Coefficient inequalities for a class of analytic functions associated with the lemniscate of Bernoulli

In this paper, a new subclass of analytic functions ML_{\lambda}^{*}  associated with the right half of the lemniscate of Bernoulli is introduced. The sharp upper bound for the Fekete-Szego functional |a_{3}-\mu a_{2}^{2}|  for both real and complex \mu are considered. Further, the sharp upper bound to the second Hankel determinant |H_{2}(1)| for the function f in the class ML_{\lambda}^{*} using Toeplitz determinant is studied. Relevances of the main results are also briefly indicated

Us among them - a study of the contemporary Polish emigration to Norway

A significant increase in migration from Poland has been observed sińce Poland joined the European Union in 2004. It has mainly been labour migration to richer countries of Western Europę. The ratę of migration has exceeded the expectations of both politicians and experts. Statistics now show that about 2 million citizens have left Poland sińce that moment (Główny Urząd Statystyczny 2011). One of the top countries which Poles choose as a target for migration is Norway. Not only do the majority of Polish immigrants lack basie skills in Norwegian, but they also lack basie skills in English. The communication problems with people who don't belong to us, those who use the same language, is one of the most important factors that contributes to the cre-ation of closed Polish ethnic enclaves. These communities try to rebuild their own identity in new countries based on the traditions and cultural codes brought from Poland, and us-them as opposite values. In this case us designates those members of a Polish minority in Norway, who follow norms accepted by the group, while Norwegians here represent them. A confrontation with the antagonists certifies one's own ideas and values. It is worth noticing that not all Polish migrants live within their ethnic groups. Poland is a rather culturally homogeneous country. This is a factor which facilitates finding one's own ethnic group in a foreign land and thereafter establishing one's place in it. Living abroad, however, changes one's identity due to foreign influence. The identity oithem changes similarly, depending on the situation. After a preliminary categorization of all the Poles as us, gradual divisions and categorizations take place within the Polish immigrant community. A significant number of Poles, usually less educated, often deliberately choose to isolate themselves from the culture of the host country. They use it as a method of retaining their own culture. Families and friends are brought from Poland in order to reproduce the lost local homeland

Differential subordination related with exponential functions

In this article, we study some first-order differential subordinations. We determine the conditions on β  such that 1 + β zp′(z) ≺ √1+cz) and 1 + β zp′(z) ≺ 1 + √(2z+ 1/2 z2  implies p(z) ≺ ez. Similarly, some results are also obtained for the expressions 1 + β zp′ (z)/p(z) and 1 + β zp′(z) / p2(z). We also give applications of these results to obtain some sufficient conditions for a function to be starlike related to exponential functions.&nbsp

ALKALI METALS ORGANIC SOLUTIONS - 39K AND 23Na NMR STUDY

Blue potassium and potassium/sodium solutions in tetrahydrofuran or tetraglyme containing various complexing agents were investigated by means of 39K and 23Na NMR. The ionic composition of the systems was determined. Relaxation behaviour of potassium solutions was presented and interpreted. A great influence of complexing agent on the magnitude of ionic interactions was revealed. The utility of Me+(crown ether) ,Me- complexes as chemical reagents and homogeneous catalysts was demonstrated

Certain results on subordinations associated with a differintegral operator

We investigate some interesting properties on subordinations for classes of multivalent analytic functions associated with a linear differintegral operator of J. Dziok [3]. Some applications and important consequences of the main results are also discussed