{"title":"A Note on the Inverse Connected <i>p</i>-Median Problem on Block Graphs","authors":"Chun-Hsiang Bai, Liqi Zhang, Jianjie Zhou","doi":"10.4236/apm.2023.134011","DOIUrl":"https://doi.org/10.4236/apm.2023.134011","url":null,"abstract":"","PeriodicalId":43512,"journal":{"name":"Advances in Pure and Applied Mathematics","volume":null,"pages":null},"PeriodicalIF":0.4,"publicationDate":"2023-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"84012095","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 constrained motion of a particle on an elliptical path is studied using Hamiltonian mechanics through Poisson bracket and Lagrangian mechanics through Euler Lagrange equation using non-natural Lagrangian. We calculate the generalized momentum pθ and we find that this quantity is not conserved and the conjugate θ coordinate is not a cyclic coordinate.
{"title":"Canonical Treatment of Elliptical Motion","authors":"Ola A. Jarab’ah","doi":"10.4236/apm.2023.139041","DOIUrl":"https://doi.org/10.4236/apm.2023.139041","url":null,"abstract":"The constrained motion of a particle on an elliptical path is studied using Hamiltonian mechanics through Poisson bracket and Lagrangian mechanics through Euler Lagrange equation using non-natural Lagrangian. We calculate the generalized momentum pθ and we find that this quantity is not conserved and the conjugate θ coordinate is not a cyclic coordinate.","PeriodicalId":43512,"journal":{"name":"Advances in Pure and Applied Mathematics","volume":null,"pages":null},"PeriodicalIF":0.0,"publicationDate":"2023-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"135699211","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 : 2023-01-01DOI: 10.4236/apm.2023.1310047
Carlos Antonio Marin-Mendoza, Rogelio Valdez-Delgado
A novel method of renormalization called Pacman renormalization allows us to study (unicritical) Siegel functions through Pacman-type functions. It has been used to investigate the Siegel parameters with combinatorially periodic rotation number in the main cardioid of the Mandelbrot set. It is already known that it can be defined a Pacman renormalization operator such that for Siegel pacmen, with combinatorially periodic rotation numbers, the operator is compact, analytic and has a unique fixed point, at which it is hyperbolic with one-dimensional unstable manifold. In this paper we observe that this Pacman renormalization operator is compact and analytic at any Siegel Pacman or Siegel map with combinatorially bounded rotation number. This allows us to define a renormalization operator on the hybrid classes of the standard Siegel pacmen to which we built its horseshoe where the operator is topologically semiconjugated to the left shift on the space of bi-infinite sequences of natural numbers bounded by some constant.
{"title":"Pacman Renormalization in Siegel Parameters of Bounded Type","authors":"Carlos Antonio Marin-Mendoza, Rogelio Valdez-Delgado","doi":"10.4236/apm.2023.1310047","DOIUrl":"https://doi.org/10.4236/apm.2023.1310047","url":null,"abstract":"A novel method of renormalization called Pacman renormalization allows us to study (unicritical) Siegel functions through Pacman-type functions. It has been used to investigate the Siegel parameters with combinatorially periodic rotation number in the main cardioid of the Mandelbrot set. It is already known that it can be defined a Pacman renormalization operator such that for Siegel pacmen, with combinatorially periodic rotation numbers, the operator is compact, analytic and has a unique fixed point, at which it is hyperbolic with one-dimensional unstable manifold. In this paper we observe that this Pacman renormalization operator is compact and analytic at any Siegel Pacman or Siegel map with combinatorially bounded rotation number. This allows us to define a renormalization operator on the hybrid classes of the standard Siegel pacmen to which we built its horseshoe where the operator is topologically semiconjugated to the left shift on the space of bi-infinite sequences of natural numbers bounded by some constant.","PeriodicalId":43512,"journal":{"name":"Advances in Pure and Applied Mathematics","volume":null,"pages":null},"PeriodicalIF":0.0,"publicationDate":"2023-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"135156132","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 : 2023-01-01DOI: 10.21494/iste.op.2023.0905
A. Kawa, S. N. Hasan, B. Wani
{"title":"Multiplicative Jordan type higher derivations of unital rings with non trivial idempotents","authors":"A. Kawa, S. N. Hasan, B. Wani","doi":"10.21494/iste.op.2023.0905","DOIUrl":"https://doi.org/10.21494/iste.op.2023.0905","url":null,"abstract":"","PeriodicalId":43512,"journal":{"name":"Advances in Pure and Applied Mathematics","volume":null,"pages":null},"PeriodicalIF":0.4,"publicationDate":"2023-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"44576398","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":"Pythagorician Divisors and Applications to Some Diophantine Equations","authors":"F. E. Tanoé, P. Kimou","doi":"10.4236/apm.2023.132003","DOIUrl":"https://doi.org/10.4236/apm.2023.132003","url":null,"abstract":"","PeriodicalId":43512,"journal":{"name":"Advances in Pure and Applied Mathematics","volume":null,"pages":null},"PeriodicalIF":0.4,"publicationDate":"2023-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"79119921","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":"Goodness-of-Fit Test for Non-Stationary and Strongly Dependent Samples","authors":"C. Crisci, G. Perera, L. Sampognaro","doi":"10.4236/apm.2023.135016","DOIUrl":"https://doi.org/10.4236/apm.2023.135016","url":null,"abstract":"","PeriodicalId":43512,"journal":{"name":"Advances in Pure and Applied Mathematics","volume":null,"pages":null},"PeriodicalIF":0.4,"publicationDate":"2023-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"79756359","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":"Exact Traveling Wave Solutions of the Generalized Fractional Differential mBBM Equation","authors":"Yuting Zhong, Renzhi Lu, Heng-Wei Su","doi":"10.4236/apm.2023.133009","DOIUrl":"https://doi.org/10.4236/apm.2023.133009","url":null,"abstract":"","PeriodicalId":43512,"journal":{"name":"Advances in Pure and Applied Mathematics","volume":null,"pages":null},"PeriodicalIF":0.4,"publicationDate":"2023-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"81903045","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}
We prove the boundedness of the multilinear operators associated to the pseudo- differential operator for the extreme cases.
