In this paper, we introduce original definitions of Smarandache ruled surfaces according to Frenet-Serret frame of a curve in E 3 . It concerns TN-Smarandache ruled surface, TB-Smarandache ruled surface, and NB-Smarandache ruled surface. We investigate theorems that give necessary and sufficient conditions for those special ruled surfaces to be developable and minimal. Furthermore, we present examples with illustrations.
{"title":"Corrigendum to “Smarandache Ruled Surfaces according to Frenet-Serret Frame of a Regular Curve in <math xmlns=\"http://www.w3.org/1998/Math/MathML\" id=\"M1\">\u0000 <msup>\u0000 <mrow>\u0000 <mi>E</mi>\u0000 </mrow>\u0000 ","authors":"Soukaina Ouarab","doi":"10.1155/2022/9849574","DOIUrl":"https://doi.org/10.1155/2022/9849574","url":null,"abstract":"In this paper, we introduce original definitions of Smarandache ruled surfaces according to Frenet-Serret frame of a curve in \u0000 \u0000 \u0000 \u0000 E\u0000 \u0000 \u0000 3\u0000 \u0000 \u0000 .\u0000 \u0000 It concerns TN-Smarandache ruled surface, TB-Smarandache ruled surface, and NB-Smarandache ruled surface. We investigate theorems that give necessary and sufficient conditions for those special ruled surfaces to be developable and minimal. Furthermore, we present examples with illustrations.","PeriodicalId":7061,"journal":{"name":"Abstract and Applied Analysis","volume":" ","pages":""},"PeriodicalIF":0.0,"publicationDate":"2022-07-11","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"48078967","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 article, we study and investigate the analytical solutions of the space-time nonlinear fractional modified KDV-Zakharov-Kuznetsov (mKDV-ZK) equation. We have got new exact solutions of the fractional mKDV-ZK equation by using first integral method; we found new types of hyperbolic solutions and trigonometric solutions by symbolic computation.
{"title":"Computational Technique to Study Analytical Solutions to the Fractional Modified KDV-Zakharov-Kuznetsov Equation","authors":"Mohamed A. Abdoon, F. Hasan, Nidal E. Taha","doi":"10.1155/2022/2162356","DOIUrl":"https://doi.org/10.1155/2022/2162356","url":null,"abstract":"In this article, we study and investigate the analytical solutions of the space-time nonlinear fractional modified KDV-Zakharov-Kuznetsov (mKDV-ZK) equation. We have got new exact solutions of the fractional mKDV-ZK equation by using first integral method; we found new types of hyperbolic solutions and trigonometric solutions by symbolic computation.","PeriodicalId":7061,"journal":{"name":"Abstract and Applied Analysis","volume":" ","pages":""},"PeriodicalIF":0.0,"publicationDate":"2022-06-20","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"49432412","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 : 2022-06-09DOI: 10.1038/d41591-022-00068-2
Karen O'Leary
{"title":"Pig-to-human transplants inch closer to reality.","authors":"Karen O'Leary","doi":"10.1038/d41591-022-00068-2","DOIUrl":"10.1038/d41591-022-00068-2","url":null,"abstract":"","PeriodicalId":7061,"journal":{"name":"Abstract and Applied Analysis","volume":"2014 1","pages":""},"PeriodicalIF":82.9,"publicationDate":"2022-06-09","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"86718348","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}
Regarding the concept of size function topology, this allows us to view the topological space X as a metric-like space. We prove the existence and uniqueness for a coupled fixed point of the map F : X × X ⟶ X satisfying some certain contractive conditions.
