A Lorentzian para-Sasakian (LP-Sasakian) space form is a kind of para-Sasakian manifold with constant $ varphi- $ holomorphic sectional curvature. The presented paper is on the curvatures of semi-invariant submanifolds of a LP-Sasakian space form. Firstly, the definition of a semi-invariant submanifold of LP-Sasakian space form is given and an example is presented. Then, using Gauss equation related to curvatures used for obtaining some important results on Ricci and scalar curvatures. Moreover, by suffering from these results conditions of distributions being Einstein have been examined. Finally, semi-invariant products of Lorentzian para-Sasakian manifolds have been considered and an important inequality for second fundamental form is proved.
{"title":"On Curvatures of Semi-invariant Submanifolds of Lorentzian Para-Sasakian Manifolds","authors":"Ramazan Sari, İ. Ünal","doi":"10.47000/tjmcs.1322351","DOIUrl":"https://doi.org/10.47000/tjmcs.1322351","url":null,"abstract":"A Lorentzian para-Sasakian (LP-Sasakian) space form is a kind of para-Sasakian manifold with constant $ varphi- $ holomorphic sectional curvature. The presented paper is on the curvatures of semi-invariant submanifolds of a LP-Sasakian space form. Firstly, the definition of a semi-invariant submanifold of LP-Sasakian space form is given and an example is presented. Then, using Gauss equation related to curvatures used for obtaining some important results on Ricci and scalar curvatures. Moreover, by suffering from these results conditions of distributions being Einstein have been examined. Finally, semi-invariant products of Lorentzian para-Sasakian manifolds have been considered and an important inequality for second fundamental form is proved.","PeriodicalId":506513,"journal":{"name":"Turkish Journal of Mathematics and Computer Science","volume":"30 1","pages":""},"PeriodicalIF":0.0,"publicationDate":"2023-12-13","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"139180801","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, it is aimed to solve the differential equation that forms a simple engineering system and transform it into the Laplace domain, and then to investigate the effectiveness of the method used to compare the solutions with the exact solutions. For this purpose, first, the solutions of a given test function with analytical and numerical Laplace inverse transform methods (Durbin, Stehfest and Talbot) are given comparatively. Although the values obtained from these three methods overlap with each other but it is observed that the Talbot inverse transform method is more suitable than the other two methods due to its lower calculation time requirement. In addition, Talbot’s method and analytical solutions to engineering problems related to the vibratory mechanical system, heat conduction problem and a single matrix block in a fractured reservoir non-isothermal gravity drainage are numerically compared. It is understood that the Talbot inverse transform method is quite effective, and this is evident from the consistency of the numerical results and analytical results of the study. The findings show that the proposed method is very suitable and the method is easy to implement without much difficulty for solving a simple engineering problem.
{"title":"Investigating the Laplace transform method's efficiency to a simple engineering problem","authors":"Huseyin Demir, İnci ÇİLİNGİR SÜNGÜ, İbrahim Keles","doi":"10.47000/tjmcs.1378857","DOIUrl":"https://doi.org/10.47000/tjmcs.1378857","url":null,"abstract":"In this study, it is aimed to solve the differential equation that forms a simple engineering system and transform it into the Laplace domain, and then to investigate the effectiveness of the method used to compare the solutions with the exact solutions. For this purpose, first, the solutions of a given test function with analytical and numerical Laplace inverse transform methods (Durbin, Stehfest and Talbot) are given comparatively. Although the values obtained from these three methods overlap with each other but it is observed that the Talbot inverse transform method is more suitable than the other two methods due to its lower calculation time requirement. In addition, Talbot’s method and analytical solutions to engineering problems related to the vibratory mechanical system, heat conduction problem and a single matrix block in a fractured reservoir non-isothermal gravity drainage are numerically compared. It is understood that the Talbot inverse transform method is quite effective, and this is evident from the consistency of the numerical results and analytical results of the study. The findings show that the proposed method is very suitable and the method is easy to implement without much difficulty for solving a simple engineering problem.","PeriodicalId":506513,"journal":{"name":"Turkish Journal of Mathematics and Computer Science","volume":"20 2","pages":""},"PeriodicalIF":0.0,"publicationDate":"2023-11-13","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"139278997","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}
Skin cancer, which can occur in any part of the human skin, is one of the common and serious types of cancer. Accurate diagnosis and segmentation of lesions are crutial to the early diagnosis. Computer-aided diagnosis make important contributions to help doctors in the diagnosis of cancer from skin images. The most important factor for such systems to reveal the accurate results is the correct feature extraction. In this study, a model for the classification of seven types of skin lesions was developed by combining the features of CNN-based feature extraction and the ABCD rule, which is widely used in the clinic. The model was evaluated on HAM10000 well-known dataset. The classification results obtained with different combinations of features and machine learning algorithms were compared. According to the results, the best classification accuracy was obtained with the Cosine Similarity Classifier with 96.4% when the features determined by CNN and the features in the ABCD rule were used together.
