Pub Date : 2020-10-03DOI: 10.37516/ADV.MATH.SCI.2020.0122
Rezaul Karim, M. A. Arefin, Amina Tahsin, Md Abdus Sattar
In this article, we have discussed the stability of second order linear and non-linear systems by characteristic roots. In the case of non-linear system, we linearize the nonlinear system under certain specified conditions and study the stability of critical points of the linearized systems. Necessary theories have been presented, applied, and illustrated with examples. A self-contained theory for a homogeneous linear system of third order is built by using the basic concept of the differential equation.
{"title":"A STUDY ABOUT STABILITY OF TWO AND THREE SPECIES POPULATION MODELS","authors":"Rezaul Karim, M. A. Arefin, Amina Tahsin, Md Abdus Sattar","doi":"10.37516/ADV.MATH.SCI.2020.0122","DOIUrl":"https://doi.org/10.37516/ADV.MATH.SCI.2020.0122","url":null,"abstract":"In this article, we have discussed the stability of second order linear and non-linear systems by characteristic roots. In the case of non-linear system, we linearize the nonlinear system under certain specified conditions and study the stability of critical points of the linearized systems. Necessary theories have been presented, applied, and illustrated with examples. A self-contained theory for a homogeneous linear system of third order is built by using the basic concept of the differential equation.","PeriodicalId":53941,"journal":{"name":"Advances and Applications in Mathematical Sciences","volume":"15 1","pages":""},"PeriodicalIF":0.0,"publicationDate":"2020-10-03","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"82438495","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 : 2020-09-07DOI: 10.37516/adv.math.sci.2020.0120
M. Akbari
In this paper, the solution of special type Voltra integral equations with single nuclei is studied. We will also consider Abelian nuclei. We will show the efficiency and simplicity of the proposed method by providing a few examples. Keywords: Integral equations, Voltra of the first type, Single cores.
{"title":"VOLTRA INTEGRAL EQUATIONS OF THE FIRST TYPE WITH SINGLE NUCLEI","authors":"M. Akbari","doi":"10.37516/adv.math.sci.2020.0120","DOIUrl":"https://doi.org/10.37516/adv.math.sci.2020.0120","url":null,"abstract":"In this paper, the solution of special type Voltra integral equations with single nuclei is studied. We will also consider Abelian nuclei. We will show the efficiency and simplicity of the proposed method by providing a few examples. Keywords: Integral equations, Voltra of the first type, Single cores.","PeriodicalId":53941,"journal":{"name":"Advances and Applications in Mathematical Sciences","volume":"3 1","pages":""},"PeriodicalIF":0.0,"publicationDate":"2020-09-07","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"82378601","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 : 2020-01-01DOI: 10.1007/978-3-030-42687-3_7
A. Haupt, T. Schultz, Mohammed Khatami, N. Tran
{"title":"Classification on Large Networks: A Quantitative Bound via Motifs and Graphons (Research)","authors":"A. Haupt, T. Schultz, Mohammed Khatami, N. Tran","doi":"10.1007/978-3-030-42687-3_7","DOIUrl":"https://doi.org/10.1007/978-3-030-42687-3_7","url":null,"abstract":"","PeriodicalId":53941,"journal":{"name":"Advances and Applications in Mathematical Sciences","volume":"279 1","pages":""},"PeriodicalIF":0.0,"publicationDate":"2020-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"86736814","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 : 2020-01-01DOI: 10.1007/978-3-030-42687-3_12
Jenna Rajchgot, M. Satriano, Wanchun Shen
{"title":"Some Combinatorial Cases of the Three Matrix Analog of Gerstenhaber’s Theorem (Research)","authors":"Jenna Rajchgot, M. Satriano, Wanchun Shen","doi":"10.1007/978-3-030-42687-3_12","DOIUrl":"https://doi.org/10.1007/978-3-030-42687-3_12","url":null,"abstract":"","PeriodicalId":53941,"journal":{"name":"Advances and Applications in Mathematical Sciences","volume":"1 1","pages":""},"PeriodicalIF":0.0,"publicationDate":"2020-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"83654423","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 : 2019-11-03DOI: 10.37516/adv.math.sci.2020.0123
Rezaul Karim, Pinakee Dey, Somi Akter, M. A. Arefin, Saikh Shahjahan Miah
The study of second-order damped nonlinear differential equations is important in the development of the theory of dynamical systems and the behavior of the solutions of the over-damped process depends on the behavior of damping forces. We aim to develop and represent a new approximate solution of a nonlinear differential system with damping force and an approximate solution of the damped nonlinear vibrating system with a varying parameter which is based on Krylov–Bogoliubov and Mitropolskii (KBM) Method and Harmonic Balance (HB) Method. By applying these methods we solve and also analyze the finding result of an example. Moreover, the solutions are obtained for different initial conditions, and figures are plotted accordingly where MATHEMATICA and C++ are used as a programming language.
