Pub Date : 2022-01-01DOI: 10.22075/IJNAA.2021.20666.2191
Farah Balaadich, E. Azroul
This work is devoted to studying the existence of solutions to systems of $p$-Laplacian type. We prove the existence of at least one weak solution, under some assumptions, by applying Galerkin's approximation and the theory of Young measures.
{"title":"Generalized $p$-Laplacian systems with lower order terms","authors":"Farah Balaadich, E. Azroul","doi":"10.22075/IJNAA.2021.20666.2191","DOIUrl":"https://doi.org/10.22075/IJNAA.2021.20666.2191","url":null,"abstract":"This work is devoted to studying the existence of solutions to systems of $p$-Laplacian type. We prove the existence of at least one weak solution, under some assumptions, by applying Galerkin's approximation and the theory of Young measures.","PeriodicalId":14240,"journal":{"name":"International Journal of Nonlinear Analysis and Applications","volume":"13 1","pages":"45-55"},"PeriodicalIF":0.0,"publicationDate":"2022-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"68118581","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 : 2022-01-01DOI: 10.22075/IJNAA.2021.21909.2302
Ishtaq Ahmad, Neyaz Ahmad
The paper deals with two different aspects of wavelet frames. First, we obtain a necessary condition on irregular wavelet frames on local fields of positive characteristic and in the second aspect, we present some results on the perturbation of wavelet frames, when we disturb the mother function of a wavelet frame or dilation parameter. All the results have been carried without the compactness of support neither on generating function nor on its Fourier transform.
{"title":"Perturbation of wavelet frames on non-Archimedean fields","authors":"Ishtaq Ahmad, Neyaz Ahmad","doi":"10.22075/IJNAA.2021.21909.2302","DOIUrl":"https://doi.org/10.22075/IJNAA.2021.21909.2302","url":null,"abstract":"The paper deals with two different aspects of wavelet frames. First, we obtain a necessary condition on irregular wavelet frames on local fields of positive characteristic and in the second aspect, we present some results on the perturbation of wavelet frames, when we disturb the mother function of a wavelet frame or dilation parameter. All the results have been carried without the compactness of support neither on generating function nor on its Fourier transform.","PeriodicalId":14240,"journal":{"name":"International Journal of Nonlinear Analysis and Applications","volume":"13 1","pages":"197-208"},"PeriodicalIF":0.0,"publicationDate":"2022-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"68119475","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 : 2022-01-01DOI: 10.22075/IJNAA.2021.22858.2422
A. Deep, Ashisha Kumar, Syed Abbas, M. Rabbani
In this paper, utilizing the technique of Petryshyn’s fixed point theorem in Banach algebra, we analyze the existence of solution for functional integral equations, which includes as special cases many functional integral equations that arise in various branches of non-linear analysis and its application. Finally, we introduce the numerical method formed by modified homotopy perturbation approach to resolving the problem with acceptable accuracy.
{"title":"Solvability and numerical method for non-linear Volterra integral equations by using Petryshyn’s fixed point theorem","authors":"A. Deep, Ashisha Kumar, Syed Abbas, M. Rabbani","doi":"10.22075/IJNAA.2021.22858.2422","DOIUrl":"https://doi.org/10.22075/IJNAA.2021.22858.2422","url":null,"abstract":"In this paper, utilizing the technique of Petryshyn’s fixed point theorem in Banach algebra, we analyze the existence of solution for functional integral equations, which includes as special cases many functional integral equations that arise in various branches of non-linear analysis and its application. Finally, we introduce the numerical method formed by modified homotopy perturbation approach to resolving the problem with acceptable accuracy.","PeriodicalId":14240,"journal":{"name":"International Journal of Nonlinear Analysis and Applications","volume":"13 1","pages":"1-28"},"PeriodicalIF":0.0,"publicationDate":"2022-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"68119514","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 : 2022-01-01DOI: 10.22075/IJNAA.2022.5463
Maysoun A. Hamel, I. Hadi
In this paper, the concepts of almost maximal submodules are fuzzified and studied. Also, three new concepts are introduced, which are: e-simple submodules, Ee-simple modules and e-maximal submodules. Then these concepts are fuzzified and studied.
{"title":"Almost maximal, e-maximal and e-simple fuzzy submodules","authors":"Maysoun A. Hamel, I. Hadi","doi":"10.22075/IJNAA.2022.5463","DOIUrl":"https://doi.org/10.22075/IJNAA.2022.5463","url":null,"abstract":"In this paper, the concepts of almost maximal submodules are fuzzified and studied. Also, three new concepts are introduced, which are: e-simple submodules, Ee-simple modules and e-maximal submodules. Then these concepts are fuzzified and studied.","PeriodicalId":14240,"journal":{"name":"International Journal of Nonlinear Analysis and Applications","volume":"13 1","pages":"103-113"},"PeriodicalIF":0.0,"publicationDate":"2022-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"68124295","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 : 2022-01-01DOI: 10.22075/IJNAA.2022.5459
T. Majeed
The main goal of this paper is investigating some types of topological groupoid and their action which denoted by LM- groupoid and M- groupoid. Some properties of these groupoid are written as proposition. We concentrated to research the relation of M- groupoid and LM- groupoid.
{"title":"Action of topological groupoid on topological space","authors":"T. Majeed","doi":"10.22075/IJNAA.2022.5459","DOIUrl":"https://doi.org/10.22075/IJNAA.2022.5459","url":null,"abstract":"The main goal of this paper is investigating some types of topological groupoid and their action which denoted by LM- groupoid and M- groupoid. Some properties of these groupoid are written as proposition. We concentrated to research the relation of M- groupoid and LM- groupoid.","PeriodicalId":14240,"journal":{"name":"International Journal of Nonlinear Analysis and Applications","volume":"13 1","pages":"85-89"},"PeriodicalIF":0.0,"publicationDate":"2022-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"68124381","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 : 2022-01-01DOI: 10.22075/IJNAA.2022.5505
Raad A. Hameed, Maan A. Rasheed, H. Mustafa, Faez N. Ghaffoori
This work is concerned with the periodic solution of a doubly degenerate Allen-Cahn equation with nonlocal terms associated with Neumann boundary conditions. Firstly, we define a new associated auxiliary problem. Secondly, the topological degree theorem is applied to prove the existence of a limit point to the auxiliary problem, where this limit point represents a nontrivial nonnegative time-periodic solution of the main studied problem. It is observed that the topological degree theorem technique plays an important role in proving the desired results. Furthermore, this technique can be applied to other similar equations with homogeneous Dirichlet or Neumann boundary conditions.
{"title":"The existence of periodic solutions to doubly degenerate Allen-Cahn equation with Neumann boundary condition","authors":"Raad A. Hameed, Maan A. Rasheed, H. Mustafa, Faez N. Ghaffoori","doi":"10.22075/IJNAA.2022.5505","DOIUrl":"https://doi.org/10.22075/IJNAA.2022.5505","url":null,"abstract":"This work is concerned with the periodic solution of a doubly degenerate Allen-Cahn equation with nonlocal terms associated with Neumann boundary conditions. Firstly, we define a new associated auxiliary problem. Secondly, the topological degree theorem is applied to prove the existence of a limit point to the auxiliary problem, where this limit point represents a nontrivial nonnegative time-periodic solution of the main studied problem. It is observed that the topological degree theorem technique plays an important role in proving the desired results. Furthermore, this technique can be applied to other similar equations with homogeneous Dirichlet or Neumann boundary conditions.","PeriodicalId":14240,"journal":{"name":"International Journal of Nonlinear Analysis and Applications","volume":"13 1","pages":"397-408"},"PeriodicalIF":0.0,"publicationDate":"2022-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"68125191","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 : 2022-01-01DOI: 10.22075/IJNAA.2022.5542
Baqer A Hakim, Ahmed Dheyaa Radhi, Fuqdan A. Al-Ibraheemi
EEG (Electroencephalogram) is brain waves measure. It is available test allowed to discover the brain functions over time. The brain troubles are evaluated by EEG. It is used to locate the activity in the brain during a seizure and to consider the patients who suffer from brain functionality problems. These troubles include tumors, coma, confusion and long-term difficulties (such as weakness associated with a stroke). The acquisition of EEG signals requires contact and liveliness and these signals are changes under stress that make so potentially unnecessary if it is acquired under menace. In this paper, an innovative and robust solution for this problem is introduced. To this end, the manner depends on models of various data compression models of information-theoretic plus the metrics symmetry related to Kolmogorov complexity. The proposed procedure compares two EEG segments and clusters the data into three groups: a corresponding record for each participant, a distinct person for each group, and self-participant. The technique was used to determine the database participant based on EEG signals. Using a distance measuring approach suggested in this scheme, a 1-NN classifier was constructed. Nearly every person in the underlying database could be accurately identified by the classifier with $96%$ accuracy
{"title":"An innovative and robust technique for human identification and authentication based on a secure clinical signals transmission","authors":"Baqer A Hakim, Ahmed Dheyaa Radhi, Fuqdan A. Al-Ibraheemi","doi":"10.22075/IJNAA.2022.5542","DOIUrl":"https://doi.org/10.22075/IJNAA.2022.5542","url":null,"abstract":"EEG (Electroencephalogram) is brain waves measure. It is available test allowed to discover the brain functions over time. The brain troubles are evaluated by EEG. It is used to locate the activity in the brain during a seizure and to consider the patients who suffer from brain functionality problems. These troubles include tumors, coma, confusion and long-term difficulties (such as weakness associated with a stroke). The acquisition of EEG signals requires contact and liveliness and these signals are changes under stress that make so potentially unnecessary if it is acquired under menace. In this paper, an innovative and robust solution for this problem is introduced. To this end, the manner depends on models of various data compression models of information-theoretic plus the metrics symmetry related to Kolmogorov complexity. The proposed procedure compares two EEG segments and clusters the data into three groups: a corresponding record for each participant, a distinct person for each group, and self-participant. The technique was used to determine the database participant based on EEG signals. Using a distance measuring approach suggested in this scheme, a 1-NN classifier was constructed. Nearly every person in the underlying database could be accurately identified by the classifier with $96%$ accuracy","PeriodicalId":14240,"journal":{"name":"International Journal of Nonlinear Analysis and Applications","volume":"13 1","pages":"603-613"},"PeriodicalIF":0.0,"publicationDate":"2022-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"68125259","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 : 2022-01-01DOI: 10.22075/IJNAA.2022.5590
A. Abdulbaqi, M. T. Younis, Younus Tahreer Younus, Ahmed J. Obaid
Electroencephalography (EEG) signals are commonly used to identify and diagnose brain disorders. Each EEG normal waveform consists of the following waveforms: Gamma(γ) wave, Beta (β) wave, Alpha (α), Theta (θ), and Delta (δ). The term Neurological Diseases ” NurDis ” is used to describe a variety of conditions that affect the nervous Epilepsy, neuro infections (bacterial and viral), brain tumors, cerebrovascular diseases, Alzheimer’s disease, and various dementias are all examples of neurological disorders. Encephalitis is one of the illnesses that affects the brain. The EEG signals used in this paper were from the CHB-MIT Scalp EEG database. The discrete wavelet transform (DWT) was utilized to extract characteristics from the filtered EEG data. Finally, classifiers such as K Nearest Neighbor (KNN) and Support vector machine (SVM) were used to categorize the EEG signals into normal and pathological signal classes using all of the computed characteristics. In order to categorize the signal in a normal and anomalous group, the KNN and SVM classifiers are employed. For both classifiers, performance assessments (accuracy, sensitivity and specificity) are determined. KNN classifier accuracy is 71.88%, whereas SVM classifier accuracy is 81.23%. The sensitivity of KNN and SVM are 80.14% and 77.31%, respectively. The KNN classification specificity is 69.62% and the SVM classification specificity is 98%. Both classifiers performance is evaluated using the confusion matrix.
{"title":"A hybrid technique for EEG signals evaluation and classification as a step towards to neurological and cerebral disorders diagnosis","authors":"A. Abdulbaqi, M. T. Younis, Younus Tahreer Younus, Ahmed J. Obaid","doi":"10.22075/IJNAA.2022.5590","DOIUrl":"https://doi.org/10.22075/IJNAA.2022.5590","url":null,"abstract":"Electroencephalography (EEG) signals are commonly used to identify and diagnose brain disorders. Each EEG normal waveform consists of the following waveforms: Gamma(γ) wave, Beta (β) wave, Alpha (α), Theta (θ), and Delta (δ). The term Neurological Diseases ” NurDis ” is used to describe a variety of conditions that affect the nervous Epilepsy, neuro infections (bacterial and viral), brain tumors, cerebrovascular diseases, Alzheimer’s disease, and various dementias are all examples of neurological disorders. Encephalitis is one of the illnesses that affects the brain. The EEG signals used in this paper were from the CHB-MIT Scalp EEG database. The discrete wavelet transform (DWT) was utilized to extract characteristics from the filtered EEG data. Finally, classifiers such as K Nearest Neighbor (KNN) and Support vector machine (SVM) were used to categorize the EEG signals into normal and pathological signal classes using all of the computed characteristics. In order to categorize the signal in a normal and anomalous group, the KNN and SVM classifiers are employed. For both classifiers, performance assessments (accuracy, sensitivity and specificity) are determined. KNN classifier accuracy is 71.88%, whereas SVM classifier accuracy is 81.23%. The sensitivity of KNN and SVM are 80.14% and 77.31%, respectively. The KNN classification specificity is 69.62% and the SVM classification specificity is 98%. Both classifiers performance is evaluated using the confusion matrix.","PeriodicalId":14240,"journal":{"name":"International Journal of Nonlinear Analysis and Applications","volume":"13 1","pages":"773-781"},"PeriodicalIF":0.0,"publicationDate":"2022-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"68125558","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 : 2022-01-01DOI: 10.22075/IJNAA.2022.5559
Sameerah Faris Khlebus, Rajaa K. Hasoun, B. T. Sabri
Cayley- Purser Algorithm is a public key algorithm invited by Sarah Flannery in 1998. The algorithm of Cayley-Purser is much faster than some public key methods like RSA but the problem of it is that it can be easily broken especially if some of the private key information is known. The solution to this problem is to modify this algorithm to be more secure than before so that it gives its utilizers the confidence of using it in encrypting important and sensitive information. In this paper, a modification to this algorithm based on using general linear groups over Galois field $GF(p^n)$, which is represented by $GL_m(GF(p^n))$ where $n$ and $m$ are positive integers and $p$ is prime, instead of $GL_2(Z_n)$ which is General linear set of inverted matrices $2 times 2$ whose entries are integers modulo $n$. This $GL_m(GF(p^n))$ ensures that the secret key of this algorithm would be very hard to be obtained. Therefore, this new modification can make the Cayley-Purser Algorithm more immune to any future attacks.
{"title":"A modification of the Cayley-Purser algorithm","authors":"Sameerah Faris Khlebus, Rajaa K. Hasoun, B. T. Sabri","doi":"10.22075/IJNAA.2022.5559","DOIUrl":"https://doi.org/10.22075/IJNAA.2022.5559","url":null,"abstract":"Cayley- Purser Algorithm is a public key algorithm invited by Sarah Flannery in 1998. The algorithm of Cayley-Purser is much faster than some public key methods like RSA but the problem of it is that it can be easily broken especially if some of the private key information is known. The solution to this problem is to modify this algorithm to be more secure than before so that it gives its utilizers the confidence of using it in encrypting important and sensitive information. In this paper, a modification to this algorithm based on using general linear groups over Galois field $GF(p^n)$, which is represented by $GL_m(GF(p^n))$ where $n$ and $m$ are positive integers and $p$ is prime, instead of $GL_2(Z_n)$ which is General linear set of inverted matrices $2 times 2$ whose entries are integers modulo $n$. This $GL_m(GF(p^n))$ ensures that the secret key of this algorithm would be very hard to be obtained. Therefore, this new modification can make the Cayley-Purser Algorithm more immune to any future attacks.","PeriodicalId":14240,"journal":{"name":"International Journal of Nonlinear Analysis and Applications","volume":"13 1","pages":"707-716"},"PeriodicalIF":0.0,"publicationDate":"2022-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"68125601","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 : 2022-01-01DOI: 10.22075/IJNAA.2022.5744
O. E. Musa, Sabah Manfi Ridha
Artificial Intelligence Algorithms have been used in recent years in many scientific fields. We suggest employing flower pollination algorithm in the environmental field to find the best estimate of the semi-parametric regression function with measurement errors in the explanatory variables and the dependent variable, where measurement errors appear frequently in fields such as chemistry, biological sciences, medicine, and epidemiological studies, rather than an exact measurement. We estimate the regression function of the semi-parametric model by estimating the parametric model and estimating the non-parametric model, the parametric model is estimated by using an instrumental variables method (Wald method, Bartlett's method, and Durbin's method), The non-parametric model is estimated by using kernel smoothing (Nadaraya Watson), K-Nearest Neighbor smoothing and Median smoothing. The Flower Pollination algorithms were employed and structured in building the ecological model and estimating the semi-parametric regression function with measurement errors in the explanatory and dependent variables, then compare the models to choose the best model used in the environmental scope measurement errors, where the comparison between the models is done using the mean square error (MSE). These methods were applied to real data on environmental pollution/ air pollution in the city of Baghdad, and the most important conclusions that we reached when using statistical methods in estimating parameters and choosing the best model, we found that the Median-Durbin model is the best as it has less MSE, but when using flower The pollination algorithm showed that the Median-Wald model is the best because it has the lowest MSE, and when we compare the statistical methods with the FPA in selecting semi-parametric models, we notice the superiority of the FP algorithm in all methods and for all models.
{"title":"Semi-parametric regression function estimation for environmental pollution with measurement error using artificial flower pollination algorithm","authors":"O. E. Musa, Sabah Manfi Ridha","doi":"10.22075/IJNAA.2022.5744","DOIUrl":"https://doi.org/10.22075/IJNAA.2022.5744","url":null,"abstract":"Artificial Intelligence Algorithms have been used in recent years in many scientific fields. We suggest employing flower pollination algorithm in the environmental field to find the best estimate of the semi-parametric regression function with measurement errors in the explanatory variables and the dependent variable, where measurement errors appear frequently in fields such as chemistry, biological sciences, medicine, and epidemiological studies, rather than an exact measurement. We estimate the regression function of the semi-parametric model by estimating the parametric model and estimating the non-parametric model, the parametric model is estimated by using an instrumental variables method (Wald method, Bartlett's method, and Durbin's method), The non-parametric model is estimated by using kernel smoothing (Nadaraya Watson), K-Nearest Neighbor smoothing and Median smoothing. The Flower Pollination algorithms were employed and structured in building the ecological model and estimating the semi-parametric regression function with measurement errors in the explanatory and dependent variables, then compare the models to choose the best model used in the environmental scope measurement errors, where the comparison between the models is done using the mean square error (MSE). These methods were applied to real data on environmental pollution/ air pollution in the city of Baghdad, and the most important conclusions that we reached when using statistical methods in estimating parameters and choosing the best model, we found that the Median-Durbin model is the best as it has less MSE, but when using flower The pollination algorithm showed that the Median-Wald model is the best because it has the lowest MSE, and when we compare the statistical methods with the FPA in selecting semi-parametric models, we notice the superiority of the FP algorithm in all methods and for all models.","PeriodicalId":14240,"journal":{"name":"International Journal of Nonlinear Analysis and Applications","volume":"13 1","pages":"1375-1389"},"PeriodicalIF":0.0,"publicationDate":"2022-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"68126364","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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