{"title":"Study on the well-posedness of stochastic Boussinesq equations with Navier boundary conditions","authors":"Chengfeng Sun, Shan Jiang, Hui Liu","doi":"10.3934/mfc.2023033","DOIUrl":"https://doi.org/10.3934/mfc.2023033","url":null,"abstract":"","PeriodicalId":93334,"journal":{"name":"Mathematical foundations of computing","volume":"1 1","pages":""},"PeriodicalIF":0.0,"publicationDate":"2023-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"70220863","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}
{"title":"Generalized interval AOR method for solving interval linear equations","authors":"Jahnabi Chakravarty, M. Saha","doi":"10.3934/mfc.2023035","DOIUrl":"https://doi.org/10.3934/mfc.2023035","url":null,"abstract":"","PeriodicalId":93334,"journal":{"name":"Mathematical foundations of computing","volume":"1 1","pages":""},"PeriodicalIF":0.0,"publicationDate":"2023-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"70221069","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, we are dealing with Cheney-Sharma Chlodovsky Durrmeyer operators and studying their approximation properties. The Bohman-Korovkin theorem is verified and estimated the convergence properties using of modulus of continuity, Lipschitz- type space, and Ditzian-Totik modulus of continuity. After that, the weighted approximation result is also given. Finally, some results related to the A-statistical convergence of the operators are obtained.
{"title":"Approximation by Durrmeyer variant of Cheney-Sharma Chlodovsky operators","authors":"Chandra Prakash, D. K. Verma, N. Deo","doi":"10.3934/mfc.2022034","DOIUrl":"https://doi.org/10.3934/mfc.2022034","url":null,"abstract":"In this paper, we are dealing with Cheney-Sharma Chlodovsky Durrmeyer operators and studying their approximation properties. The Bohman-Korovkin theorem is verified and estimated the convergence properties using of modulus of continuity, Lipschitz- type space, and Ditzian-Totik modulus of continuity. After that, the weighted approximation result is also given. Finally, some results related to the A-statistical convergence of the operators are obtained.","PeriodicalId":93334,"journal":{"name":"Mathematical foundations of computing","volume":"148 1","pages":"535-545"},"PeriodicalIF":0.0,"publicationDate":"2023-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"73438969","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}
Constructing neural networks for function approximation is a classical and longstanding topic in approximation theory, so is it in learning theory. In this paper, we are going to construct a deep neural network with three hidden layers using sigmoid function to approximate and learn the piecewise smooth functions, respectively. In particular, we prove that the constructed deep sigmoid nets can reach the optimal approximation rate in approximating the piecewise smooth functions with controllable parameters but without saturation. Similar results can also be obtained in learning theory, that is, the constructed deep sigmoid nets can also realize the optimal learning rates in learning the piecewise smooth functions. The above two obtained results underlie the advantages of deep sigmoid nets and provide theoretical assessment for deep learning.
{"title":"Learning and approximating piecewise smooth functions by deep sigmoid neural networks","authors":"Xia Liu","doi":"10.3934/mfc.2023039","DOIUrl":"https://doi.org/10.3934/mfc.2023039","url":null,"abstract":"Constructing neural networks for function approximation is a classical and longstanding topic in approximation theory, so is it in learning theory. In this paper, we are going to construct a deep neural network with three hidden layers using sigmoid function to approximate and learn the piecewise smooth functions, respectively. In particular, we prove that the constructed deep sigmoid nets can reach the optimal approximation rate in approximating the piecewise smooth functions with controllable parameters but without saturation. Similar results can also be obtained in learning theory, that is, the constructed deep sigmoid nets can also realize the optimal learning rates in learning the piecewise smooth functions. The above two obtained results underlie the advantages of deep sigmoid nets and provide theoretical assessment for deep learning.","PeriodicalId":93334,"journal":{"name":"Mathematical foundations of computing","volume":"298 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2023-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"135699848","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}
Autism spectrum disorder (ASD) is a type of mental health disorder, and its prevalence worldwide is estimated at about one in 100 children. Accurate diagnosis of ASD as early as possible is very important for the treatment of patients in clinical applications. ABIDE Ⅰ dataset as a repository of ASD is used much for developing classifiers for ASD from typical controls. In this paper, we mainly consider three types of correlations including Pearson correlation, partial correlation, and tangent correlation together based on different numbers of regions of interest (ROIs) from only one atlas, and then twelve deep neural network models are used to train 884 subjects with 5, 10, 15, 20-fold cross-validation on two types of split methods including stratified and non-stratified methods. We first consider six metrics to compare the model performance among the split methods. The six metrics are F1-Score, precision, recall, accuracy, and specificity, area under the precision-recall curve (PRAUC), and area under the Receiver Characteristic Operator curve (ROCAUC). The study achieved the highest accuracy rate of 71.94% for 5-fold cross-validation, 72.64% for 10-fold cross-validation, 72.96% for 15-fold cross-validation, and 73.43% for 20-fold cross-validation.
