Anjan Biswas, José Vega-Guzmán, Yakup Yildirim, Asim Asiri
This paper recovers optical solitons to the dispersive concatenation model that is studied with Kerr law of self-phase modulation. The method of undetermined coefficients is the adopted integration algorithm, enabling this retrieval possible. A full spectrum of optical solitons is recovered. The parameter constraints for the existence of the solitons, that naturally emerge during the course of their derivation, are also presented. The practical applications of this research include advancements in optical communication, nonlinear optics, and optical signal processing, as well as the potential for optimizing optical soliton-based technologies. In our current work, we have achieved the following novel findings: optical soliton recovery, integration algorithm innovation, and parameter constraints.
{"title":"Optical Solitons for the Dispersive Concatenation Model: Undetermined Coefficients","authors":"Anjan Biswas, José Vega-Guzmán, Yakup Yildirim, Asim Asiri","doi":"10.37256/cm.4420233618","DOIUrl":"https://doi.org/10.37256/cm.4420233618","url":null,"abstract":"This paper recovers optical solitons to the dispersive concatenation model that is studied with Kerr law of self-phase modulation. The method of undetermined coefficients is the adopted integration algorithm, enabling this retrieval possible. A full spectrum of optical solitons is recovered. The parameter constraints for the existence of the solitons, that naturally emerge during the course of their derivation, are also presented. The practical applications of this research include advancements in optical communication, nonlinear optics, and optical signal processing, as well as the potential for optimizing optical soliton-based technologies. In our current work, we have achieved the following novel findings: optical soliton recovery, integration algorithm innovation, and parameter constraints.","PeriodicalId":29767,"journal":{"name":"Contemporary Mathematics","volume":"52 3","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2023-11-07","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"135476493","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}
Mathematics and statistics have a significant impact on the advancement of most trending sciences like machine learning, artificial intelligence, and data science. In this article, we use the Stacking Ensemble Machine Learning Algorithm (SEMLA) to predict heart disease, considering accuracy (acc), diagnostic odds ratio (Dor), F1_score, Matthews correlation coefficient (Mcc), receiver operating characteristics-area under curve (roc-auc), and logloss (log_loss). The data is analyzed using classification learning techniques. We have considered sex, age, cholesterol, fasting blood sugar, the highest rate of heartbeat, type of chest pain, resting electrocardiogram (ECG), angina, depression induced by exercise, peak exercise measurement, major vessel number, a disorder in the blood, and a target attribute to represent the presence and absence of disorders. The approach used allows for the prediction of heart disease and the management of worst-case scenarios. In comparison with the existing models, our proposed model has outperformed other models with an accuracy of 97.28%.
{"title":"Stacking Ensemble Machine Learning Algorithm with an Application to Heart Disease Prediction","authors":"Ruhi Fatima, Sabeena Kazi, Asifa Tassaddiq, Nilofer Farhat, Humera Naaz, Sumera Jabeen","doi":"10.37256/cm.4420232390","DOIUrl":"https://doi.org/10.37256/cm.4420232390","url":null,"abstract":"Mathematics and statistics have a significant impact on the advancement of most trending sciences like machine learning, artificial intelligence, and data science. In this article, we use the Stacking Ensemble Machine Learning Algorithm (SEMLA) to predict heart disease, considering accuracy (acc), diagnostic odds ratio (Dor), F1_score, Matthews correlation coefficient (Mcc), receiver operating characteristics-area under curve (roc-auc), and logloss (log_loss). The data is analyzed using classification learning techniques. We have considered sex, age, cholesterol, fasting blood sugar, the highest rate of heartbeat, type of chest pain, resting electrocardiogram (ECG), angina, depression induced by exercise, peak exercise measurement, major vessel number, a disorder in the blood, and a target attribute to represent the presence and absence of disorders. The approach used allows for the prediction of heart disease and the management of worst-case scenarios. In comparison with the existing models, our proposed model has outperformed other models with an accuracy of 97.28%.","PeriodicalId":29767,"journal":{"name":"Contemporary Mathematics","volume":"12 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2023-11-06","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"135634371","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}
Ahmed H. Arnous, Anjan Biswas, Yakup Yildirim, Asim Asiri
This study recovers quiescent optical solitons within a complex concatenation model featuring nonlinear chromatic dispersion and differential group delay. It employs the sine-Gordon equation approach and the projective Riccati equation scheme. The results include the successful recovery of soliton solutions and the identification of parameter restrictions for their existence. The novelty lies in the application of these methods to this specific problem, offering valuable insights for optical communication system design.
