Pub Date : 2022-10-05DOI: 10.14738/tmlai.105.13171
Y. S. Ayala
In this article, we prove that initial value problem associated to the non homogeneous third order equation in periodic Sobolev spaces has a local so- lution in [0, T ] with T > 0, and the solution has continuous dependence with respect to the initial data and the non homogeneous part of the problem. We do this in a intuitive way using Fourier theory and introducing a Co - Semi- group inspired by the work of Iorio [1] and Santiago [6]. Also, we prove the uniqueness solution of the homogeneous third order equa- tion, using its conservative property, inspired by the work of Iorio [1] and Santiago [7]. Finally, we study its generalization to n-th order equation.
{"title":"Existence and Continuous Dependence of the Local Solution of Non Homogeneous Third Order Equation and Generalizations","authors":"Y. S. Ayala","doi":"10.14738/tmlai.105.13171","DOIUrl":"https://doi.org/10.14738/tmlai.105.13171","url":null,"abstract":"\u0000 \u0000 \u0000In this article, we prove that initial value problem associated to the non homogeneous third order equation in periodic Sobolev spaces has a local so- lution in [0, T ] with T > 0, and the solution has continuous dependence with respect to the initial data and the non homogeneous part of the problem. We do this in a intuitive way using Fourier theory and introducing a Co - Semi- group inspired by the work of Iorio [1] and Santiago [6]. Also, we prove the uniqueness solution of the homogeneous third order equa- tion, using its conservative property, inspired by the work of Iorio [1] and Santiago [7]. Finally, we study its generalization to n-th order equation. \u0000 \u0000 \u0000","PeriodicalId":119801,"journal":{"name":"Transactions on Machine Learning and Artificial Intelligence","volume":"53 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2022-10-05","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"122390700","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 : 2022-09-29DOI: 10.14738/tmlai.105.13049
D. Karimanzira, Linda Ritzau, Katharina Emde
Modeling of rainfall-runoff is very critical for flood prediction studies in decision making for disaster management. Deep learning methods have proven to be very useful in hydrological prediction. To increase their acceptance in the hydrological community, they must be physic-informed and show some interpretability. They are several ways this can be achieved e.g. by learning from a fully-trained hydrological model which assumes the availability of the hydrological model or to use physic-informed data. In this work we developed a Graph Attention Network (GAT) with learnable Adjacency Matrix coupled with a Bi-directional Gated Temporal Convolutional Neural Network (2DGAT-BiLSTM). Physic-informed data with spatial information from Digital Elevation Model and geographical data is used to train it. Besides, precipitation, evapotranspiration and discharge, the model utilizes the catchment area characteristic information, such as instantaneous slope, soil type, drainage area etc. The method is compared to two different current developments in deep learning structures for streamflow prediction, which also utilize all the spatial and temporal information in an integrated way. One, namely Graph Neural Rainfall-Runoff Models (GNRRM) uses timeseries prediction on each node and a Graph Neural Network (GNN) to route the information to the target node and another one called STA-LSTM is based on Spatial and temporal Attention Mechanism and Long Short Term Memory (LSTM) for prediction. The different methods were compared in their performance in predicting the flow at several points of a pilot catchment area. With an average prediction NSE and KGE of 0.995 and 0.981, respectively for 2DGAT-BiLSTM, it could be shown that graph attention mechanism and learning the adjacency matrix for spatial information can boost the model performance and robustness, and bring interpretability and with the inclusion of domain knowledge the acceptance of the models.