{"title":"APPROXIMATE SOLUTIONS OF DAMPED NON LINEAR SYSTEM WITH VARYING PARAMETER AND DAMPING FORCE","authors":"Rezaul Karim, Pinakee Dey, Somi Akter, M. A. Arefin, Saikh Shahjahan Miah","doi":"10.37516/adv.math.sci.2020.0123","DOIUrl":"https://doi.org/10.37516/adv.math.sci.2020.0123","url":null,"abstract":"The study of second-order damped nonlinear differential equations is important in the development of the theory of dynamical systems and the behavior of the solutions of the over-damped process depends on the behavior of damping forces. We aim to develop and represent a new approximate solution of a nonlinear differential system with damping force and an approximate solution of the damped nonlinear vibrating system with a varying parameter which is based on Krylov–Bogoliubov and Mitropolskii (KBM) Method and Harmonic Balance (HB) Method. By applying these methods we solve and also analyze the finding result of an example. Moreover, the solutions are obtained for different initial conditions, and figures are plotted accordingly where MATHEMATICA and C++ are used as a programming language.","PeriodicalId":53941,"journal":{"name":"Advances and Applications in Mathematical Sciences","volume":"8 1","pages":""},"PeriodicalIF":0.0,"publicationDate":"2019-11-03","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"90093384","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 : 2019-08-26DOI: 10.1007/978-3-030-42687-3_15
V. Hoang, M. Radosz
{"title":"A Note on Singularity Formation for a Nonlocal Transport Equation (Research)","authors":"V. Hoang, M. Radosz","doi":"10.1007/978-3-030-42687-3_15","DOIUrl":"https://doi.org/10.1007/978-3-030-42687-3_15","url":null,"abstract":"","PeriodicalId":53941,"journal":{"name":"Advances and Applications in Mathematical Sciences","volume":"35 1","pages":""},"PeriodicalIF":0.0,"publicationDate":"2019-08-26","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"75604076","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 : 2019-07-17DOI: 10.37516/adv.math.sci.2019.0080
Maan A. Rasheed
In this paper, we consider some blow-up properties of a semilinear heat equation, where the nonlinear term is of exponential type, subject to the zero Dirichletboundary conditions, defined in a ball in 𝑅 𝑛 . Firstly, we study the blow-up set showing that the blow-up can only occur at a single point. Secondly, the upper blow-up rate estimate is derived.
{"title":"SOME BLOW-UP PROPERTIES OF A SEMILINEAR HEAT EQUATION","authors":"Maan A. Rasheed","doi":"10.37516/adv.math.sci.2019.0080","DOIUrl":"https://doi.org/10.37516/adv.math.sci.2019.0080","url":null,"abstract":"In this paper, we consider some blow-up properties of a semilinear heat equation, where the nonlinear term is of exponential type, subject to the zero Dirichletboundary conditions, defined in a ball in 𝑅 𝑛 . Firstly, we study the blow-up set showing that the blow-up can only occur at a single point. Secondly, the upper blow-up rate estimate is derived.","PeriodicalId":53941,"journal":{"name":"Advances and Applications in Mathematical Sciences","volume":"7 1","pages":""},"PeriodicalIF":0.0,"publicationDate":"2019-07-17","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"83279520","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 : 2019-07-01DOI: 10.37516/adv.math.sci.2019.0067
S. K. Malhotra, Sarita Prakash, S. Shukla
The purpose of this paper is to introduce the notion of set-valued (𝛼, 𝑝)- weak contractions in cone metric spaces over Banach algebra and to prove some fixed point theorems for such mappings. The fixed point results of this paper generalize and extend several known fixed point results on cone metric spaces. An example in support of our results is given.
