<abstract>
<title style='display:none'>Abstract</title>
This paper proposes a mathematical model of multiple regression analysis of basketball shooting percentage. We give the numerical solution for the shooting angle under given solution conditions by solving the equation. From this, the optimal shooting speed and cut-off shooting speed under the shooting at a given point are obtained. At the same time, we analyze the laws of basketball movement in several different forms of rotation. The article combines Matlab software for verification to get the best angle of entry and the best shooting distance and speed.
</abstract>

Basketball Shooting Rate Based on Multiple Regression Logical-Mathematical Algorithm

<abstract><title style='display:none'>Abstract</title>In the paper we present results of accuracy evaluation of numerous numerical algorithms for the numerical approximation of the Inverse Laplace Transform. The selected algorithms represent diverse lines of approach to this problem and include methods by Stehfest, Abate and Whitt, Vlach and Singhai, De Hoog, Talbot, Zakian and a one in which the FFT is applied for the Fourier series convergence acceleration. We use C++ and Python languages with arbitrary precision mathematical libraries to address some crucial issues of numerical implementation. The test set includes Laplace transforms considered as difficult to compute as well as some others commonly applied in fractional calculus. Evaluation results enable to conclude that the Talbot method which involves deformed Bromwich contour integration, the De Hoog and the Abate and Whitt methods using Fourier series expansion with accelerated convergence can be assumed as general purpose high-accuracy algorithms. They can be applied to a wide variety of inversion problems.</abstract>

Review of numerical methods for NumILPT with computational accuracy assessment for fractional calculus

<abstract><title style='display:none'>Abstract</title>In computational chemistry, the molecular structures are modelled as graphs which are called the molecular graphs. In these graphs, each vertex represents an atom and each edge denotes covalent bound between atoms. It is shown that the topological indices defined on the molecular graphs can reflect the chemical characteristics of chemical compounds and drugs. In this paper, we report several degree based indices of some widely used chemical molecular structures by means of edge dividing technology.</abstract>

Degree-based indices computation for special chemical molecular structures using edge dividing method

<abstract><title style='display:none'>Abstract</title>In this paper we study a nonlinear multi-dimensional partial differential equation, namely, a generalized second extended (3+1)-dimensional Jimbo-Miwa equation. We perform symmetry reductions of this equation until it reduces to a nonlinear fourth-order ordinary differential equation. The general solution of this ordinary differential equation is obtained in terms of the Weierstrass zeta function. Also travelling wave solutions are derived using the simplest equation method. Finally, the conservation laws of the underlying equation are computed by employing the conservation theorem due to Ibragimov, which include conservation of energy and conservation of momentum laws.</abstract>

Solutions and conservation laws of a generalized second extended (3+1)-dimensional Jimbo-Miwa equation

<abstract><title style='display:none'>Abstract</title>In this paper, we use a time splitting method with higher-order accuracy for the solutions (in space variables) of a class of two-dimensional semi-linear parabolic equations. Galerkin-Chebyshev pseudo spectral method is used for discretization of the spatial derivatives, and implicit Euler method is used for temporal discretization. In addition, we use this novel method to solve the well-known semi-linear Poisson-Boltzmann (PB) model equation and obtain solutions with higher-order accuracy. Furthermore, we compare the results obtained by our method for the semi-linear parabolic equation with the available analytical results in the literature for some special cases, and found excellent agreement. Furthermore, our new technique is also applicable for three-dimensional problems.</abstract>

Galerkin-Chebyshev Pseudo Spectral Method and a Split Step New Approach for a Class of Two dimensional Semi-linear Parabolic Equations of Second Order

<abstract><title style='display:none'>Abstract</title>In this paper we study a (2+1)-dimensional coupling system with the Korteweg-de Vries equation, which is associated with non-semisimple matrix Lie algebras. Its Lax-pair and bi-Hamiltonian formulation were obtained and presented in the literature. We utilize Lie symmetry analysis along with the (<italic>G</italic>′/<italic>G</italic>)–expansion method to obtain travelling wave solutions of this system. Furthermore, conservation laws are constructed using the multiplier method.</abstract>

Travelling waves and conservation laws of a (2+1)-dimensional coupling system with Korteweg-de Vries equation

