Rosa Maza-Quiroga, Karl Thurnhofer-Hemsi, Domingo López-Rodríguez, Ezequiel López-Rubio
This paper investigates the distribution characteristics of Fourier, discrete cosine, and discrete sine transform coefficients in T1 MRI images. This paper reveals their adherence to Benford’s law, characterized by a logarithmic distribution of first digits. The impact of Rician noise on the first digit distribution is examined, which causes deviations from the ideal distribution. A novel methodology is proposed for noise level estimation, employing metrics such as the Bhattacharyya distance, Kullback–Leibler divergence, total variation distance, Hellinger distance, and Jensen–Shannon divergence. Supervised learning techniques utilize these metrics as regressors. Evaluations on MRI scans from several datasets coming from a wide range of different acquisition devices of 1.5 T and 3 T, comprising hundreds of patients, validate the adherence of noiseless T1 MRI frequency domain coefficients to Benford’s law. Through rigorous experimentation, our methodology has demonstrated competitiveness with established noise estimation techniques, even surpassing them in numerous conducted experiments. This research empirically supports the application of Benford’s law in transforms, offering a reliable approach for noise estimation in denoising algorithms and advancing image quality assessment.
本文研究了 T1 MRI 图像中傅立叶、离散余弦和离散正弦变换系数的分布特征。本文揭示了它们遵循本福德定律的情况，即首位数字呈对数分布。本文研究了里森噪声对首位数字分布的影响，这种噪声会导致首位数字偏离理想分布。利用巴塔查里亚距离、库尔贝克-莱布勒发散、总变异距离、海林格距离和詹森-香农发散等指标，提出了一种用于噪声水平估计的新方法。监督学习技术利用这些指标作为回归因子。对来自 1.5 T 和 3 T 不同采集设备的多个数据集（包括数百名患者）的磁共振成像扫描进行评估，验证了无噪声 T1 磁共振成像频域系数与本福德定律的一致性。通过严格的实验，我们的方法证明了与现有噪声估计技术的竞争力，甚至在大量实验中超过了它们。这项研究从经验上支持了本福德定律在变换中的应用，为去噪算法中的噪声估计提供了一种可靠的方法，并推进了图像质量评估。
{"title":"Regression of the Rician Noise Level in 3D Magnetic Resonance Images from the Distribution of the First Significant Digit","authors":"Rosa Maza-Quiroga, Karl Thurnhofer-Hemsi, Domingo López-Rodríguez, Ezequiel López-Rubio","doi":"10.3390/axioms12121117","DOIUrl":"https://doi.org/10.3390/axioms12121117","url":null,"abstract":"This paper investigates the distribution characteristics of Fourier, discrete cosine, and discrete sine transform coefficients in T1 MRI images. This paper reveals their adherence to Benford’s law, characterized by a logarithmic distribution of first digits. The impact of Rician noise on the first digit distribution is examined, which causes deviations from the ideal distribution. A novel methodology is proposed for noise level estimation, employing metrics such as the Bhattacharyya distance, Kullback–Leibler divergence, total variation distance, Hellinger distance, and Jensen–Shannon divergence. Supervised learning techniques utilize these metrics as regressors. Evaluations on MRI scans from several datasets coming from a wide range of different acquisition devices of 1.5 T and 3 T, comprising hundreds of patients, validate the adherence of noiseless T1 MRI frequency domain coefficients to Benford’s law. Through rigorous experimentation, our methodology has demonstrated competitiveness with established noise estimation techniques, even surpassing them in numerous conducted experiments. This research empirically supports the application of Benford’s law in transforms, offering a reliable approach for noise estimation in denoising algorithms and advancing image quality assessment.","PeriodicalId":53148,"journal":{"name":"Axioms","volume":"28 11","pages":""},"PeriodicalIF":2.0,"publicationDate":"2023-12-13","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"139004886","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Junchi Ma, Bart Wiegmans, Xifu Wang, Kai Yang, Lijun Jiang
Inland ports are gaining more and more attention as important hubs for inland cities to promote foreign trade. However, studies on the evaluation of inland ports are lacking. In this work, we aim to construct an index system and propose a multi-criteria group decision-making method to comprehensively evaluate the development of inland ports. Unlike previous studies, using pressure–state–response model as a reference, we built up a demand–risk–power–potential framework for the index system proposed in this study. To determine the different weights for each indicator, which is a typical multi-criteria decision-making problem, we innovatively combined the decision-making trial and evaluation laboratory (DEMATEL) and the Bayesian best–worst method (BBWM) based on their distinct advantages in dealing with data coupling and group decision-making. In addition, this work introduces a case study of inland ports in the Huaihai Economy Zone to validate the efficacy of the proposed evaluation model and method. After calculating and obtaining the comprehensive scores and rankings of each inland port in this case, we compared the evaluation results with those under the BBWM, TOPSIS, and CRITIC methodologies, and found that the results under the DEMATEL–BBWM methodology can provide better differentiation for inland port evaluation results. Moreover, based on the evaluation results, a performance–importance matrix is formulated to identify the areas requiring attention in the development process of each inland port. Subsequently, rational managerial insights are put forward to achieve the sustainable development of inland ports in the Huaihai Economy Zone.
