Pub Date : 2023-03-27DOI: 10.11648/j.mcs.20230802.12
Chonghu Wang, Xin Lai, Rongge Yu, Yaxuan Zheng, Bao-Ping Liu
: Digraphs are generalization of graphs in which each edge is given one or two directions. For each digraph, there exists a transitive digraph containing it. Moreover, all the formal linear combinations of allowed elementary paths form a basis of the path complex for a transitive digraph. Hence, the study of discrete Morse theory on transitive digraphs is very important for the further study of discrete Morse theory on general digraphs. As we know, the definition of discrete Morse function on a digraph is different from that on a simplical complex or a cell complex: each discrete Morse function on a digraph is a discrete flat Witten-Morse function. In this paper, we deform the usual boundary operator, replacing it with a boundary operator with parameters and consider the induced Laplace operators. In addition, we consider the eigenvectors of the eigenvalues of the Laplace operator that approach to zero when the parameters approach infinity, define the generation space of these eigenvectors, and further give the Witten complex of digraphs. Finally, we prove that for a transitive digraph, Witten complex approaches to its Morse complex. However, for general digraphs, the structure of Morse complex is not as simple as that of transitive digraphs and the critical path is not directly related to the eigenvector with zero eigenvalue of Laplace operator. This is explained in the last part of the paper.
{"title":"Witten Complex of Transitive Digraph and Its Convergence","authors":"Chonghu Wang, Xin Lai, Rongge Yu, Yaxuan Zheng, Bao-Ping Liu","doi":"10.11648/j.mcs.20230802.12","DOIUrl":"https://doi.org/10.11648/j.mcs.20230802.12","url":null,"abstract":": Digraphs are generalization of graphs in which each edge is given one or two directions. For each digraph, there exists a transitive digraph containing it. Moreover, all the formal linear combinations of allowed elementary paths form a basis of the path complex for a transitive digraph. Hence, the study of discrete Morse theory on transitive digraphs is very important for the further study of discrete Morse theory on general digraphs. As we know, the definition of discrete Morse function on a digraph is different from that on a simplical complex or a cell complex: each discrete Morse function on a digraph is a discrete flat Witten-Morse function. In this paper, we deform the usual boundary operator, replacing it with a boundary operator with parameters and consider the induced Laplace operators. In addition, we consider the eigenvectors of the eigenvalues of the Laplace operator that approach to zero when the parameters approach infinity, define the generation space of these eigenvectors, and further give the Witten complex of digraphs. Finally, we prove that for a transitive digraph, Witten complex approaches to its Morse complex. However, for general digraphs, the structure of Morse complex is not as simple as that of transitive digraphs and the critical path is not directly related to the eigenvector with zero eigenvalue of Laplace operator. This is explained in the last part of the paper.","PeriodicalId":45497,"journal":{"name":"Journal of Mathematics and Computer Science-JMCS","volume":"33 1","pages":""},"PeriodicalIF":2.5,"publicationDate":"2023-03-27","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"86772916","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 : 2023-03-09DOI: 10.11648/j.mcs.20230802.11
Dalabaev Umurdin, Hasanova Dilfuza
{"title":"Construction of an Approximate-Analytical Solution for Boundary Value Problems of a Parabolic Equation","authors":"Dalabaev Umurdin, Hasanova Dilfuza","doi":"10.11648/j.mcs.20230802.11","DOIUrl":"https://doi.org/10.11648/j.mcs.20230802.11","url":null,"abstract":"","PeriodicalId":45497,"journal":{"name":"Journal of Mathematics and Computer Science-JMCS","volume":"11 1","pages":""},"PeriodicalIF":2.5,"publicationDate":"2023-03-09","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"89030318","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
{"title":"Theoretical study and numerical simulation for a mathematical model of diffusive cancer with effect of stem cell therapy and chemotherapy","authors":"N. Aljahdaly, N. A. Almushaity","doi":"10.22436/jmcs.030.04.04","DOIUrl":"https://doi.org/10.22436/jmcs.030.04.04","url":null,"abstract":"","PeriodicalId":45497,"journal":{"name":"Journal of Mathematics and Computer Science-JMCS","volume":" ","pages":""},"PeriodicalIF":2.5,"publicationDate":"2023-02-18","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"46736286","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
{"title":"Generalized m -preinvexity on fractal set and related local fractional integral inequalities with applications","authors":"S. Al-Sa'di, M. Bibi, M. Muddassar, S. Kermausuor","doi":"10.22436/jmcs.030.04.05","DOIUrl":"https://doi.org/10.22436/jmcs.030.04.05","url":null,"abstract":"","PeriodicalId":45497,"journal":{"name":"Journal of Mathematics and Computer Science-JMCS","volume":" ","pages":""},"PeriodicalIF":2.5,"publicationDate":"2023-02-18","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"43595293","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
