Contemporary Mathematics (Singapore)

This paper introduces the Kolmogorov-Arnold Credit Informed Network Orchestration (KACINO), a novel framework proposed to comprehensively structure and analyze the carbon dynamic system. By synthesizing dynamic processes such as carbon emission and sequestration, a credit information of carbon dynamics is built accumulation, KACINO provides a holistic approach to model the complexities inherent in carbon dynamics. Through systematic analysis and scenario simulations, KACINO facilitates informed policy recommendations aimed at optimizing carbon credit utilization and achieving sustainable environmental outcomes. This paper outlines the theoretical foundation, methodology, and practical applications of KACINO, highlighting its potential to support transformative strategies in climate change mitigation and sustainable development.

Charles Z. Liu

None Farookh Hussain

None Ying Zhang

None Lu Qin

Contemporary Mathematics

Kolmogorov-Arnold Representation Based Informed Orchestration in Solving Partial Differential Equations for Carbon Balance Sustainability

基于Kolmogorov-Arnold表示的智能编排在解决碳平衡可持续性偏微分方程中的应用

We introduce a certain subclass of analytic functions in the open unit disk U involving the q-derivative operator. Some convolution results and Fekete-Szegö inequalities for the analytic functions belonging to this class are derived. We have also provided some results as corollaries of our theorems.

Amnah E. Shammaky

Tamer M. Seoudy

On a General Subclass of &lt;i&gt;q&lt;/i&gt;-Starlike and &lt;i&gt;q&lt;/i&gt;-Convex Analytic Functions

关于一类广义的&lt;i&gt;q&lt;/i&gt;-星形和&lt;i&gt;q&lt;/i&gt;-凸解析函数

Maize plays a significant role in the African diet and is one of the main staple foods in many parts of the continent. Accurate yield estimations ensure an adequate food supply, contributing to food security and reducing the risk of food shortages. They also enable market planning and price setting. Machine learning is well known as one of the most advanced statistical methods for predicting crop yields. This paper provides extensive experiment results of machine learning models on maize production. Thirteen basic supervised learning algorithms classified into classic and ensemble learning are compared using three datasets of different sizes and from various sources (Kaggle, Zenodo). These datasets are from three main origins: experimentation, specifically covering crop data with 240 observations; predictions on crop yield from the FAO (Food and Agriculture Organization) and World Data Bank with 4,121 observations; and historical data from China with 975 observations. The metrics used to evaluate the models are the coefficient of determination, the mean absolute error, the root mean square error, and the explained variance score. Moreover, permutation importance is used on the best models to identify the most relevant predictors for the models according to the data. The results show that extremely randomized trees (ERT) and extreme gradient boosting (XGBoost) are more suitable for predicting maize yield with a coefficient of determination between 0.75 and 0.96 and 0.73 and 0.96, respectively. With the other metrics, the ERT model shows a low performance. Its training time varies between 2,547 and 7,814 seconds as obtained from a computer with characteristics of HP core i5, CPU @ 1.00 GHz, 1.9 GHz, and 8 GB RAM under 134 Windows 10. ERT and XGBoost are best suited to these databases of varying dimensions, making them perfect for predicting maize yield and streamlining decision-making processes.

Souand P.G. Tahi

Castro G. Hounmenou

Vinasetan Ratheil Houndji

Romain Glèlè Kakaï

An Experimental Analysis of Traditional Machine Learning Algorithms for Maize Yield Prediction

基于传统机器学习算法的玉米产量预测实验分析

This work is concerned with the existence of solutions to a nonlinear fractional hybrid thermostat model in the settings of Atangana-Baleanu derivatives. We also consider the boundary conditions of this model in the form of hybrid conditions. Imposing some suitable conditions on the given data, we establish the existence result of continuous solutions based on the Dhage fixed-point theorem in Banach algebra. Moreover, an example is constructed to illustrate our theoretical result.

Kiran Kumar Saha

N. Sukavanam

On the Existence of Solutions to a Fractional Hybrid Thermostat Model

关于分数阶混合恒温器模型解的存在性

In this paper, the controllability of nonlinear impulsive fractional dynamical system with delays in state and control is analyzed by using a delayed Mittag Leffler (M-L) function. Controllability Grammian matrix is used to establish the controllability of linear system. The sufficient conditions of the considered nonlinear system are derived by utilizing the fixed point techniques. Finally, an example is provided for the illustration of the obtained result.

G. Arthi

S. Gopika

Controllability of Impulsive Nonlinear Fractional Dynamical System with Delays in State and Control

具有状态和控制时滞的脉冲非线性分数阶动力系统的可控性

The initial objective of the paper is to propose an explicit relationship between the fractal dimension and fractal numerical integration of curves approximated through fractal interpolation from a discrete set of data points. Once the proposed relation is established, it is shown to be accurate by considering the data points of certain functions. The conventionalbox-counting dimension method has several drawbacks including the proper positioning of the boxes and determining the size of the boxes. The proposed relation becomes significant for such situations in providing the accurate determination of fractal dimension. Secondly, the paper aims to apply the derived relationship in the evaluation of two integral transforms of fractal interpolation functions, namely, the Fourier transform and the Laplace transform. The two integral transforms have been provided with alternate expressions, primarily, using the fractal dimension of fractal interpolation functions. Finally, considering these newly derived expressions and the proposed relation between fractal dimension and fractal numerical integration, this paper provides another method for the evaluation of the two integral transforms. This newly introduced method calculates the two integral transforms, via the fractal numerical integration of fractal interpolation functions.

