Pub Date : 2019-08-09DOI: 10.12697/ACUTM.2019.23.06
N. Irmak, L. Szalay
Let Lm denote the mth Lucas number. We show that the solutions to the diophantine equation (2t/k) = Lm, in non-negative integers t, k ≤ 2t−1, and m, are (t, k, m) = (1, 1, 0), (2, 1, 3), and (a, 0, 1) with non-negative integers a.
设Lm表示第m个Lucas数。我们证明了在非负整数t, k≤2t - 1和m下，diophantine方程(2t/k) = Lm的解为(t, k, m) =(1,1,0)，(2,1,3)和(a, 0,1)，且非负整数为a。
{"title":"Lucas numbers of the form (2t/k)","authors":"N. Irmak, L. Szalay","doi":"10.12697/ACUTM.2019.23.06","DOIUrl":"https://doi.org/10.12697/ACUTM.2019.23.06","url":null,"abstract":"Let Lm denote the mth Lucas number. We show that the solutions to the diophantine equation (2t/k) = Lm, in non-negative integers t, k ≤ 2t−1, and m, are (t, k, m) = (1, 1, 0), (2, 1, 3), and (a, 0, 1) with non-negative integers a.","PeriodicalId":42426,"journal":{"name":"Acta et Commentationes Universitatis Tartuensis de Mathematica","volume":"144 1 1","pages":""},"PeriodicalIF":0.3,"publicationDate":"2019-08-09","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"80999694","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 : 2019-08-09DOI: 10.12697/ACUTM.2019.23.02
U. De, D. Dey
The object of the present paper is to characterize Ricci pseudosymmetric and Ricci semisymmetric almost Kenmotsu manifolds with (k; μ)-, (k; μ)′-, and generalized (k; μ)-nullity distributions. We also characterize (k; μ)-almost Kenmotsu manifolds satisfying the condition R ⋅ S = LꜱQ(g; S2).
{"title":"Pseudo-symmetric structures on almost Kenmotsu manifolds with nullity distributions","authors":"U. De, D. Dey","doi":"10.12697/ACUTM.2019.23.02","DOIUrl":"https://doi.org/10.12697/ACUTM.2019.23.02","url":null,"abstract":"The object of the present paper is to characterize Ricci pseudosymmetric and Ricci semisymmetric almost Kenmotsu manifolds with (k; μ)-, (k; μ)′-, and generalized (k; μ)-nullity distributions. We also characterize (k; μ)-almost Kenmotsu manifolds satisfying the condition R ⋅ S = LꜱQ(g; S2).","PeriodicalId":42426,"journal":{"name":"Acta et Commentationes Universitatis Tartuensis de Mathematica","volume":"11 1","pages":""},"PeriodicalIF":0.3,"publicationDate":"2019-08-09","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"81527031","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 : 2019-06-12DOI: 10.12697/ACUTM.2020.24.06
A. Makhlouf, Ahmed Zahari
The purpose of this paper is to study the structure and the algebraic varieties of Hom-associative algebras. We characterize multiplicative simple Hom-associative algebras and give some examples deforming the 2 × 2-matrix algebra to simple Hom-associative algebras. We provide a classification of n-dimensional Hom-associative algebras for n ≤ 3. Then we study irreducible components using deformation theory.
{"title":"Structure and classification of Hom-associative algebras","authors":"A. Makhlouf, Ahmed Zahari","doi":"10.12697/ACUTM.2020.24.06","DOIUrl":"https://doi.org/10.12697/ACUTM.2020.24.06","url":null,"abstract":"The purpose of this paper is to study the structure and the algebraic varieties of Hom-associative algebras. We characterize multiplicative simple Hom-associative algebras and give some examples deforming the 2 × 2-matrix algebra to simple Hom-associative algebras. We provide a classification of n-dimensional Hom-associative algebras for n ≤ 3. Then we study irreducible components using deformation theory.","PeriodicalId":42426,"journal":{"name":"Acta et Commentationes Universitatis Tartuensis de Mathematica","volume":"57 1","pages":""},"PeriodicalIF":0.3,"publicationDate":"2019-06-12","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"84874468","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 : 2019-04-08DOI: 10.12697/acutm.2022.26.04
Silvio Capobianco
We prove an analogue of Fekete's subadditivity lemma for functions of several real variables which are subadditive in each variable taken singularly. This extends both the classical case for subadditive functions of one real variable, and a similar result for functions of integer variables. While doing so, we prove that the functions with the property mentioned above are bounded in every closed and bounded subset of their domain. The arguments expand on those in Chapter 6 of E. Hille's 1948 textbook.