{"title":"Coupled Fixed Point Theorems in Topological Spaces with Size Function Topology","authors":"G. Sunyeekhan","doi":"10.1155/2022/5858050","DOIUrl":"https://doi.org/10.1155/2022/5858050","url":null,"abstract":"Regarding the concept of size function topology, this allows us to view the topological space \u0000 \u0000 X\u0000 \u0000 as a metric-like space. We prove the existence and uniqueness for a coupled fixed point of the map \u0000 \u0000 F\u0000 :\u0000 X\u0000 ×\u0000 X\u0000 ⟶\u0000 X\u0000 \u0000 satisfying some certain contractive conditions.","PeriodicalId":7061,"journal":{"name":"Abstract and Applied Analysis","volume":" ","pages":""},"PeriodicalIF":0.0,"publicationDate":"2022-06-03","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"42928367","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, a discretization of a three-dimensional fractional-order prey-predator model has been investigated with Holling type III functional response. All its fixed points are determined; also, their local stability is investigated. We extend the discretized system to an optimal control problem to get the optimal harvesting amount. For this, the discrete-time Pontryagin’s maximum principle is used. Finally, numerical simulation results are given to confirm the theoretical outputs as well as to solve the optimality problem.
{"title":"Discretization Fractional-Order Biological Model with Optimal Harvesting","authors":"Barhoom Noor S. Sh., Sadiq Al-Nassir","doi":"10.1155/2022/8171037","DOIUrl":"https://doi.org/10.1155/2022/8171037","url":null,"abstract":"In this paper, a discretization of a three-dimensional fractional-order prey-predator model has been investigated with Holling type III functional response. All its fixed points are determined; also, their local stability is investigated. We extend the discretized system to an optimal control problem to get the optimal harvesting amount. For this, the discrete-time Pontryagin’s maximum principle is used. Finally, numerical simulation results are given to confirm the theoretical outputs as well as to solve the optimality problem.","PeriodicalId":7061,"journal":{"name":"Abstract and Applied Analysis","volume":" ","pages":""},"PeriodicalIF":0.0,"publicationDate":"2022-05-28","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"48083134","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 : 2022-05-17DOI: 10.1093/gigascience/giac037
Mohamed Amgad, Lamees A Atteya, Hagar Hussein, Kareem Hosny Mohammed, Ehab Hafiz, Maha A T Elsebaie, Ahmed M Alhusseiny, Mohamed Atef AlMoslemany, Abdelmagid M Elmatboly, Philip A Pappalardo, Rokia Adel Sakr, Pooya Mobadersany, Ahmad Rachid, Anas M Saad, Ahmad M Alkashash, Inas A Ruhban, Anas Alrefai, Nada M Elgazar, Ali Abdulkarim, Abo-Alela Farag, Amira Etman, Ahmed G Elsaeed, Yahya Alagha, Yomna A Amer, Ahmed M Raslan, Menatalla K Nadim, Mai A T Elsebaie, Ahmed Ayad, Liza E Hanna, Ahmed Gadallah, Mohamed Elkady, Bradley Drumheller, David Jaye, David Manthey, David A Gutman, Habiba Elfandy, Lee A D Cooper
Background: Deep learning enables accurate high-resolution mapping of cells and tissue structures that can serve as the foundation of interpretable machine-learning models for computational pathology. However, generating adequate labels for these structures is a critical barrier, given the time and effort required from pathologists.
Results: This article describes a novel collaborative framework for engaging crowds of medical students and pathologists to produce quality labels for cell nuclei. We used this approach to produce the NuCLS dataset, containing >220,000 annotations of cell nuclei in breast cancers. This builds on prior work labeling tissue regions to produce an integrated tissue region- and cell-level annotation dataset for training that is the largest such resource for multi-scale analysis of breast cancer histology. This article presents data and analysis results for single and multi-rater annotations from both non-experts and pathologists. We present a novel workflow that uses algorithmic suggestions to collect accurate segmentation data without the need for laborious manual tracing of nuclei. Our results indicate that even noisy algorithmic suggestions do not adversely affect pathologist accuracy and can help non-experts improve annotation quality. We also present a new approach for inferring truth from multiple raters and show that non-experts can produce accurate annotations for visually distinctive classes.
