On logarithmic coefficients of some close-to-convex functions

The logarithmic coefficients $\gamma_n$ of an analytic and univalent function $f$ in the unit disk $\mathbb{D}=\{z\in\mathbb{C}:|z|<1\}$ with the normalization $f(0)=0=f'(0)-1$ is defined by $\log \frac{f(z)}{z}= 2\sum_{n=1}^{\infty} \gamma_n z^n$. Recently, D.K. Thomas [On the logarithmic coefficients of close to convex functions, {\it Proc. Amer. Math. Soc.} {\bf 144} (2016), 1681--1687] proved that $|\gamma_3|\le \frac{7}{12}$ for functions in a subclass of close-to-convex functions (with argument $0$) and claimed that the estimate is sharp by providing a form of a extremal function. In the present paper, we pointed out that such extremal functions do not exist and the estimate is not sharp by providing a much more improved bound for the whole class of close-to-convex functions (with argument $0$). We also determine a sharp upper bound of $|\gamma_3|$ for close-to-convex functions (with argument $0$) with respect to the Koebe function.Comment: 13 page

Contributing Factors to Under-Five Child Malnutrition in Rural Bangladesh

Background and objectives: Bangladesh has the highest malnutrition rates in the world. The main objective of this study is to identify and determine the main factors for child malnutrition among children under the age 5 years in rural Bangladesh. Material and methods: This research was conducted in rural areas at Meherpur district in Bangladesh. Convenience sampling method is used and 85 under 5 child information is collected through a structured questionnaire. The information’s of child’s are gathered from the mothers of the child. Malnourished children is measured by using APLS method and WHO Child Growth Standard Median Index. Binary logistic regression model is used to find out the key factors of malnutrition. Results: It is found that family income, maintain proper diet during pregnancy period, proper diet maintain for children have negative significant (p\u3c0.05) effect on child malnutrition. Conclusion: The magnitude of the child’s malnutrition still is of great concern in Bangladesh. Since, poverty, imbalanced diet during pregnancy period and imbalanced diet for under 5 children influences to malnutrition are significantly associated with high prevalence of malnutrition, so government and people should reduce these factor to reduce malnutrition in rural area of Bangladesh

Alteplase administration for acute ischemic stroke (AIS) in ER - a 5-year review

ER visits for AIS grown in last 10 years by 25% Ongoing effort by AHA/ASA to improve access to care with early stroke recognition and awareness Time is brain; rate of thrombolysis with alteplase (ALT) should increase with better EMS systems, awareness, and educatio