{"title":"Fekete's lemma for componentwise subadditive functions of two or more real variables","authors":"Silvio Capobianco","doi":"10.12697/acutm.2022.26.04","DOIUrl":"https://doi.org/10.12697/acutm.2022.26.04","url":null,"abstract":"We prove an analogue of Fekete's subadditivity lemma for functions of several real variables which are subadditive in each variable taken singularly. This extends both the classical case for subadditive functions of one real variable, and a similar result for functions of integer variables. While doing so, we prove that the functions with the property mentioned above are bounded in every closed and bounded subset of their domain. The arguments expand on those in Chapter 6 of E. Hille's 1948 textbook.","PeriodicalId":42426,"journal":{"name":"Acta et Commentationes Universitatis Tartuensis de Mathematica","volume":"85 1","pages":""},"PeriodicalIF":0.3,"publicationDate":"2019-04-08","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"89704561","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 : 2019-01-02DOI: 10.12697/ACUTM.2018.22.21
H. Özgen
See PDF
看到PDF
{"title":"On two integrability methods","authors":"H. Özgen","doi":"10.12697/ACUTM.2018.22.21","DOIUrl":"https://doi.org/10.12697/ACUTM.2018.22.21","url":null,"abstract":"<jats:p>See PDF</jats:p>","PeriodicalId":42426,"journal":{"name":"Acta et Commentationes Universitatis Tartuensis de Mathematica","volume":"26 1","pages":""},"PeriodicalIF":0.3,"publicationDate":"2019-01-02","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"85077326","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 : 2019-01-02DOI: 10.12697/ACUTM.2018.22.15
S. Dragomir
Some inequalities of Hermite–Hadamard type for HH-convex functions defined on positive intervals are given. Applications for special means are also provided.
{"title":"Inequalities of Hermite–Hadamard type for HH-convex functions","authors":"S. Dragomir","doi":"10.12697/ACUTM.2018.22.15","DOIUrl":"https://doi.org/10.12697/ACUTM.2018.22.15","url":null,"abstract":"Some inequalities of Hermite–Hadamard type for HH-convex functions defined on positive intervals are given. Applications for special means are also provided.","PeriodicalId":42426,"journal":{"name":"Acta et Commentationes Universitatis Tartuensis de Mathematica","volume":"52 1","pages":""},"PeriodicalIF":0.3,"publicationDate":"2019-01-02","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"84737322","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 : 2019-01-02DOI: 10.12697/ACUTM.2018.22.25
G. Pettere, I. Voronova, I. Zariņa
In applications tail dependence is an important property of a copula. Bivariate tail dependence is investigated in many papers, but multivariate tail dependence has not been studied widely. We define multivariate upper and lower tail dependence coefficients as limits of the probability that values of one marginal will be large if at least one of other marginals will be as large also. Further we derive some relations between introduced tail dependence and bivariate tail dependence coefficients. Applications have shown that the multivariate t-copula has been successfully used in practice because of its tail dependence property. Therefore, t-copula can be used as an alternative method for risk assessment under Solvency II for insurance models. We have paid attention to the properties of the introduced multivariate tail dependence coefficient for t-copula and examine it in the simulation experiment.
{"title":"Behaviour of multivariate tail dependence coefficients","authors":"G. Pettere, I. Voronova, I. Zariņa","doi":"10.12697/ACUTM.2018.22.25","DOIUrl":"https://doi.org/10.12697/ACUTM.2018.22.25","url":null,"abstract":"In applications tail dependence is an important property of a copula. Bivariate tail dependence is investigated in many papers, but multivariate tail dependence has not been studied widely. We define multivariate upper and lower tail dependence coefficients as limits of the probability that values of one marginal will be large if at least one of other marginals will be as large also. Further we derive some relations between introduced tail dependence and bivariate tail dependence coefficients. Applications have shown that the multivariate t-copula has been successfully used in practice because of its tail dependence property. Therefore, t-copula can be used as an alternative method for risk assessment under Solvency II for insurance models. We have paid attention to the properties of the introduced multivariate tail dependence coefficient for t-copula and examine it in the simulation experiment.","PeriodicalId":42426,"journal":{"name":"Acta et Commentationes Universitatis Tartuensis de Mathematica","volume":"36 1","pages":""},"PeriodicalIF":0.3,"publicationDate":"2019-01-02","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"85405462","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 : 2019-01-02DOI: 10.12697/ACUTM.2018.22.24
Feng Qi (祁锋)
By virtue of the Faá di Bruno formula, properties of the Stirling numbers and the Bell polynomials of the second kind, the binomial inversion formula, and other techniques in combinatorial analysis, the author finds a simple, meaningful, and signicant expression for coefficients in a family of nonlinear ordinary differential equations.