{"title":"Catchment Area Multi-Streamflow Multiple Hours Ahead Forecast Based on Deep Learning","authors":"D. Karimanzira, Linda Ritzau, Katharina Emde","doi":"10.14738/tmlai.105.13049","DOIUrl":"https://doi.org/10.14738/tmlai.105.13049","url":null,"abstract":"Modeling of rainfall-runoff is very critical for flood prediction studies in decision making for disaster management. Deep learning methods have proven to be very useful in hydrological prediction. To increase their acceptance in the hydrological community, they must be physic-informed and show some interpretability. They are several ways this can be achieved e.g. by learning from a fully-trained hydrological model which assumes the availability of the hydrological model or to use physic-informed data. In this work we developed a Graph Attention Network (GAT) with learnable Adjacency Matrix coupled with a Bi-directional Gated Temporal Convolutional Neural Network (2DGAT-BiLSTM). Physic-informed data with spatial information from Digital Elevation Model and geographical data is used to train it. Besides, precipitation, evapotranspiration and discharge, the model utilizes the catchment area characteristic information, such as instantaneous slope, soil type, drainage area etc. The method is compared to two different current developments in deep learning structures for streamflow prediction, which also utilize all the spatial and temporal information in an integrated way. One, namely Graph Neural Rainfall-Runoff Models (GNRRM) uses timeseries prediction on each node and a Graph Neural Network (GNN) to route the information to the target node and another one called STA-LSTM is based on Spatial and temporal Attention Mechanism and Long Short Term Memory (LSTM) for prediction. The different methods were compared in their performance in predicting the flow at several points of a pilot catchment area. With an average prediction NSE and KGE of 0.995 and 0.981, respectively for 2DGAT-BiLSTM, it could be shown that graph attention mechanism and learning the adjacency matrix for spatial information can boost the model performance and robustness, and bring interpretability and with the inclusion of domain knowledge the acceptance of the models.","PeriodicalId":119801,"journal":{"name":"Transactions on Machine Learning and Artificial Intelligence","volume":"25 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2022-09-29","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"128393035","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 : 2022-09-29DOI: 10.14738/tmlai.105.13170
Francis Kwadade-Cudjoe
E-Commerce has been going on since Netscape.com introduced the idea in 1995 when www was invented. Businesses / consumers that have been immersed in e-commerce transaction have reaped the benefits associated with such technological break-through, as consumers sit at comfort of their homes to transact business. However, the impediment that has hindered other businesses / consumers to transform to this technological business approach has been the trust associated with carrying out business; consumer trust across global cultures has been contentious. Authors, including Hofstede, Gefen et al. and Greenberg et al. have done research on culture differences across the globe and how these differences could affect behaviours towards accepting e-commerce for transacting business. There is therefore, the need for a global digital guideline / policy to protect all consumers and businesses that trade on the internet. Such a policy would hopefully allay the fears amongst nations’ cultures having difficulty in imbibing this wholesome technological advancement for enhanced business transaction. Conducting business transaction through brick-and-mortar approach is archaic and cumbersome and should be faded out completely.
{"title":"Consumer Trust in B2C Ecommerce Strategy for Contemporary Business Transaction is Paramount for Sustaining the Emerging Commerce Market. Indicate the Similarities and Differences Between Traditional and Ecommerce Markets and Provide the Conduct of Consumer Trust Across Cultures, Globally","authors":"Francis Kwadade-Cudjoe","doi":"10.14738/tmlai.105.13170","DOIUrl":"https://doi.org/10.14738/tmlai.105.13170","url":null,"abstract":"E-Commerce has been going on since Netscape.com introduced the idea in 1995 when www was invented. Businesses / consumers that have been immersed in e-commerce transaction have reaped the benefits associated with such technological break-through, as consumers sit at comfort of their homes to transact business. However, the impediment that has hindered other businesses / consumers to transform to this technological business approach has been the trust associated with carrying out business; consumer trust across global cultures has been contentious. Authors, including Hofstede, Gefen et al. and Greenberg et al. have done research on culture differences across the globe and how these differences could affect behaviours towards accepting e-commerce for transacting business. There is therefore, the need for a global digital guideline / policy to protect all consumers and businesses that trade on the internet. Such a policy would hopefully allay the fears amongst nations’ cultures having difficulty in imbibing this wholesome technological advancement for enhanced business transaction. Conducting business transaction through brick-and-mortar approach is archaic and cumbersome and should be faded out completely. ","PeriodicalId":119801,"journal":{"name":"Transactions on Machine Learning and Artificial Intelligence","volume":"210 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2022-09-29","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"126511342","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 : 2022-09-24DOI: 10.14738/tmlai.105.13126
S. Gornale, G. Patil, R. Benne
Using advanced digital technologies and photo editing software, document images, such as typed and handwritten documents, can be manipulated in a variety of ways. The most common method of document forgery is adding or removing information. As a result of the changes made to document images, there is misinformation and misbelief in document images. Forgery detection with multiple forgery operations is challenging issue. As a result, special consideration is given in this work to the ten-class problem, in which a text can be altered using multiple forgery types. The characteristics are computed using RGB color components and GLCM texture descriptors. The method is effective for distinguishing between genuine and forged document images. A classification rate of 95.8% for forged handwritten documents and 93.11% for forged printed document images are obtained respectively. The obtained results are promising and competitive with state-of- art techniques reported in the literature.
