Coefficient estimates for some classes of functions associated with qq-function theory

In this paper, for every $q\in(0,1)$, we obtain the Herglotz representation theorem and discuss the Bieberbach type problem for the class of $q$-convex functions of order $\alpha, 0\le\alpha<1$. In addition, we discuss the Fekete-szeg\"o problem and the Hankel determinant problem for the class of $q$-starlike functions, leading to couple of conjectures for the class of $q$-starlike functions of order $\alpha, 0\le\alpha<1$.Comment: 12 page

A generalization of starlike functions of order alpha

For every $q\in(0,1)$ and $0\le \alpha<1$ we define a class of analytic functions, the so-called $q$-starlike functions of order $\alpha$, on the open unit disk. We study this class of functions and explore some inclusion properties with the well-known class of starlike functions of order $\alpha$. The paper is also devoted to the discussion on the Herglotz representation formula for analytic functions $zf'(z)/f(z)$ when $f(z)$ is $q$-starlike of order $\alpha$. As an application we also discuss the Bieberbach conjecture problem for the $q$-starlike functions of order $\alpha$. Further application includes the study of the order of $q$-starlikeness of the well-known basic hypergeometric functions introduced by Heine.Comment: 13 pages, 4 figures, submitted to a journa

Correlation between ultrasonography measured transcerebellar diameter of foetus with early and late gestational age

Background: Traditionally, the gestational age of the foetus is determined from the date of the last menstrual period. Prediction of gestational age (GA) based on sonographic foetal parameters is perhaps the cornerstone in modern obstetrics and continues to remain an important component in the management of pregnancies with foetuses who have growth disturbances. The objective of the study was to study the correlation between foetal transcerebellar diameter (TCD) and pregnancy age, addressing early and late gestation periods.Methods: This prospective observational study was conducted in the 100 pregnant women. Ultrasound examination for TCD and gestation age was done between 20-28 weeks of gestation and between 30-36 weeks of gestation. For the measurement of TCD transverse view of the foetal intracranium was obtained. Statistical analysis was performed using suitable tests.Results: Mean age of the women was 24.82+3.31 and 85% women were in age group 21-30. The mean TCD in early gestational age i.e. 20-28 weeks was 24.7 ± 3.86 and in late gestational age i.e. 30-36 weeks was 39.31 ± 2.51. Median TCD increases from 20.35 mm at 20 weeks to 41.7 mm at 36 weeks of gestation. The correlation coefficient between gestational age and TCD was 0.971, which indicated high degree of relation with p value <0.0001.Conclusions: This study shows linear relationship between TCD and gestational age at 20-28 weeks & 30-36 weeks. So, TCD is a reliable method of gestational age determination in early as well as in late pregnancy

Acute abdomen after hysterosalpingography-flare up of subclinical abdominal Kochs or endometriosis, a diagnostic dilemma

Here we present the case report of a patient of infertility with endometriosis and undiagnosed underlying abdominal Kochs that exacerbated after hysterosalpingography (HSG), presenting as acute abdomen and causing a diagnostic dilemma. (HSG) is a diagnostic test used to evaluate the fallopian tubes and uterus. HSG is contraindicated in FGTB as it can result in flare-up of subclinical infection. However, it is often performed as part of infertility workup in unsuspected cases. In our patient the unsuspected preexisting abdominal Kochs got flared up after extravasation of the contrast material during HSG resulting in formation of pus and diffuse peritonitis. Explorative laparotomy was taken after 1 week of conservative management and pus drained along with ovarian cystectomy. The patient was started on antitubercular treatment postoperatively and recovered well

Recurrent vulval fibroepithelial polyp with pregnancy: a rare presentation

A fibroepithelial polyp (FEP) is a relatively uncommon benign condition of vulva, mainly of reactive origin, occurs in women of reproductive age, mostly during pregnancy. Here is a case which presented with bilateral vulval mass, for that she underwent surgical excision. Histopathological examination revealed bilateral fibroepithelial vulval polyp. After 4 years of uneventful interval same female came with term pregnancy with a huge vulval mass on left side, having similar characteristic features as previous one. Emergency cesarean section followed by excision of polyp in the same sitting done. Histopathological report confirmed the finding of fibroepithelial polyp this time also. Only few cases of recurrent fibroepithelial polyp of vulva associated with pregnancy have been reported till date

Producing Copper Powder from Copper Bleed Solution by Hydrogen Reduction

This paper deals with the bench scale investigation on the hydrogen reduction of a highly acidic copper bleed solution.(CBS), generated in an Indian copper smelter, to produce highly pure copper powder. A titanium-lined autoclave of 1 L capacity was used for this study. After the optimization of the parameters for the recovery of copper powder, hydrogen reduction of copper was done in a larger autoclave to validate the results