Pub Date : 2021-08-01DOI: 10.32513/tmj/19322008139
H. Waghamore, S. Vijaylaxmi
In this paper, we deal with meromorphic functions and its kth derivative. We consider a set of roots of unity, which shares the functions of the form (fnP(f))(k) and (gnP(g))(k) and obtain uniqueness results which improves the results of V. H. An and H. H. Khoai. Also, by introducing the concept of weighted sharing, we obtain analogous results from these authors.
{"title":"Weighted sharing of a set and uniqueness of meromorphic functions with derivatives","authors":"H. Waghamore, S. Vijaylaxmi","doi":"10.32513/tmj/19322008139","DOIUrl":"https://doi.org/10.32513/tmj/19322008139","url":null,"abstract":"In this paper, we deal with meromorphic functions and its kth derivative. We consider a set of roots of unity, which shares the functions of the form (fnP(f))(k) and (gnP(g))(k) and obtain uniqueness results which improves the results of V. H. An and H. H. Khoai. Also, by introducing the concept of weighted sharing, we obtain analogous results from these authors.","PeriodicalId":43977,"journal":{"name":"Tbilisi Mathematical Journal","volume":null,"pages":null},"PeriodicalIF":0.5,"publicationDate":"2021-08-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"43220972","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 : 2021-08-01DOI: 10.32513/tmj/19322008155
Bilel Selikh, A. Chillali, Douadi Mihoubi, N. Ghadbane
Let F3d is the finite field of order 3d with d be a positive integer, we consider A4:=F3d[e]=F3d[X]/(X4) is a finite quotient ring, where e4=0. In this paper, we will show an example of encryption and decryption. Firstly, we will present the elliptic curve over this ring. In addition, we study the algorithmic properties by proposing effective implementations for representing the elements and the group law. Precisely, we give a numerical example of cryptography (encryption and decryption) by using two methods with a secret key.
{"title":"ECC over the ring F3d[ε],ε4=0 by using two methods","authors":"Bilel Selikh, A. Chillali, Douadi Mihoubi, N. Ghadbane","doi":"10.32513/tmj/19322008155","DOIUrl":"https://doi.org/10.32513/tmj/19322008155","url":null,"abstract":"Let F3d is the finite field of order 3d with d be a positive integer, we consider A4:=F3d[e]=F3d[X]/(X4) is a finite quotient ring, where e4=0. In this paper, we will show an example of encryption and decryption. Firstly, we will present the elliptic curve over this ring. In addition, we study the algorithmic properties by proposing effective implementations for representing the elements and the group law. Precisely, we give a numerical example of cryptography (encryption and decryption) by using two methods with a secret key.","PeriodicalId":43977,"journal":{"name":"Tbilisi Mathematical Journal","volume":null,"pages":null},"PeriodicalIF":0.5,"publicationDate":"2021-08-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"42879246","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 : 2021-08-01DOI: 10.32513/tmj/19322008142
Ulviye Demirbileko, V. Ala, K. Mamedov
The nonlinear conformable time-fractional modified Camassa-Holm (MCH) equation plays an important role in physics. It is an interesting model to define change waves with weak nonlinearity. The aim of this study is to present the new exact solutions of conformable time-fractional MCH equation. For this purpose, an effective method which is the Improved Bernoulli Sub-Equation Function Method (IBSEFM) has been used. The 2D and 3D graphs and contour surfaces acquired from the values of the solutions are plotted by the aid of mathematics software. The obtained results confirm that IBSEFM is a powerful mathematical tool to solve nonlinear conformable time-fractional partial differential equations arising in mathematical physics.