{"title":"Document Image Forgery Detection Using RGB Color Channel","authors":"S. Gornale, G. Patil, R. Benne","doi":"10.14738/tmlai.105.13126","DOIUrl":"https://doi.org/10.14738/tmlai.105.13126","url":null,"abstract":"Using advanced digital technologies and photo editing software, document images, such as typed and handwritten documents, can be manipulated in a variety of ways. The most common method of document forgery is adding or removing information. As a result of the changes made to document images, there is misinformation and misbelief in document images. Forgery detection with multiple forgery operations is challenging issue. As a result, special consideration is given in this work to the ten-class problem, in which a text can be altered using multiple forgery types. The characteristics are computed using RGB color components and GLCM texture descriptors. The method is effective for distinguishing between genuine and forged document images. A classification rate of 95.8% for forged handwritten documents and 93.11% for forged printed document images are obtained respectively. The obtained results are promising and competitive with state-of- art techniques reported in the literature.\u0000 ","PeriodicalId":119801,"journal":{"name":"Transactions on Machine Learning and Artificial Intelligence","volume":"7 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2022-09-24","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"128081130","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 : 2022-09-03DOI: 10.14738/tmlai.104.13100
D. De Groff, P. Neelakanta
In the contexts of deep learning (DL) considered in artificial intelligence (AI) efforts, relevant machine learning (ML) algorithms adopted refer to using a class of deep artificial neural network (ANN) that supports a learning process exercised with an enormous set of input data (labeled and/or unlabeled) so to predict at the output details on accurate features of labeled data present in the input data set. In the present study, a deep ANN is proposed thereof conceived with certain novel considerations: The proposed deep architecture consists of a large number of consequently placed structures of paired-layers. Each layer hosts identical number of neuronal units for computation and the neuronal units are massively interconnected across the entire network. Further, each paired-layer is independently subjected to unsupervised learning (USL). Hence, commencing from the input layer-pair, the excitatory (input) data supplied flows across the interconnected neurons of paired layers, terminating eventually at the final pair of layers, where the output is recovered. That is, the converged neuronal states at any given pair is iteratively passed on to the next pair and so on. The USL suite involves collectively gathering the details of neural information across a pair of the layers constituting the network. This summed data is then limited with a specific choice of a squashing (sigmoidal) function; and, the resulting scaled value is used to adjust the coefficients of interconnection weights seeking a convergence criterion. The associated learning rate on weight adjustment is uniquely designed to facilitate fast learning towards convergence. The unique aspects of deep learning proposed here refer to: (i) Deducing the learning coefficient with a compatible algorithm so as to realize a fast convergence; and, (ii) the adopted sigmoidal function in the USL loop conforms to the heuristics of the so-called Langevin-Neelakanta machine. The paper describes the proposed deep ANN architecture with necessary details on structural considerations, sigmoidal selection, prescribing required learning rate and operational (training and predictive phase) routines. Results are furnished to demonstrate the performance efficacy of the test ANN.
