Pub Date : 2019-04-01DOI: 10.4067/S0719-06462019000100021
Yogesh J. Bagul, C. Chesneau
The prime goal of this paper is to establish sharp lower and upper bounds for useful functions such as the exponential functions, with a focus on exp(−x2), the trigonometric functions (cosine and sine) and the hyperbolic functions (cosine and sine). The bounds obtained for hyperbolic cosine are very sharp. New proofs, refinements as well as new results are offered. Some graphical and numerical results illustrate the findings.
{"title":"Some New Simple Inequalities Involving Exponential, Trigonometric and Hyperbolic Functions","authors":"Yogesh J. Bagul, C. Chesneau","doi":"10.4067/S0719-06462019000100021","DOIUrl":"https://doi.org/10.4067/S0719-06462019000100021","url":null,"abstract":"The prime goal of this paper is to establish sharp lower and upper bounds for useful functions such as the exponential functions, with a focus on exp(−x2), the trigonometric functions (cosine and sine) and the hyperbolic functions (cosine and sine). The bounds obtained for hyperbolic cosine are very sharp. New proofs, refinements as well as new results are offered. Some graphical and numerical results illustrate the findings.","PeriodicalId":36416,"journal":{"name":"Cubo","volume":" ","pages":""},"PeriodicalIF":0.5,"publicationDate":"2019-04-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"46196235","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 : 2019-04-01DOI: 10.4067/S0719-06462019000100001
M. Belishev, A. Vakulenko
Let Ω be a smooth compact oriented 3-dimensional Riemannian manifold with boundary. A quaternion field is a pair q = {α, u} of a function α and a vector field u on Ω. A field q is harmonic if α, u are continuous in Ω and ∇α = rot u, div u = 0 holds into Ω. The space 𝒞(Ω) of harmonic fields is a subspace of the Banach algebra 𝒬 (Ω) of continuous quaternion fields with the point-wise multiplication qq′ = {αα′ − u · u ′ , αu′ + α ′u + u ∧ u ′ }. We prove a Stone-Weierstrass type theorem: the subalgebra ∨𝒞(Ω) generated by harmonic fields is dense in 𝒬 (Ω). Some results on 2-jets of harmonic functions and the uniqueness sets of harmonic fields are provided. Comprehensive study of harmonic fields is motivated by possible applications to inverse problems of mathematical physics.
设Ω为具有边界的光滑紧致三维黎曼流形。四元数域是一个函数α和Ω上的向量域u的一对q = {α， u}。如果α， u在Ω中连续且∇α = rot u, div u = 0在Ω中成立，则场q是调和的。调和场的空间 (Ω)是连续四元数场的Banach代数𝒬(Ω)的子空间，其点向乘法qq ' = {αα ' - u·u '， αu ' + α ' u + u∧u '}。我们证明了一个Stone-Weierstrass型定理:谐波场产生的子代数在𝒬(Ω)上是稠密的;给出了调和函数的2-射流和调和场的唯一性集的一些结果。谐波的全面研究是由可能应用于数学物理的反问题。
{"title":"On algebraic and uniqueness properties of harmonic quaternion fields on 3d manifolds","authors":"M. Belishev, A. Vakulenko","doi":"10.4067/S0719-06462019000100001","DOIUrl":"https://doi.org/10.4067/S0719-06462019000100001","url":null,"abstract":"Let Ω be a smooth compact oriented 3-dimensional Riemannian manifold with boundary. A quaternion field is a pair q = {α, u} of a function α and a vector field u on Ω. A field q is harmonic if α, u are continuous in Ω and ∇α = rot u, div u = 0 holds into Ω. The space 𝒞(Ω) of harmonic fields is a subspace of the Banach algebra 𝒬 (Ω) of continuous quaternion fields with the point-wise multiplication qq′ = {αα′ − u · u ′ , αu′ + α ′u + u ∧ u ′ }. We prove a Stone-Weierstrass type theorem: the subalgebra ∨𝒞(Ω) generated by harmonic fields is dense in 𝒬 (Ω). Some results on 2-jets of harmonic functions and the uniqueness sets of harmonic fields are provided. Comprehensive study of harmonic fields is motivated by possible applications to inverse problems of mathematical physics.","PeriodicalId":36416,"journal":{"name":"Cubo","volume":" ","pages":""},"PeriodicalIF":0.5,"publicationDate":"2019-04-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"44828297","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 : 2018-12-14DOI: 10.4067/s0719-06462021000300369
R. Hidalgo
An structural decomposition of function groups, in terms of the Klein-Maskit combination theorems, was provided by Maskit in the middle of the 70's. A similar decomposition works for extended function groups, but it seems not to be stated in the existing literature. The aim of this paper is to state and prove such a decomposition structure.