{"title":"Quiescent Optical Solitons for the Concatenation Model Having Nonlinear Chromatic Dispersion with Differential Group Delay","authors":"Ahmed H. Arnous, Anjan Biswas, Yakup Yildirim, Asim Asiri","doi":"10.37256/cm.4420233596","DOIUrl":"https://doi.org/10.37256/cm.4420233596","url":null,"abstract":"This study recovers quiescent optical solitons within a complex concatenation model featuring nonlinear chromatic dispersion and differential group delay. It employs the sine-Gordon equation approach and the projective Riccati equation scheme. The results include the successful recovery of soliton solutions and the identification of parameter restrictions for their existence. The novelty lies in the application of these methods to this specific problem, offering valuable insights for optical communication system design.","PeriodicalId":29767,"journal":{"name":"Contemporary Mathematics","volume":"128 S196","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2023-11-03","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"135818803","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}
In this study, we employ a rational Jacobi collocation technique to effectively address linear time-fractional subdiffusion and reaction sub-diffusion equations. The semi-analytic approximation solution, in this case, represents the spatial and temporal variables as a series of rational Jacobi polynomials. Subsequently, we apply the operational collocation method to convert the target equations into a system of algebraic equations. A comprehensive investigation into the convergence properties of the dual series expansion employed in this approximation is conducted, demonstrating the robustness of the numerical method put forth. To illustrate the method's accuracy and practicality, we present several numerical examples. The advantages of this method are: high accuracy, efficiency, applicability, and high rate of convergence.
{"title":"Jacobi Rational Operational Approach for Time-Fractional Sub-Diffusion Equation on a Semi-Infinite Domain","authors":"R. M. Hafez, Y. H. Youssri, A. G. Atta","doi":"10.37256/cm.4420233594","DOIUrl":"https://doi.org/10.37256/cm.4420233594","url":null,"abstract":"In this study, we employ a rational Jacobi collocation technique to effectively address linear time-fractional subdiffusion and reaction sub-diffusion equations. The semi-analytic approximation solution, in this case, represents the spatial and temporal variables as a series of rational Jacobi polynomials. Subsequently, we apply the operational collocation method to convert the target equations into a system of algebraic equations. A comprehensive investigation into the convergence properties of the dual series expansion employed in this approximation is conducted, demonstrating the robustness of the numerical method put forth. To illustrate the method's accuracy and practicality, we present several numerical examples. The advantages of this method are: high accuracy, efficiency, applicability, and high rate of convergence.","PeriodicalId":29767,"journal":{"name":"Contemporary Mathematics","volume":"1 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2023-10-30","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"136018941","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}
This paper deals with a nonlinear ordinary differential system of second order. In the paper, qualitative properties of solutions of the system called asymptotic stability (AS), uniform stability (US), boundedness, ultimately boundedness (UB) and integrability of solutions, are investigated by using the second method of Lyapunov. We give four new qualitative results and an example as a numerical application of the results. The results of this article extend and improve some earlier ones in the literature.
{"title":"New Qualitative Outcomes for Ordinary Differential Systems of Second Order","authors":"Melek Gözen","doi":"10.37256/cm.5120243045","DOIUrl":"https://doi.org/10.37256/cm.5120243045","url":null,"abstract":"This paper deals with a nonlinear ordinary differential system of second order. In the paper, qualitative properties of solutions of the system called asymptotic stability (AS), uniform stability (US), boundedness, ultimately boundedness (UB) and integrability of solutions, are investigated by using the second method of Lyapunov. We give four new qualitative results and an example as a numerical application of the results. The results of this article extend and improve some earlier ones in the literature.","PeriodicalId":29767,"journal":{"name":"Contemporary Mathematics","volume":"13 12","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2023-10-27","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"136261789","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}
There is no single set in an imaginary space, for which an exact mathematical definition would not exist by the mathematical symmetry laws. We discuss a theory in which appears an imaginary number axis strictly defifined at the level of imaginary space, allowing one to formulate and prove the theorem on the basis of its internal disclosure. This new theory of a set makes it possible to introduce a notion of the full compactness of sets of an imaginary space, confirming their availability in the defined symmetry of elements of a definitely symmetrical line.
{"title":"Fully Regular Sets of an Imaginary Space","authors":"Rasulkhozha S. Sharafiddinov","doi":"10.37256/cm.4420232405","DOIUrl":"https://doi.org/10.37256/cm.4420232405","url":null,"abstract":"There is no single set in an imaginary space, for which an exact mathematical definition would not exist by the mathematical symmetry laws. We discuss a theory in which appears an imaginary number axis strictly defifined at the level of imaginary space, allowing one to formulate and prove the theorem on the basis of its internal disclosure. This new theory of a set makes it possible to introduce a notion of the full compactness of sets of an imaginary space, confirming their availability in the defined symmetry of elements of a definitely symmetrical line.","PeriodicalId":29767,"journal":{"name":"Contemporary Mathematics","volume":"34 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2023-10-26","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"134908074","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}
We studied the Lax type integrability of the Calogero-Degasperis nonlinear dynamical system, possessing only one local conserved quantity. Based on the gradientholonomic integrability approach there are stated tboth the bi-Hamiltonian structure of the Calogero-Degasperis dynamical system and isomorphism of its symmetries group to the semidirect product of the diffeomorphism group of the circle and the abelian group of functions on it. We also constructed a rich algebra of non-Hamiltonian symmetries, related to the Bäcklund transformed general symmetries of the corresponding linearization of the Calogero-Degasperis dynamical system. There is also analyzed in detail the inverse problem of classifying integrable generalized Calogero-Degasperis type dynamical systems a priori possessing a finite number of conserved quantities.
