Showing papers in "Annales Umcs, Mathematica in 2013"
TL;DR: In this article, some results related to extremal problems with free poles on radial systems are generalized by applying the known methods of geometric function theory of complex variable, and sufficiently good numerical results for γ are obtained.
Abstract: Some results related to extremal problems with free poles on radial systems are generalized. They are obtained by applying the known methods of geometric function theory of complex variable. Sufficiently good numerical results for γ are obtained.
5 citations
TL;DR: In this article, explicit examples of Loewner chains generated by continuous driving measures are studied, and the shape of growing Loewer hulls is analyzed in terms of the properties of driving measures.
Abstract: We study explicit examples of Loewner chains generated by absolutely continuous driving measures, and discuss how properties of driving measures are reflected in the shapes of the growing Loewner hulls.
4 citations
TL;DR: In this paper, the class of analytic functions G(α, γ), which is a subset of gamma-starlike functions introduced by Lewandowski, Miller and Zlotkiewicz in Gamma starlike functions, was considered.
Abstract: In this work we consider the class of analytic functions G(α, γ), which is a subset of gamma-starlike functions introduced by Lewandowski, Miller and Zlotkiewicz in Gamma starlike functions, Ann. Univ. Mariae Curie- Sklodowska, Sect. A 28 (1974), 53-58. We discuss the order of strongly starlikeness and the order of strongly convexity in this subclass.
2 citations
TL;DR: For functions of the form f(z) = zp + √ √ n = 1}^{infty} a_{p + n} zp+n}, the authors obtained sharp bounds for some coefficients functionals in certain subclasses of starlike functions.
Abstract: For functions of the form \[f(z) = z^{p} + \sum_{n = 1}^{\infty} a_{p + n} z^{p + n}\] we obtain sharp bounds for some coefficients functionals in certain subclasses of starlike functions. Certain applications of our main results are also given. In particular, Fekete-Szego-like inequality for classes of functions defined through extended fractional differintegrals are obtained.
2 citations
TL;DR: In this paper, the curvatures of the intersection curve of three spacelike hypersurfaces given by their parametric equations in four-dimensional Minkowski space were computed.
Abstract: In this paper, we compute the Frenet vectors and the curvatures of the spacelike intersection curve of three spacelike hypersurfaces given by their parametric equations in four-dimensional Minkowski space \(E_1^4\).
2 citations
TL;DR: In this article, the generalized Meixner-Pollaczek polynomials (GMP) were defined and studied, and a generalization of the Gegenbauer polynomial was proposed.
Abstract: The extremal functions \(f_0(z)\) realizing the maxima of some functionals (e.g. \(\max|a_3|\), and \(\max{arg f^{'}(z)}\)) within the so-called universal linearly invariant family \(U_\alpha\) (in the sense of Pommerenke [10]) have such a form that \(f_0^{'}(z)\) looks similar to generating function for Meixner-Pollaczek (MP) polynomials [2], [8]. This fact gives motivation for the definition and study of the generalized Meixner-Pollaczek (GMP) polynomials \(P_n^\lambda(x;\theta,\psi)\) of a real variable \(x\) as coefficients of \[G^\lambda(x;\theta,\psi;z)=\frac{1}{(1-ze^{i\theta})^{\lambda-ix}(1-ze^{i\psi})^{\lambda+ix}}=\sum_{n=0}^\infty P_n^\lambda (x;\theta,\psi)z^n,\ |z| 0\), \(\theta \in (0,\pi)\), \(\psi \in \mathbb{R}\). In the case \(\psi=-\theta\) we have the well-known (MP) polynomials. The cases \(\psi=\pi-\theta\) and \(\psi=\pi+\theta\) leads to new sets of polynomials which we call quasi-Meixner-Pollaczek polynomials and strongly symmetric Meixner-Pollaczek polynomials. If \(x=0\), then we have an obvious generalization of the Gegenbauer polynomials. The properties of (GMP) polynomials as well as of some families of holomorphic functions \(|z|<1\) defined by the Stieltjes-integral formula, where the function \(zG^{\lambda}(x; \theta, \psi;z)\) is a kernel, will be discussed.
2 citations
TL;DR: In this article, the authors estimate the growth order of the n-th derivative Cauchy integrals at a point in terms of the distance between the point and the boundary of the domain.
Abstract: In this paper, we shall estimate the growth order of the n-th derivative Cauchy integrals at a point in terms of the distance between the point and the boundary of the domain. By using the estimate, we shall generalize Plemelj–Sokthoski theorem. We also consider the boundary behavior of generalized Cauchy integrals on compact bordered Riemann surfaces.