{"title":"A Hybrid DEMATEL and Bayesian Best–Worst Method Approach for Inland Port Development Evaluation","authors":"Junchi Ma, Bart Wiegmans, Xifu Wang, Kai Yang, Lijun Jiang","doi":"10.3390/axioms12121116","DOIUrl":"https://doi.org/10.3390/axioms12121116","url":null,"abstract":"Inland ports are gaining more and more attention as important hubs for inland cities to promote foreign trade. However, studies on the evaluation of inland ports are lacking. In this work, we aim to construct an index system and propose a multi-criteria group decision-making method to comprehensively evaluate the development of inland ports. Unlike previous studies, using pressure–state–response model as a reference, we built up a demand–risk–power–potential framework for the index system proposed in this study. To determine the different weights for each indicator, which is a typical multi-criteria decision-making problem, we innovatively combined the decision-making trial and evaluation laboratory (DEMATEL) and the Bayesian best–worst method (BBWM) based on their distinct advantages in dealing with data coupling and group decision-making. In addition, this work introduces a case study of inland ports in the Huaihai Economy Zone to validate the efficacy of the proposed evaluation model and method. After calculating and obtaining the comprehensive scores and rankings of each inland port in this case, we compared the evaluation results with those under the BBWM, TOPSIS, and CRITIC methodologies, and found that the results under the DEMATEL–BBWM methodology can provide better differentiation for inland port evaluation results. Moreover, based on the evaluation results, a performance–importance matrix is formulated to identify the areas requiring attention in the development process of each inland port. Subsequently, rational managerial insights are put forward to achieve the sustainable development of inland ports in the Huaihai Economy Zone.","PeriodicalId":53148,"journal":{"name":"Axioms","volume":"23 12","pages":""},"PeriodicalIF":2.0,"publicationDate":"2023-12-13","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"139004972","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
J. Sánchez-Pérez, Joaquín Solano-Ramírez, Enrique Castro, M. Conesa, Fulgencio Marín-García, G. García-Ros
The Burgers–Huxley equation is important because it involves the phenomena of accumulation, drag, diffusion, and the generation or decay of species, which are common in various problems in science and engineering, such as heat transmission, the diffusion of atmospheric contaminants, etc. On the other hand, the mathematical technique of nondimensionalisation has proven to be very useful in the appropriate grouping of the variables involved in a physical–chemical phenomenon and in obtaining universal solutions to different complex engineering problems. Therefore, a deep analysis using this technique of the Burgers–Huxley equation and its possible boundary conditions can facilitate a common understanding of these problems through the appropriate grouping of variables and propose common universal solutions. Thus, in this case, the technique is applied to obtain a universal solution for Dirichlet and symmetric boundary conditions. The validation of the methodology is carried out by comparing different cases, where the coefficients or the value of the boundary condition are varied, with the results obtained through a numerical simulation. Furthermore, one of the cases presented presents a boundary condition that changes at a certain time. Finally, after applying the technique, it is studied which phenomenon is predominant, concluding that from a certain value diffusion predominates, with the rest being practically negligible.