{"title":"Skin Lesion Classification Using Convolutional Neural Network and ABCD Rule","authors":"Ezgi Kestek, Mehmet Emin Aktan, E. Akdogan","doi":"10.47000/tjmcs.1249300","DOIUrl":"https://doi.org/10.47000/tjmcs.1249300","url":null,"abstract":"Skin cancer, which can occur in any part of the human skin, is one of the common and serious types of cancer. Accurate diagnosis and segmentation of lesions are crutial to the early diagnosis. Computer-aided diagnosis make important contributions to help doctors in the diagnosis of cancer from skin images. The most important factor for such systems to reveal the accurate results is the correct feature extraction. In this study, a model for the classification of seven types of skin lesions was developed by combining the features of CNN-based feature extraction and the ABCD rule, which is widely used in the clinic. The model was evaluated on HAM10000 well-known dataset. The classification results obtained with different combinations of features and machine learning algorithms were compared. According to the results, the best classification accuracy was obtained with the Cosine Similarity Classifier with 96.4% when the features determined by CNN and the features in the ABCD rule were used together.","PeriodicalId":506513,"journal":{"name":"Turkish Journal of Mathematics and Computer Science","volume":"17 1","pages":""},"PeriodicalIF":0.0,"publicationDate":"2023-11-06","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"139288165","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}
The object of the present paper is to study Quasi-concircularly flat and $phi-$quasi-concircularly flat generalized Sasakian-space-forms. Also, we consider generalized Sasakian-space-forms satisfying the condition $P(xi, X).widetilde{V}=0, widetilde{V}(xi, X).P=0, $ and $widetilde{V}(xi, X).widetilde{V}=0$ and we obtain some important results. Finally, we give an example.
{"title":"Quasi-Concircular Curvature Tensor on Generalized Sasakian Space-Forms","authors":"Rana Pratap Singh Yadav, Bhagwat Prasad","doi":"10.47000/tjmcs.1194308","DOIUrl":"https://doi.org/10.47000/tjmcs.1194308","url":null,"abstract":"The object of the present paper is to study Quasi-concircularly flat and $phi-$quasi-concircularly flat generalized Sasakian-space-forms. Also, we consider generalized Sasakian-space-forms satisfying the condition $P(xi, X).widetilde{V}=0, widetilde{V}(xi, X).P=0, $ and $widetilde{V}(xi, X).widetilde{V}=0$ and we obtain some important results. Finally, we give an example.","PeriodicalId":506513,"journal":{"name":"Turkish Journal of Mathematics and Computer Science","volume":"121 1","pages":""},"PeriodicalIF":0.0,"publicationDate":"2023-11-03","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"139289727","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}
ABsTRACT. The rapid surge in social media usage has augmented the significance and value of data available on these platforms. As a result, analyzing community sentiment and opinions related to various topics and events using social media data has become increasingly crucial. However, the sheer volume of data produced on social media platforms surpasses human processing capabilities. Consequently, artificial intelligence-based models became frequently employed in social media analysis. In this study, deep learning (DL) and machine learning (ML) methods are applied to assess user opinions regarding airlines, and the effectiveness of these methods in social media analysis is comparatively discussed based on the performance results obtained. Due to the imbalanced nature of the dataset, synthetic data is produced using the Synthetic Minority Over-Sampling Technique (SMOTE) to enhance model performance. Before the SMOTE process, the dataset containing 14640 data points expanded to 27534 data points after the SMOTE process. The experimental results demonstrate that Support Vector Machines (SVM) achieved the highest performance among all methods with accuracy, precision, recall, and F-score values of 0.79 in the pre-SMOTE (imbalanced dataset). In contrast, Random Forest (RF) obtained the best performance among all methods, with accuracy, precision, recall, and F-score values of 0.88 in the post-SMOTE (balanced data set). Moreover, experimental findings demonstrate that SMOTE led to performance improvements in ML and DL models, ranging from a minimum of 3% to a maximum of 24% increase in F-Score metric.
