Pub Date : 2024-07-16DOI: 10.3389/fams.2024.1384559
A. M. Hassan, O. Moaaz, Sameh S. Askar, Ahmad M. Alshamrani
This study primarily seeks to expand upon these developments by encompassing neutral differential equations of mixed type, incorporating both delay and advanced terms, particularly in the case of the canonical operator. The presented results are derived from the application of the comparison method, Riccati transformation, and integral averaging technique. These methodologies lead to substantial improvements and extensions of existing results found in the literature. Additionally, illustrative examples are provided to demonstrate the practical implications of the developed criteria.
{"title":"Oscillatory behavior of solutions of second-order non-linear differential equations with mixed non-linear neutral terms","authors":"A. M. Hassan, O. Moaaz, Sameh S. Askar, Ahmad M. Alshamrani","doi":"10.3389/fams.2024.1384559","DOIUrl":"https://doi.org/10.3389/fams.2024.1384559","url":null,"abstract":"This study primarily seeks to expand upon these developments by encompassing neutral differential equations of mixed type, incorporating both delay and advanced terms, particularly in the case of the canonical operator. The presented results are derived from the application of the comparison method, Riccati transformation, and integral averaging technique. These methodologies lead to substantial improvements and extensions of existing results found in the literature. Additionally, illustrative examples are provided to demonstrate the practical implications of the developed criteria.","PeriodicalId":507585,"journal":{"name":"Frontiers in Applied Mathematics and Statistics","volume":null,"pages":null},"PeriodicalIF":0.0,"publicationDate":"2024-07-16","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"141642778","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2024-07-15DOI: 10.3389/fams.2024.1414899
S. L. Cheru, G. Duressa, T. Mekonnen
This study presents an (ε, μ)−uniform numerical method for a two-parameter singularly perturbed time-delayed parabolic problems. The proposed approach is based on a fitted operator finite difference method. The Crank–Nicolson method is used on a uniform mesh to discretize the time variables initially. Subsequently, the resulting semi-discrete scheme is further discretized in space using Simpson's 1/3rd rule. Finally, the finite difference approximation of the first derivatives is applied. The method is unique in that it is not dependent on delay terms, asymptotic expansions, or fitted meshes. The fitting factor's value, which is used to account for abrupt changes in the solution, is calculated using the theory of singular perturbations. The developed scheme is demonstrated to be second-order accurate and uniformly convergent. The proposed method's applicability is validated by three model examples, which yielded more accurate results than some other methods found in the literature.
{"title":"Numerical integration method for two-parameter singularly perturbed time delay parabolic problem","authors":"S. L. Cheru, G. Duressa, T. Mekonnen","doi":"10.3389/fams.2024.1414899","DOIUrl":"https://doi.org/10.3389/fams.2024.1414899","url":null,"abstract":"This study presents an (ε, μ)−uniform numerical method for a two-parameter singularly perturbed time-delayed parabolic problems. The proposed approach is based on a fitted operator finite difference method. The Crank–Nicolson method is used on a uniform mesh to discretize the time variables initially. Subsequently, the resulting semi-discrete scheme is further discretized in space using Simpson's 1/3rd rule. Finally, the finite difference approximation of the first derivatives is applied. The method is unique in that it is not dependent on delay terms, asymptotic expansions, or fitted meshes. The fitting factor's value, which is used to account for abrupt changes in the solution, is calculated using the theory of singular perturbations. The developed scheme is demonstrated to be second-order accurate and uniformly convergent. The proposed method's applicability is validated by three model examples, which yielded more accurate results than some other methods found in the literature.","PeriodicalId":507585,"journal":{"name":"Frontiers in Applied Mathematics and Statistics","volume":null,"pages":null},"PeriodicalIF":0.0,"publicationDate":"2024-07-15","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"141648507","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2024-07-10DOI: 10.3389/fams.2024.1408381
D. Devianto, Elsa Wahyuni, M. Maiyastri, Mutia Yollanda
This study aimed to explore big-time series data on agricultural commodities with an autocorrelation model comprising long-term processes, seasonality, and the impact of exogenous variables. Among the agricultural commodities with a large amount of data, chili prices exemplified criteria for long-term memory, seasonality, and the impact of various factors on production as an exogenous variable. These factors included the month preceding the new year and the week before the Eid al-Fitr celebration in Indonesia. To address the factors affecting price fluctuations, the Seasonal Autoregressive Fractionally Integrated Moving Average (SARFIMA) model was used to manage seasonality and long-term memory effects in the big data analysis. It improved with the addition of exogenous variables called SARFIMAX (SARFIMA with exogenous variables is known as SARFIMAX). After comparing the accuracy of both models, it was discovered that the SARFIMAX performed better, indicating the influence of seasonality and previous chili prices for an extended period in conjunction with exogenous variables. The SARFIMAX model gives an improvement in model accuracy by adding the effect of exogenous variables. Consequently, this observation concerning price dynamics established the cornerstone for maintaining the sustainability of chili supply even with the big data case.
