Solution Of Problem Research Articles

Facilitating Students' Cognitive Engagement in Online Asynchronous Discussion Within a Remote English Foreign Language Learning Environment

This study examined the cognitive presence of students in an asynchronous online discussion in the Second Language Acquisition (SLA) course. The course combined synchronous meetings through Zoom sessions to support student participation in asynchronous discussions. The study involved a cohort of 36 participants from the two remote extended campuses of Pattimura University in Maluku. Through content analysis, two key aspects were examined: (1) student participation rates, and (2) the extent of students’ cognitive presence within the discussions. The content analysis findings revealed that although each student made a minimum of two contributions per topic during online asynchronous discussions, they exhibited a moderately high level of cognition, incorporating problem recognition, exploration, integration, and solution, not only in individual messages but also in the overall exchange of information within the discussion thread. These findings suggest that a combination of synchronous meetings through Zoom sessions, tailored prompts, feedback, and social interactions enhances students' active engagement and utilization of cognitive skills in online asynchronous discussions. Keywords: online asynchronous discussion, English foreign language learning, cognitive presence

Advancing nonlinear problem solutions: Newton-like iterative techniques for varied convergence orders using homotopy perturbation

Abstract Iterative methods are crucial in numerical analysis for approximating solutions to nonlinear problems encountered in various fields, such as biomathematics, thermodynamics, chemical engineering, and fluid mechanics. This paper introduces innovative iterative methods of convergence orders three and six to eight, developed using the homotopy perturbation technique (HPT). We address the limitations of traditional derivative-based methods by incorporating divided differences, resulting in derivative-free schemes with optimal convergence properties. We present four newly designed algorithms (HPM1, HPM2, HPM3, and HPM4) and provide a comprehensive convergence analysis. Numerical simulations and basins of attraction demonstrate the superior performance of the proposed methods compared to existing methods of the same order. The proposed methods exhibit faster convergence and larger basins of attraction, making them highly effective for solving nonlinear equations. Our new numerical methods rely on approximations and iterative processes, with each small step bringing us closer to the exact solution. Exploring these numerical methods encourages us to apply mathematics to solve challenging problems in physics, engineering, finance, and more.

Development of Multimedia Teaching Content for Basketball in High School

Background and Aim: In the continuous development of information technology, the global education sector has been greatly impacted by the globalization of information, the application of modern information technology can be seen everywhere, which will profoundly change education. Modern information technology with network and multimedia technology as the core has been applied in physical education teaching in schools and universities. It is necessary to reform and upgrade the traditional education mode and develop multimedia teaching methods. Therefore, this research was to develop multimedia teaching content for basketball in high school, to promote the use of multimedia technology in physical education teaching. Materials and Methods: The survey included 516 students and 35 teachers from 10 high schools in Guangzhou, questionnaire was used to investigate the current situation of basketball teaching. Then, 7 teachers were interviewed to consult the problem solutions, and the indicator contents of multimedia teaching content for basketball in high school was constructed by literature review and content analysis. Through 19 Delphi experts’ consensus, multimedia teaching content for basketball in high school was established. Finally, 9 experts were invited to confirm the developed multimedia teaching content by the Connoisseurship method. In this research, mean, standard deviation and coefficient of variation were used to analyze the data. Results: After two rounds of Delphi method investigation, statistics, and modification, there are 92 indicators suitable for using multimedia in high school basketball teaching content. The content of high school multimedia basketball teaching is designed and includes the origin and development of basketball, sports injuries, and prevention, basic movement of a basketball player, dribble technique, one-handed marching shot, basic movement of a basketball player, basic basketball rules, shoot technique, pass technique, defend technique, breakthrough technique, advanced dribbling, steal technique, zone cooperation, pick and roll and defense, attacking match, fast break and defense, one-on-one check, offensive zone defense. Conclusion: The multimedia teaching content for basketball high school in Guangzhou was effective and appropriate, and can be integrated into the teaching plan.

Multiplicity of solutions for p-Laplacian Kirchhoff problems with singular nonlinearity

In this paper, we prove the existence of solutions for [Formula: see text]-Laplacian Kirchhoff problems with singular nonlinearity. More precisely, we use the Nehari manifold method and the analysis of the fibering maps in order to prove the existence of nonnegative solutions for such problem.

