Pub Date : 2020-12-30DOI: 10.37622/ADSA/15.2.2020.265-269
B. Shin, Hwajoon Kim
We consider the form of the third partial derivative test for functions of three variables. The methods used are Hessian matrix and Taylor expansion. This study was conducted for the purpose of providing an orderly tool to alleviate the computational hassle for related research of the future. Mathematics Subject Classification: 35A22, 44A10
{"title":"The form of the Third Partial Derivative Test for Functions of Three Variables","authors":"B. Shin, Hwajoon Kim","doi":"10.37622/ADSA/15.2.2020.265-269","DOIUrl":"https://doi.org/10.37622/ADSA/15.2.2020.265-269","url":null,"abstract":"We consider the form of the third partial derivative test for functions of three variables. The methods used are Hessian matrix and Taylor expansion. This study was conducted for the purpose of providing an orderly tool to alleviate the computational hassle for related research of the future. Mathematics Subject Classification: 35A22, 44A10","PeriodicalId":36469,"journal":{"name":"Advances in Dynamical Systems and Applications","volume":"96 1","pages":""},"PeriodicalIF":0.0,"publicationDate":"2020-12-30","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"90326545","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 : 2020-12-30DOI: 10.37622/ADSA/15.2.2020.231-247
J. Aramaki
In this paper, we show the existence of a weak solution to the Maxwell-Stokes type equation by the penalty method introduced by Temam. Our approximate equation is nonlinear and contains so called p-curl system. Furthermore, we obtain the continuous dependence of the weak solution on the data.
{"title":"Existence of a Weak Solution to the Maxwell-Stokes Type Equation by the Penalty Method","authors":"J. Aramaki","doi":"10.37622/ADSA/15.2.2020.231-247","DOIUrl":"https://doi.org/10.37622/ADSA/15.2.2020.231-247","url":null,"abstract":"In this paper, we show the existence of a weak solution to the Maxwell-Stokes type equation by the penalty method introduced by Temam. Our approximate equation is nonlinear and contains so called p-curl system. Furthermore, we obtain the continuous dependence of the weak solution on the data.","PeriodicalId":36469,"journal":{"name":"Advances in Dynamical Systems and Applications","volume":"14 1","pages":""},"PeriodicalIF":0.0,"publicationDate":"2020-12-30","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"74109008","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 : 2020-12-22DOI: 10.37622/adsa/15.2.2020.153-169
N. M., K. S. Subrahamanian Moosath
In this paper, first we study the rough Liouville equivalence of non-degenerate integrable Hamiltonian systems with two degrees of freedom using geometric skeleton. Then consider the rough Liouville equivalence using molecules and show that both the approaches are equivalent. Classification: MSC 37J15. MSC 37J35
{"title":"Rough Liouville Equivalence of Integrable Hamiltonian Systems","authors":"N. M., K. S. Subrahamanian Moosath","doi":"10.37622/adsa/15.2.2020.153-169","DOIUrl":"https://doi.org/10.37622/adsa/15.2.2020.153-169","url":null,"abstract":"In this paper, first we study the rough Liouville equivalence of non-degenerate integrable Hamiltonian systems with two degrees of freedom using geometric skeleton. Then consider the rough Liouville equivalence using molecules and show that both the approaches are equivalent. Classification: MSC 37J15. MSC 37J35","PeriodicalId":36469,"journal":{"name":"Advances in Dynamical Systems and Applications","volume":"240 1","pages":""},"PeriodicalIF":0.0,"publicationDate":"2020-12-22","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"74651968","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 : 2020-12-22DOI: 10.37622/adsa/15.2.2020.143-151
Fernando Mejías, J. Vielma, Á. Guale
In this paper a recent topological approach to the Collatz conjecture is shown. Also known as “the 3 x + 1 problem”, the Collatz conjecture establishes that for every natural number n , there exists a natural number r such that the r -fold composite κ r ( n ) = 1 , where κ : N → N is the function defined as x/ 2 if x is even and as 3 x + 1 if x is odd. This map κ induces the so called primal topology τ κ on N . We prove that the space ( N , τ κ ) is path-connected and compact if and only if the Collatz conjecture is true.