{"title":"Autism spectrum disorder (ASD) classification with three types of correlations based on ABIDE Ⅰ data","authors":"Donglin Wang, Xin Yang, Wandi Ding","doi":"10.3934/mfc.2023042","DOIUrl":"https://doi.org/10.3934/mfc.2023042","url":null,"abstract":"Autism spectrum disorder (ASD) is a type of mental health disorder, and its prevalence worldwide is estimated at about one in 100 children. Accurate diagnosis of ASD as early as possible is very important for the treatment of patients in clinical applications. ABIDE Ⅰ dataset as a repository of ASD is used much for developing classifiers for ASD from typical controls. In this paper, we mainly consider three types of correlations including Pearson correlation, partial correlation, and tangent correlation together based on different numbers of regions of interest (ROIs) from only one atlas, and then twelve deep neural network models are used to train 884 subjects with 5, 10, 15, 20-fold cross-validation on two types of split methods including stratified and non-stratified methods. We first consider six metrics to compare the model performance among the split methods. The six metrics are F1-Score, precision, recall, accuracy, and specificity, area under the precision-recall curve (PRAUC), and area under the Receiver Characteristic Operator curve (ROCAUC). The study achieved the highest accuracy rate of 71.94% for 5-fold cross-validation, 72.64% for 10-fold cross-validation, 72.96% for 15-fold cross-validation, and 73.43% for 20-fold cross-validation.","PeriodicalId":93334,"journal":{"name":"Mathematical foundations of computing","volume":"49 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2023-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"136367263","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}
{"title":"Convergence theorems in Orlicz and Bögel continuous functions spaces by means of Kantorovich discrete type sampling operators","authors":"Serkan Ayan, N. Ispir","doi":"10.3934/mfc.2022056","DOIUrl":"https://doi.org/10.3934/mfc.2022056","url":null,"abstract":"","PeriodicalId":93334,"journal":{"name":"Mathematical foundations of computing","volume":"25 1","pages":"354-368"},"PeriodicalIF":0.0,"publicationDate":"2023-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"78885437","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 bionic polarization integrated navigation system includes three-axis gyroscopes, three-axis accelerometers, three-axis magnetometers, and polarization sensors, which provide pitch, roll, and yaw. When the magnetometers are interfered or the polarization sensors are obscured, the accuracy of attitude will be decreased due to abnormal measurement. To improve the accuracy of attitude of the integrated navigation system under these complex environments, an adaptive complementary filter based on DQN (Deep Q-learning Network) is proposed. The complementary filter is first designed to fuse the measurements from the gyroscopes, accelerometers, magnetometers, and polarization sensors. Then, a reward function of the bionic polarization integrated navigation system is defined as the function of the absolute value of the attitude angle error. The action-value function is introduced by a fully-connected network obtained by historical sensor data training. The strategy can be calculated by the deep Q-learning network and the action that optimal action-value function is obtained. Based on the optimized action, three types of integration are switched automatically to adapt to the different environments. Three cases of simulations are conducted to validate the effectiveness of the proposed algorithm. The results show that the adaptive attitude determination of bionic polarization integrated navigation system based on DQN can improve the accuracy of the attitude estimation.