{"title":"The seasonal model of chili price movement with the effect of long memory and exogenous variables for improving time series model accuracy","authors":"D. Devianto, Elsa Wahyuni, M. Maiyastri, Mutia Yollanda","doi":"10.3389/fams.2024.1408381","DOIUrl":"https://doi.org/10.3389/fams.2024.1408381","url":null,"abstract":"This study aimed to explore big-time series data on agricultural commodities with an autocorrelation model comprising long-term processes, seasonality, and the impact of exogenous variables. Among the agricultural commodities with a large amount of data, chili prices exemplified criteria for long-term memory, seasonality, and the impact of various factors on production as an exogenous variable. These factors included the month preceding the new year and the week before the Eid al-Fitr celebration in Indonesia. To address the factors affecting price fluctuations, the Seasonal Autoregressive Fractionally Integrated Moving Average (SARFIMA) model was used to manage seasonality and long-term memory effects in the big data analysis. It improved with the addition of exogenous variables called SARFIMAX (SARFIMA with exogenous variables is known as SARFIMAX). After comparing the accuracy of both models, it was discovered that the SARFIMAX performed better, indicating the influence of seasonality and previous chili prices for an extended period in conjunction with exogenous variables. The SARFIMAX model gives an improvement in model accuracy by adding the effect of exogenous variables. Consequently, this observation concerning price dynamics established the cornerstone for maintaining the sustainability of chili supply even with the big data case.","PeriodicalId":507585,"journal":{"name":"Frontiers in Applied Mathematics and Statistics","volume":null,"pages":null},"PeriodicalIF":0.0,"publicationDate":"2024-07-10","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"141659297","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2024-07-10DOI: 10.3389/fams.2024.1434012
Aziz Elmire, Aziz Ait Bassou, M. Hlyal, Jamila el Alami
In this paper, we present a model detailing the benefits of two competing firms in a duopoly market, where profit maximization is linked to their production levels using the Cournot method. Our primary objective is to develop a collaborative strategy within the framework of open innovation to optimize their profits. Furthermore, we analyze how these firms can integrate an additional source of revenue in the form of intellectual property, without negatively impacting their open innovation strategies. To achieve this, we conducted a dynamic study of these strategies by introducing this intellectual property, to assess the impact of its components, such as patent licensing fees and royalties, on the equilibrium of strategies adopted by these firms. Our aim is to provide recommendations for optimal management of this intellectual property, thus enabling firms to fully leverage its benefits while preserving their competitive position in the market.