Conclusions: This study is the most extensive systematic exploration of the large-scale use of wisdom-of-the-crowd approaches to generate data for computational pathology applications.
{"title":"NuCLS: A scalable crowdsourcing approach and dataset for nucleus classification and segmentation in breast cancer.","authors":"Mohamed Amgad, Lamees A Atteya, Hagar Hussein, Kareem Hosny Mohammed, Ehab Hafiz, Maha A T Elsebaie, Ahmed M Alhusseiny, Mohamed Atef AlMoslemany, Abdelmagid M Elmatboly, Philip A Pappalardo, Rokia Adel Sakr, Pooya Mobadersany, Ahmad Rachid, Anas M Saad, Ahmad M Alkashash, Inas A Ruhban, Anas Alrefai, Nada M Elgazar, Ali Abdulkarim, Abo-Alela Farag, Amira Etman, Ahmed G Elsaeed, Yahya Alagha, Yomna A Amer, Ahmed M Raslan, Menatalla K Nadim, Mai A T Elsebaie, Ahmed Ayad, Liza E Hanna, Ahmed Gadallah, Mohamed Elkady, Bradley Drumheller, David Jaye, David Manthey, David A Gutman, Habiba Elfandy, Lee A D Cooper","doi":"10.1093/gigascience/giac037","DOIUrl":"10.1093/gigascience/giac037","url":null,"abstract":"<p><strong>Background: </strong>Deep learning enables accurate high-resolution mapping of cells and tissue structures that can serve as the foundation of interpretable machine-learning models for computational pathology. However, generating adequate labels for these structures is a critical barrier, given the time and effort required from pathologists.</p><p><strong>Results: </strong>This article describes a novel collaborative framework for engaging crowds of medical students and pathologists to produce quality labels for cell nuclei. We used this approach to produce the NuCLS dataset, containing >220,000 annotations of cell nuclei in breast cancers. This builds on prior work labeling tissue regions to produce an integrated tissue region- and cell-level annotation dataset for training that is the largest such resource for multi-scale analysis of breast cancer histology. This article presents data and analysis results for single and multi-rater annotations from both non-experts and pathologists. We present a novel workflow that uses algorithmic suggestions to collect accurate segmentation data without the need for laborious manual tracing of nuclei. Our results indicate that even noisy algorithmic suggestions do not adversely affect pathologist accuracy and can help non-experts improve annotation quality. We also present a new approach for inferring truth from multiple raters and show that non-experts can produce accurate annotations for visually distinctive classes.</p><p><strong>Conclusions: </strong>This study is the most extensive systematic exploration of the large-scale use of wisdom-of-the-crowd approaches to generate data for computational pathology applications.</p>","PeriodicalId":7061,"journal":{"name":"Abstract and Applied Analysis","volume":"2014 1","pages":""},"PeriodicalIF":3.5,"publicationDate":"2022-05-17","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://www.ncbi.nlm.nih.gov/pmc/articles/PMC9112766/pdf/","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"86746186","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"OA","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
In this paper, we introduce generalized α , ψ -contraction mappings in the setting of rectangular b -metric spaces and established existence and uniqueness of fixed points for the mappings introduced. Our results extend and generalize related fixed point results in the existing literature. We derive some consequences and corollaries from our obtained results. Also, we provide examples in support of our main findings. Furthermore, we determined a solution to an integral equation by applying our obtained results.