{"title":"Analysis of the Burgers–Huxley Equation Using the Nondimensionalisation Technique: Universal Solution for Dirichlet and Symmetry Boundary Conditions","authors":"J. Sánchez-Pérez, Joaquín Solano-Ramírez, Enrique Castro, M. Conesa, Fulgencio Marín-García, G. García-Ros","doi":"10.3390/axioms12121113","DOIUrl":"https://doi.org/10.3390/axioms12121113","url":null,"abstract":"The Burgers–Huxley equation is important because it involves the phenomena of accumulation, drag, diffusion, and the generation or decay of species, which are common in various problems in science and engineering, such as heat transmission, the diffusion of atmospheric contaminants, etc. On the other hand, the mathematical technique of nondimensionalisation has proven to be very useful in the appropriate grouping of the variables involved in a physical–chemical phenomenon and in obtaining universal solutions to different complex engineering problems. Therefore, a deep analysis using this technique of the Burgers–Huxley equation and its possible boundary conditions can facilitate a common understanding of these problems through the appropriate grouping of variables and propose common universal solutions. Thus, in this case, the technique is applied to obtain a universal solution for Dirichlet and symmetric boundary conditions. The validation of the methodology is carried out by comparing different cases, where the coefficients or the value of the boundary condition are varied, with the results obtained through a numerical simulation. Furthermore, one of the cases presented presents a boundary condition that changes at a certain time. Finally, after applying the technique, it is studied which phenomenon is predominant, concluding that from a certain value diffusion predominates, with the rest being practically negligible.","PeriodicalId":53148,"journal":{"name":"Axioms","volume":"8 10","pages":""},"PeriodicalIF":2.0,"publicationDate":"2023-12-11","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"138980866","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Nikola Kadoić, Nina Begičević Ređep, Dragana Kupres
Creating policy measures is the final step in the process of e-learning roadmap development. Policy measures can be seen as long-term activities that need to be implemented and constantly upgraded to achieve strategic goals. For resource allocation, it is useful to prioritize policy measures. Prioritization can be implemented using multi-criteria decision-making methods. This paper analyzes policy measures in the Maldives National University’s e-learning roadmap using the social network analysis process (SNAP), which includes the analytic hierarchy process (AHP), the decision-making trial and evaluation laboratory (DEMATEL), and the PageRank centrality. In policy measure evaluation, there were more than 20 participants: persons with managerial functions at the Maldives National University (MNU) (deans, heads of departments) and persons in lecturer and researcher positions. By using the AHP, participants prioritized policy measures with respect to their importance to them. By using the DEMATEL, participants identified and prioritized policy measures with respect to their effect on other measures. Finally, by using the SNAP, it was possible to determine the prioritization list for resource allocation since it aggregates the aspects of the policy measures, their importance, and their effect on other measures.
{"title":"Using SNAP to Analyze Policy Measures in e-Learning Roadmaps","authors":"Nikola Kadoić, Nina Begičević Ređep, Dragana Kupres","doi":"10.3390/axioms12121110","DOIUrl":"https://doi.org/10.3390/axioms12121110","url":null,"abstract":"Creating policy measures is the final step in the process of e-learning roadmap development. Policy measures can be seen as long-term activities that need to be implemented and constantly upgraded to achieve strategic goals. For resource allocation, it is useful to prioritize policy measures. Prioritization can be implemented using multi-criteria decision-making methods. This paper analyzes policy measures in the Maldives National University’s e-learning roadmap using the social network analysis process (SNAP), which includes the analytic hierarchy process (AHP), the decision-making trial and evaluation laboratory (DEMATEL), and the PageRank centrality. In policy measure evaluation, there were more than 20 participants: persons with managerial functions at the Maldives National University (MNU) (deans, heads of departments) and persons in lecturer and researcher positions. By using the AHP, participants prioritized policy measures with respect to their importance to them. By using the DEMATEL, participants identified and prioritized policy measures with respect to their effect on other measures. Finally, by using the SNAP, it was possible to determine the prioritization list for resource allocation since it aggregates the aspects of the policy measures, their importance, and their effect on other measures.","PeriodicalId":53148,"journal":{"name":"Axioms","volume":"88 3","pages":""},"PeriodicalIF":2.0,"publicationDate":"2023-12-11","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"138978580","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Fahd Masood, O. Moaaz, Ghada AlNemer, H. El-Metwally
This paper delves into the investigation of quasi-linear neutral differential equations in the third-order canonical case. In this study, we refine the relationship between the solution and its corresponding function, leading to improved preliminary results. These enhanced results play a crucial role in excluding the existence of positive solutions to the investigated equation. By building upon the improved preliminary results, we introduce novel criteria that shed light on the nature of these solutions. These criteria help to distinguish whether the solutions exhibit oscillatory behavior or tend toward zero. Moreover, we present oscillation criteria for all solutions. To demonstrate the relevance of our results, we present an illustrative example. This example validates the theoretical framework we have developed and offers practical insights into the behavior of solutions for quasi-linear third-order neutral differential equations.