{"title":"Dynamic study of the duopoly market stability based on open innovation rate integration and intellectual property","authors":"Aziz Elmire, Aziz Ait Bassou, M. Hlyal, Jamila el Alami","doi":"10.3389/fams.2024.1434012","DOIUrl":"https://doi.org/10.3389/fams.2024.1434012","url":null,"abstract":"In this paper, we present a model detailing the benefits of two competing firms in a duopoly market, where profit maximization is linked to their production levels using the Cournot method. Our primary objective is to develop a collaborative strategy within the framework of open innovation to optimize their profits. Furthermore, we analyze how these firms can integrate an additional source of revenue in the form of intellectual property, without negatively impacting their open innovation strategies. To achieve this, we conducted a dynamic study of these strategies by introducing this intellectual property, to assess the impact of its components, such as patent licensing fees and royalties, on the equilibrium of strategies adopted by these firms. Our aim is to provide recommendations for optimal management of this intellectual property, thus enabling firms to fully leverage its benefits while preserving their competitive position in the market.","PeriodicalId":507585,"journal":{"name":"Frontiers in Applied Mathematics and Statistics","volume":null,"pages":null},"PeriodicalIF":0.0,"publicationDate":"2024-07-10","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"141661376","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2024-07-05DOI: 10.3389/fams.2024.1376558
Ehsan Zohreh Bojnourdi, Arash Mansoori, Samira Jowkar, Mina Alvandi Ghiasvand, Ghazal Rezaei, Seyed Ali Tabatabaei, S. B. Razavian, Mohammad Mehdi Keshvari
The subject of predicting global crude oil prices is well recognized in academic circles. The notion of hybrid modeling suggests that the integration of several methodologies has the potential to optimize advantages while reducing limitations. Consequently, hybrid techniques are extensively used in contemporary research. In this paper, a novel decompose-ensemble prediction approach is proposed by integrating various optimization algorithms, namely biography-based optimization (BBO), backtracking search algorithm (BSA), teaching-learning-based algorithm (TLBO), cuckoo optimization algorithm (COA), multi-verse optimization (MVO), and multilayer perceptron (MLP). Furthermore, the aforementioned approaches, namely BBO-MLP, BSA-MLP, and TLBO-MLP, include the de-compose-ensemble technique into the individual artificial intelligence model in order to enhance the accuracy of predictions. In order to validate the findings, the forecast is conducted using the authoritative data on oil prices. This study will use three primary indicators, including EMA 20, EMA 60, EMA 100, ROC, and AUC assessments, to assess and evaluate the efficacy of the five methodologies under investigation. The below findings are derived from the conducted research: Based on the achieved AUC values of 0.9567 and 0.9429, it can be concluded that using a multi-verse optimization technique is considered the most suitable strategy for effectively handling the dataset pertaining to crude oil revenue. The next four approaches likewise have a significant AUC value, surpassing 0.8. The AUC values for the BBO-MLP, BSA-MLP, TLBO-MLP, and COA-MLP approaches were obtained as follows: (0.874 and 0.792) for training and testing stages, (0.809 and 0.792) for training and testing stages, (0.9353 and 0.9237) for training and testing stages, and (0.9092 and 0.8927) for training and testing stages, respectively. This model has the potential to contribute to the resolution of default probability and is very valuable to the credit card industry. Broadly speaking, this novel forecasting approach serves as a notable predictor of crude oil prices.