摘要。社交媒体使用量的快速激增增强了这些平台上可用数据的重要性和价值。因此，利用社交媒体数据分析与各种话题和事件相关的社区情绪和观点变得越来越重要。然而，社交媒体平台上产生的大量数据超出了人类的处理能力。因此，基于人工智能的模型经常被用于社交媒体分析。本研究将深度学习（DL）和机器学习（ML）方法应用于评估用户对航空公司的意见，并根据所获得的性能结果比较讨论了这些方法在社交媒体分析中的有效性。由于数据集的不平衡性，我们使用合成少数群体过度采样技术（SMOTE）生成合成数据，以提高模型性能。在进行 SMOTE 处理之前，数据集包含 14640 个数据点，经过 SMOTE 处理后，数据集扩大到 27534 个数据点。实验结果表明，在所有方法中，支持向量机（SVM）在 SMOTE 前（不平衡数据集）的准确度、精确度、召回率和 F 分数值均为 0.79，取得了最高的性能。相比之下，随机森林（RF）在所有方法中表现最佳，在后 SMOTE（平衡数据集）中的准确度、精确度、召回率和 F 分数均为 0.88。此外，实验结果表明，SMOTE 提高了 ML 和 DL 模型的性能，F-Score 指标的提高幅度最小为 3%，最大为 24%。
{"title":"Social Media User Opinion Analysis Using Deep Learning and Machine Learning Methods: A Case Study on Airlines","authors":"Ömer Ayberk Şencan, I. Atacak","doi":"10.47000/tjmcs.1368430","DOIUrl":"https://doi.org/10.47000/tjmcs.1368430","url":null,"abstract":"ABsTRACT. The rapid surge in social media usage has augmented the significance and value of data available on these platforms. As a result, analyzing community sentiment and opinions related to various topics and events using social media data has become increasingly crucial. However, the sheer volume of data produced on social media platforms surpasses human processing capabilities. Consequently, artificial intelligence-based models became frequently employed in social media analysis. In this study, deep learning (DL) and machine learning (ML) methods are applied to assess user opinions regarding airlines, and the effectiveness of these methods in social media analysis is comparatively discussed based on the performance results obtained. Due to the imbalanced nature of the dataset, synthetic data is produced using the Synthetic Minority Over-Sampling Technique (SMOTE) to enhance model performance. Before the SMOTE process, the dataset containing 14640 data points expanded to 27534 data points after the SMOTE process. The experimental results demonstrate that Support Vector Machines (SVM) achieved the highest performance among all methods with accuracy, precision, recall, and F-score values of 0.79 in the pre-SMOTE (imbalanced dataset). In contrast, Random Forest (RF) obtained the best performance among all methods, with accuracy, precision, recall, and F-score values of 0.88 in the post-SMOTE (balanced data set). Moreover, experimental findings demonstrate that SMOTE led to performance improvements in ML and DL models, ranging from a minimum of 3% to a maximum of 24% increase in F-Score metric.","PeriodicalId":506513,"journal":{"name":"Turkish Journal of Mathematics and Computer Science","volume":"31 1","pages":""},"PeriodicalIF":0.0,"publicationDate":"2023-10-31","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"139309594","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}
The object of this article is to study a quarter-symmetric non-metric connection in the tangent bundle and induced metric and connection on submanifold of co-dimension 2 and hypersurface concerning the quarter-symmetric non-metric connection in the tangent bundle. The Weingarten equations concerning the quarter-symmetric non-metric connection on a submanifold of co-dimension 2 and the hypersurface in the tangent bundle are obtained. Finally, authors deduce the Riemannian curvature tensor and Gauss and Codazzi equations on a submanifold of co-dimension 2 and hypersurface of the Riemannian manifold concerning the quarter-symmetric non-metric connection in the tangent bundle.