{"title":"More Effective Criteria for Testing the Asymptotic and Oscillatory Behavior of Solutions of a Class of Third-Order Functional Differential Equations","authors":"Fahd Masood, O. Moaaz, Ghada AlNemer, H. El-Metwally","doi":"10.3390/axioms12121112","DOIUrl":"https://doi.org/10.3390/axioms12121112","url":null,"abstract":"This paper delves into the investigation of quasi-linear neutral differential equations in the third-order canonical case. In this study, we refine the relationship between the solution and its corresponding function, leading to improved preliminary results. These enhanced results play a crucial role in excluding the existence of positive solutions to the investigated equation. By building upon the improved preliminary results, we introduce novel criteria that shed light on the nature of these solutions. These criteria help to distinguish whether the solutions exhibit oscillatory behavior or tend toward zero. Moreover, we present oscillation criteria for all solutions. To demonstrate the relevance of our results, we present an illustrative example. This example validates the theoretical framework we have developed and offers practical insights into the behavior of solutions for quasi-linear third-order neutral differential equations.","PeriodicalId":53148,"journal":{"name":"Axioms","volume":"21 S1","pages":""},"PeriodicalIF":2.0,"publicationDate":"2023-12-11","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"138978697","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Francisco Miguel García-Olmedo, Antonio Jesús Rodríguez-Salas, P. González-Rodelas
In this paper, we give a basic structure theorem based on the study of extreme cases for the value of ≺ (the classical precedence relation between ultrafilters), i.e., ≺=∅ and no isolated element in ≺. This gives rise, respectively, to the temporal varieties O and W, with the result that O generates a variety of temporal algebras. We also characterize the simple temporal algebras by means of arithmetical properties related to basical temporal operators; we conclude that the simplicity of the temporal algebra lies in being able to make 0 any element less than 1 by repeated application to it of the L operator. We then present an algebraic construction similar to a product but in which the temporal operations are not defined componentwise. This new “product” is shown to be useful in the study of algebra order and finding of bounds by means of something similar to a lifting process. Finally, we give an alternative proof of an already known result on atoms counting in free temporal algebras.