{"title":"On the Lie-Algebraic Integrability of the Calogero-Degasperis Dynamical System and Its Generalizations","authors":"Anatolij K. Prykarpatski, Victor A. Bovdi","doi":"10.37256/cm.4420232955","DOIUrl":"https://doi.org/10.37256/cm.4420232955","url":null,"abstract":"We studied the Lax type integrability of the Calogero-Degasperis nonlinear dynamical system, possessing only one local conserved quantity. Based on the gradientholonomic integrability approach there are stated tboth the bi-Hamiltonian structure of the Calogero-Degasperis dynamical system and isomorphism of its symmetries group to the semidirect product of the diffeomorphism group of the circle and the abelian group of functions on it. We also constructed a rich algebra of non-Hamiltonian symmetries, related to the Bäcklund transformed general symmetries of the corresponding linearization of the Calogero-Degasperis dynamical system. There is also analyzed in detail the inverse problem of classifying integrable generalized Calogero-Degasperis type dynamical systems a priori possessing a finite number of conserved quantities.","PeriodicalId":29767,"journal":{"name":"Contemporary Mathematics","volume":"43 4","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2023-10-25","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"135218947","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}
Ismailkhan Enayathulla Khan, Rajendran Paramasivam
In this article, we aim to provide a solution for the Markovian Erlang non-constricted queue that takes into account encouraged arrival, balking feedback strategy, and customer retention, all in a steady state. Our approach involved using an iterative technique to determine the probability of “n” customers in the system occupying stage “s”, the probability of an empty system, and the efficiency of the queuing system. To illustrate the relationship between probability and these additional concepts, we present numerical data.
{"title":"Markovian Erlang Non-Constricted Single-Channel with Encouraged Arrival in Steady State with Balking, Feedback Strategy, and Customer Retention","authors":"Ismailkhan Enayathulla Khan, Rajendran Paramasivam","doi":"10.37256/cm.4420232964","DOIUrl":"https://doi.org/10.37256/cm.4420232964","url":null,"abstract":"In this article, we aim to provide a solution for the Markovian Erlang non-constricted queue that takes into account encouraged arrival, balking feedback strategy, and customer retention, all in a steady state. Our approach involved using an iterative technique to determine the probability of “n” customers in the system occupying stage “s”, the probability of an empty system, and the efficiency of the queuing system. To illustrate the relationship between probability and these additional concepts, we present numerical data.","PeriodicalId":29767,"journal":{"name":"Contemporary Mathematics","volume":"11 5","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2023-10-25","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"135217352","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}
S. Sivasankar, R. Udhayakumar, V. Muthukumaran, S. Al-Omari
In this manuscript, we present a collection of suitable requirements for the approximate controllability outcomes of impulsive second-order stochastic neutral differential evolution systems. We use the ideas from the sine and cosine functions and the fixed point strategy to demonstrate the primary findings. The analysis then moves to second-order nonlocal stochastic neutral differential systems. Eventually, in order to make our topic more useful, we will provide an epistemological implementation.
{"title":"Approximate Controllability Outcomes of Impulsive Second-Order Stochastic Neutral Differential Evolution Systems","authors":"S. Sivasankar, R. Udhayakumar, V. Muthukumaran, S. Al-Omari","doi":"10.37256/cm.4420233253","DOIUrl":"https://doi.org/10.37256/cm.4420233253","url":null,"abstract":"In this manuscript, we present a collection of suitable requirements for the approximate controllability outcomes of impulsive second-order stochastic neutral differential evolution systems. We use the ideas from the sine and cosine functions and the fixed point strategy to demonstrate the primary findings. The analysis then moves to second-order nonlocal stochastic neutral differential systems. Eventually, in order to make our topic more useful, we will provide an epistemological implementation.","PeriodicalId":29767,"journal":{"name":"Contemporary Mathematics","volume":"21 2","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2023-10-25","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"135217656","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}
京公网安备 11010802042870号
京ICP备2023020795号-1
扫码关注我们
求助内容：
应助结果提醒方式：