Band 70, Heft 4

We study relative normality properties in locales. We identify localic maps that preserve and ones that reflect various relative normality properties.

In this paper, we prove some conditional results about the order of zero at central point s = 1/2 of the Rankin-Selberg L -function L ( s , π f × π͠ ′ f ). Then, we give an upper bound for the height of the first zero with positive imaginary part of L ( s , π f × π͠ ′ f ). We apply our results to automorphic L -functions.

In this paper, we develop a new method based on Newton polygon and graded polynomials, similar to the known one based on Newton polygon and residual polynomials. This new method allows us the factorization of any monic polynomial in any henselian valued field. As applications, we give a new proof of Hensel’s lemma and a theorem on prime ideal factorization.

Given a subdirectly irreducible ∗-regular ring R , we show that R is a homomorphic image of a regular ∗-subring of an ultraproduct of the (simple) eRe , e in the minimal ideal of R ; moreover, R (with unit) is directly finite if all eRe are unit-regular. For any subdirect product of artinian ∗-regular rings we construct a unit-regular and ∗-clean extension within its variety.

In the paper, we give new improvements of the reverse Hölder and Minkowski integral inequalities. These new results in special case yield the Pólya-Szegö’s inequality and reverse Minkowski’s inequality, respectively.

In this paper, we are mainly interested to study the generalization of typically real functions in the unit disk. We study some coefficient inequalities concerning this class of functions. In particular, we find the Zalcman conjecture for generalized typically real functions.

Dynamics of composition of entire functions is well related to it's factors, as it is known that for entire functions f and g , fog has wandering domain if and only if gof has wandering domain. However the Fatou components may have different structures and properties. In this paper we have shown the existence of domains with all possibilities of wandering and periodic in given angular region θ .

In this paper, we use the novel idea of incorporating the recently derived formula for the fourth coefficient of Carathéodory functions, in place of the routine triangle inequality to achieve the sharp bounds of the Hankel determinants H 3 (1) and H 2 (3) for the well known class 𝓢𝓛 * of starlike functions associated with the right lemniscate of Bernoulli. Apart from that the sharp bound of the Zalcman functional: |a32− a5|$\begin{array}{} |a_3^2-a_5| \end{array}$ for the class 𝓢𝓛 * is also estimated. Further, a couple of interesting results of 𝓢𝓛 * are also discussed.

In this article, we prove a new generalization of uniqueness theorems for meromorphic mappings of a complete Kähler manifold M into ℙ n (ℂ) sharing hyperplanes in general position with a general condition on the intersections of the inverse images of these hyperplanes.

In this paper, we prove a global well-posedness of the three-dimensional incompressible Navier-Stokes equation under initial data, which belongs to the Lei-Lin-Gevrey space Za,σ − 1$\begin{array}{} Z^{-1}_{a,\sigma} \end{array}$(ℝ 3 ) and if the norm of the initial data in the Lei-Lin space 𝓧 −1 is controlled by the viscosity. Moreover, we will show that the norm of this global solution in the Lei-Lin-Gevrey space decays to zero as time approaches to infinity.

In this paper, we prove the boundedness of the B n maximal operator and B n singular integral operators associated with the Laplace-Bessel differential operator Δ B n on variable exponent Lebesgue spaces.

Kaimakamis and Panagiotidou in [Taiwanese J. Math. 18 (6) (2014), 1991–1998] proposed an open question: are there real hypersurfaces in nonflat complex space forms whose ∗-Ricci tensor satisfies the condition of 𝔻-parallelism? In this short note, we present an affirmative answer and prove that a three-dimensional real hypersurface in a nonflat complex space form has 𝔻-parallel ∗-Ricci tensor if and only if it is locally congruent to either a geodesic hypersphere of radius r in ℂ H 2 ( c ) with tanh⁡ (|c|2r)=12$\begin{array}{} \displaystyle \tanh(\frac{\sqrt{|c|}}{2}r) = \frac{1}{2} \end{array}$ or a ruled real hypersurface.