本文基于对≺（超滤波器之间的经典优先关系）值极端情况的研究，给出了一个基本结构定理，即≺=∅且≺中无孤立元素。这就分别产生了时空变项 O 和 W，结果是 O 产生了一个时空代数变项。我们还通过与基本时态算子相关的算术性质来描述简单时态代数的特征；我们得出结论：时态代数的简单性在于，通过对它重复应用 L 算子，可以使任何小于 1 的元素为 0。然后，我们提出了一种类似于积的代数结构，但其中的时态运算不是按分量定义的。这种新的 "乘积 "在研究代数阶和通过类似于提升过程的方法寻找边界时非常有用。最后，我们给出了关于自由时态代数中原子计数的已知结果的另一种证明。
{"title":"Certain Bounds of Formulas in Free Temporal Algebras","authors":"Francisco Miguel García-Olmedo, Antonio Jesús Rodríguez-Salas, P. González-Rodelas","doi":"10.3390/axioms12121111","DOIUrl":"https://doi.org/10.3390/axioms12121111","url":null,"abstract":"In this paper, we give a basic structure theorem based on the study of extreme cases for the value of ≺ (the classical precedence relation between ultrafilters), i.e., ≺=∅ and no isolated element in ≺. This gives rise, respectively, to the temporal varieties O and W, with the result that O generates a variety of temporal algebras. We also characterize the simple temporal algebras by means of arithmetical properties related to basical temporal operators; we conclude that the simplicity of the temporal algebra lies in being able to make 0 any element less than 1 by repeated application to it of the L operator. We then present an algebraic construction similar to a product but in which the temporal operations are not defined componentwise. This new “product” is shown to be useful in the study of algebra order and finding of bounds by means of something similar to a lifting process. Finally, we give an alternative proof of an already known result on atoms counting in free temporal algebras.","PeriodicalId":53148,"journal":{"name":"Axioms","volume":"39 8","pages":""},"PeriodicalIF":2.0,"publicationDate":"2023-12-11","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"138979755","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Transformations are much used to connect complicated nonlinear differential equations to simple equations with known exact solutions. Two examples of this are the Hopf–Cole transformation and the simple equations method. In this article, we follow an idea that is opposite to the idea of Hopf and Cole: we use transformations in order to transform simpler linear or nonlinear differential equations (with known solutions) to more complicated nonlinear differential equations. In such a way, we can obtain numerous exact solutions of nonlinear differential equations. We apply this methodology to the classical parabolic differential equation (the wave equation), to the classical hyperbolic differential equation (the heat equation), and to the classical elliptic differential equation (Laplace equation). In addition, we use the methodology to obtain exact solutions of nonlinear ordinary differential equations by means of the solutions of linear differential equations and by means of the solutions of the nonlinear differential equations of Bernoulli and Riccati. Finally, we demonstrate the capacity of the methodology to lead to exact solutions of nonlinear partial differential equations on the basis of known solutions of other nonlinear partial differential equations. As an example of this, we use the Korteweg–de Vries equation and its solutions. Traveling wave solutions of nonlinear differential equations are of special interest in this article. We demonstrate the existence of the following phenomena described by some of the obtained solutions: (i) occurrence of the solitary wave–solitary antiwave from the solution, which is zero at the initial moment (analogy of an occurrence of particle and antiparticle from the vacuum); (ii) splitting of a nonlinear solitary wave into two solitary waves (analogy of splitting of a particle into two particles); (iii) soliton behavior of some of the obtained waves; (iv) existence of solitons which move with the same velocity despite the different shape and amplitude of the solitons.
{"title":"On the Method of Transformations: Obtaining Solutions of Nonlinear Differential Equations by Means of the Solutions of Simpler Linear or Nonlinear Differential Equations","authors":"N. Vitanov","doi":"10.3390/axioms12121106","DOIUrl":"https://doi.org/10.3390/axioms12121106","url":null,"abstract":"Transformations are much used to connect complicated nonlinear differential equations to simple equations with known exact solutions. Two examples of this are the Hopf–Cole transformation and the simple equations method. In this article, we follow an idea that is opposite to the idea of Hopf and Cole: we use transformations in order to transform simpler linear or nonlinear differential equations (with known solutions) to more complicated nonlinear differential equations. In such a way, we can obtain numerous exact solutions of nonlinear differential equations. We apply this methodology to the classical parabolic differential equation (the wave equation), to the classical hyperbolic differential equation (the heat equation), and to the classical elliptic differential equation (Laplace equation). In addition, we use the methodology to obtain exact solutions of nonlinear ordinary differential equations by means of the solutions of linear differential equations and by means of the solutions of the nonlinear differential equations of Bernoulli and Riccati. Finally, we demonstrate the capacity of the methodology to lead to exact solutions of nonlinear partial differential equations on the basis of known solutions of other nonlinear partial differential equations. As an example of this, we use the Korteweg–de Vries equation and its solutions. Traveling wave solutions of nonlinear differential equations are of special interest in this article. We demonstrate the existence of the following phenomena described by some of the obtained solutions: (i) occurrence of the solitary wave–solitary antiwave from the solution, which is zero at the initial moment (analogy of an occurrence of particle and antiparticle from the vacuum); (ii) splitting of a nonlinear solitary wave into two solitary waves (analogy of splitting of a particle into two particles); (iii) soliton behavior of some of the obtained waves; (iv) existence of solitons which move with the same velocity despite the different shape and amplitude of the solitons.","PeriodicalId":53148,"journal":{"name":"Axioms","volume":"84 12","pages":""},"PeriodicalIF":2.0,"publicationDate":"2023-12-08","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"138586701","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Vicente Borja-Jaimes, Manuel Adam-Medina, Jarniel García-Morales, Alan Cruz-Rojas, Alfredo Gil-Velasco, Antonio Coronel-Escamilla