{"title":"A Topological Path to the Collatz Conjecture: A historical point of view","authors":"Fernando Mejías, J. Vielma, Á. Guale","doi":"10.37622/adsa/15.2.2020.143-151","DOIUrl":"https://doi.org/10.37622/adsa/15.2.2020.143-151","url":null,"abstract":"In this paper a recent topological approach to the Collatz conjecture is shown. Also known as “the 3 x + 1 problem”, the Collatz conjecture establishes that for every natural number n , there exists a natural number r such that the r -fold composite κ r ( n ) = 1 , where κ : N → N is the function defined as x/ 2 if x is even and as 3 x + 1 if x is odd. This map κ induces the so called primal topology τ κ on N . We prove that the space ( N , τ κ ) is path-connected and compact if and only if the Collatz conjecture is true.","PeriodicalId":36469,"journal":{"name":"Advances in Dynamical Systems and Applications","volume":"74 1","pages":""},"PeriodicalIF":0.0,"publicationDate":"2020-12-22","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"91282659","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 : 2020-12-22DOI: 10.37622/adsa/15.2.2020.199-215
V. Rusanov, A. Daneev, Yu. É. Linke, P. A. Plesnyov
On the basis of tensor production of the real Hilbert spaces, functionalgeometric conditions (necessary and sufficient) are given for the existence of a differential realization model for experimental data of an "inputoutput" type describing the dynamic behavior of the "black box" in the class of controllable bilinear nonstationary ordinary differential equations of the second order with delay (including non-autonomous quasi-linear hyperbolic models) in the separable Hilbert space. Incidentally, the topological-metric conditions of continuity of the projectivization of the entropic RayleighRitz operator are substantiated with calculating the fundamental group of its image. The results obtained give incentives to develop a qualitative theory of non-linear structural identification of polylinear non-autonomous differential systems of higher orders with delay, as the tools of mathematical modeling for the weaklystructured neurodynamic processes.
{"title":"Existence of a Bilinear Delay Differential Realization of Nonlinear Neurodynamic Process in the Constructions of Entropic Rayleigh Ritz Operator","authors":"V. Rusanov, A. Daneev, Yu. É. Linke, P. A. Plesnyov","doi":"10.37622/adsa/15.2.2020.199-215","DOIUrl":"https://doi.org/10.37622/adsa/15.2.2020.199-215","url":null,"abstract":"On the basis of tensor production of the real Hilbert spaces, functionalgeometric conditions (necessary and sufficient) are given for the existence of a differential realization model for experimental data of an \"inputoutput\" type describing the dynamic behavior of the \"black box\" in the class of controllable bilinear nonstationary ordinary differential equations of the second order with delay (including non-autonomous quasi-linear hyperbolic models) in the separable Hilbert space. Incidentally, the topological-metric conditions of continuity of the projectivization of the entropic RayleighRitz operator are substantiated with calculating the fundamental group of its image. The results obtained give incentives to develop a qualitative theory of non-linear structural identification of polylinear non-autonomous differential systems of higher orders with delay, as the tools of mathematical modeling for the weaklystructured neurodynamic processes.","PeriodicalId":36469,"journal":{"name":"Advances in Dynamical Systems and Applications","volume":"182 1","pages":""},"PeriodicalIF":0.0,"publicationDate":"2020-12-22","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"77668777","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 : 2020-12-22DOI: 10.37622/adsa/15.2.2020.187-197
G. Vasilyev, O. Kuzichkin, D. Surzhik
Thermoelectric modules (TEM) based on Peltier elements have a number of advantages compared to classic compressor cooling systems based on refrigerants. Increasing the efficiency of TEM is associated with the search for new thermoelectric materials with improved properties and the use of temperature control systems for these modules. The complexity of modeling, analysis and synthesis of thermoelectric systems (TES) is determined by the significantly nonlinear characteristics of Peltier elements in a wide range of temperatures and control currents, as well as the influence of switching effects in pulse control. It is proposed to analyze the dynamic modes of TES using a spectral technique based on the approximation of the system characteristics by piecewise linear functions. This allowed us to obtain generalized expressions of transients for any order of the studied pulse system and arbitrary character of non-linearity, taking into account switching effects. The functional diagram and model of the current control system flowing through the Peltier element are presented. Dynamic modes of pulse TEM control systems with transfer functions of continuous parts of the 1st, 2nd and 3rd orders are simulated. The developed mathematical apparatus is the basis for further optimization and synthesis of TEM control systems.
