{"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":"32 1","pages":""},"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}
{"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":"20 1","pages":""},"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":"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":"91 1","pages":""},"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}
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":"1 1","pages":""},"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.2022.0837
H. Marzougui
The global structure of divergence-free vector fields on closed surfaces is investigated. We prove that if M is a closed surface and V is a divergence-free C-vector field with finitely many singularities on M then every orbit L of V is one of the following types: (i) a singular point, (ii) a periodic orbit, (iii) a closed (non periodic) orbit in M∗ = M − Sing(V), (iv) a locally dense orbit, where Sing(V) denotes the set of singular points of V . On the other hand, we show that the complementary in M of periodic components and minimal components is a compact invariant subset consisting of singularities and closed (non compact) orbits in M∗. These results extend those of T. Ma and S. Wang in [Discrete Contin. Dynam. Systems, 7 (2001), 431–445] established when the divergence-free vector field V is regular that is all its singular points are non-degenerate. 2010 Mathematics Subject Classification. Primary: 37A, 37B20, 37C10, 37E35
{"title":"Limit sets and global dynamic for 2-D divergence-free vector fields","authors":"H. Marzougui","doi":"10.21494/iste.op.2022.0837","DOIUrl":"https://doi.org/10.21494/iste.op.2022.0837","url":null,"abstract":"The global structure of divergence-free vector fields on closed surfaces is investigated. We prove that if M is a closed surface and V is a divergence-free C-vector field with finitely many singularities on M then every orbit L of V is one of the following types: (i) a singular point, (ii) a periodic orbit, (iii) a closed (non periodic) orbit in M∗ = M − Sing(V), (iv) a locally dense orbit, where Sing(V) denotes the set of singular points of V . On the other hand, we show that the complementary in M of periodic components and minimal components is a compact invariant subset consisting of singularities and closed (non compact) orbits in M∗. These results extend those of T. Ma and S. Wang in [Discrete Contin. Dynam. Systems, 7 (2001), 431–445] established when the divergence-free vector field V is regular that is all its singular points are non-degenerate. 2010 Mathematics Subject Classification. Primary: 37A, 37B20, 37C10, 37E35","PeriodicalId":43512,"journal":{"name":"Advances in Pure and Applied Mathematics","volume":" ","pages":""},"PeriodicalIF":0.4,"publicationDate":"2022-06-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"48781940","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":" ","pages":""},"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}
Pub Date : 2022-02-26DOI: 10.4236/apm.2022.1212054
N. Tsirivas
Let θ be a fixed positive number, θ ∈ (0, 1) and let λ = (λn)n∈N be a fixed sequence of non-zero complex numbers, so that λn→∞. We shall apply the functions gn : [0, θ]× C→C, defined as gn((t, z)) = z + λne for each (t, z) ∈ [0, θ]× C. We shall consider the space C([0, θ]× C) of continuous functions on [0, θ]× C, as endowed with the topology of uniform convergence on compacta and let ρ be the usual metric in C([0, θ]×C). For an entire function f ∈ H(C) we shall denote that f̄ : [0, θ]× C→C, f̄((t, z)) = f(z) for every (t, z) ∈ [0, θ]× C. We will prove that the equation: lim n→+∞ ρ((x ◦ gyn , f̄)) = 0 does not have any solution (x, yn) where x ∈ H(C) and yn is an strictly increasing subsequence of natural numbers and f ∈ H(C) is a given non-constant entire function. When f is a constant entire function, then the above equation has infinitely several solutions, according to a result provided by G. Costakis.