In the present manuscript, we design a fractional multi-order high-gain observer to estimate temperature in a double pipe heat exchange process. For comparison purposes and since we want to prove that when using our novel technique, the estimation is more robust than the classical approach, we design a non-fractional high-gain observer, and then we compare the performance of both observers. We consider three scenarios: The first one considers the estimation of the system states by measuring only one output with no noise added on it and under ideal conditions. Second, we add noise to the measured output and then reconstruct the system states, and, third, in addition to the noise, we increase the gain parameter in both observers (non-fractional and fractional) due to the fact that we want to prove that the robustness changes in this parameter. The results showed that, using our approach, the estimated states can be recovered under noise circumstances in the measured output and under parameter change in the observer, contrary to using classical (non-fractional) observers where the states cannot be recovered. In all our tests, we used the normalized root-mean-square, integral square error, and integral absolute error indices, resulting in a better performance for our approach than that obtained using the classical approach. We concluded that our fractional multi-order high-gain observer is more robust to input noise than the classical high-gain observer.
{"title":"A Novel Fractional Multi-Order High-Gain Observer Design to Estimate Temperature in a Heat Exchange Process","authors":"Vicente Borja-Jaimes, Manuel Adam-Medina, Jarniel García-Morales, Alan Cruz-Rojas, Alfredo Gil-Velasco, Antonio Coronel-Escamilla","doi":"10.3390/axioms12121107","DOIUrl":"https://doi.org/10.3390/axioms12121107","url":null,"abstract":"In the present manuscript, we design a fractional multi-order high-gain observer to estimate temperature in a double pipe heat exchange process. For comparison purposes and since we want to prove that when using our novel technique, the estimation is more robust than the classical approach, we design a non-fractional high-gain observer, and then we compare the performance of both observers. We consider three scenarios: The first one considers the estimation of the system states by measuring only one output with no noise added on it and under ideal conditions. Second, we add noise to the measured output and then reconstruct the system states, and, third, in addition to the noise, we increase the gain parameter in both observers (non-fractional and fractional) due to the fact that we want to prove that the robustness changes in this parameter. The results showed that, using our approach, the estimated states can be recovered under noise circumstances in the measured output and under parameter change in the observer, contrary to using classical (non-fractional) observers where the states cannot be recovered. In all our tests, we used the normalized root-mean-square, integral square error, and integral absolute error indices, resulting in a better performance for our approach than that obtained using the classical approach. We concluded that our fractional multi-order high-gain observer is more robust to input noise than the classical high-gain observer.","PeriodicalId":53148,"journal":{"name":"Axioms","volume":"4 5","pages":""},"PeriodicalIF":2.0,"publicationDate":"2023-12-08","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"138589636","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
This paper investigates the capability of undirected graphs (UGs) to represent a set of Conditional Independence (CI) statements derived from a given probability distribution of a random vector. While it is established that certain axioms can govern this set, providing sufficient conditions for UGs to capture specific CI statements, our focus is on covariance and concentration graphs. These remain the only known families of UGs capable of describing CI statements. We explore the issue of complete representation of CI statements through their corresponding covariance and concentration graphs. Two parameters are defined, one each from the covariance and concentration graphs, to determine the limitations concerning the cardinality of the conditioning subset that the graph can represent. We establish a relationship between these parameters and the cardinality of the separators in each graph, providing a straightforward computational method to evaluate them. In conclusion, we enhance the aforementioned procedure and introduce criteria to ascertain, without additional computations, whether the graphs can fully represent a given set of CI statements. We demonstrate that either the concentration or the covariance graph forms a cycle, and when considered in conjunction, they can represent the entire relation. These criteria also enable us, in specific cases, to deduce the covariance graph from the concentration graph and vice versa.