{"title":"Predicting successful trading in the West Texas Intermediate crude oil cash market with machine learning nature-inspired swarm-based approaches","authors":"Ehsan Zohreh Bojnourdi, Arash Mansoori, Samira Jowkar, Mina Alvandi Ghiasvand, Ghazal Rezaei, Seyed Ali Tabatabaei, S. B. Razavian, Mohammad Mehdi Keshvari","doi":"10.3389/fams.2024.1376558","DOIUrl":"https://doi.org/10.3389/fams.2024.1376558","url":null,"abstract":"The subject of predicting global crude oil prices is well recognized in academic circles. The notion of hybrid modeling suggests that the integration of several methodologies has the potential to optimize advantages while reducing limitations. Consequently, hybrid techniques are extensively used in contemporary research. In this paper, a novel decompose-ensemble prediction approach is proposed by integrating various optimization algorithms, namely biography-based optimization (BBO), backtracking search algorithm (BSA), teaching-learning-based algorithm (TLBO), cuckoo optimization algorithm (COA), multi-verse optimization (MVO), and multilayer perceptron (MLP). Furthermore, the aforementioned approaches, namely BBO-MLP, BSA-MLP, and TLBO-MLP, include the de-compose-ensemble technique into the individual artificial intelligence model in order to enhance the accuracy of predictions. In order to validate the findings, the forecast is conducted using the authoritative data on oil prices. This study will use three primary indicators, including EMA 20, EMA 60, EMA 100, ROC, and AUC assessments, to assess and evaluate the efficacy of the five methodologies under investigation. The below findings are derived from the conducted research: Based on the achieved AUC values of 0.9567 and 0.9429, it can be concluded that using a multi-verse optimization technique is considered the most suitable strategy for effectively handling the dataset pertaining to crude oil revenue. The next four approaches likewise have a significant AUC value, surpassing 0.8. The AUC values for the BBO-MLP, BSA-MLP, TLBO-MLP, and COA-MLP approaches were obtained as follows: (0.874 and 0.792) for training and testing stages, (0.809 and 0.792) for training and testing stages, (0.9353 and 0.9237) for training and testing stages, and (0.9092 and 0.8927) for training and testing stages, respectively. This model has the potential to contribute to the resolution of default probability and is very valuable to the credit card industry. Broadly speaking, this novel forecasting approach serves as a notable predictor of crude oil prices.","PeriodicalId":507585,"journal":{"name":"Frontiers in Applied Mathematics and Statistics","volume":null,"pages":null},"PeriodicalIF":0.0,"publicationDate":"2024-07-05","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"141674024","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2024-07-02DOI: 10.3389/fams.2024.1374832
Martyna Lukaszewicz, Brian Dennis
Predicting the timing of phenological events is important in agriculture, especially high-revenue products. A project sponsored by USDA-ARS had the objective of adapting a previously developed model for estimating proportions of insects in different development stages as a function of temperature (degree) and time (days) for predicting bloom in almond orchards. Data for the model normally form a two-way table of counts, with rows corresponding to sample percentages of different development stages and columns to sampling times. In this study, we report a technique developed to estimate sample sizes of multinomial and product multinomial models using a method of moments and determine the empirical coverage of sample size. This study aims to determine an appropriate sample size for data collection. This involves establishing a sampling distribution for the Pearson statistic, defined as the product of the sample size and the deviance of empirical proportions from population proportions. The intended outcome is to predict the optimal timing for harvesting crops at desired development stages when coupled with the phenology model, for which variability of the maximum likelihood estimates of the phenology model depends on sample size.