2 citations
TL;DR: In this paper, the authors considered a Cauchy type integral taking values in a three-dimensional harmonic algebra with two-dimensional radical and established sufficient conditions for an existence of limiting values of this integral on the curve of integration.
Abstract: We consider a certain analog of Cauchy type integral taking values in a three-dimensional harmonic algebra with two-dimensional radical. We establish sufficient conditions for an existence of limiting values of this integral on the curve of integration.
2 citations
TL;DR: In this article, a family of polynomials P with only one zero lying outside the complex plane C is studied and criteria for P to satisfy implying that each of P and Phas has at least one critical point outside C.
Abstract: Let D denote the unit disk {z : |z| < 1} in the complex plane C. In this paper, we study a family of polynomials P with only one zero lying outside D. We establish criteria for P to satisfy implying that each of P and Phas exactly one critical point outside D.
1 citations
TL;DR: In this article, the authors studied the maximal abelian extension of a local field with exponent p − 1 and its maximal p-abelian extension, especially the description of their Galois groups in solvable case.
Abstract: Let K be a local field with finite residue field of characteristic p. This paper is devoted to the study of the maximal abelian extension of K of exponent p − 1 and its maximal p-abelian extension, especially the description of their Galois groups in solvable case. Then some properties of local fields in general case are studied too.
1 citations
TL;DR: In this paper, the authors point out certain flaws in two papers published in the Ann. Univ. Mariae Curie-Sklodowska Sect. A, one in 2009 and the other in 2011.
Abstract: We point out certain flaws in two papers published in Ann. Univ. Mariae Curie-Sklodowska Sect. A, one in 2009 and the other in 2011. We discuss in detail the validity of the results in the two papers in question.
TL;DR: In this paper, a representation of the mapping class group of genus 2 surface in terms of a coordinate system of the Teichmuller space defined by trace functions was obtained.
Abstract: We obtain a representation of the mapping class group of genus 2 surface in terms of a coordinate system of the Teichmuller space defined by trace functions.
TL;DR: In this paper, the problem of transforming projectable-projectable classical torsion-free linear connections into classical linear connections on fibred-fibred manifolds was reduced to finding natural operators for the problem.
Abstract: We describe all \(\mathcal{F}^2\mathcal{M}_{m_1,m_2,n_1,n_2}\)-natural operators \(D\colon Q^{\tau}_{proj-proj} \rightsquigarrow QT^*\) transforming projectable-projectable classical torsion-free linear connections \(
abla\) on fibred-fibred manifolds \(Y\) into classical linear connections \(D(
abla)\) on cotangent bundles \(T^*Y\) of \(Y\). We show that this problem can be reduced to finding \(\mathcal{F}^2 \mathcal{M}_{m_1,m_2,n_1,n_2}\)-natural operators \(D\colon Q^{\tau}_{proj-proj}\rightsquigarrow (T^*,\otimes^pT^*\otimes\otimes^q T)\) for \(p=2\), \(q=1\) and \(p=3\), \(q=0\).
TL;DR: In this paper, the authors present new inequalities of L_p norms for sums of positive functions, which are useful for investigation of convergence of simple partial fractions in L_P(L_p(mathbb{R}).
Abstract: We present new inequalities of \(L_p\) norms for sums of positive functions. These inequalities are useful for investigation of convergence of simple partial fractions in \(L_p(\mathbb{R})\).
TL;DR: In this paper, the class of analytic functions of the form (p(z) = 1+c_nz^n+c_{n+1}z^{n+ 1}+\dots'' in the open unit disc (U) were studied.
Abstract: Let \(\mathcal{P}_n\) denote the class of analytic functions \(p(z)\) of the form \(p(z)=1+c_nz^n+c_{n+1}z^{n+1}+\dots\) in the open unit disc \(\mathbb{U}\). Applying the result by S. S. Miller and P. T. Mocanu (J. Math. Anal. Appl. 65 (1978), 289-305), some interesting properties for \(p(z)\) concerned with Caratheodory functions are discussed. Further, some corollaries of the results concerned with the result due to M. Obradovic and S. Owa (Math. Nachr. 140 (1989), 97-102) are shown.
TL;DR: In this article, the authors studied the convexity order and coefficients of a general integral operator with analytic functions from the class of starlike functions of order α and the class CVH(β).
Abstract: The purpose of this paper is to study some properties related to convexity order and coefficients estimation for a general integral operator. We find the convexity order for this operator, using the analytic functions from the class of starlike functions of order α and from the class CVH(β) and also we estimate the first two coefficients for functions obtained by this operator applied on the class CVH(β). 1. Preliminary and definitions. We consider the class of analytic func- tions f (z), in the open unit disk, U = {z ∈ C : |z| < 1}, having the form: