The aim of this article is to demonstrate the invariance of the probability of return to the origin on the locally compact groups by quasi isometries. This is a generalization of a theorem of Ch. Pittet and L.Salof-Coste who established this invariance in the case of discrete groups finitely generated.
{"title":"Stability of probability of return on locally compact groups under quasi-isometry","authors":"Barmaki Mohammed, Ftouhi Mostafa, D. Gretete","doi":"10.52846/ami.v48i1.1327","DOIUrl":"https://doi.org/10.52846/ami.v48i1.1327","url":null,"abstract":"The aim of this article is to demonstrate the invariance of the probability of return to the origin on the locally compact groups by quasi isometries. This is a generalization of a theorem of Ch. Pittet and L.Salof-Coste who established this invariance in the case of discrete groups finitely generated.","PeriodicalId":43654,"journal":{"name":"Annals of the University of Craiova-Mathematics and Computer Science Series","volume":null,"pages":null},"PeriodicalIF":1.0,"publicationDate":"2021-06-30","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"78156915","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}
"Purpose: Explore the efficiency of two convolutional neural networks in helping physicians in establishing colon cancer diagnosis from histopathological image scans. Methods: The dataset used in this study contains 357 histopathological image slides that ranged from benign cases to colon cancer grade three. The slides were collected by doctors at the Emergency Hospital of Craiova, Romania. The study proposes a statistical framework that studies the performances of two convolutional neural networks AlexNet and GoogleNet. Results: AlexNet has revealed a competitive accuracy in comparison with GoogleNet. To prove the robustness of the AlexNet in fair terms, we have performed a thorough statistical analysis of its performance. Conclusions: On this particular dataset which contains histopathological image scans regarding colon cancer, the convolutional neural network AlexNet proved to be superior to GoogleNet. "
{"title":"A statistical framework for evaluating convolutional neural networks. Application to colon cancer","authors":"L. Popa","doi":"10.52846/ami.v48i1.1449","DOIUrl":"https://doi.org/10.52846/ami.v48i1.1449","url":null,"abstract":"\"Purpose: Explore the efficiency of two convolutional neural networks in helping physicians in establishing colon cancer diagnosis from histopathological image scans. Methods: The dataset used in this study contains 357 histopathological image slides that ranged from benign cases to colon cancer grade three. The slides were collected by doctors at the Emergency Hospital of Craiova, Romania. The study proposes a statistical framework that studies the performances of two convolutional neural networks AlexNet and GoogleNet. Results: AlexNet has revealed a competitive accuracy in comparison with GoogleNet. To prove the robustness of the AlexNet in fair terms, we have performed a thorough statistical analysis of its performance. Conclusions: On this particular dataset which contains histopathological image scans regarding colon cancer, the convolutional neural network AlexNet proved to be superior to GoogleNet. \"","PeriodicalId":43654,"journal":{"name":"Annals of the University of Craiova-Mathematics and Computer Science Series","volume":null,"pages":null},"PeriodicalIF":1.0,"publicationDate":"2021-06-30","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"87947124","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 shall o¤er some new inequalities related to Hermite-Hadamard inequalities for differentiable convex functions involving generalized fractional integrals. Some of our new results are the extension of the previously established results.
{"title":"On some inequalities related to fractional Hermite-Hadamard type for differentiable convex functions","authors":"H. Budak, Hasan Kara, M. Ali, M. E. Kiriș","doi":"10.52846/ami.v48i1.1369","DOIUrl":"https://doi.org/10.52846/ami.v48i1.1369","url":null,"abstract":"In this paper, we shall o¤er some new inequalities related to Hermite-Hadamard inequalities for differentiable convex functions involving generalized fractional integrals. Some of our new results are the extension of the previously established results.","PeriodicalId":43654,"journal":{"name":"Annals of the University of Craiova-Mathematics and Computer Science Series","volume":null,"pages":null},"PeriodicalIF":1.0,"publicationDate":"2021-06-30","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"90722069","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 define the topological versions of the concepts of crossed module over generalized groups, which is called generalized crossed module, and generalized group-groupoid. We construct the categories of the topological generalized crossed modules and their homomorphisms and of the topological generalized group-groupoid and homomorphisms between them. We also obtain some characterizations related to the concepts of topological generalized crossed module and topological generalized group-groupoid. Finally, at the end of the work, we prove that the category of topological generalized crossed modules is equivalent to that of topological generalized group-groupoids whose object sets are commutative topological generalized groups.
{"title":"On the topological generalized crossed modules","authors":"M. H. Gürsoy","doi":"10.52846/ami.v48i1.1287","DOIUrl":"https://doi.org/10.52846/ami.v48i1.1287","url":null,"abstract":"In this paper, we define the topological versions of the concepts of crossed module over generalized groups, which is called generalized crossed module, and generalized group-groupoid. We construct the categories of the topological generalized crossed modules and their homomorphisms and of the topological generalized group-groupoid and homomorphisms between them. We also obtain some characterizations related to the concepts of topological generalized crossed module and topological generalized group-groupoid. Finally, at the end of the work, we prove that the category of topological generalized crossed modules is equivalent to that of topological generalized group-groupoids whose object sets are commutative topological generalized groups.","PeriodicalId":43654,"journal":{"name":"Annals of the University of Craiova-Mathematics and Computer Science Series","volume":null,"pages":null},"PeriodicalIF":1.0,"publicationDate":"2021-06-30","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"72382615","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
This research paper focuses on defining the relationships between the sets of strongly lacunary summable and lacunary statistically convergent sequences by using different modulus functions f and g under certain conditions and different orders. Furthermore, for some special modulus functions, we establish the relations between the sets of strongly f-lacunary summable sequences and strongly f-lacunary summable sequences of order alpha.
{"title":"On strong lacunary summability of order α with respect to modulus functions","authors":"I. S. Ibrahim, R. Çolak","doi":"10.52846/ami.v48i1.1399","DOIUrl":"https://doi.org/10.52846/ami.v48i1.1399","url":null,"abstract":"This research paper focuses on defining the relationships between the sets of strongly lacunary summable and lacunary statistically convergent sequences by using different modulus functions f and g under certain conditions and different orders. Furthermore, for some special modulus functions, we establish the relations between the sets of strongly f-lacunary summable sequences and strongly f-lacunary summable sequences of order alpha.","PeriodicalId":43654,"journal":{"name":"Annals of the University of Craiova-Mathematics and Computer Science Series","volume":null,"pages":null},"PeriodicalIF":1.0,"publicationDate":"2021-06-30","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"83904068","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
This research focus on the determination of the numerical solution for the mathematical model of Fokker-Planck equations utilizing a new method, in which Sumudu transformation and homotopy analysis method (SHAM) are used together. By SHAM analytical series solution of any mathematical model including fractional derivative can be obtained. By this method, we constructed the solution of fractional Fokker-Planck equations in Caputo and Caputo-Fabrizio senses. The results show that this method is advantageous and applicable to form the series resolution of the fractional mathematical models.
{"title":"Analysis of fractional Fokker-Planck equation with Caputo and Caputo-Fabrizio derivatives","authors":"Süleyman Çetinkaya, A. Demir, D. Baleanu","doi":"10.52846/ami.v48i1.1473","DOIUrl":"https://doi.org/10.52846/ami.v48i1.1473","url":null,"abstract":"This research focus on the determination of the numerical solution for the mathematical model of Fokker-Planck equations utilizing a new method, in which Sumudu transformation and homotopy analysis method (SHAM) are used together. By SHAM analytical series solution of any mathematical model including fractional derivative can be obtained. By this method, we constructed the solution of fractional Fokker-Planck equations in Caputo and Caputo-Fabrizio senses. The results show that this method is advantageous and applicable to form the series resolution of the fractional mathematical models.","PeriodicalId":43654,"journal":{"name":"Annals of the University of Craiova-Mathematics and Computer Science Series","volume":null,"pages":null},"PeriodicalIF":1.0,"publicationDate":"2021-06-30","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"72388639","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}
Consider a robot which is investigating in a space exhibited by a graph (network), and which needs to know its current location. It can grant a sign to find how far it is from each among a lot of fixed places of interest (tourist spots or landmarks). We study the problem of calculating the minimum number of tourist spots required, and where they ought to be set, with the ultimate objective that the robot can generally decide its location. The set of nodes where the places of interest are placed is known as the metric basis of the graph, and the cardinality of tourist spots is known as the location number (or metric dimension) of the graph. Another graph invariant related to resolving set (say $mathfrak{L}$) is the fault-tolerant resolving set $mathfrak{L}^{ast}$, in which the expulsion of a discretionary vertex from $mathfrak{L}$ keeps up the resolvability. The problem of characterizing the classes of plane graphs with a bounded fault-tolerant metric dimension is of great interest nowadays. In this article, we obtain the fault-tolerant metric dimension of three interminable classes of symmetrical plane graphs, that are found to be constant for each of these three families of the plane graphs. We set lower and upper bounds for the fault-tolerant metric dimension of these three classes of the plane graphs.