{"title":"A Novel Deep Learning ANN Supported on Langevin-Neelakanta Machine","authors":"D. De Groff, P. Neelakanta","doi":"10.14738/tmlai.104.13100","DOIUrl":"https://doi.org/10.14738/tmlai.104.13100","url":null,"abstract":"In the contexts of deep learning (DL) considered in artificial intelligence (AI) efforts, relevant machine learning (ML) algorithms adopted refer to using a class of deep artificial neural network (ANN) that supports a learning process exercised with an enormous set of input data (labeled and/or unlabeled) so to predict at the output details on accurate features of labeled data present in the input data set. In the present study, a deep ANN is proposed thereof conceived with certain novel considerations: The proposed deep architecture consists of a large number of consequently placed structures of paired-layers. Each layer hosts identical number of neuronal units for computation and the neuronal units are massively interconnected across the entire network. Further, each paired-layer is independently subjected to unsupervised learning (USL). Hence, commencing from the input layer-pair, the excitatory (input) data supplied flows across the interconnected neurons of paired layers, terminating eventually at the final pair of layers, where the output is recovered. That is, the converged neuronal states at any given pair is iteratively passed on to the next pair and so on. The USL suite involves collectively gathering the details of neural information across a pair of the layers constituting the network. This summed data is then limited with a specific choice of a squashing (sigmoidal) function; and, the resulting scaled value is used to adjust the coefficients of interconnection weights seeking a convergence criterion. The associated learning rate on weight adjustment is uniquely designed to facilitate fast learning towards convergence. The unique aspects of deep learning proposed here refer to: (i) Deducing the learning coefficient with a compatible algorithm so as to realize a fast convergence; and, (ii) the adopted sigmoidal function in the USL loop conforms to the heuristics of the so-called Langevin-Neelakanta machine. The paper describes the proposed deep ANN architecture with necessary details on structural considerations, sigmoidal selection, prescribing required learning rate and operational (training and predictive phase) routines. Results are furnished to demonstrate the performance efficacy of the test ANN.","PeriodicalId":119801,"journal":{"name":"Transactions on Machine Learning and Artificial Intelligence","volume":"1 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2022-09-03","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"128766286","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 : 2022-08-23DOI: 10.14738/tmlai.104.12854
Eric Michel DEUSSOM DJOMADJI, Bequerelle MATEMTSAP MBOU, Aurelle Tchagna Kouanou, M. Ekonde Sone, Parfait Bayonbog
Fraud in telecommunications networks is a constantly growing phenomenon that causes enormous financial losses for both the individual user and the telecommunications operators. We can denote many researchers who have proposed various approaches to provide a solution to this problem, but still need to be improve to ensure the efficiency. Detecting fraud is difficult and, it's no surprise that many frauds schemes have serious limitations. Different types of fraud may require different systems, each with different procedures, parameter adjustments, database interfaces, and case management tools and capabilities. This article uses the K-Means algorithm to handle fraud detection based on Call Detail Record (CDR) and traffic analysis in a telecommunication industry. Our algorithm consists to compare traffic and CDR generated in the network and check if there is abnormal behavior and if yes, our model is used to confirm if users suspecting of fraud are really fraudster or not. To build our model we used real word CDR data collected in November 2021. Our model associates the Differential Privacy model to encrypt users' personal information, and the k-means algorithm to group users into different clusters. Those clusters represent non fraud users having similar characteristics based on criteria used to build the model. Users having abnormal behavior that can be assimilated to fraudsters are those who are far from the different clusters center. Thanks to a representation in a plan, we better visualize user’s behavior. We validated our model by evaluating our segmentation method. The interpretation of the results shows sufficiently that our approach allows to obtain better results. Our approach can be used by all telecommunications operator to reduce the impact of fraud on internet services.