{"title":"An application of improved Bernoulli sub-equation function method to the nonlinear conformable time-fractional equation","authors":"Ulviye Demirbileko, V. Ala, K. Mamedov","doi":"10.32513/tmj/19322008142","DOIUrl":"https://doi.org/10.32513/tmj/19322008142","url":null,"abstract":"The nonlinear conformable time-fractional modified Camassa-Holm (MCH) equation plays an important role in physics. It is an interesting model to define change waves with weak nonlinearity. The aim of this study is to present the new exact solutions of conformable time-fractional MCH equation. For this purpose, an effective method which is the Improved Bernoulli Sub-Equation Function Method (IBSEFM) has been used. The 2D and 3D graphs and contour surfaces acquired from the values of the solutions are plotted by the aid of mathematics software. The obtained results confirm that IBSEFM is a powerful mathematical tool to solve nonlinear conformable time-fractional partial differential equations arising in mathematical physics.","PeriodicalId":43977,"journal":{"name":"Tbilisi Mathematical Journal","volume":null,"pages":null},"PeriodicalIF":0.5,"publicationDate":"2021-08-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"48415126","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 : 2021-08-01DOI: 10.32513/tmj/19322008154
H. Arabyani
In 1940, P. Hall introduced the concept of isoclinism of groups. Heidarian et al. studied the concept of n-isoclinism of pairs of groups. In this paper, we investigate the concept of n-isoclinism between two pairs of groups and give some relations between the notions of n-isoclinism of groups and n-isoclinism of pairs of groups.
{"title":"Some remarks on n-isoclinic pairs of groups","authors":"H. Arabyani","doi":"10.32513/tmj/19322008154","DOIUrl":"https://doi.org/10.32513/tmj/19322008154","url":null,"abstract":"In 1940, P. Hall introduced the concept of isoclinism of groups. Heidarian et al. studied the concept of n-isoclinism of pairs of groups. In this paper, we investigate the concept of n-isoclinism between two pairs of groups and give some relations between the notions of n-isoclinism of groups and n-isoclinism of pairs of groups.","PeriodicalId":43977,"journal":{"name":"Tbilisi Mathematical Journal","volume":null,"pages":null},"PeriodicalIF":0.5,"publicationDate":"2021-08-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"69696588","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 : 2021-08-01DOI: 10.32513/tmj/19322008143
Furkan Yildirim
Using projection (submersion) of the cotangent bundle T*M over a manifold M, we define a semi-tensor (pull-back) bundle tM of type (p,q). The purpose of this paper is to investigate horizontal lifts of vector fields in a special class of semi-tensor (pull-back) bundle tM of type (p,q).
{"title":"Horizontal lift problems in a pull-back bundle of tensor bundles defined by projection of the cotangent bundles","authors":"Furkan Yildirim","doi":"10.32513/tmj/19322008143","DOIUrl":"https://doi.org/10.32513/tmj/19322008143","url":null,"abstract":"Using projection (submersion) of the cotangent bundle T*M over a manifold M, we define a semi-tensor (pull-back) bundle tM of type (p,q). The purpose of this paper is to investigate horizontal lifts of vector fields in a special class of semi-tensor (pull-back) bundle tM of type (p,q).","PeriodicalId":43977,"journal":{"name":"Tbilisi Mathematical Journal","volume":null,"pages":null},"PeriodicalIF":0.5,"publicationDate":"2021-08-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"44808937","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 : 2021-08-01DOI: 10.32513/tmj/19322008153
E. Pişkin, F. Ekinci
{"title":"Global existence of solutions for a coupled viscoelastic plate equation with degenerate damping terms","authors":"E. Pişkin, F. Ekinci","doi":"10.32513/tmj/19322008153","DOIUrl":"https://doi.org/10.32513/tmj/19322008153","url":null,"abstract":"","PeriodicalId":43977,"journal":{"name":"Tbilisi Mathematical Journal","volume":null,"pages":null},"PeriodicalIF":0.5,"publicationDate":"2021-08-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"43973811","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 : 2021-08-01DOI: 10.32513/tmj/19322008152
T. Biswas, C. Biswas
In this paper we aim to establish some results depending on the comparative growth properties of composite transcendental entire or meromorphic functions and some special type of differential polynomials generated by one of the factors on the basis of generalized order α,β and generalized lower order α,β where α and β are continuous non-negative functions defined on −∞,+∞.