Let X be a completely regular topological space. For each closed non-vanishing ideal H of C B ( X ), the normed algebra of all bounded continuous scalar-valued mappings on X equipped with pointwise addition and multiplication and the supremum norm, we study its spectrum, denoted by 𝔰𝔭( H ). We make a correspondence between algebraic properties of H and topological properties of 𝔰𝔭( H ). This continues some previous studies, in which topological properties of 𝔰𝔭( H ) such as the Lindelöf property, paracompactness, σ -compactness and countable compactness have been made into correspondence with algebraic properties of H . We study here other compactness properties of 𝔰𝔭( H ) such as weak paracompactness, sequential compactness and pseudocompactness. We also study the ideal isomorphisms between two non-vanishing closed ideals of C B ( X ).

A generalization of the Lindley distribution namely, Lindley negative-binomial distribution, is introduced. The Lindley and the exponentiated Lindley distributions are considered as sub-models of the proposed distribution. The proposed model has flexible density and hazard rate functions. The density function can be decreasing, right-skewed, left-skewed and approximately symmetric. The hazard rate function possesses various shapes including increasing, decreasing and bathtub. Furthermore, the survival and hazard rate functions have closed form representations which make this model tractable for censored data analysis. Some general properties of the proposed model are studied such as ordinary and incomplete moments, moment generating function, mean deviations, Lorenz and Bonferroni curve. The maximum likelihood and the Bayesian estimation methods are utilized to estimate the model parameters. In addition, a small simulation study is conducted in order to evaluate the performance of the estimation methods. Two real data sets are used to illustrate the applicability of the proposed model.

The James function, also known as the “log5 method”, assigns a probability to the result of a competition between two teams based on their respective winning percentages. This paper, which builds on earlier work of the authors and Steven J. Miller, explores the analogous situation where a single team or player competes simultaneously against multiple opponents.

This paper proposes a new extended Lindley distribution, which has a more flexible density and hazard rate shapes than the Lindley and Power Lindley distributions, based on the mixture distribution structure in order to model with new distribution characteristics real data phenomena. Its some distributional properties such as the shapes, moments, quantile function, Bonferonni and Lorenz curves, mean deviations and order statistics have been obtained. Characterizations based on two truncated moments, conditional expectation as well as in terms of the hazard function are presented. Different estimation procedures have been employed to estimate the unknown parameters and their performances are compared via Monte Carlo simulations. The flexibility and importance of the proposed model are illustrated by two real data sets.

This study introduces the Poisson-Bilal distribution and its associated two models for modeling the over-dispersed count data sets. The Poisson-Bilal distribution has tractable properties and explicit forms for its statistical properties. A new over-dispersed count regression model and integer-valued autoregressive process with flexible innovation distribution are defined and studied comprehensively. Two real data sets are analyzed to prove empirically the importance of proposed models. Empirical findings show that the Poisson-Bilal distribution has important application fields in time series and regression modeling.

Convergence models of interest rates are used to model a situation, where a country is going to enter a monetary union and its short rate is affected by the short rate in the monetary union. In addition, Wiener processes which model random shocks in the behaviour of the short rates can be correlated. In this paper we consider a stochastic correlation in a selected convergence model. A stochastic correlation has been already studied in different contexts in financial mathematics, therefore we distinguish differences which come from modelling interest rates by a convergence model. We provide meaningful properties which a correlation model should satisfy and afterwards we study the problem of solving the partial differential equation for the bond prices. We find its solution in a separable form, where the term coming from the stochastic correlation is given in its series expansion for a high value of the correlation.

Let 𝓐 be a ⋆-algebra, δ : 𝓐 → 𝓐 be a linear map, and z ∈ 𝓐 be fixed. We consider the condition that δ satisfies xδ ( y ) ⋆ + δ ( x ) y ⋆ = δ ( z ) ( x ⋆ δ ( y ) + δ ( x ) ⋆ y = δ ( z )) whenever xy ⋆ = z ( x ⋆ y = z ), and under several conditions on 𝓐, δ and z we characterize the structure of δ . In particular, we prove that if 𝓐 is a Banach ⋆-algebra, δ is a continuous linear map, and z is a left (right) separating point of 𝓐, then δ is a Jordan derivation. Our proof is based on complex variable techniques. Also, we describe a linear map δ satisfying the above conditions with z = 0 on two classes of ⋆-algebras: zero product determined algebras and standard operator algebras.