{"title":"Machine learning-based approach for designing and implementing a collaborative fraud detection model through CDR and traffic analysis","authors":"Eric Michel DEUSSOM DJOMADJI, Bequerelle MATEMTSAP MBOU, Aurelle Tchagna Kouanou, M. Ekonde Sone, Parfait Bayonbog","doi":"10.14738/tmlai.104.12854","DOIUrl":"https://doi.org/10.14738/tmlai.104.12854","url":null,"abstract":"Fraud in telecommunications networks is a constantly growing phenomenon that causes enormous financial losses for both the individual user and the telecommunications operators. We can denote many researchers who have proposed various approaches to provide a solution to this problem, but still need to be improve to ensure the efficiency. Detecting fraud is difficult and, it's no surprise that many frauds schemes have serious limitations. Different types of fraud may require different systems, each with different procedures, parameter adjustments, database interfaces, and case management tools and capabilities. This article uses the K-Means algorithm to handle fraud detection based on Call Detail Record (CDR) and traffic analysis in a telecommunication industry. Our algorithm consists to compare traffic and CDR generated in the network and check if there is abnormal behavior and if yes, our model is used to confirm if users suspecting of fraud are really fraudster or not. To build our model we used real word CDR data collected in November 2021. Our model associates the Differential Privacy model to encrypt users' personal information, and the k-means algorithm to group users into different clusters. Those clusters represent non fraud users having similar characteristics based on criteria used to build the model. Users having abnormal behavior that can be assimilated to fraudsters are those who are far from the different clusters center. Thanks to a representation in a plan, we better visualize user’s behavior. We validated our model by evaluating our segmentation method. The interpretation of the results shows sufficiently that our approach allows to obtain better results. Our approach can be used by all telecommunications operator to reduce the impact of fraud on internet services.","PeriodicalId":119801,"journal":{"name":"Transactions on Machine Learning and Artificial Intelligence","volume":"90 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2022-08-23","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"115345800","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 : 2022-08-23DOI: 10.14738/tmlai.104.12831
Md. Afzalur Rahaman, H. Mahmud
Automatic Essay Grading (AEG) is one of the exciting research topics in the field of adopting technology in education. In the education system assessment of student’s answer script is a critical job of teachers; yet doing so consumes a significant amount of their time and prevents them from working on other tasks. In addition, evaluating a large number of exam scripts is error-prone, inefficient, and tedious. Natural Language Processing (NLP), has created such an opportunity to make the computer learn about written text data and make important decisions based on the learned model. Similarly, it is possible to make a computer be able to assess an answering script based on the model used to train our computer to learn about answers to predefined short questions. In this paper, we propose a deep learning architecture with a combination of Con- volutional Neural Network (CNN) and Bidirectional Long Short Term Memory (BiLSTM) which has the ability to perform both handwritten answers recogni- tion and grading them as accurately as a human expert grader.
{"title":"Automated Evaluation of Handwritten Answer Script Using Deep Learning Approach","authors":"Md. Afzalur Rahaman, H. Mahmud","doi":"10.14738/tmlai.104.12831","DOIUrl":"https://doi.org/10.14738/tmlai.104.12831","url":null,"abstract":"\u0000\u0000\u0000Automatic Essay Grading (AEG) is one of the exciting research topics in the field of adopting technology in education. In the education system assessment of student’s answer script is a critical job of teachers; yet doing so consumes a significant amount of their time and prevents them from working on other tasks. In addition, evaluating a large number of exam scripts is error-prone, inefficient, and tedious. Natural Language Processing (NLP), has created such an opportunity to make the computer learn about written text data and make important decisions based on the learned model. Similarly, it is possible to make a computer be able to assess an answering script based on the model used to train our computer to learn about answers to predefined short questions. In this paper, we propose a deep learning architecture with a combination of Con- volutional Neural Network (CNN) and Bidirectional Long Short Term Memory (BiLSTM) which has the ability to perform both handwritten answers recogni- tion and grading them as accurately as a human expert grader.\u0000\u0000\u0000","PeriodicalId":119801,"journal":{"name":"Transactions on Machine Learning and Artificial Intelligence","volume":"65 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2022-08-23","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"133293043","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 : 2022-08-10DOI: 10.14738/tmlai.104.12792
Pham Thanh Nga
Currently, there are about 100 law training institutions in Vietnam. In 2019, Vietnamese law training institutions established a network. This activity is very necessary to support each other in the process of law training between the law training institutions. In this article, the author will mention and present the problem of technology application and recommend solutions in sharing resource activities between law training institutions in Vietnam for the next period.