<abstract>
<title style='display:none'>Abstract</title>
The enhancement of children’s education quality necessitates a high level of teacher moral literacy. This paper employs data mining techniques to elaborate on the Classification and Regression Tree (CART) model within logistic regression and decision tree algorithms. Data pertinent to elementary school education were collected via questionnaires, followed by data cleaning and segmentation. The parameters of the CART model were optimized using a Bayesian algorithm, and its efficacy was validated through a dataset to support the exploration of factors influencing the developmental level of children’s education. Additionally, data regarding teachers’ moral literacy were gathered and analyzed using binary logistic regression within the logistic regression framework. The analysis revealed that the accuracy of the CART decision tree model reached 90%, with the error converging to zero at 50 trees. Key determinants such as willpower and communication abilities in children’s education were influenced by exercise duration, time spent in interest classes, gender, and parents’ educational levels. The mean score for teachers’ moral literacy was 4.349±0.465. Notably, teachers with low salary satisfaction exhibited a moral literacy level that was only 0.517 times that of their counterparts with high salary satisfaction. Establishing a scientifically sound and reasonable salary management system is crucial. Such a system can ignite teachers’ enthusiasm for teaching, substantially enhancing their moral literacy, which in turn positively impacts the level of children’s educational development.
</abstract>

A Perspective on the Current Situation of Children’s Education and Teachers’ Moral Cultivation Combined with Decision Tree Algorithm

<abstract>
<title style='display:none'>Abstract</title>
With the development of informatization and digitalization, the transformation of intelligent manufacturing has become the focus. This paper builds an evaluation system based on the scientific evaluation method of the development level of smart manufacturing and the real demand situation. It establishes an evaluation model of intelligent manufacturing MES systems by combining the GA-BP algorithm. Then, a SeqGAN generative adversarial network is used to expand the real samples. The evaluation model was trained and validated by constructing a training model through the BP neural network, taking the sample data of evaluation indexes as the network input and the seven labels from Industry 1.0 to Industry 4.0 as the network output. The results show that the classification accuracy of the model is above 98%, and all of them have achieved good results. In the actual case evaluation, it is judged that the intelligent manufacturing MES system of Company Z is in the range of industry 3.0 to 3.5, and this result is very close to the manual evaluation of the factory field survey. The synthesis shows that the model is reasonable and effective and has important guiding significance for the evaluation of enterprise intelligent manufacturing MES systems.
</abstract>

Research on evaluation system and method of MES system for intelligent manufacturing

<abstract>
<title style='display:none'>Abstract</title>
The combination of VR technology and art exhibition promotes a new form of art exhibition and enriches the multi-sensory experience of visitors. After analyzing the development form of VR art exhibition and the design process of VR art exhibition, this paper puts forward the solution countermeasures of using the sparse 3D map to optimize the presentation of virtual reality visualization scene, refining the 3D scene model and improving the presentation of the surface scene based on the Possion reconstruction for the lack of development of interactive experience in VR art exhibition. As well as based on the dimensions of interactive experiences, Kinect somatosensory interaction technology is used to update the interactive experience design in VR art exhibition planning. Explore the optimization effect of VR art exhibition planning, analyze the visitors’ interactive experience task completion time, participation, and interactive experience degree, and put forward effective countermeasures for the future development of VR art exhibitions. The mean value of scores of VR exhibitions and offline exhibitions are 5.887 and 5.657, respectively, with a difference of 0.23 and a total score difference of 2.07, which indicates that the art exhibition constructed on the basis of VR has a better sense of experience.
</abstract>

Application and Challenges of Virtual Reality (VR) in Art Exhibition Planning

<abstract>
<title style='display:none'>Abstract</title>
In the contemporary digital economy, digital trade barriers have emerged as significant external risks for enterprises engaging in international business despite the digital economy’s role as a critical driver of international commerce. This study examines the relationship between digital trade barriers and international business through a theoretical model, investigating the influence mechanisms of digital trade barriers alongside other factors. Utilizing data from several countries spanning from 2015 to 2022, this research employs correlation analysis, benchmark regression, and robustness tests within a constructed benchmark regression model to explore the impact of digital trade barriers on international business. The findings indicate a significant negative correlation between digital trade barriers and international commerce, with a 1% increase in the trade restriction index of digital services resulting in a 0.217% decrease in international commerce (p&lt;0.01). Additionally, while R&amp;D intensity and total trade have positive effects on the development of international commerce, trade openness appears to have a negative impact. Given these results, it is recommended that governments enhance the construction of digital service trade systems and actively engage in the formulation and convergence of international regulations. Simultaneously, enterprises should elevate their technological capabilities related to digitization to effectively navigate and mitigate the impacts of digital trade barriers.
</abstract>

Research on the Impact of Digital Trade Barriers on International Business and Countermeasures

