. The major novelty, however, is the extension of the technique to virtually any shape or segment delimiting a planar domain, be it linear, a circular arc, or a higher order curve. Full article

Recently, the fixed-point theorem for fuzzy contractive mappings has been investigated within the framework of intuitionistic fuzzy metric-like spaces. This interesting topic was explored through the utilization of G-Cauchy sequences as defined by Grabiec. The aim of this study is to enhance the aforementioned results in a few aspects. Initially, the proof of the fixed-point theorem is simplified and condensed, allowing for potential generalization to papers focusing on similar fixed-point analyses. Furthermore, instead of G-Cauchy sequences, the classical Cauchy sequences proposed by George and Veeramani are examined, incorporating an additional condition on the fuzzy metric. Within this context, a solution to an old unresolved question posed by Gregory and Sapena is provided. The findings are reinforced by relevant examples. Finally, the introduced fuzzy metrics are applied to the field of image processing. Full article

In free probability, the theory of Cauchy–Stieltjes Kernel (CSK) families has recently been introduced. This theory is about a set of probability measures defined using the Cauchy kernel similarly to natural exponential families in classical probability that are defined by means of the exponential kernel. Within the context of CSK families, this article presents certain features of the Marchenko–Pastur law based on the Fermi convolution and the t-deformed free convolution. The Marchenko–Pastur law holds significant theoretical and practical implications in various fields, particularly in the analysis of random matrices and their applications in statistics, signal processing, and machine learning. In the specific context of CSK families, our study of the Marchenko–Pastur law is summarized as follows: Let ${\mathcal{K}}_{+}(\mu )=\{Q_m^{\mu }(dx);m\in (m_0^{\mu },m_{+}^{\mu })\}$ be the CSK family generated by a non-degenerate probability measure $\mu$ with support bounded from above. Denote by ${\left(Q_m^{\mu }\right)}^{•s}$ the Fermi convolution power of order $s>0$ of the measure $Q_m^{\mu }$. We prove that if ${\left(Q_m^{\mu }\right)}^{•s}\in {\mathcal{K}}_{+}(\mu )$, then $\mu$ is of the Marchenko–Pastur type law. The same result is obtained if we replace the Fermi convolution • with the t-deformed free convolution $\begin{array}{|c|}\hline t\\ \hline\end{array}$. Full article

The paper concerns a nonlinear second-order parabolic evolution equation, one of the well-known objects of mathematical physics, which describes the processes of high-temperature thermal conductivity, nonlinear diffusion, filtration of liquid in a porous medium and some other processes in continuum mechanics. A particular case of it is the well-known porous medium equation. Unlike previous studies, we consider the case of several spatial variables. We construct and study solutions that describe disturbances propagating over a zero background with a finite speed, usually called ‘diffusion-wave-type solutions’. Such effects are atypical for parabolic equations and appear since the equation degenerates on manifolds where the desired function vanishes. The paper pays special attention to exact solutions of the required type, which can be expressed as either explicit or implicit formulas, as well as a reduction of the partial differential equation to an ordinary differential equation that cannot be integrated in quadratures. In this connection, Cauchy problems for second-order ordinary differential equations arise, inheriting the singularities of the original formulation. We prove the existence of continuously differentiable solutions for them. A new example, an analog of the classic example by S.V. Kovalevskaya for the considered case, is constructed. We also proved a new existence and uniqueness theorem of heat-wave-type solutions in the class of piece-wise analytic functions, generalizing previous ones. During the proof, we transit to the hodograph plane, which allows us to overcome the analytical difficulties. Full article

Hyperbolic complete monotonicity property ($\mathrm{HCM}$) is a way to check if a distribution is a generalized gamma ($\mathrm{GGC}$), hence is infinitely divisible. In this work, we illustrate to which extent the Mittag-Leffler functions $E_{\alpha },\alpha \in (0,2]$, enjoy the $\mathrm{HCM}$ property, and then intervene deeply in the probabilistic context. We prove that for suitable $\alpha$ and complex numbers z, the real and imaginary part of the functions $x\mapsto E_{\alpha }\left(zx\right)$, are tightly linked to the stable distributions and to the generalized Cauchy kernel. Full article

The presence of active hydrothermal vent fields near residential areas and their possible link to volcanic activity poses a potential hazard to the environment, society, and the economy. By capitalizing on Autonomous Underwater Vehicle sampling methodologies and applying the Generalized Moments Method model for geological and physical processes in these environments, we shed light on the underlying dynamics shaping the physicochemical characteristics of the vents. In this study, we focus on the Northern Caldera of Santorini and, more specifically, on the recorded CTD data (Conductivity, Temperature, Depth). The data sets were collected in 2017 in Santorini using an Autonomous Underwater Vehicle during the GEOMAR POS510 mission. Our research shows that the active vent field within the caldera probably follows a multifractal behavior and exhibits a weak memory effect. Depth Profiles and Time Series show similar behavior among conductivity and temperature. The variance and moments of both parameters underline the existence of two different mechanisms governing the behavior of the vent field. Finally, the structure function shows that changes in the time series are described by a Cauchy–Lorentz distribution. Full article

With the continuous development and complexity of industrial systems, various types of industrial equipment and systems face increasing risks of failure during operation. Important to these systems is fault warning technology, which can timely detect anomalies before failures and take corresponding preventive measures, thereby reducing production interruptions and maintenance costs, improving production efficiency, and enhancing equipment reliability. Machine learning techniques have proven highly effective for fault detection in modern production processes. Among numerous machine learning algorithms, the generalized neural network stands out due to its simplicity, effectiveness, and applicability to various fault warning scenarios. However, the increasing complexity of systems and equipment presents significant challenges to the generalized neural network. In real-world scenarios, it suffers from drawbacks such as difficulties in determining parameters and getting trapped in local optima, which affect its ability to meet the requirements of high efficiency and accuracy. To overcome these issues, this paper proposes a fault warning method based on an enhanced sand cat swarm optimization algorithm combined with a generalized neural network. First, we develop an enhanced sand cat swarm optimization algorithm that incorporates an improved chaotic mapping initialization strategy, as well as Cauchy mutation and reverse elite strategies based on adaptive selection. Subsequently, we utilize this algorithm to optimize the generalized neural network and determine its optimal parameters, effectively improving the accuracy and reliability of system fault warnings. The proposed method is validated using actual industrial system data, specifically for generator fault warning, and is demonstrated to outperform other advanced fault warning techniques. This research provides valuable insights and promising directions for enhancing industrial fault warning capabilities. Full article

In an emergency situation, fast and efficient logistics and distribution are essential for minimizing the impact of a disaster and for safeguarding property. When selecting a distribution center location, time satisfaction needs to be considered, in addition to the general cost factor. The improved jellyfish search algorithm (CIJS), which simulates the bionics of jellyfish foraging, is applied to solve the problem of an emergency logistics and distribution center site selection model considering time satisfaction. The innovation of the CIJS is mainly reflected in two aspects. First, when initializing the population, the two-level logistic map method is used instead of the original logistic map method to improve the diversity and uniform distribution of the population. Second, in the jellyfish search process, a Cauchy strategy is introduced to determine the moving distance of internal motions, which improves the global search capability and prevents the search from falling into local optimal solutions. The superiority of the improved algorithm was verified by testing 20 benchmark functions and applying them to site selection problems of different dimensions. The performance of the CIJS was compared to that of heuristic algorithms through the iterative convergence graph of the algorithm. The experimental results show that the CIJS has higher solution accuracy and faster solution speed than PSO, the WOA, and JS. Full article