{"title":"Method for Modeling Dynamic Modes of Nonlinear Control Systems for Thermoelectric Modules","authors":"G. Vasilyev, O. Kuzichkin, D. Surzhik","doi":"10.37622/adsa/15.2.2020.187-197","DOIUrl":"https://doi.org/10.37622/adsa/15.2.2020.187-197","url":null,"abstract":"Thermoelectric modules (TEM) based on Peltier elements have a number of advantages compared to classic compressor cooling systems based on refrigerants. Increasing the efficiency of TEM is associated with the search for new thermoelectric materials with improved properties and the use of temperature control systems for these modules. The complexity of modeling, analysis and synthesis of thermoelectric systems (TES) is determined by the significantly nonlinear characteristics of Peltier elements in a wide range of temperatures and control currents, as well as the influence of switching effects in pulse control. It is proposed to analyze the dynamic modes of TES using a spectral technique based on the approximation of the system characteristics by piecewise linear functions. This allowed us to obtain generalized expressions of transients for any order of the studied pulse system and arbitrary character of non-linearity, taking into account switching effects. The functional diagram and model of the current control system flowing through the Peltier element are presented. Dynamic modes of pulse TEM control systems with transfer functions of continuous parts of the 1st, 2nd and 3rd orders are simulated. The developed mathematical apparatus is the basis for further optimization and synthesis of TEM control systems.","PeriodicalId":36469,"journal":{"name":"Advances in Dynamical Systems and Applications","volume":"32 1","pages":""},"PeriodicalIF":0.0,"publicationDate":"2020-12-22","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"75573737","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 find a new connection between nth degree polynomial mod p congruence with n roots and higher order Fibonacci and Lucas sequences. We shall first discuss about the recent work been done in sequences and their connection to polynomial congruence and then find out new relations between particular recurrence relation and the congruence of the sequences
{"title":"Sequences and Polynomial Congruence","authors":"Darrell Cox, Sourangshu Ghosh","doi":"10.31219/osf.io/3hwzq","DOIUrl":"https://doi.org/10.31219/osf.io/3hwzq","url":null,"abstract":"In this paper we shall find a new connection between nth degree polynomial mod p congruence with n roots and higher order Fibonacci and Lucas sequences. We shall first discuss about the recent work been done in sequences and their connection to polynomial congruence and then find out new relations between particular recurrence relation and the congruence of the sequences","PeriodicalId":36469,"journal":{"name":"Advances in Dynamical Systems and Applications","volume":"1 1","pages":""},"PeriodicalIF":0.0,"publicationDate":"2020-12-18","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"75004181","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 : 2020-06-30DOI: 10.37622/adsa/15.1.2020.73-82
S. K. Tiwari, Ayush S Saxena, S. Bhaumik
{"title":"Coupled Fixed Point Theorem for Mapping Satisfying Integral Type Contraction on Cone Metric Space","authors":"S. K. Tiwari, Ayush S Saxena, S. Bhaumik","doi":"10.37622/adsa/15.1.2020.73-82","DOIUrl":"https://doi.org/10.37622/adsa/15.1.2020.73-82","url":null,"abstract":"","PeriodicalId":36469,"journal":{"name":"Advances in Dynamical Systems and Applications","volume":"9 1","pages":""},"PeriodicalIF":0.0,"publicationDate":"2020-06-30","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"74400870","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 : 2020-06-01DOI: 10.37622/adsa/15.1.2020.1-15
V. Khan, Abdullah A. H. Makharesh, Mohammad Faisal Khan, Sameera A. A. Abdullah, Kamal M. A. S. Alshlool
Recently, the notion of Iλ–convergence in an intuitionistic fuzzy n–normed spaces was introduced by Konwar et al. [N. Konwar and P. Debnath. Iλ–convergence in intuitionistic fuzzy n-normed linear space. 07 2016]. In this article with the help of the notion Iλ–convergence , we introduce some new Orlicz sequence spaces. Further, we examine some topological properties on these spaces.
{"title":"On Intuitionistic Fuzzy n–Normed I –Convergence of Sequence spaces Defined by Orlicz Function","authors":"V. Khan, Abdullah A. H. Makharesh, Mohammad Faisal Khan, Sameera A. A. Abdullah, Kamal M. A. S. Alshlool","doi":"10.37622/adsa/15.1.2020.1-15","DOIUrl":"https://doi.org/10.37622/adsa/15.1.2020.1-15","url":null,"abstract":"Recently, the notion of Iλ–convergence in an intuitionistic fuzzy n–normed spaces was introduced by Konwar et al. [N. Konwar and P. Debnath. Iλ–convergence in intuitionistic fuzzy n-normed linear space. 07 2016]. In this article with the help of the notion Iλ–convergence , we introduce some new Orlicz sequence spaces. Further, we examine some topological properties on these spaces.","PeriodicalId":36469,"journal":{"name":"Advances in Dynamical Systems and Applications","volume":"32 1","pages":""},"PeriodicalIF":0.0,"publicationDate":"2020-06-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"88053639","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 : 2019-06-05DOI: 10.37622/adsa/14.1.2019.83-118
K. Ramkumar, A. G. Amoussou, C. Ogouyandjou, M. Diop
In this paper, we investigate the existence of mild solutions for a class of stochastic functional differential impulsive equations with infinite delay on Hilbert space. The results are obtained by using the Banach fixed point theorem and Krasnoselskii–Schaefer type fixed point theorem combined with theories of resolvent operators. In the end as an application, an example has been presented to illustrate the results obtained.
{"title":"Existence and Uniqueness of Mild Solutions of Stochastic Partial Integro-Differential Impulsive Equations with Infinite Delay via Resolvent Operator","authors":"K. Ramkumar, A. G. Amoussou, C. Ogouyandjou, M. Diop","doi":"10.37622/adsa/14.1.2019.83-118","DOIUrl":"https://doi.org/10.37622/adsa/14.1.2019.83-118","url":null,"abstract":"In this paper, we investigate the existence of mild solutions for a class of stochastic functional differential impulsive equations with infinite delay on Hilbert space. The results are obtained by using the Banach fixed point theorem and Krasnoselskii–Schaefer type fixed point theorem combined with theories of resolvent operators. In the end as an application, an example has been presented to illustrate the results obtained.","PeriodicalId":36469,"journal":{"name":"Advances in Dynamical Systems and Applications","volume":"11 1","pages":""},"PeriodicalIF":0.0,"publicationDate":"2019-06-05","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"83016365","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}
京公网安备 11010802042870号
京ICP备2023020795号-1
扫码关注我们
求助内容：
应助结果提醒方式：