{"title":"Rotationally symmetrical plane graphs and their Fault-tolerant metric dimension","authors":"S. Sharma, V. K. Bhat","doi":"10.52846/ami.v48i1.1447","DOIUrl":"https://doi.org/10.52846/ami.v48i1.1447","url":null,"abstract":"Consider a robot which is investigating in a space exhibited by a graph (network), and which needs to know its current location. It can grant a sign to find how far it is from each among a lot of fixed places of interest (tourist spots or landmarks). We study the problem of calculating the minimum number of tourist spots required, and where they ought to be set, with the ultimate objective that the robot can generally decide its location. The set of nodes where the places of interest are placed is known as the metric basis of the graph, and the cardinality of tourist spots is known as the location number (or metric dimension) of the graph. Another graph invariant related to resolving set (say $mathfrak{L}$) is the fault-tolerant resolving set $mathfrak{L}^{ast}$, in which the expulsion of a discretionary vertex from $mathfrak{L}$ keeps up the resolvability. The problem of characterizing the classes of plane graphs with a bounded fault-tolerant metric dimension is of great interest nowadays. In this article, we obtain the fault-tolerant metric dimension of three interminable classes of symmetrical plane graphs, that are found to be constant for each of these three families of the plane graphs. We set lower and upper bounds for the fault-tolerant metric dimension of these three classes of the plane graphs.","PeriodicalId":43654,"journal":{"name":"Annals of the University of Craiova-Mathematics and Computer Science Series","volume":null,"pages":null},"PeriodicalIF":1.0,"publicationDate":"2021-06-30","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"73956501","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}
Anderson L. A. de Araujo, S. Heidarkhani, G. Afrouzi, S. Moradi
We study the existence of at least one weak solution for p(x)-Kirchhoff-type problems of nonhomogeneous Neumann conditions. Our technical approach is based on variational methods. Some examples are presented to demonstrate the application of our main results.
{"title":"A variational approach for nonlocal problems with variable exponent and nonhomogeneous Neumann conditions","authors":"Anderson L. A. de Araujo, S. Heidarkhani, G. Afrouzi, S. Moradi","doi":"10.52846/ami.v48i1.1365","DOIUrl":"https://doi.org/10.52846/ami.v48i1.1365","url":null,"abstract":"We study the existence of at least one weak solution for p(x)-Kirchhoff-type problems of nonhomogeneous Neumann conditions. Our technical approach is based on variational methods. Some examples are presented to demonstrate the application of our main results.","PeriodicalId":43654,"journal":{"name":"Annals of the University of Craiova-Mathematics and Computer Science Series","volume":null,"pages":null},"PeriodicalIF":1.0,"publicationDate":"2021-06-30","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"76439590","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 will introduce a new notion, that of $K$-Integral operator frames in the set of all bounded linear operators noted $mathcal{B}(H)$, where $H$ is a separable Hilbert space. Also, we prove some results of integral $K$-operator frame. Lastly we will establish some new properties for the perturbation and stability for an integral $K$-operator frames for $mathcal{B}(H)$.
{"title":"Integral K-operator frames for B(H)","authors":"H. Labrigui, M. Rossafi, A. Touri, S. Kabbaj","doi":"10.52846/ami.v48i1.1385","DOIUrl":"https://doi.org/10.52846/ami.v48i1.1385","url":null,"abstract":"In this paper, we will introduce a new notion, that of $K$-Integral operator frames in the set of all bounded linear operators noted $mathcal{B}(H)$, where $H$ is a separable Hilbert space. Also, we prove some results of integral $K$-operator frame. Lastly we will establish some new properties for the perturbation and stability for an integral $K$-operator frames for $mathcal{B}(H)$.","PeriodicalId":43654,"journal":{"name":"Annals of the University of Craiova-Mathematics and Computer Science Series","volume":null,"pages":null},"PeriodicalIF":1.0,"publicationDate":"2021-06-30","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"89007214","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}
Seyed Arash Shahraeini, S. Tabrizi, C. Spulbar, Ramona Birau, Amir Karbassi Yazdi
Nowadays, ECAs have a crucial role in the export of production, creating job opportunities for countries and growth of economic indicators.This research aims first to estimate the performance of ECAs based on covering all countries of the world and ranking the countries based on the issue of export credit according to their performance and clustering techniques. For evaluation performance of these ECAs, clustering techniques are used to put them in the categories according to their performance between 2005 to 2020 in the fourth quarter. The context of clustering shows the rank of each cluster, and then exporters can choose a better choice from them. Moreover, for reinsurance,other ECAs can find out which ECAs have high performance. The result indicates that ranking the ECAs and show the performance of each cluster.
{"title":"New Data Mining approach for clustering Export Credit Agencies (ECAs) based on performance criteria: a bibliometric citation analysis for the period 2005 to 2020","authors":"Seyed Arash Shahraeini, S. Tabrizi, C. Spulbar, Ramona Birau, Amir Karbassi Yazdi","doi":"10.52846/ami.v48i1.1579","DOIUrl":"https://doi.org/10.52846/ami.v48i1.1579","url":null,"abstract":"Nowadays, ECAs have a crucial role in the export of production, creating job opportunities for countries and growth of economic indicators.This research aims first to estimate the performance of ECAs based on covering all countries of the world and ranking the countries based on the issue of export credit according to their performance and clustering techniques. For evaluation performance of these ECAs, clustering techniques are used to put them in the categories according to their performance between 2005 to 2020 in the fourth quarter. The context of clustering shows the rank of each cluster, and then exporters can choose a better choice from them. Moreover, for reinsurance,other ECAs can find out which ECAs have high performance. The result indicates that ranking the ECAs and show the performance of each cluster.","PeriodicalId":43654,"journal":{"name":"Annals of the University of Craiova-Mathematics and Computer Science Series","volume":null,"pages":null},"PeriodicalIF":1.0,"publicationDate":"2021-06-30","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"82803418","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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