{"title":"Uniform Convergence of Translation Operators","authors":"N. Tsirivas","doi":"10.4236/apm.2022.1212054","DOIUrl":"https://doi.org/10.4236/apm.2022.1212054","url":null,"abstract":"Let θ be a fixed positive number, θ ∈ (0, 1) and let λ = (λn)n∈N be a fixed sequence of non-zero complex numbers, so that λn→∞. We shall apply the functions gn : [0, θ]× C→C, defined as gn((t, z)) = z + λne for each (t, z) ∈ [0, θ]× C. We shall consider the space C([0, θ]× C) of continuous functions on [0, θ]× C, as endowed with the topology of uniform convergence on compacta and let ρ be the usual metric in C([0, θ]×C). For an entire function f ∈ H(C) we shall denote that f̄ : [0, θ]× C→C, f̄((t, z)) = f(z) for every (t, z) ∈ [0, θ]× C. We will prove that the equation: lim n→+∞ ρ((x ◦ gyn , f̄)) = 0 does not have any solution (x, yn) where x ∈ H(C) and yn is an strictly increasing subsequence of natural numbers and f ∈ H(C) is a given non-constant entire function. When f is a constant entire function, then the above equation has infinitely several solutions, according to a result provided by G. Costakis.","PeriodicalId":43512,"journal":{"name":"Advances in Pure and Applied Mathematics","volume":"81 1","pages":""},"PeriodicalIF":0.4,"publicationDate":"2022-02-26","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"81390146","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":"A Method for the Squaring of a Circle","authors":"Lyndon O. Barton","doi":"10.4236/apm.2022.129041","DOIUrl":"https://doi.org/10.4236/apm.2022.129041","url":null,"abstract":"","PeriodicalId":43512,"journal":{"name":"Advances in Pure and Applied Mathematics","volume":"28 1","pages":""},"PeriodicalIF":0.4,"publicationDate":"2022-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"72845435","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 : 2022-01-01DOI: 10.4236/apm.2022.1212055
G. Cirier
{"title":"A Probabilistic Approach of the Poincaré-Bendixon Problem in R<sup><i>d</i></sup>","authors":"G. Cirier","doi":"10.4236/apm.2022.1212055","DOIUrl":"https://doi.org/10.4236/apm.2022.1212055","url":null,"abstract":"","PeriodicalId":43512,"journal":{"name":"Advances in Pure and Applied Mathematics","volume":"25 1","pages":""},"PeriodicalIF":0.4,"publicationDate":"2022-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"74457440","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}
Möbius transformations, which are one-to-one mappings of onto have remarkable geometric properties susceptible to be visualized by drawing pictures. Not the same thing can be said about m-Möbius transformations m f mapping m onto . Even for the simplest entity, the pre-image by m f of a unique point, there is no way of visualization. Pre-images by m f of figures from are like ghost figures in m . This paper is about handling those ghost figures. We succeeded in doing it and proving theorems about them by using their projections onto the coordinate planes. The most im-portant achievement is the proof in that context of a theorem similar to the symmetry principle for Möbius transformations. It is like saying that the images by m-Möbius transformations of symmetric ghost points with respect to ghost circles are symmetric points with respect to the image circles. Vectors in m are well known and vector calculus in m is familiar, yet the pre-image by m f of a vector from is a different entity which materializes by projections into vectors in the coordinate planes. In this paper, we study the interface between those entities and the vectors in m . Finally, we have shown that the uniqueness theorem for Möbius transformations and the property of preserving the cross-ratio of four points
{"title":"Some Geometric Properties of the <i>m</i>-Möbius Transformations","authors":"D. Ghisa","doi":"10.4236/apm.2022.123013","DOIUrl":"https://doi.org/10.4236/apm.2022.123013","url":null,"abstract":"Möbius transformations, which are one-to-one mappings of onto have remarkable geometric properties susceptible to be visualized by drawing pictures. Not the same thing can be said about m-Möbius transformations m f mapping m onto . Even for the simplest entity, the pre-image by m f of a unique point, there is no way of visualization. Pre-images by m f of figures from are like ghost figures in m . This paper is about handling those ghost figures. We succeeded in doing it and proving theorems about them by using their projections onto the coordinate planes. The most im-portant achievement is the proof in that context of a theorem similar to the symmetry principle for Möbius transformations. It is like saying that the images by m-Möbius transformations of symmetric ghost points with respect to ghost circles are symmetric points with respect to the image circles. Vectors in m are well known and vector calculus in m is familiar, yet the pre-image by m f of a vector from is a different entity which materializes by projections into vectors in the coordinate planes. In this paper, we study the interface between those entities and the vectors in m . Finally, we have shown that the uniqueness theorem for Möbius transformations and the property of preserving the cross-ratio of four points","PeriodicalId":43512,"journal":{"name":"Advances in Pure and Applied Mathematics","volume":"1 1","pages":""},"PeriodicalIF":0.4,"publicationDate":"2022-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"79578607","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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