本文研究了无向图（UGs）表示由给定随机向量概率分布衍生出的一组条件独立性（CI）声明的能力。虽然已经确定某些公理可以支配这组图，为无向图捕捉特定的 CI 语句提供了充分条件，但我们的重点是协方差图和浓度图。这些仍然是唯一已知的能够描述 CI 语句的 UG 系列。我们探讨了通过相应的协方差图和浓度图完整表示 CI 语句的问题。我们定义了两个参数，分别来自协方差图和浓度图，以确定图所能表示的条件子集的心率限制。我们在这些参数和每个图中分离器的卡片数之间建立了一种关系，并提供了一种直接的计算方法来评估这些参数。总之，我们改进了上述程序，并引入了标准，无需额外计算即可确定图形是否能完全代表给定的 CI 语句集。我们证明，无论是浓度图还是协方差图，都能形成一个循环，如果结合起来考虑，它们就能代表整个关系。在特定情况下，这些标准还能让我们从浓度图推导出协方差图，反之亦然。
{"title":"Describing Conditional Independence Statements Using Undirected Graphs","authors":"D. Malouche","doi":"10.3390/axioms12121109","DOIUrl":"https://doi.org/10.3390/axioms12121109","url":null,"abstract":"This paper investigates the capability of undirected graphs (UGs) to represent a set of Conditional Independence (CI) statements derived from a given probability distribution of a random vector. While it is established that certain axioms can govern this set, providing sufficient conditions for UGs to capture specific CI statements, our focus is on covariance and concentration graphs. These remain the only known families of UGs capable of describing CI statements. We explore the issue of complete representation of CI statements through their corresponding covariance and concentration graphs. Two parameters are defined, one each from the covariance and concentration graphs, to determine the limitations concerning the cardinality of the conditioning subset that the graph can represent. We establish a relationship between these parameters and the cardinality of the separators in each graph, providing a straightforward computational method to evaluate them. In conclusion, we enhance the aforementioned procedure and introduce criteria to ascertain, without additional computations, whether the graphs can fully represent a given set of CI statements. We demonstrate that either the concentration or the covariance graph forms a cycle, and when considered in conjunction, they can represent the entire relation. These criteria also enable us, in specific cases, to deduce the covariance graph from the concentration graph and vice versa.","PeriodicalId":53148,"journal":{"name":"Axioms","volume":"93 ","pages":""},"PeriodicalIF":2.0,"publicationDate":"2023-12-08","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"139010914","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Over a field of characteristic p>3, let KO(n,n+1;t̲) denote the odd contact Lie superalgebra. In this paper, the super-biderivations of odd Contact Lie superalgebra KO(n,n+1;t̲) are studied. Let TKO be a torus of KO(n,n+1;t̲), which is an abelian subalgebra of KO(n,n+1;t̲). By applying the weight space decomposition approach of KO(n,n+1;t̲) with respect to TKO, we show that all skew-symmetric super-biderivations of KO(n,n+1;t̲) are inner super-biderivations.
{"title":"A Note on Finite Dimensional Odd Contact Lie Superalgebra in Prime Characteristic","authors":"Xiaoning Xu, Qiyuan Wang","doi":"10.3390/axioms12121108","DOIUrl":"https://doi.org/10.3390/axioms12121108","url":null,"abstract":"Over a field of characteristic p>3, let KO(n,n+1;t̲) denote the odd contact Lie superalgebra. In this paper, the super-biderivations of odd Contact Lie superalgebra KO(n,n+1;t̲) are studied. Let TKO be a torus of KO(n,n+1;t̲), which is an abelian subalgebra of KO(n,n+1;t̲). By applying the weight space decomposition approach of KO(n,n+1;t̲) with respect to TKO, we show that all skew-symmetric super-biderivations of KO(n,n+1;t̲) are inner super-biderivations.","PeriodicalId":53148,"journal":{"name":"Axioms","volume":"34 18","pages":""},"PeriodicalIF":2.0,"publicationDate":"2023-12-08","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"138588789","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
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