Acta et Commentationes Universitatis Tartuensis de Mathematica 2019-01-22T07:41:44+00:00 Enno Kolk Open Journal Systems <p><em>Acta et Commentationes Universitatis Tartuensis de Mathematica&nbsp;</em>(ACUTM) is an international journal of pure and applied mathematics.</p> On a class of N(k)-mixed generalized quasi-Einstein manifolds 2019-01-22T07:41:44+00:00 Arindam Bhattacharyya Sampa Pahan <p>The objective of the present paper is to study N(<em>k</em>)-mixed generalized quasi-Einstein manifolds. We prove the existence of these manifolds. Later we establish some curvature properties of N(<em>k</em>)-mixed generalized quasi-Einstein manifolds under certain conditions. In the last section, we give two examples of N(<em>k</em>)-mixed generalized quasi-Einstein manifolds.</p> 2019-01-02T10:32:22+00:00 ##submission.copyrightStatement## Inequalities of Hermite–Hadamard type for HH-convex functions 2019-01-22T07:41:44+00:00 Sever Silvestru Dragomir <p>Some inequalities of Hermite–Hadamard type for <em>HH</em>-convex functions defined on positive intervals are given. Applications for special means are also provided.</p> 2019-01-02T10:39:06+00:00 ##submission.copyrightStatement## Matrix transformations related to I-convergent sequences 2019-01-22T07:41:43+00:00 Enno Kolk <p>Characterized are matrix transformations related to certain subsets of the space of ideal convergent sequences. Obtained here results are connected with the previous investigations of the author on some transformations defined by infinite matrices of bounded linear operators.</p> 2019-01-02T13:55:52+00:00 ##submission.copyrightStatement## On new extensions of the generalized Hermite matrix polynomials 2019-01-22T07:41:43+00:00 Ayman Shehata <p>Various families of generating matrix functions have been established in diverse ways. The objective of the present paper is to investigate these generalized Hermite matrix polynomials, and derive some important results for them, such as, the generating matrix functions, matrix recurrence relations, an expansion of <em>x<sup>n</sup>I</em>, finite summation formulas, addition theorems, integral representations, fractional calculus operators, and certain other implicit summation formulae.</p> 2019-01-02T14:02:13+00:00 ##submission.copyrightStatement## Boundedness of the L-index in a direction of entire solutions of second order partial differential equation 2019-01-22T07:41:42+00:00 Andriy Bandura Oleh Skaskiv <p>See PDF</p> 2019-01-02T14:08:27+00:00 ##submission.copyrightStatement## Asymptotics of approximation of conjugate functions by Poisson integrals 2019-01-22T07:41:41+00:00 Yu. I. Kharkevych K. V. Pozharska <p>We obtain a decomposition of the upper bound for the deviation of Poisson integrals of conjugate periodic functions. The decomposition enables one to provide the Kolmogorov–Nikol'skii constants of an arbitrary order.</p> 2019-01-02T14:14:07+00:00 ##submission.copyrightStatement## Second approximation of local functions in ideal topological spaces 2019-01-22T07:41:41+00:00 Md. Monirul Islam Shyamapada Modak <p>This paper gives a new dimension to discuss the local function in ideal topological spaces. We calculate error operators for various type of local functions and introduce more perfect approximation of the local functions for discussing their properties. We have also reached a topological space with the help of semi-closure.</p> 2019-01-02T14:21:12+00:00 ##submission.copyrightStatement## On two integrability methods 2019-01-22T07:41:40+00:00 H. N. Özgen <p>See PDF</p> 2019-01-02T14:26:05+00:00 ##submission.copyrightStatement## Extremal tricyclic, tetracyclic, and pentacyclic graphs with respect to the Narumi–Katayama index 2019-01-22T07:41:40+00:00 Ali Reza Ashrafi Mehdi Eliasi Ali Ghalavand Ottorino Ori <p>See PDF</p> 2019-01-02T14:33:01+00:00 ##submission.copyrightStatement## On concircular curvature tensor in a Lorentzian α-Sasakian manifold with respect to the quarter-symmetric non-metric connection 2019-01-22T07:41:39+00:00 Abdul Haseeb Rajendra Prasad <p>In the present paper, some properties of concircular curvature tensor in a Lorentzian <em>α</em>-Sasakian manifold with respect to the quarter-symmetric non-metric connection have been studied.</p> 2019-01-02T14:38:36+00:00 ##submission.copyrightStatement## Simplifying coefficients in a family of nonlinear ordinary differential equations 2019-01-22T07:41:39+00:00 Feng Qi <p>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.</p> 2019-01-02T14:45:09+00:00 ##submission.copyrightStatement## Behaviour of multivariate tail dependence coefficients 2019-01-22T07:41:38+00:00 Gaida Pettere Irina Voronova Ilze Zariņa <p>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 <em>t</em>-copula has been successfully used in practice because of its tail dependence property. Therefore, <em>t</em>-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 <em>t</em>-copula and examine it in the simulation experiment.</p> 2019-01-02T14:52:16+00:00 ##submission.copyrightStatement## Empirical cumulant function based parameter estimation in stable laws 2019-01-22T07:41:37+00:00 Annika Krutto <p>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.</p> 2019-01-02T14:57:36+00:00 ##submission.copyrightStatement##