None M. P. Aparna

None P. Paramanathan

Fractal Dimension Through Numerical Integration of Fractal Interpolation Functions

分形插值函数数值积分中的分形维数

This work examines a mathematical model of diabetes mellitus and its consequences in a population using fractional differential equations. It attempts to solve the problem using a nonstandard way because standard finite difference numerical methods can result in numerical instabilities. The nonstandard finite difference scheme (NSFDS), which satisfies dynamical consistency, is the recommended nonstandard method for discretising the model. To demonstrate the stability of the model at the equilibrium points, analyses of both discrete and continuous models are performed.Stability analysis is carried out at the discretised models equilibrium point using the Schur-Cohn criterion. Consequently, the models asymptotically stable state is demonstrated. Furthermore, by contrasting the stability for various step sizes with conventional techniques like Finite Difference Scheme (FDS), the benefits of the NSFDS are shown. The NSFDS has been shown to converge at bigger step sizes. Furthermore, a graphical comparison is shown between the numerical findings acquired by the NSFDS and the FDS. It is noted that the NSFDS is accurate.

Said Al Kathiri

Farah Aini Abdullah

Nur Nadiah Abd Hamid

Eihab Bashier

Altaf A Bhat

Danish A Sunny

Applications of the Nonstandard Finite Difference Method to a Fractional Model Explaining Diabetes Mellitus and Its Complications

非标准有限差分法在解释糖尿病及其并发症的分数阶模型中的应用

Planar vector fields can be visualized using their tangent lines. It is shown that orthogonality between these curves and their associated orthogonal trajectories can be classified as well-ordered or irregular. Criterion for this taxonomy is the Global Curvature vector (a quantity involving the local curvatures of the two sets of lines) and in particular its rotation, . The latter, which has been termed Geometric Vorticity is an important quantity for the characterization of a two-dimensional vector field. Depending on the kinematical constraints the field is subjected to, can either vanish (well-ordered orthogonality) or not (irregular case). The main theorem of the study asserts that every Laplacian vector field is geometrically irrotational ( = 0) and therefore well-ordered. Conversely, well-ordered orthogonal nets (which are sets of curves admitting zero geometric vorticity) can always be attributed to a Laplacian vector field. The necessary and sufficient condition for this behavior is the harmonicity of their angle function φ (∆φ = 0), which is defined as the angle of incidence of the field lines. This provides a pure geometric criterion a vector field should fulfill, in order to satisfy the Laplace conditions. It connects its “appearance” with its “nature”, thus allowing the experimentalist to study the violation of continuity and irrotationality in physical processes by mere observation.

Ioannis Dimitriou

Geometric Vorticity and the Twofold Nature of Orthogonality

几何涡量与正交性的双重本质

Fullerenes are polyhedral molecules composed solely of carbon atoms, available in various sizes and shapes. These structures can also be depicted as graphs, with the vertices symbolizing the atoms and the edges representing the bonds between them. A fullerene graph is defined as a 3-connected, 3-regular planar graph that consists only of pentagonal and hexagonal faces. This paper examines the perfect 2- and 3-coloring of fullerene graphs, with a particular focus on irreducible fullerenes. The proposed approach begins by obtaining the adjacency matrix of the graphs and then comparing its eigenvalues with those of the parameter matrices. If the eigenvalues of a parameter matrix are a subset of the graph's eigenvalues, we retain these matrices for further analysis to determine their suitability for perfect coloring.

Mehdi Alaeiyan

Mozhgan Keyhani

Murtadha Ali Shabee‏b

Perfect Coloring of Graphs Related to Irreducible Fullerenes in Carbon Structures

与碳结构中不可约富勒烯相关的图的完美着色

Parameters identification algorithms are formulated for the system of equations of Rőssler's type. The problem is solved for the cases of complete and incomplete information about functions of the system. If there is complete information about the state variables, it is possible to apply the algorithms discussed to any system of linear or nonlinear ordinary differential equations of arbitrary order in the Cauchy form that linearly depends on the unknown parameters (or groups of unknown parameters). The problems of parameter identification in the case of incomplete information about the state variables must be solved individually, depending on the possibility (or impossibility) of eliminating unknown steady states from the system of equations. Most real-world problems in fields such as chemical kinetics, mathematical ecology, predator-prey dynamics in game reserves, and the spread of infectious diseases belong to this class of problems, in which the algorithms discussed demonstrate their applicability. In the present paper the case of one unknown function is considered. Lemmas about possibilities on complete and incomplete parameter identification are formulated and proven. The algorithms of the parameter identification are formulated in the process of the constructive proofs of the lemmas. Numerical examples and graphs of solutions are considered which demonstrate efficiency and accuracy of the developed algorithms. In the proposed paper, the integration approach is used instead of the differential approach because it allows for the smoothing of discrete data, thereby reducing the estimation errors of the unknown parameters.

G. T. Sedebo

T. T. Mthombeni

M. Y. Shatalov

A. A. Adeniji

Parameter Identification and Prediction of the Rőssler System with Complete and Incomplete Information: Two Known and One Unknown State Variables

具有完整和不完整信息的Rőssler系统的参数识别与预测：两个已知和一个未知状态变量

Abbreviation
Journal Impact	0.74
Quartiles(Global)	MATHEMATICS, APPLIED(Q4)

Publication Information	Publisher: Universal Wiser Publisher，Publishing cycle: ，Journal Type: journal，Open Access Journals: No
Basic data	Year of publication: 2019，Proportion of original research papers: 96.67%，Self Citation Rate:， Gold OA Rate: 0.00%

Contemporary Mathematics (Singapore)

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