{"title":"On tangent bundles of submanifolds of a Riemannian manifold endowed with quarter-symmetric non-metric connection","authors":"Mohammad Nazrul Islam Khan, Lovejoy Das","doi":"10.47000/tjmcs.1355887","DOIUrl":"https://doi.org/10.47000/tjmcs.1355887","url":null,"abstract":"The object of this article is to study a quarter-symmetric non-metric connection in the tangent bundle and induced metric and connection on submanifold of co-dimension 2 and hypersurface concerning the quarter-symmetric non-metric connection in the tangent bundle. The Weingarten equations concerning the quarter-symmetric non-metric connection on a submanifold of co-dimension 2 and the hypersurface in the tangent bundle are obtained. Finally, authors deduce the Riemannian curvature tensor and Gauss and Codazzi equations on a submanifold of co-dimension 2 and hypersurface of the Riemannian manifold concerning the quarter-symmetric non-metric connection in the tangent bundle.","PeriodicalId":506513,"journal":{"name":"Turkish Journal of Mathematics and Computer Science","volume":"79 1","pages":""},"PeriodicalIF":0.0,"publicationDate":"2023-10-07","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"139321961","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 work, we construct the sequence spaces $c_{0}(Q)$, $c(Q)$, $ell_{infty}(Q)$ and $ell_{p}(Q)$ derived by the domain of quadruple band matrix, which generalizes the matrices $Delta^{3}$, $B(r,s,t)$, $Delta^{2}$, $B(r,s)$, $Delta$, where $Delta^{3}$, $B(r,s,t)$, $Delta^{2}$, $B(r,s)$ and $Delta$ are called third order difference, triple band, second order difference, double band and difference matrix, in turn. Also, we investigate some topological properties and some inclusion relations related to those spaces. Furthermore, we give the Schauder basis of the spaces $c_{0}(Q)$, $c(Q)$ and $ell_{p}(Q)$, and determine $alpha-beta-$ and $gamma-$duals of those spaces. Lastly, we characterize some matrix classes related to some of those spaces.
{"title":"Four New Sequence Spaces Obtained From The Domain Of Quadruple Band Matrix Operator","authors":"M. Bi̇şgi̇n","doi":"10.47000/tjmcs.1274395","DOIUrl":"https://doi.org/10.47000/tjmcs.1274395","url":null,"abstract":"In this work, we construct the sequence spaces $c_{0}(Q)$, $c(Q)$, $ell_{infty}(Q)$ and $ell_{p}(Q)$ derived by the domain of quadruple band matrix, which generalizes the matrices $Delta^{3}$, $B(r,s,t)$, $Delta^{2}$, $B(r,s)$, $Delta$, where $Delta^{3}$, $B(r,s,t)$, $Delta^{2}$, $B(r,s)$ and $Delta$ are called third order difference, triple band, second order difference, double band and difference matrix, in turn. Also, we investigate some topological properties and some inclusion relations related to those spaces. Furthermore, we give the Schauder basis of the spaces $c_{0}(Q)$, $c(Q)$ and $ell_{p}(Q)$, and determine $alpha-beta-$ and $gamma-$duals of those spaces. Lastly, we characterize some matrix classes related to some of those spaces.","PeriodicalId":506513,"journal":{"name":"Turkish Journal of Mathematics and Computer Science","volume":"64 1","pages":""},"PeriodicalIF":0.0,"publicationDate":"2023-10-07","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"139322016","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 the modified quadratic Lorenz attractor is introduced in geometric multiplicative calculus. The new system is analyzed and discussed for the chaotic behaviour in detail. The equilibria points, the eigenvalues of the multiplicative Jacobian, and the Lyapunov exponents are determined. The numerical simulations are conducted using the Runge-Kutta method in the framework of geometric multiplicative calculus highlighting the chaotic behaviour.