{"title":"Adaptive attitude determination of bionic polarization integrated navigation system based on reinforcement learning strategy","authors":"HuiYi Bao, Tao Du, Luyue Sun","doi":"10.3934/mfc.2022014","DOIUrl":"https://doi.org/10.3934/mfc.2022014","url":null,"abstract":"The bionic polarization integrated navigation system includes three-axis gyroscopes, three-axis accelerometers, three-axis magnetometers, and polarization sensors, which provide pitch, roll, and yaw. When the magnetometers are interfered or the polarization sensors are obscured, the accuracy of attitude will be decreased due to abnormal measurement. To improve the accuracy of attitude of the integrated navigation system under these complex environments, an adaptive complementary filter based on DQN (Deep Q-learning Network) is proposed. The complementary filter is first designed to fuse the measurements from the gyroscopes, accelerometers, magnetometers, and polarization sensors. Then, a reward function of the bionic polarization integrated navigation system is defined as the function of the absolute value of the attitude angle error. The action-value function is introduced by a fully-connected network obtained by historical sensor data training. The strategy can be calculated by the deep Q-learning network and the action that optimal action-value function is obtained. Based on the optimized action, three types of integration are switched automatically to adapt to the different environments. Three cases of simulations are conducted to validate the effectiveness of the proposed algorithm. The results show that the adaptive attitude determination of bionic polarization integrated navigation system based on DQN can improve the accuracy of the attitude estimation.","PeriodicalId":93334,"journal":{"name":"Mathematical foundations of computing","volume":"96 1","pages":"161-177"},"PeriodicalIF":0.0,"publicationDate":"2023-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"82211802","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}
M. López-Pellicer, S. López-Alfonso, S. Moll-López
{"title":"Revisiting Mazur separable quotient problem (1932)","authors":"M. López-Pellicer, S. López-Alfonso, S. Moll-López","doi":"10.3934/mfc.2022063","DOIUrl":"https://doi.org/10.3934/mfc.2022063","url":null,"abstract":"","PeriodicalId":93334,"journal":{"name":"Mathematical foundations of computing","volume":"156 1","pages":"453-459"},"PeriodicalIF":0.0,"publicationDate":"2023-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"77479829","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}
{"title":"Output feedback control of interval type-2 T-S fuzzy fractional order systems subject to actuator saturation","authors":"Taoqi Deng, Xuefeng Zhang, Zhe Wang","doi":"10.3934/mfc.2023025","DOIUrl":"https://doi.org/10.3934/mfc.2023025","url":null,"abstract":"","PeriodicalId":93334,"journal":{"name":"Mathematical foundations of computing","volume":"1 1","pages":""},"PeriodicalIF":0.0,"publicationDate":"2023-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"70220953","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 determine the necessary and sufficient convolution conditions for the starlike functions on the open unit disk and related to some geometric aspects of the function begin{document}$ tanh z $end{document}. We also determine sharp bounds on second and third order Hermitian-Toeplitz determinants for such functions. Further, we compute estimates on some initial coefficients and the Hankel determinants of third and fourth order. In addition, using the concept of Briot-Bouquet type differential subordination, we establish a subordination inclusion involving Bernardi integral operator.
We determine the necessary and sufficient convolution conditions for the starlike functions on the open unit disk and related to some geometric aspects of the function begin{document}$ tanh z $end{document}. We also determine sharp bounds on second and third order Hermitian-Toeplitz determinants for such functions. Further, we compute estimates on some initial coefficients and the Hankel determinants of third and fourth order. In addition, using the concept of Briot-Bouquet type differential subordination, we establish a subordination inclusion involving Bernardi integral operator.
{"title":"Starlike functions associated with $ tanh z $ and Bernardi integral operator","authors":"Pratima Rai, A. Çetinkaya, Sushil Kumar","doi":"10.3934/mfc.2022032","DOIUrl":"https://doi.org/10.3934/mfc.2022032","url":null,"abstract":"<p style='text-indent:20px;'>We determine the necessary and sufficient convolution conditions for the starlike functions on the open unit disk and related to some geometric aspects of the function <inline-formula><tex-math id=\"M8\">begin{document}$ tanh z $end{document}</tex-math></inline-formula>. We also determine sharp bounds on second and third order Hermitian-Toeplitz determinants for such functions. Further, we compute estimates on some initial coefficients and the Hankel determinants of third and fourth order. In addition, using the concept of Briot-Bouquet type differential subordination, we establish a subordination inclusion involving Bernardi integral operator.</p>","PeriodicalId":93334,"journal":{"name":"Mathematical foundations of computing","volume":"29 1","pages":"573-585"},"PeriodicalIF":0.0,"publicationDate":"2023-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"73022462","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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