Some Remarks About Forward and Inverse Modelling in Hydrology, Within a General Conceptual Framework

The solution to inverse problems is crucial for model calibration and to provide a good basis for model results to be reliable. This paper is based on a recently proposed conceptual framework for the development and application of mathematical models that require the solution of forward and inverse problems. The focus of this paper is on the discussion of some terminology related to the results of forward problems and their reanalysis, on the use of the proposed framework to revise and generalise some methods of solutions of the inverse problem, and to provide a non-standard insight in some aspects about the Bayesian approach to model calibration.

Stability estimates of Nyström discretizations of Helmholtz decomposition boundary integral equation formulations for the solution of Navier scattering problems in two dimensions with Dirichlet boundary conditions

Abstract Helmholtz decompositions of elastic fields is a common approach for the solution of Navier scattering problems. Used in the context of boundary integral equations (BIE), this approach affords solutions of Navier problems via the simpler Helmholtz boundary integral operators (BIOs). Approximations of Helmholtz Dirichlet-to-Neumann (DtN) can be employed within a regularizing combined field strategy to deliver BIE formulations of the second kind for the solution of Navier scattering problems in two dimensions with Dirichlet boundary conditions, at least in the case of smooth boundaries. Unlike the case of scattering and transmission Helmholtz problems, the approximations of the DtN maps we use in the Helmholtz decomposition BIE in the Navier case require incorporation of lower order terms in their pseudodifferential asymptotic expansions. The presence of these lower order terms in the Navier regularized BIE formulations complicates the stability analysis of their Nyström discretizations in the framework of global trigonometric interpolation and the Kussmaul–Martensen kernel singularity splitting strategy. The main difficulty stems from compositions of pseudodifferential operators of opposite orders, whose Nyström discretization must be performed with care via pseudodifferential expansions beyond the principal symbol. The error analysis is significantly simpler in the case of arclength boundary parametrizations and considerably more involved in the case of general smooth parametrizations that are typically encountered in the description of one-dimensional closed curves.

Self-learning salp swarm algorithm for global optimization and its application in multi-layer perceptron model training

Optimization problems are common across various fields, and one effective solution is the swarm intelligence algorithm.It is essential for the algorithm to deliver high-quality solutions for problems with varying characteristics. However, most existing swarm intelligence rely on fixed and monotonic search strategies, which limits their ability to handle the diverse and complex situations encountered when solving real-world optimization problems with unknown fitness landscapes. To extend the applicability of swarm intelligence and thus offer users an efficient black-box optimizer for various applications, a novel self-learning mechanism is proposed and applied to the Salp Swarm Algorithm (SSA) to develop the self-learning salp swarm algorithm (SLSSA) in this paper. In SLSSA, four distinct search strategies, including a novel multiple food sources search strategy, are adopted to strengthen the search agents’ abilities to conquer various difficulties in the search space. To improve the efficiency of the search process, the self-learning strategy dynamically determines the execution probability of each search strategy according to the quality of solutions it produced previously. Moreover, a parameter setting method is proposed in this paper, which eliminates the need for a trial-and-error approach and allows for straightforward configuration of the parameters that optimize the performance of SLSSA. In comparison with several highly regarded state-of-the-art peer algorithms, the performance of SLSSA in solving the CEC2014 benchmark functions was thoroughly examined. Subsequently, SLSSA was applied to train multi-layer perceptron classifiers and test on the UCI machine-learning datasets. The experimental results and analysis on benchmark functions and multi-layer perceptron classifier training problems demonstrate that SLSSA outperforms the competing algorithms in terms of solution accuracy, stability, and overall convergence speed. Moreover, computational time comparisons reveal that SLSSA achieves significant performance improvement with only a marginal increase in time cost compared to the original SSA.