<abstract>
<title style='display:none'>Abstract</title>
The core of translation is language conversion, but it should be more of an aesthetic experience, a transformation of different ways of thinking. This paper proposes a neural semantic analysis method for English translation based on text similarity calculation. The technique uses a large-scale corpus to train the vector space model of words, establishes a concept-context matrix through the term-document matrix, and determines each value of the concept vector with a weight according to the literary translation in the knowledge base. The information extraction and evaluation of the English-translated text through semantic similarity calculation provides a theoretical basis for the subsequent analysis of style conversion and linguistic, and aesthetic reproduction of the English-translated text. The study will take the Lin Yutang translation and the Ricardian translation of The Analects of Confucius as an example to develop the analysis of style transformation and reproduction of linguistic beauty of the English-translated text from both lexical and syntactic levels. The results show that the lexical density of Lin Yutang’s translation is 0.5866, while that of Rie Jacob’s translation is 0.5334, with the former significantly larger than the latter. It shows that Lin Yutang’s translation of The Analects of Confucius adopts a naturalization strategy, i.e., To disseminate Chinese culture in a way that is authentic, familiar to English readers, and easy to understand, so as to make his linguistic expression more emotional.
</abstract>

Stylistic Conversion and Linguistic Beauty Reproduction in English Translation-Based on Neurosemantic Analysis

<abstract>
<title style='display:none'>Abstract</title>
In this paper, texture mapping technology is utilized to enhance the virtual reality piano teaching situation, and the piano classroom teaching data is integrated through big data statistical analysis methods. A deep neural network based on BERT+BiLSTM+CRF is used to train a named entity recognition model and complete the construction of a knowledge graph for piano subject data. Then, deep learning methods are used to extract the piano subject data and construct a visualized knowledge graph for the piano subject. Analyze the use of the Piano Smart Classroom teaching platform and the development of a blended teaching mode. The design requirements of the piano intelligent teaching platform are planned from two aspects: platform user roles and platform use cases, and the overall design of the piano intelligent teaching platform is carried out. The use of piano teaching video samples is a tool for calculating the teaching language ratio, analyzing the teaching interactions between teachers and students, and comparing the number of interactions between traditional teaching and smart classroom teaching. Analyze the effectiveness of piano-smart classroom teaching in three dimensions: cognition, emotion, and skill. The mean value of the specific content score of piano intelligent classroom teaching is 3.82, which is the single item with the highest mean value, and the piano teaching classroom supported by smart technology can show the piano teaching content more comprehensively.
</abstract>

Practical Exploration of Smart Classroom in Piano Teaching

<abstract><title style='display:none'>Abstract</title>In this paper, our aim is to generalize the truncated M-fractional derivative which was recently introduced [Sousa and de Oliveira, A new truncated M-fractional derivative type unifying some fractional derivative types with classical properties, Inter. of Jour. Analy. and Appl., 16 (1), 83–96, 2018]. To do that, we used generalized M-series, which has a more general form than Mittag-Leffler and hypergeometric functions. We called this generalization as truncated ℳ-series fractional derivative. This new derivative generalizes several fractional derivatives and satisfies important properties of the integer-order derivatives. Finally, we obtain the analytical solutions of some ℳ-series fractional differential equations.</abstract>

A generalization of truncated M-fractional derivative and applications to fractional differential equations

<abstract>
<title style='display:none'>Abstract</title>
In this study, we present some new results for the time fractional mixed boundary value problems. We consider a generalization of the Heat - conduction problem in two dimensions that arises during the manufacturing of p - n junctions. Constructive examples are also provided throughout the paper. The main purpose of this article is to present mathematical results that are useful to researchers in a variety of fields.
</abstract>

Complete Solution For The Time Fractional Diffusion Problem With Mixed Boundary Conditions by Operational Method

<abstract>
<title style='display:none'>Abstract</title>
In this manuscript, the application of the extended sinh-Gordon equation expansion method to the Davey-Stewartson equation and the (2+1)-dimensional nonlinear complex coupled Maccari system is presented. The Davey-Stewartson equation arises as a result of multiple-scale analysis of modulated nonlinear surface gravity waves propagating over a horizontal seabed and the (2+1)-dimensional nonlinear complex coupled Maccari equation describes the motion of the isolated waves, localized in a small part of space, in many fields such as hydrodynamic, plasma physics, nonlinear optics. We successfully construct some soliton, singular soliton and singular periodic wave solutions to these two nonlinear complex models. The 2D, 3D and contour graphs to some of the obtained solutions are presented.
</abstract>

On the exact solutions to some system of complex nonlinear models

Editorial for papers to honor the memory of Professor Anatole M.Stepin 1940-2020

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 Applied Mathematics and Nonlinear Sciences has been classified in the 3rd place with the result of 2.7 JCI metrics in Mathematics, Applied Category...