{"title":"The structure of extended function groups","authors":"R. Hidalgo","doi":"10.4067/s0719-06462021000300369","DOIUrl":"https://doi.org/10.4067/s0719-06462021000300369","url":null,"abstract":"An structural decomposition of function groups, in terms of the Klein-Maskit combination theorems, was provided by Maskit in the middle of the 70's. A similar decomposition works for extended function groups, but it seems not to be stated in the existing literature. The aim of this paper is to state and prove such a decomposition structure.","PeriodicalId":36416,"journal":{"name":"Cubo","volume":" ","pages":""},"PeriodicalIF":0.5,"publicationDate":"2018-12-14","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"42738838","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 : 2018-10-01DOI: 10.4067/s0719-06462018000300081
J. Bochi
A generalization of Rokhlin’s Tower Lemma is presented. The Maximal Ergodic Theorem is then obtained as a corollary. We also use the generalized Rokhlin lemma, this time combined with a subadditive version of Kac’s formula, to deduce a subadditive version of the Maximal Ergodic Theorem due to Silva and Thieullen. In both the additive and subadditive cases, these maximal theorems immediately imply that “heavy” points have positive probability. We use heaviness to prove the pointwise ergodic theorems of Birkhoff and Kingman.
{"title":"The basic ergodic theorems, yet again","authors":"J. Bochi","doi":"10.4067/s0719-06462018000300081","DOIUrl":"https://doi.org/10.4067/s0719-06462018000300081","url":null,"abstract":"A generalization of Rokhlin’s Tower Lemma is presented. The Maximal Ergodic Theorem is then obtained as a corollary. We also use the generalized Rokhlin lemma, this time combined with a subadditive version of Kac’s formula, to deduce a subadditive version of the Maximal Ergodic Theorem due to Silva and Thieullen. \u0000In both the additive and subadditive cases, these maximal theorems immediately imply that “heavy” points have positive probability. We use heaviness to prove the pointwise ergodic theorems of Birkhoff and Kingman.","PeriodicalId":36416,"journal":{"name":"Cubo","volume":" ","pages":""},"PeriodicalIF":0.5,"publicationDate":"2018-10-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://sci-hub-pdf.com/10.4067/s0719-06462018000300081","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"45433203","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 : 2018-10-01DOI: 10.4067/S0719-06462018000300031
E. Ballico
A +line is a scheme R ⊂ ℙr with a line as its reduction L = Rred which is the union of L and a tangent vector v ⊈ L with vred ∈ L. Here we prove in arbitrary characteristic that for r ≥ 4 a general union of lines and +lines has maximal rank. We use the case r = 3 proved by myself in a previous paper and adapt the characteristic zero proof of the case r > 3 given in the same paper.
{"title":"Postulation of general unions of lines and +lines in positive characteristic","authors":"E. Ballico","doi":"10.4067/S0719-06462018000300031","DOIUrl":"https://doi.org/10.4067/S0719-06462018000300031","url":null,"abstract":"A +line is a scheme R ⊂ ℙr with a line as its reduction L = Rred which is the union of L and a tangent vector v ⊈ L with vred ∈ L. Here we prove in arbitrary characteristic that for r ≥ 4 a general union of lines and +lines has maximal rank. We use the case r = 3 proved by myself in a previous paper and adapt the characteristic zero proof of the case r > 3 given in the same paper.","PeriodicalId":36416,"journal":{"name":"Cubo","volume":" ","pages":""},"PeriodicalIF":0.5,"publicationDate":"2018-10-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://sci-hub-pdf.com/10.4067/S0719-06462018000300031","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"48390888","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 : 2018-10-01DOI: 10.4067/S0719-06462018000300049
A. Ardjouni, A. Djoudi
This paper is mainly concerned the global asymptotic stability of the zero solution of a class of nonlinear neutral dynamic equations in C1rd. By converting the nonlinear neutral dynamic equation into an equivalent integral equation, our main results are obtained via the Banach contraction mapping principle. The results obtained here extend the work of Yazgan, Tunc and Atan [17].
{"title":"Study of global asymptotic stability in nonlinear neutral dynamic equations on time scales","authors":"A. Ardjouni, A. Djoudi","doi":"10.4067/S0719-06462018000300049","DOIUrl":"https://doi.org/10.4067/S0719-06462018000300049","url":null,"abstract":"This paper is mainly concerned the global asymptotic stability of the zero solution of a class of nonlinear neutral dynamic equations in C1rd. By converting the nonlinear neutral dynamic equation into an equivalent integral equation, our main results are obtained via the Banach contraction mapping principle. The results obtained here extend the work of Yazgan, Tunc and Atan [17].","PeriodicalId":36416,"journal":{"name":"Cubo","volume":" ","pages":""},"PeriodicalIF":0.5,"publicationDate":"2018-10-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://sci-hub-pdf.com/10.4067/S0719-06462018000300049","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"43899402","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 : 2018-10-01DOI: 10.4067/S0719-06462018000300001
G. Anastassiou
In this article we present multivariate basic approximation by a Kantorovich-Shilkret type quasi-interpolation neural network operator with respect to supremum norm. This is done with rates using the multivariate modulus of continuity. We approximate continuous and bounded functions on ℝN, N ∈ ℕ. When they are additionally uniformly continuous we derive pointwise and uniform convergences.