Sharp estimates of solutions of free boundary problems with nonlocal diffusion

Sharp estimates of solutions of free boundary problems with nonlocal diffusion

Generalized Laplace Transform with Adomian Decomposition Method for Solving Fractional Differential Equations Involving ψ-Caputo Derivative

In this study, we introduced the ψ-Laplace transform Adomian decomposition method, which is a combination of the efficient Adomian decomposition method with the generalization of the classical Laplace transform to treat fractional differential equations with respect to another function, ψ, in the Caputo sense. To validate the effectiveness of this method, we applied the derived recurrent scheme of the ψ-Laplace Adomian decomposition on several test numerical problems, including a real-life scenario in pharmacokinetics that models the movement of drug concentration in human blood. The solutions obtained closely matched the known solutions for the test problems. Additionally, in the pharmacokinetics case, the results were consistent with the available physical data. Consequently, this method simplifies the verification of numerous related aspects and proves advantageous in solving various ψ-fractional differential equations.

Numerical study of the influence of temperature data error on the determination of frictional heat generation

Subject of research: determination of the friction torque and functions of the specific intensity of heat generation in system of sliding bearings. The purpose of the study: To develop a method for determining the friction torque in sliding bearings using temperature data. Based on computational experiments, study the influence of errors in temperature data on the solution of the inverse problem. Methods and object of research: A system of sliding bearings made of a polymer composite material on which a rotating shaft rests is considered. A mathematical model of the thermal process in the considered system of friction units is presented, taking into account the spatial distribution of temperature and its change over time. The temperature is measured at several points in each bearing. Frictional heat generation is determined by solving the inverse heat conduction problem from the condition that the measured and calculated temperatures are close. To ensure continuous data processing and determine the friction torque during long-term tests, the inverse problem of determining the friction torque from temperature data is solved at successive short time intervals. Then the resulting solutions are «glued together». The main results of the study: With such a restoration, the discrepancy between the specified and restored functions of the specific intensity of heat generation is 10–15 % with an error level in temperature data of 10 %. The developed algorithm for solving the inverse problem of thermal conductivity can be used to determine the friction torques in real systems of self-lubricating sliding bearings.

Collective PES Contracts Can Motivate Institutional Creation to Conserve Forests: Experimental Evidence

ABSTRACTIncentives are a widely used tool for addressing deforestation and are often implemented as collective contracts. Local institutions are crucial to the solution of collective action problems associated with forest conservation, but we still have little knowledge of how to encourage institutional creation through policy. Since collective contracts do not eliminate freeriding incentives, we argue that their success hinges on their ability to stimulate the creation of institutions for collective action. To test these ideas, we analyze data from an incentivized lab‐in‐the‐field experimental collective action game played with natural resource users in four developing countries. The experiment simulates management of a common forest, and groups were randomly assigned to a conservation incentive payment condition. We observe how much group members attempt to coordinate on the creation of institutional rules and find experimental evidence that an external incentive program can stimulate the endogenous creation of informal institutions.

Markets of agro-industrial complex products in conditions of geoeconomic fragmentation of the international trade

For decades, international trade has contributed to the reduction of global poverty and the income gap between countries, and the development of intercountry exchange of agricultural products has largely ensured the solution of problems of poverty and food security. At the same time, at the present stage, a high degree of dependence of many developing countries on food imports has occured, while its global exporters have faced a number of restrictions on the supply of their agricultural products. This article analyses the impact of geoeconomic fragmentation of the international trade on the development of exports and imports of products of the agro-industrial complex (hereinafter referred to as AIC). In particular, the problems of competition in the world agro-food markets are discussed in a new context, since the growing problems of monopolisation in certain segments of the AIC disrupt the stability of agricultural markets. Exclusive attention is paid to the key aspects of the application of non-tariff measures in regulating trade of the agricultural products, which, in addition to the protective role, can have a distorting effect on world prices. Our analysis places particular emphasis on the hidden costs of global agri-food systems, which necessitate their rapid modernisation to ensure sustainability in the development of the agricultural markets and to address global food security issues.