{"title":"Technology Solutions to Improve the Efficiency of Resource Sharing Among Law Training Institutions in Vietnam","authors":"Pham Thanh Nga","doi":"10.14738/tmlai.104.12792","DOIUrl":"https://doi.org/10.14738/tmlai.104.12792","url":null,"abstract":"Currently, there are about 100 law training institutions in Vietnam. In 2019, Vietnamese law training institutions established a network. This activity is very necessary to support each other in the process of law training between the law training institutions. In this article, the author will mention and present the problem of technology application and recommend solutions in sharing resource activities between law training institutions in Vietnam for the next period.","PeriodicalId":119801,"journal":{"name":"Transactions on Machine Learning and Artificial Intelligence","volume":"23 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2022-08-10","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"121632202","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 : 2022-07-23DOI: 10.14738/tmlai.104.12959
M. Wolf, Franccois Wolf
We study the factorization of the numbers N=X^2+c, where c is a fixed constant, and this independently of the value of gcd(X,c). We prove the existence of a family of sequences with arithmetic difference (Un,Zn) generating factorizations, i.e. such that: (Un)^2+c= ZnZn+1. The different properties demonstrated allow us to establish new factorization methods by a subset of prime numbers and to define a prime sieve. An algorithm is presented on this basis and leads to empirical results which suggest a positive answer to Landau's 4th problem.
{"title":"On the Factorization of Numbers of the Form X^2+c","authors":"M. Wolf, Franccois Wolf","doi":"10.14738/tmlai.104.12959","DOIUrl":"https://doi.org/10.14738/tmlai.104.12959","url":null,"abstract":"We study the factorization of the numbers N=X^2+c, where c is a fixed constant, and this independently of the value of gcd(X,c). We prove the existence of a family of sequences with arithmetic difference (Un,Zn) generating factorizations, i.e. such that: (Un)^2+c= ZnZn+1. The different properties demonstrated allow us to establish new factorization methods by a subset of prime numbers and to define a prime sieve. An algorithm is presented on this basis and leads to empirical results which suggest a positive answer to Landau's 4th problem.","PeriodicalId":119801,"journal":{"name":"Transactions on Machine Learning and Artificial Intelligence","volume":"47 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2022-07-23","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"116922118","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 : 2022-07-15DOI: 10.14738/tmlai.104.12596
Y. S. Ayala
In this article we prove that the Cauchy problem associated to third order equation in periodic Sobolev spaces is globally well posed. We do this in an intuitive way using Fourier theory and in a fine version using groups theory. Also, we study its generalization to n-th order equation.
{"title":"Wellposedness of a Cauchy Problem Associated to Third Order Equation","authors":"Y. S. Ayala","doi":"10.14738/tmlai.104.12596","DOIUrl":"https://doi.org/10.14738/tmlai.104.12596","url":null,"abstract":"\u0000 \u0000 \u0000In this article we prove that the Cauchy problem associated to third order equation in periodic Sobolev spaces is globally well posed. We do this in an intuitive way using Fourier theory and in a fine version using groups theory. Also, we study its generalization to n-th order equation. \u0000 \u0000 \u0000","PeriodicalId":119801,"journal":{"name":"Transactions on Machine Learning and Artificial Intelligence","volume":"60 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2022-07-15","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"132267981","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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