{"title":"Fixed Point Results for Generalized <math xmlns=\"http://www.w3.org/1998/Math/MathML\" id=\"M1\">\u0000 <mfenced open=\"(\" close=\")\">\u0000 <mrow>\u0000 <mi>α</mi>\u0000 <mo>,</mo>\u0000 <mi>ψ</mi>\u0000 ","authors":"Mustefa Abduletif Mamud, Kidane Koyas Tola","doi":"10.1155/2022/9370083","DOIUrl":"https://doi.org/10.1155/2022/9370083","url":null,"abstract":"In this paper, we introduce generalized \u0000 \u0000 \u0000 \u0000 α\u0000 ,\u0000 ψ\u0000 \u0000 \u0000 \u0000 -contraction mappings in the setting of rectangular \u0000 \u0000 b\u0000 \u0000 -metric spaces and established existence and uniqueness of fixed points for the mappings introduced. Our results extend and generalize related fixed point results in the existing literature. We derive some consequences and corollaries from our obtained results. Also, we provide examples in support of our main findings. Furthermore, we determined a solution to an integral equation by applying our obtained results.","PeriodicalId":7061,"journal":{"name":"Abstract and Applied Analysis","volume":" ","pages":""},"PeriodicalIF":0.0,"publicationDate":"2022-04-05","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"46727596","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 finite element approach was utilized in this study to solve numerically the two-dimensional time-dependent heat transfer equation coupled with the Darcy flow. The Picard-Lindelöf Theorem was used to prove the existence and uniqueness of the solution. The prior and posterior error estimates are then derived for the numerical scheme. Numerical examples were provided to show the effectiveness of the theoretical results. The essential code development in this study was done using MATLAB computer simulation.
{"title":"Numerical Solution of the Heat Transfer Equation Coupled with the Darcy Flow Using the Finite Element Method","authors":"Mohammed Hirpho","doi":"10.1155/2022/5108445","DOIUrl":"https://doi.org/10.1155/2022/5108445","url":null,"abstract":"The finite element approach was utilized in this study to solve numerically the two-dimensional time-dependent heat transfer equation coupled with the Darcy flow. The Picard-Lindelöf Theorem was used to prove the existence and uniqueness of the solution. The prior and posterior error estimates are then derived for the numerical scheme. Numerical examples were provided to show the effectiveness of the theoretical results. The essential code development in this study was done using MATLAB computer simulation.","PeriodicalId":7061,"journal":{"name":"Abstract and Applied Analysis","volume":" ","pages":""},"PeriodicalIF":0.0,"publicationDate":"2022-04-05","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"44118868","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 ill-posed Helmholtz equation with inhomogeneous boundary deflection in a Hilbert space is regularized using the divergence regularization method (DRM). The DRM includes a positive integer scaler that homogenizes the inhomogeneous boundary deflection in the Helmholtz equation’s Cauchy issue. This guarantees the existence and uniqueness of the equation’s solution. To reestablish the stability of the regularized Helmholtz equation and regularized Cauchy boundary conditions, the DRM uses its regularization term 1 + α 2 m e m , where α > 0 is the regularization parameter. As a result, DRM restores all three Hadamard requirements for well-posedness.
利用散度正则化方法对Hilbert空间中具有非均匀边界偏转的不适定Helmholtz方程进行了正则化。DRM包括一个正整数定标器，用于均匀化亥姆霍兹方程柯西问题中的非均匀边界偏转。这保证了方程解的存在性和唯一性。为了重新建立正则化亥姆霍兹方程和正则化柯西边界条件的稳定性，DRM使用其正则化项1+α2 m e m，其中α>0是正则化参数。因此，DRM恢复了Hadamard对适定性的所有三个要求。