{"title":"Comparative growth properties of special type of differential polynomial generated by entire and meromorphic functions on the basis of their generalized order α,β","authors":"T. Biswas, C. Biswas","doi":"10.32513/tmj/19322008152","DOIUrl":"https://doi.org/10.32513/tmj/19322008152","url":null,"abstract":"In this paper we aim to establish some results depending on the comparative growth properties of composite transcendental entire or meromorphic functions and some special type of differential polynomials generated by one of the factors on the basis of generalized order α,β and generalized lower order α,β where α and β are continuous non-negative functions defined on −∞,+∞.","PeriodicalId":43977,"journal":{"name":"Tbilisi Mathematical Journal","volume":null,"pages":null},"PeriodicalIF":0.5,"publicationDate":"2021-08-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"46302838","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 : 2021-08-01DOI: 10.32513/tmj/19322008147
K. Khelil, A. Ardjouni, A. Djoudi
In this work, we use the Banach fixed point theorem to establish new results on the stability and asymptotic stability of the zero solution for a neutral integro-dynamic equation on time scales. The results obtained here extend those due to Yankson. We end by giving two examples to illustrate our work.
{"title":"Stability for neutral integro-dynamic equations with multiple functional delays on time scales","authors":"K. Khelil, A. Ardjouni, A. Djoudi","doi":"10.32513/tmj/19322008147","DOIUrl":"https://doi.org/10.32513/tmj/19322008147","url":null,"abstract":"In this work, we use the Banach fixed point theorem to establish new results on the stability and asymptotic stability of the zero solution for a neutral integro-dynamic equation on time scales. The results obtained here extend those due to Yankson. We end by giving two examples to illustrate our work.","PeriodicalId":43977,"journal":{"name":"Tbilisi Mathematical Journal","volume":null,"pages":null},"PeriodicalIF":0.5,"publicationDate":"2021-08-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"45964449","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 : 2021-08-01DOI: 10.32513/tmj/19322008144
S. Butt, A. Kashuri, Muhammad Nadeem
The aim of this paper is to establish some new inequalities of Hermite-Hadamard and Fejer type using generalized h−convex and generalized (h1,h2)–convex functions on the co-ordinates. Some known results are recaptured from our results as special cases.
{"title":"Generalized integral inequalities for convex functions on the co-ordinates","authors":"S. Butt, A. Kashuri, Muhammad Nadeem","doi":"10.32513/tmj/19322008144","DOIUrl":"https://doi.org/10.32513/tmj/19322008144","url":null,"abstract":"The aim of this paper is to establish some new inequalities of Hermite-Hadamard and Fejer type using generalized h−convex and generalized (h1,h2)–convex functions on the co-ordinates. Some known results are recaptured from our results as special cases.","PeriodicalId":43977,"journal":{"name":"Tbilisi Mathematical Journal","volume":null,"pages":null},"PeriodicalIF":0.5,"publicationDate":"2021-08-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"42096172","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 : 2021-08-01DOI: 10.32513/tmj/19322008140
A. Kashuri, Muhammad Raees, M. Anwar
In this paper, we establish some new Hermite-Hadamard integral inequalities for m-convex functions via (p,q)-calculus. Also, some known results are recaptured as special cases from our results. At the end, a briefly conclusion is given.
{"title":"New integral inequalities involving m—convex functions in (p,q)—calculus","authors":"A. Kashuri, Muhammad Raees, M. Anwar","doi":"10.32513/tmj/19322008140","DOIUrl":"https://doi.org/10.32513/tmj/19322008140","url":null,"abstract":"In this paper, we establish some new Hermite-Hadamard integral inequalities for m-convex functions via (p,q)-calculus. Also, some known results are recaptured as special cases from our results. At the end, a briefly conclusion is given.","PeriodicalId":43977,"journal":{"name":"Tbilisi Mathematical Journal","volume":null,"pages":null},"PeriodicalIF":0.5,"publicationDate":"2021-08-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"47983583","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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