{"title":"A Modified Quadratic Lorenz Attractor in Geometric Multiplicative Calculus","authors":"Bugce EMİNAGA TATLİCİOGLU","doi":"10.47000/tjmcs.1249554","DOIUrl":"https://doi.org/10.47000/tjmcs.1249554","url":null,"abstract":"In this study the modified quadratic Lorenz attractor is introduced in geometric multiplicative calculus. The new system is analyzed and discussed for the chaotic behaviour in detail. The equilibria points, the eigenvalues of the multiplicative Jacobian, and the Lyapunov exponents are determined. The numerical simulations are conducted using the Runge-Kutta method in the framework of geometric multiplicative calculus highlighting the chaotic behaviour.","PeriodicalId":506513,"journal":{"name":"Turkish Journal of Mathematics and Computer Science","volume":"28 1","pages":""},"PeriodicalIF":0.0,"publicationDate":"2023-09-20","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"139338366","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 paper, invariant submanifolds of a para-Sasakian manifold are studied. For a para-Sasakian manifold, pseudoparallel, 2-pseudoparallel, Ricci generalized pseudoparallel and 2-Ricci generalized pseudoparalel cases are considered and new results are obtained. The necessary and sufficient are given for an invriant submanifold to be totally geodesic under the some conditions.
{"title":"Pseudoparallel Invariant Submanifolds of a Para-Sasakian Manifold","authors":"Tuğba Mert, M. Atc̣eken","doi":"10.47000/tjmcs.1124668","DOIUrl":"https://doi.org/10.47000/tjmcs.1124668","url":null,"abstract":"In this paper, invariant submanifolds of a para-Sasakian manifold are studied. For a para-Sasakian manifold, pseudoparallel, 2-pseudoparallel, Ricci generalized pseudoparallel and 2-Ricci generalized pseudoparalel cases are considered and new results are obtained. The necessary and sufficient are given for an invriant submanifold to be totally geodesic under the some conditions.","PeriodicalId":506513,"journal":{"name":"Turkish Journal of Mathematics and Computer Science","volume":"33 1","pages":""},"PeriodicalIF":0.0,"publicationDate":"2023-09-15","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"139339784","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}
New first order and second order energy preserving schemes are proposed for the Zakharov system. The methods are fully implicit and semi-explicit. It has been found that the first order method is also mass conserving. Concrete schemes have been applied to simulate the soliton evolution of the Zakharov system. Numerical results show that the proposed methods capture the remarkable features of the Zakharov equation. We obtained that the semi-explicit methods are more efficient than the fully implicit methods. Numerical results also show that the new energy preserving schemes well simulate the soliton evolution of the Zakharov system.
{"title":"New conservative schemes for Zakharov equation","authors":"Ayhan Aydin, Bahaa Ahmed Khalaf Sabawe","doi":"10.47000/tjmcs.1226770","DOIUrl":"https://doi.org/10.47000/tjmcs.1226770","url":null,"abstract":"New first order and second order energy preserving schemes are proposed for the Zakharov system. The methods are fully implicit and semi-explicit. It has been found that the first order method is also mass conserving. Concrete schemes have been applied to simulate the soliton evolution of the Zakharov system. Numerical results show that the proposed methods capture the remarkable features of the Zakharov equation. We obtained that the semi-explicit methods are more efficient than the fully implicit methods. Numerical results also show that the new energy preserving schemes well simulate the soliton evolution of the Zakharov system.","PeriodicalId":506513,"journal":{"name":"Turkish Journal of Mathematics and Computer Science","volume":"81 1","pages":""},"PeriodicalIF":0.0,"publicationDate":"2023-09-06","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"139342204","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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