{"title":"Quantitative Approximation by a Kantorovich-Shilkret quasi-interpolation neural network operator","authors":"G. Anastassiou","doi":"10.4067/S0719-06462018000300001","DOIUrl":"https://doi.org/10.4067/S0719-06462018000300001","url":null,"abstract":"In this article we present multivariate basic approximation by a Kantorovich-Shilkret type quasi-interpolation neural network operator with respect to supremum norm. This is done with rates using the multivariate modulus of continuity. We approximate continuous and bounded functions on ℝN, N ∈ ℕ. When they are additionally uniformly continuous we derive pointwise and uniform convergences.","PeriodicalId":36416,"journal":{"name":"Cubo","volume":" ","pages":""},"PeriodicalIF":0.5,"publicationDate":"2018-10-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://sci-hub-pdf.com/10.4067/S0719-06462018000300001","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"46203640","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 : 2018-10-01DOI: 10.4067/S0719-06462018000300065
I. Argyros, S. George
The convergence order of iterative methods is determined using high order derivatives and Taylor series, and without providing computable error bounds, uniqueness of the solution results or information on how to choose the initial point. We address all these problems by using hypotheses only on the first derivative. Moreover, to achieve all these we present our technique using a comparison between the convergence radii of Jarratt’s fourth order method and another method of the same convergence order.
{"title":"Ball comparison between Jarratt’s and other fourth order method for solving equations","authors":"I. Argyros, S. George","doi":"10.4067/S0719-06462018000300065","DOIUrl":"https://doi.org/10.4067/S0719-06462018000300065","url":null,"abstract":"The convergence order of iterative methods is determined using high order derivatives and Taylor series, and without providing computable error bounds, uniqueness of the solution results or information on how to choose the initial point. We address all these problems by using hypotheses only on the first derivative. Moreover, to achieve all these we present our technique using a comparison between the convergence radii of Jarratt’s fourth order method and another method of the same convergence order.","PeriodicalId":36416,"journal":{"name":"Cubo","volume":" ","pages":""},"PeriodicalIF":0.5,"publicationDate":"2018-10-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://sci-hub-pdf.com/10.4067/S0719-06462018000300065","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"48636557","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 : 2018-10-01DOI: 10.4067/S0719-06462018000300037
Yadab ChandraMandal, S. Hui
The Riemannian manifolds whose metric is Yamabe soliton with potential vector field as torse forming admitting Riemannian connection, semisymmetric metric connection and projective semisymmetric connection have been studied. An example is constructed to verify the theorem concerning Riemannian connection.
{"title":"Yamabe Solitons with potential vector field as torse forming","authors":"Yadab ChandraMandal, S. Hui","doi":"10.4067/S0719-06462018000300037","DOIUrl":"https://doi.org/10.4067/S0719-06462018000300037","url":null,"abstract":"The Riemannian manifolds whose metric is Yamabe soliton with potential vector field as torse forming admitting Riemannian connection, semisymmetric metric connection and projective semisymmetric connection have been studied. An example is constructed to verify the theorem concerning Riemannian connection.","PeriodicalId":36416,"journal":{"name":"Cubo","volume":" ","pages":""},"PeriodicalIF":0.5,"publicationDate":"2018-10-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://sci-hub-pdf.com/10.4067/S0719-06462018000300037","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"48201485","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 : 2018-09-12DOI: 10.4067/S0719-06462022000100037
Robert Auffarth, G. Arteche, Pablo Quezada
Let $A$ be an abelian surface and let $G$ be a finite group of automorphisms of $A$ fixing the origin. Assume that the analytic representation of $G$ is irreducible. We give a classification of the pairs $(A,G)$ such that the quotient $A/G$ is smooth. In particular, we prove that $A=E^2$ with $E$ an elliptic curve and that $A/Gsimeqmathbb P^2$ in all cases. Moreover, for fixed $E$, there are only finitely many pairs $(E^2,G)$ up to isomorphism. This completes the classification of smooth quotients of abelian varieties by finite groups started by the first two authors.
{"title":"Smooth quotients of abelian surfaces by finite groups that fix the origin","authors":"Robert Auffarth, G. Arteche, Pablo Quezada","doi":"10.4067/S0719-06462022000100037","DOIUrl":"https://doi.org/10.4067/S0719-06462022000100037","url":null,"abstract":"Let $A$ be an abelian surface and let $G$ be a finite group of automorphisms of $A$ fixing the origin. Assume that the analytic representation of $G$ is irreducible. We give a classification of the pairs $(A,G)$ such that the quotient $A/G$ is smooth. In particular, we prove that $A=E^2$ with $E$ an elliptic curve and that $A/Gsimeqmathbb P^2$ in all cases. Moreover, for fixed $E$, there are only finitely many pairs $(E^2,G)$ up to isomorphism. This completes the classification of smooth quotients of abelian varieties by finite groups started by the first two authors.","PeriodicalId":36416,"journal":{"name":"Cubo","volume":" ","pages":""},"PeriodicalIF":0.5,"publicationDate":"2018-09-12","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"45248329","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：