{"title":"Using a Divergence Regularization Method to Solve an Ill-Posed Cauchy Problem for the Helmholtz Equation","authors":"B. Barnes, Anthony Y. Aidoo, J. Ackora-Prah","doi":"10.1155/2022/4628634","DOIUrl":"https://doi.org/10.1155/2022/4628634","url":null,"abstract":"The ill-posed Helmholtz equation with inhomogeneous boundary deflection in a Hilbert space is regularized using the divergence regularization method (DRM). The DRM includes a positive integer scaler that homogenizes the inhomogeneous boundary deflection in the Helmholtz equation’s Cauchy issue. This guarantees the existence and uniqueness of the equation’s solution. To reestablish the stability of the regularized Helmholtz equation and regularized Cauchy boundary conditions, the DRM uses its regularization term \u0000 \u0000 \u0000 \u0000 1\u0000 +\u0000 \u0000 \u0000 α\u0000 \u0000 \u0000 2\u0000 m\u0000 \u0000 \u0000 \u0000 \u0000 \u0000 \u0000 e\u0000 \u0000 \u0000 m\u0000 \u0000 \u0000 \u0000 , where \u0000 \u0000 α\u0000 >\u0000 0\u0000 \u0000 is the regularization parameter. As a result, DRM restores all three Hadamard requirements for well-posedness.","PeriodicalId":7061,"journal":{"name":"Abstract and Applied Analysis","volume":"9 1","pages":""},"PeriodicalIF":0.0,"publicationDate":"2022-03-29","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"41245291","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}
Nirenberg proposed a problem as to whether or not a continuous and expansive operator (where is a Hilbert space) is surjective if . I shall give a positive answer for the problem provided that is unbounded. For contents related to this paper, the reader is referred to the remarks and the study of Asfaw (2021). The present paper gives a complete answer for the problem that has been open for about 47 years.
{"title":"A Positive Answer on Nirenberg’s Problem on Expansive Mappings in Hilbert Spaces","authors":"Teffera M. Asfaw","doi":"10.1155/2022/9487405","DOIUrl":"https://doi.org/10.1155/2022/9487405","url":null,"abstract":"<jats:p>Nirenberg proposed a problem as to whether or not a continuous and expansive operator <jats:inline-formula>\u0000 <math xmlns=\"http://www.w3.org/1998/Math/MathML\" id=\"M1\">\u0000 <mi>T</mi>\u0000 <mo>:</mo>\u0000 <mi>X</mi>\u0000 <mo>⟶</mo>\u0000 <mi>X</mi>\u0000 </math>\u0000 </jats:inline-formula> (where <jats:inline-formula>\u0000 <math xmlns=\"http://www.w3.org/1998/Math/MathML\" id=\"M2\">\u0000 <mi>X</mi>\u0000 </math>\u0000 </jats:inline-formula> is a Hilbert space) is surjective if <jats:inline-formula>\u0000 <math xmlns=\"http://www.w3.org/1998/Math/MathML\" id=\"M3\">\u0000 <mover>\u0000 <mrow>\u0000 <mi>R</mi>\u0000 <mfenced open=\"(\" close=\")\">\u0000 <mrow>\u0000 <mi>T</mi>\u0000 </mrow>\u0000 </mfenced>\u0000 </mrow>\u0000 <mrow>\u0000 <mo>∘</mo>\u0000 </mrow>\u0000 </mover>\u0000 <mo>≠</mo>\u0000 <mo>∅</mo>\u0000 </math>\u0000 </jats:inline-formula>. I shall give a positive answer for the problem provided that <jats:inline-formula>\u0000 <math xmlns=\"http://www.w3.org/1998/Math/MathML\" id=\"M4\">\u0000 <mover>\u0000 <mrow>\u0000 <mi>R</mi>\u0000 <mfenced open=\"(\" close=\")\">\u0000 <mrow>\u0000 <mi>T</mi>\u0000 </mrow>\u0000 </mfenced>\u0000 </mrow>\u0000 <mrow>\u0000 <mo>∘</mo>\u0000 </mrow>\u0000 </mover>\u0000 </math>\u0000 </jats:inline-formula> is unbounded. For contents related to this paper, the reader is referred to the remarks and the study of Asfaw (2021). The present paper gives a complete answer for the problem that has been open for about 47 years.</jats:p>","PeriodicalId":7061,"journal":{"name":"Abstract and Applied Analysis","volume":" ","pages":""},"PeriodicalIF":0.0,"publicationDate":"2022-03-17","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"46548834","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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