{"title":"Determination of sample size for a multinomial model coupled with the phenology model","authors":"Martyna Lukaszewicz, Brian Dennis","doi":"10.3389/fams.2024.1374832","DOIUrl":"https://doi.org/10.3389/fams.2024.1374832","url":null,"abstract":"Predicting the timing of phenological events is important in agriculture, especially high-revenue products. A project sponsored by USDA-ARS had the objective of adapting a previously developed model for estimating proportions of insects in different development stages as a function of temperature (degree) and time (days) for predicting bloom in almond orchards. Data for the model normally form a two-way table of counts, with rows corresponding to sample percentages of different development stages and columns to sampling times. In this study, we report a technique developed to estimate sample sizes of multinomial and product multinomial models using a method of moments and determine the empirical coverage of sample size. This study aims to determine an appropriate sample size for data collection. This involves establishing a sampling distribution for the Pearson statistic, defined as the product of the sample size and the deviance of empirical proportions from population proportions. The intended outcome is to predict the optimal timing for harvesting crops at desired development stages when coupled with the phenology model, for which variability of the maximum likelihood estimates of the phenology model depends on sample size.","PeriodicalId":507585,"journal":{"name":"Frontiers in Applied Mathematics and Statistics","volume":null,"pages":null},"PeriodicalIF":0.0,"publicationDate":"2024-07-02","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"141687253","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2024-06-05DOI: 10.3389/fams.2024.1344158
Sina Abbasi, Umar Muhammad Modibbo, Hamed Jafari Kolashlou, Irfan Ali, Nader Kavousi
In the last several decades, Iran’s ecosystem has suffered due to the careless usage of natural resources. Cities have grown in an uneven and non-normative way, and poor project management has been a major issue, particularly in large cities. An even greater number of environmental factors and engineering regulations are not relevant to projects. Because of this, in order to ascertain a project’s environmental impact, an environmental impact assessment (EIA), is required. Using the rapid impact assessment matrix (RIAM) is one method of applying it to EIA. Reducing subjectivity brings objectivity and transparency. During the COVID-19 pandemic, a thorough EIA was carried out for the Tehran project utilizing the RIAM and other possibilities. This research is the first to combine the methodology that was discussed during the incident. Through the use of the RIAM technique, the environmental impact of COVID-19 was to be quantified in this inquiry. The research examined lockdown procedures and the COVID-19 pandemic to create an EIA indicator. In a real-world case study conducted in Tehran, Iran, the impact of the initiative was evaluated using the RIAM methodology during the COVID-19 epidemic. The results demonstrated that COVID-19 had both beneficial and harmful effects. Decision-makers were effectively informed about the COVID-19 pandemic’s environmental consequences on people and the environment, as well as how to minimize negative effects, according to the EIA technique that used RIAM. This is the first research to integrate the EIA during a crisis, such as the COVID-19 pandemic, with the RIAM approach.
{"title":"Environmental impact assessment with rapid impact assessment matrix method: during disaster conditions","authors":"Sina Abbasi, Umar Muhammad Modibbo, Hamed Jafari Kolashlou, Irfan Ali, Nader Kavousi","doi":"10.3389/fams.2024.1344158","DOIUrl":"https://doi.org/10.3389/fams.2024.1344158","url":null,"abstract":"In the last several decades, Iran’s ecosystem has suffered due to the careless usage of natural resources. Cities have grown in an uneven and non-normative way, and poor project management has been a major issue, particularly in large cities. An even greater number of environmental factors and engineering regulations are not relevant to projects. Because of this, in order to ascertain a project’s environmental impact, an environmental impact assessment (EIA), is required. Using the rapid impact assessment matrix (RIAM) is one method of applying it to EIA. Reducing subjectivity brings objectivity and transparency. During the COVID-19 pandemic, a thorough EIA was carried out for the Tehran project utilizing the RIAM and other possibilities. This research is the first to combine the methodology that was discussed during the incident. Through the use of the RIAM technique, the environmental impact of COVID-19 was to be quantified in this inquiry. The research examined lockdown procedures and the COVID-19 pandemic to create an EIA indicator. In a real-world case study conducted in Tehran, Iran, the impact of the initiative was evaluated using the RIAM methodology during the COVID-19 epidemic. The results demonstrated that COVID-19 had both beneficial and harmful effects. Decision-makers were effectively informed about the COVID-19 pandemic’s environmental consequences on people and the environment, as well as how to minimize negative effects, according to the EIA technique that used RIAM. This is the first research to integrate the EIA during a crisis, such as the COVID-19 pandemic, with the RIAM approach.","PeriodicalId":507585,"journal":{"name":"Frontiers in Applied Mathematics and Statistics","volume":null,"pages":null},"PeriodicalIF":0.0,"publicationDate":"2024-06-05","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"141383637","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2024-05-21DOI: 10.3389/fams.2024.1376010
N. Nieto-Marín, C. C. Nieto-Marín, I. Nieto-Marín, J. A. Nieto
We describe the genetic code in terms of numbers that help us to find several dual symmetries. Our formulation can even be rewritten regarding the up-down and right-left dual concepts. We argue that our work may bring many topological tools to studying the DNA molecule, including the Grassmann-Plücker coordinates, which are important in mathematical and physical contexts.