在极端情况下，证明了与伪微分算子相关的多线性算子的有界性。
{"title":"Boundedness for Multilinear Operators of Pseudo-Differential Operators","authors":"Lanzhe Liu","doi":"10.7153/JMI-04-20","DOIUrl":"https://doi.org/10.7153/JMI-04-20","url":null,"abstract":"We prove the boundedness of the multilinear operators associated to the pseudo- differential operator for the extreme cases.","PeriodicalId":43512,"journal":{"name":"Advances in Pure and Applied Mathematics","volume":null,"pages":null},"PeriodicalIF":0.4,"publicationDate":"2023-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"76669178","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 : 2022-06-01DOI: 10.21494/iste.op.2022.0839
B. Rao, Shilpa N.
This paper mainly concerns about establishing the Bruck conjecture for differential-difference polynomial generated by an entire function. The polynomial considered is of finite order and involves the entire function f(z) and its shift f(z + c) where c ∈ C. Suitable examples are given to prove the sharpness of sharing exceptional values of Borel and Nevanlinna. 2020 Mathematics Subject Classification. 30D35
{"title":"A result on Bruck Conjecture related to Shift Polynomials","authors":"B. Rao, Shilpa N.","doi":"10.21494/iste.op.2022.0839","DOIUrl":"https://doi.org/10.21494/iste.op.2022.0839","url":null,"abstract":"This paper mainly concerns about establishing the Bruck conjecture for differential-difference polynomial generated by an entire function. The polynomial considered is of finite order and involves the entire function f(z) and its shift f(z + c) where c ∈ C. Suitable examples are given to prove the sharpness of sharing exceptional values of Borel and Nevanlinna. 2020 Mathematics Subject Classification. 30D35","PeriodicalId":43512,"journal":{"name":"Advances in Pure and Applied Mathematics","volume":null,"pages":null},"PeriodicalIF":0.4,"publicationDate":"2022-06-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"43531491","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 : 2022-06-01DOI: 10.21494/iste.op.2022.0840
R. Alsaedi, K. Ali, A. Ghanmi
This paper is concerned with the existence of solutions for the following class of singular fourth order elliptic equations { Δ ( |x|p(x)|Δu|p(x)−2Δu ) = a(x)u−γ(x) + λf(x, u), in Ω, u = Δu = 0, on ∂Ω. where Ω is a smooth bounded domain in R , γ : Ω → (0, 1) be a continuous function, f ∈ C(Ω × R), p : Ω −→ (1,∞) and a is a function that is almost everywhere positive in Ω . Using variational techniques combined with the theory of the generalized Lebesgue-Sobolev spaces, we prove the existence at least one nontrivial weak solution. 2020 Mathematics Subject Classification. 46E35,26A45,28A12.
{"title":"Existence Results for Singular p(x)-Laplacian Equation","authors":"R. Alsaedi, K. Ali, A. Ghanmi","doi":"10.21494/iste.op.2022.0840","DOIUrl":"https://doi.org/10.21494/iste.op.2022.0840","url":null,"abstract":"This paper is concerned with the existence of solutions for the following class of singular fourth order elliptic equations { Δ ( |x|p(x)|Δu|p(x)−2Δu ) = a(x)u−γ(x) + λf(x, u), in Ω, u = Δu = 0, on ∂Ω. where Ω is a smooth bounded domain in R , γ : Ω → (0, 1) be a continuous function, f ∈ C(Ω × R), p : Ω −→ (1,∞) and a is a function that is almost everywhere positive in Ω . Using variational techniques combined with the theory of the generalized Lebesgue-Sobolev spaces, we prove the existence at least one nontrivial weak solution. 2020 Mathematics Subject Classification. 46E35,26A45,28A12.","PeriodicalId":43512,"journal":{"name":"Advances in Pure and Applied Mathematics","volume":null,"pages":null},"PeriodicalIF":0.4,"publicationDate":"2022-06-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"43932187","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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