The Logic and Application of Greedy Algorithms

Abstract. Being easy to implement and offering faster solutions, the greedy algorithms have widely been used in solving combinatorial optimization problems in computer science and many practical applications, such as resource allocation and data compression. This paper aims at analyzing the definitions, theory, and application of greedy algorithms in computer science as well as their logic and efficacy in numerous situations. In this analysis, concepts such as the greedy choice property and optimal substructure are examined as essential to understanding how greedy algorithms operate. The provided analysis mainly assumes prior knowledge of concepts and problems like the Fractional Knapsack problem and the Shortest Path problem solution as well as some practical problems, for example, resource allocation and the exact coin change problem. Analytical data and real applications are used to analyze the performance of greedy algorithms vis-a-vis other categories, such as the dynamic programming paradigm. The results reveal that greedy algorithms have the potential for great efficiency while also being restricted by certain parameters. They are ideal in the following aspects pertaining to computational aspects, that is, speed, ease of implementation, and applicability to large datasets. But they do not necessarily promise strong optimality in certain situations. The conclusion notes that greedy algorithms deserve further applications when the specified conditions are met and states that the effectiveness of these conditions needs to be studied.

Equilibria of large random Lotka-Volterra systems with vanishing species: a mathematical approach.

Ecosystems with a large number of species are often modelled as Lotka-Volterra dynamical systems built around a large interaction matrix with random part. Under some known conditions, a global equilibrium exists and is unique. In this article, we rigorously study its statistical properties in the large dimensional regime. Such an equilibrium vector is known to be the solution of a so-called Linear Complementarity Problem. We describe its statistical properties by designing an Approximate Message Passing (AMP) algorithm, a technique that has recently aroused an intense research effort in the fields of statistical physics, machine learning, or communication theory. Interaction matrices based on the Gaussian Orthogonal Ensemble, or following a Wishart distribution are considered. Beyond these models, the AMP approach developed in this article has the potential to describe the statistical properties of equilibria associated to more involved interaction matrix models.

Конструктивные алгоритмы автоматизированного решения позиционных задач

This paper presents the theoretical foundations for an approach to automated solutions of positional problems involving intersections of geometric objects in Euclidean space. A conceptual framework is developed based on concepts and definitions related to the equivalence relation known in set theory. This framework includes: an equivalence relation defined on the set of geometric objects in Euclidean space; the dimension and factorization of the object set, represented as a collection of equivalence classes; and the projected factor set of space. A set-theoretic basis for representing the projection operation is provided, enabling the development of constructive algorithms to solve positional problems involving intersections of spatial geometric objects. These algorithms have been implemented within the KOMPAS-3D CAD environment. The theoretical foundations and analysis of the algorithm functionality establish definitions for "geometric modeling" and "3D modeling." The proposed approach to automating positional problem solutions essentially constitutes a 3D model of these solutions through the creation of a virtual model. The paper includes examples of automated 3D solutions to intersection problems, descriptions of the algorithms used in their design, and examples of practical applications of these algorithms.

Primary healthcare as a strategy for eliminating hepatitis C: the METRIC toolkit.

This paper presents the development of the METRIC toolkit, aimed at enhancing primary healthcare interventions in the context of hepatitis C control, thus contributing to the World Health Organization's global strategy to achieve the elimination of the disease by 2030. At the global level, most people living with hepatitis C are unaware of their condition. As such, the eradication of hepatitis C necessitates comprehensive strategies within primary healthcare settings, as it provides an opportunity to reach the general population, facilitates the identification of potential patients who may be unfamiliar with hepatitis C, and guides them toward adequate care. Herein, we propose the METRIC toolkit as a means to optimize the efficiency and efficacy of healthcare services dedicated to hepatitis C control. The development of the METRIC toolkit was guided by a thorough review of pertinent literature, focusing on primary healthcare interventions in hepatitis C control. Key components were identified, encompassing systematic problem identification, solution formulation, outcome evaluation, and feedback integration. The METRIC toolkit represents a valuable resource for strengthening primary healthcare interventions in hepatitis C control. By fostering a culture of continuous improvement and data-driven decision-making, this framework holds promise in advancing the global agenda towards hepatitis C elimination. However, its successful application requires careful consideration of contextual factors and ongoing adaptation to local needs and circumstances.