{"title":"SOME FIXED POINT THEOREMS FOR SET-VALUED (a, p)-WEAK CONTRACTIONS IN CONE METRIC SPACES OVER BANACH ALGEBRA","authors":"S. K. Malhotra, Sarita Prakash, S. Shukla","doi":"10.37516/adv.math.sci.2019.0067","DOIUrl":"https://doi.org/10.37516/adv.math.sci.2019.0067","url":null,"abstract":"The purpose of this paper is to introduce the notion of set-valued (𝛼, 𝑝)- weak contractions in cone metric spaces over Banach algebra and to prove some fixed point theorems for such mappings. The fixed point results of this paper generalize and extend several known fixed point results on cone metric spaces. An example in support of our results is given.","PeriodicalId":53941,"journal":{"name":"Advances and Applications in Mathematical Sciences","volume":"158 1","pages":""},"PeriodicalIF":0.0,"publicationDate":"2019-07-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"80135924","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 : 2019-07-01DOI: 10.1007/978-3-030-42687-3_9
Anyu Zhang, B. Stigler
{"title":"The Number of Gröbner Bases in Finite Fields (Research)","authors":"Anyu Zhang, B. Stigler","doi":"10.1007/978-3-030-42687-3_9","DOIUrl":"https://doi.org/10.1007/978-3-030-42687-3_9","url":null,"abstract":"","PeriodicalId":53941,"journal":{"name":"Advances and Applications in Mathematical Sciences","volume":"54 1","pages":""},"PeriodicalIF":0.0,"publicationDate":"2019-07-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"78372557","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 : 2019-07-01DOI: 10.37516/adv.math.sci.2019.0061
R. Vigneswaran, S. Kajanthan
Various iteration schemes are proposed by various authors to solve nonlinear equations arising in the implementation of implicit Runge-Kutta methods. In this paper, a class of s-step non-linear scheme based on projection method is proposed to accelerate the convergence rate of those linear iteration schemes. In this scheme, sequence of numerical solutions is updated after each sub-step is completed. For 2-stage Gauss method, upper bound for the spectral radius of its iteration matrix was obtained in the left half complex plane. This result is extended to 3-stage and 4-stage Gauss methods by transforming the coefficient matrix and the iteration matrix to a block diagonal form. Finally, some numerical experiments are carried out to confirm the obtained theoretical results.
{"title":"A CLASS OF S-STEP NON-LINEAR ITERATION SCHEME BASED ON PROJECTION METHOD FOR GAUSS METHOD","authors":"R. Vigneswaran, S. Kajanthan","doi":"10.37516/adv.math.sci.2019.0061","DOIUrl":"https://doi.org/10.37516/adv.math.sci.2019.0061","url":null,"abstract":"Various iteration schemes are proposed by various authors to solve nonlinear equations arising in the implementation of implicit Runge-Kutta methods. In this paper, a class of s-step non-linear scheme based on projection method is proposed to accelerate the convergence rate of those linear iteration schemes. In this scheme, sequence of numerical solutions is updated after each sub-step is completed. For 2-stage Gauss method, upper bound for the spectral radius of its iteration matrix was obtained in the left half complex plane. This result is extended to 3-stage and 4-stage Gauss methods by transforming the coefficient matrix and the iteration matrix to a block diagonal form. Finally, some numerical experiments are carried out to confirm the obtained theoretical results.","PeriodicalId":53941,"journal":{"name":"Advances and Applications in Mathematical Sciences","volume":"15 1","pages":""},"PeriodicalIF":0.0,"publicationDate":"2019-07-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"78371811","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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