利用组合分析中的fa di Bruno公式、Stirling数和第二类Bell多项式的性质、二项式反演公式等方法，得到了一类非线性常微分方程中系数的一个简单、有意义、有意义的表达式。
{"title":"Simplifying coefficients in a family of nonlinear ordinary differential equations","authors":"Feng Qi (祁锋)","doi":"10.12697/ACUTM.2018.22.24","DOIUrl":"https://doi.org/10.12697/ACUTM.2018.22.24","url":null,"abstract":"By virtue of the Faá di Bruno formula, properties of the Stirling numbers and the Bell polynomials of the second kind, the binomial inversion formula, and other techniques in combinatorial analysis, the author finds a simple, meaningful, and signicant expression for coefficients in a family of nonlinear ordinary differential equations.","PeriodicalId":42426,"journal":{"name":"Acta et Commentationes Universitatis Tartuensis de Mathematica","volume":"31 1","pages":""},"PeriodicalIF":0.3,"publicationDate":"2019-01-02","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"88768580","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 : 2019-01-02DOI: 10.12697/ACUTM.2018.22.23
A. Haseeb, R. Prasad
In the present paper, some properties of concircular curvature tensor in a Lorentzian α-Sasakian manifold with respect to the quarter-symmetric non-metric connection have been studied.
{"title":"On concircular curvature tensor in a Lorentzian α-Sasakian manifold with respect to the quarter-symmetric non-metric connection","authors":"A. Haseeb, R. Prasad","doi":"10.12697/ACUTM.2018.22.23","DOIUrl":"https://doi.org/10.12697/ACUTM.2018.22.23","url":null,"abstract":"In the present paper, some properties of concircular curvature tensor in a Lorentzian α-Sasakian manifold with respect to the quarter-symmetric non-metric connection have been studied.","PeriodicalId":42426,"journal":{"name":"Acta et Commentationes Universitatis Tartuensis de Mathematica","volume":"34 5-8","pages":""},"PeriodicalIF":0.3,"publicationDate":"2019-01-02","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"72454969","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 : 2019-01-02DOI: 10.12697/ACUTM.2018.22.26
Annika Krutto
Stable distributions are a subclass of infinitely divisible distributions that form the only family of possible limiting distributions for sums of independent identically distributed random variables. A challenging problem is estimating their parameters because many have densities with no explicit form and infinite moments. To address this problem, a class of closed-form estimators, called cumulant estimators, has been introduced. Cumulant estimators are derived from the logarithm of empirical characteristic function at two arbitrary distinct positive real arguments. This paper extends cumulant estimators in two directions: (i) it is proved that they are asymptotically normal and (ii) a sample based rule for selecting the two arguments is proposed. Extensive simulations show that under the provided selection rule, the closed-form cumulant estimators generally outperform the well-known algorithmic methods.
{"title":"Empirical cumulant function based parameter estimation in stable laws","authors":"Annika Krutto","doi":"10.12697/ACUTM.2018.22.26","DOIUrl":"https://doi.org/10.12697/ACUTM.2018.22.26","url":null,"abstract":"Stable distributions are a subclass of infinitely divisible distributions that form the only family of possible limiting distributions for sums of independent identically distributed random variables. A challenging problem is estimating their parameters because many have densities with no explicit form and infinite moments. To address this problem, a class of closed-form estimators, called cumulant estimators, has been introduced. Cumulant estimators are derived from the logarithm of empirical characteristic function at two arbitrary distinct positive real arguments. This paper extends cumulant estimators in two directions: (i) it is proved that they are asymptotically normal and (ii) a sample based rule for selecting the two arguments is proposed. Extensive simulations show that under the provided selection rule, the closed-form cumulant estimators generally outperform the well-known algorithmic methods.","PeriodicalId":42426,"journal":{"name":"Acta et Commentationes Universitatis Tartuensis de Mathematica","volume":"80 1","pages":""},"PeriodicalIF":0.3,"publicationDate":"2019-01-02","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"86623193","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：