我们用数字来描述遗传密码，这有助于我们找到几种对偶对称性。我们的表述甚至可以根据上下和左右对偶概念进行改写。我们认为，我们的工作可以为研究 DNA 分子带来许多拓扑学工具，包括格拉斯曼-普吕克坐标，这在数学和物理方面都很重要。
{"title":"Hidden dual mathematical symmetry in the genetic code","authors":"N. Nieto-Marín, C. C. Nieto-Marín, I. Nieto-Marín, J. A. Nieto","doi":"10.3389/fams.2024.1376010","DOIUrl":"https://doi.org/10.3389/fams.2024.1376010","url":null,"abstract":"We describe the genetic code in terms of numbers that help us to find several dual symmetries. Our formulation can even be rewritten regarding the up-down and right-left dual concepts. We argue that our work may bring many topological tools to studying the DNA molecule, including the Grassmann-Plücker coordinates, which are important in mathematical and physical contexts.","PeriodicalId":507585,"journal":{"name":"Frontiers in Applied Mathematics and Statistics","volume":null,"pages":null},"PeriodicalIF":0.0,"publicationDate":"2024-05-21","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"141116440","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2024-05-16DOI: 10.3389/fams.2024.1397374
Ivan Kovalyov, Oleksandra Levina
Let J be a symmetric Jacobi matrix associated with some Toda lattice. We find conditions for Jacobi matrix J to admit factorization J = LU (or J = 𝔘𝔏) with L (or 𝔏) and U (or 𝔘) being lower and upper triangular two-diagonal matrices, respectively. In this case, the Darboux transformation of J is the symmetric Jacobi matrix J(p) = UL (or J(d) = 𝔏𝔘), which is associated with another Toda lattice. In addition, we found explicit transformation formulas for orthogonal polynomials, m-functions and Toda lattices associated with the Jacobi matrices and their Darboux transformations.
{"title":"Darboux transformation of symmetric Jacobi matrices and Toda lattices","authors":"Ivan Kovalyov, Oleksandra Levina","doi":"10.3389/fams.2024.1397374","DOIUrl":"https://doi.org/10.3389/fams.2024.1397374","url":null,"abstract":"Let J be a symmetric Jacobi matrix associated with some Toda lattice. We find conditions for Jacobi matrix J to admit factorization J = LU (or J = 𝔘𝔏) with L (or 𝔏) and U (or 𝔘) being lower and upper triangular two-diagonal matrices, respectively. In this case, the Darboux transformation of J is the symmetric Jacobi matrix J(p) = UL (or J(d) = 𝔏𝔘), which is associated with another Toda lattice. In addition, we found explicit transformation formulas for orthogonal polynomials, m-functions and Toda lattices associated with the Jacobi matrices and their Darboux transformations.","PeriodicalId":507585,"journal":{"name":"Frontiers in Applied Mathematics and Statistics","volume":null,"pages":null},"PeriodicalIF":0.0,"publicationDate":"2024-05-16","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"140971391","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2024-05-14DOI: 10.3389/fams.2024.1420155
Scott E. Field, Sigal Gottlieb, Gaurav Khanna
{"title":"Editorial: Advances in computational relativity","authors":"Scott E. Field, Sigal Gottlieb, Gaurav Khanna","doi":"10.3389/fams.2024.1420155","DOIUrl":"https://doi.org/10.3389/fams.2024.1420155","url":null,"abstract":"","PeriodicalId":507585,"journal":{"name":"Frontiers in Applied Mathematics and Statistics","volume":null,"pages":null},"PeriodicalIF":0.0,"publicationDate":"2024-05-14","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"140981810","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
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