{"title":"On the elliptical solutions of models connected to the short pulse equation","authors":"S. Jamal, R. Champala","doi":"10.22436/jmcs.030.04.07","DOIUrl":"https://doi.org/10.22436/jmcs.030.04.07","url":null,"abstract":"","PeriodicalId":45497,"journal":{"name":"Journal of Mathematics and Computer Science-JMCS","volume":" ","pages":""},"PeriodicalIF":2.5,"publicationDate":"2023-02-18","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"47168830","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
{"title":"Generalised Hermite-Hadamard type inequalities for ( s , r ) -convex functions in mixed kind with applications","authors":"F. Mehmood, F. Nawaz, A. Soleev","doi":"10.22436/jmcs.030.04.06","DOIUrl":"https://doi.org/10.22436/jmcs.030.04.06","url":null,"abstract":"","PeriodicalId":45497,"journal":{"name":"Journal of Mathematics and Computer Science-JMCS","volume":" ","pages":""},"PeriodicalIF":2.5,"publicationDate":"2023-02-18","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"46815981","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 : 2023-02-10DOI: 10.11648/j.mcs.20230801.13
Paschal Bisong Nyiam, A. Salhi
: Multiple Objective Linear Programming (MOLP) problems are usually solved by exact methods. However, nature-inspired population based stochastic algorithms such as the plant propagation algorithm are becoming more and more prominent. This paper applies the multiple objective plant propagation algorithm (MOPPA) and nondominated sorting genetic algorithm II (NSGA-II) for the first time to MOLP and compares their outcomes with those of prominent exact methods. Computational results from a collection of 51 existing MOLP instances suggests that MOPPA compares favourably with four of the most prominent exact methods namely extended multiple objective simplex algorithm (EMSA), affine scaling interior MOLP algorithm (ASIMOLP), Benson’s outer-approximation algorithm (BOA) and parametric simplex algorithm (PSA)
{"title":"Application of the Plant Propagation Algorithm and NSGA-II to Multiple Objective Linear Programming","authors":"Paschal Bisong Nyiam, A. Salhi","doi":"10.11648/j.mcs.20230801.13","DOIUrl":"https://doi.org/10.11648/j.mcs.20230801.13","url":null,"abstract":": Multiple Objective Linear Programming (MOLP) problems are usually solved by exact methods. However, nature-inspired population based stochastic algorithms such as the plant propagation algorithm are becoming more and more prominent. This paper applies the multiple objective plant propagation algorithm (MOPPA) and nondominated sorting genetic algorithm II (NSGA-II) for the first time to MOLP and compares their outcomes with those of prominent exact methods. Computational results from a collection of 51 existing MOLP instances suggests that MOPPA compares favourably with four of the most prominent exact methods namely extended multiple objective simplex algorithm (EMSA), affine scaling interior MOLP algorithm (ASIMOLP), Benson’s outer-approximation algorithm (BOA) and parametric simplex algorithm (PSA)","PeriodicalId":45497,"journal":{"name":"Journal of Mathematics and Computer Science-JMCS","volume":"47 1","pages":""},"PeriodicalIF":2.5,"publicationDate":"2023-02-10","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"89159141","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
{"title":"Generalized neutrosophic ideal convergent sequence spaces","authors":"M. Ahmad, M. I. Idrisi, A. Sirohi","doi":"10.22436/jmcs.030.04.03","DOIUrl":"https://doi.org/10.22436/jmcs.030.04.03","url":null,"abstract":"","PeriodicalId":45497,"journal":{"name":"Journal of Mathematics and Computer Science-JMCS","volume":" ","pages":""},"PeriodicalIF":2.5,"publicationDate":"2023-02-09","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"44341970","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
{"title":"On the existence and stability of Caputo Volterra-Fredholm systems","authors":"S. A. Jameel","doi":"10.22436/jmcs.030.04.02","DOIUrl":"https://doi.org/10.22436/jmcs.030.04.02","url":null,"abstract":"","PeriodicalId":45497,"journal":{"name":"Journal of Mathematics and Computer Science-JMCS","volume":" ","pages":""},"PeriodicalIF":2.5,"publicationDate":"2023-02-09","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"47768853","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
{"title":"Connectedness, local connectedness, and components on bipolar soft generalized topological spaces","authors":"H. Saleh, Baravan A. Asaad, R. A. Mohammed","doi":"10.22436/jmcs.030.04.01","DOIUrl":"https://doi.org/10.22436/jmcs.030.04.01","url":null,"abstract":"","PeriodicalId":45497,"journal":{"name":"Journal of Mathematics and Computer Science-JMCS","volume":" ","pages":""},"PeriodicalIF":2.5,"publicationDate":"2023-02-09","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"48157645","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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