Reduced basis method for the elastic scattering by multiple shape-parametric open arcs in two dimensions

We consider the elastic scattering problem by multiple disjoint arcs or cracks in two spatial dimensions. A key aspect of our approach lies in the parametric description of each arc's shape, which is controlled by a potentially high-dimensional, possibly countably infinite, set of parameters. We are interested in the efficient approximation of the parameter-to-solution map employing model order reduction techniques, specifically the reduced basis method. Initially, we utilize boundary potentials to transform the boundary value problem, originally posed in an unbounded domain, into a system of boundary integral equations set on the parametrically defined open arcs. Our aim is to construct a rapid surrogate for solving this problem. To achieve this, we adopt the two-phase paradigm of the reduced basis method. In the offline phase, we compute solutions for this problem under the assumption of complete decoupling among arcs for various shapes. Leveraging these high-fidelity solutions and Proper Orthogonal Decomposition (POD), we construct a reduced-order basis tailored to the single arc problem. Subsequently, in the online phase, when computing solutions for the multiple arc problem with a new parametric input, we utilize the aforementioned basis for each individual arc. To expedite the offline phase, we employ a modified version of the Empirical Interpolation Method (EIM) to compute a precise and cost-effective affine representation of the interaction terms between arcs. Finally, we present a series of numerical experiments demonstrating the advantages of our proposed method in terms of both accuracy and computational efficiency.

Qualitative analysis of fourth-order hyperbolic equations

We investigate the qualitative properties of weak solutions to the boundary value problems for fourth-order linear hyperbolic equations with constant coefficients in a plane bounded domain convex with respect to characteristics. Our main scope is to prove some analog of the maximum principle, solvability, uniqueness and regularity results for weak solutions of initial and boundary value problems in the space L2. The main novelty of this paper is to establish some analog of the maximum principle for fourth-order hyperbolic equations. This question is very important due to natural physical interpretation and helps to establish the qualitative properties for solutions (uniqueness and existence results for weak solutions). The challenge to prove the maximum principle for weak solutions remains more complicated and at that time becomes more interesting in the case of fourth-order hyperbolic equations, especially, in the case of non-classical boundary value problems with data of weak regularity. Unlike second-order equations, qualitative analysis of solutions to fourth-order equations is not a trivial problem, since not only a solution is involved in boundary or initial conditions, but also its high- order derivatives. Other difficulty concerns the concept of weak solution of the boundary value problems with L2 – data. Such solutions do not have usual traces, thus, we have to use a special notion for traces to poss correctly the boundary value problems. This notion is traces associated with operator L or L-traces. We also derive an interesting interpretation (as periodicity of characteristic billiard or the John's mapping) of the Fredholm's property violation. Finally, we discuss some potential challenges in applying the results and proposed methods.

Application of iron oxide and its composites containing carbon nanoparticles to the solution of environmental problems

The radioactive materials and the secondary waste after a nuclear power plant accident pose a big environmental problem. The nontoxic iron oxide and iron oxyhydroxide, and their composites with carbon materials were applied to solve the problem. Coal oxide produced by modified Brodie method using coal, NaOH, and γ-Fe2O3 were treated by a hydrothermal process. When the diluted dispersion mixture was treated with SrCl2, the composite particles were attracted to a magnet. On the other hand, the composite without SrCl2 was not attracted. This means only the SrCl2-adsorbed composite can be recovered by a magnet. Hematite doped with various amounts of Nb was synthesized. Its catalytic activities for photo-Fenton reaction were investigated for degradation of methylene blue (MB) in the presence of H2O2 under visible light. Nb-doped hematite calcined at 600 ºC produced smaller particles and showed higher catalytic activity than those calcined at 700 ºC. It was shown that the sample with higher Nb doping showed a better catalytic activity, i.e., the sample with 40 atomic percent of Nb calcined at 600 ºC has the highest catalytic activity. The hematite with 7.4 atomic percent of Nb calcined at 600 ºC showed unique characteristics since it has rapid decomposition rate of MB as well as ferrimagnetic-like characteristics, which makes it separable by a magnet. The polymorphism of iron(III) oxyhydroxide was controlled by adding acetic acid, ethylenediamine, and citric acid. The lepidocrocite obtained by adding the additive of citric acid resulted in the presence of citric acid in the particles and revealed a large specific surface area and negative Zeta potential, which showed an extremely high catalytic activity of MB decomposition for photo-Fenton reaction.

The Different Approach of Solution for Multi-objective Fractional Programming Problems Under Fuzzy Environment

The Different Approach of Solution for Multi-objective Fractional Programming Problems Under Fuzzy Environment