Bilinear Spherical Maximal Functions of Product Type

In this paper we introduce and study a bilinear spherical maximal function of product type in the spirit of bilinear Calderón–Zygmund theory. This operator is different from the bilinear spherical maximal function considered by Geba et al. in (Math Res Lett20(4):675–694, 2013). We deal with lacunary and full versions of this operator, and prove weighted estimates with respect to genuine bilinear weights beyond the Banach range. Our results are implied by sharp sparse domination for both the operators,following ideas by Lacey (J Anal Math 139(2):613–635, 2019). In the case of the lacunary maximal operator we also use interpolation of analytic families of operators to address the weighted boundedness for the whole range of tuplesRYC2018-025477-I Ikerbasqu

A study of femoral bicondylar angle in Udaipur, India zone

Background: Human body consists of 206 bones; among which femur. The thigh bone is considered as the biggest and strongest bone of the body. The bone contains a femoral bicondylar angle which helps in maintaining the balance and certain movements of the body. Those movements are essential to stand upright and erect; therefore, helps in balancing the posture of the body. Bicondylar angle shows various gestures and characteristics essential for describing the necessary ailments of the human skeleton. Thus, the present study is designed with an aim to measure and compare the bicondylar angle of femur both in males and females in Udaipur, Rajasthan, India zone.Methods: Totally, 96 bones were studied- 48 males and 48 females’ bones in 2 years duration. The study was carried out in the Department of Anatomy of Geetanjali Medical College and Hospital and R.N.T. Medical College. The bicondylar angle was measured with a suitable apparatus comprising of compass, Digital Vernier Calliper, scale and protector (Figure 1) along with osteometric board. Bicondylar angle of male and female bone was calculated using SPSS software.Results: The study shows that the bicondylar angle of left femur was greater than right femur in both the genders, but their side differences was statistically insignificant (p>0.05).Conclusions: Hence, the bicondylar angle of female is larger than in comparison to males and these results can put emphasis/light on the orthopaedic clinicians and surgeons to know the etiology of osteometric diseases

Invariant Random Approximation in Nonconvex Domain

Random fixed point results in the setup of compact and weakly compact domain of Banach spaces which is not necessary starshaped have been obtained in the present work. Invariant random approximation results have also been determined asits application. In this way, random version of invariant approximation results due toMukherjee and Som [13] and Singh [17] have been given.DOI : http://dx.doi.org/10.22342/jims.15.2.45.69-7

Iron meteorite fall at Bhuka village, Barmer District, Rajasthan

This article does not have an abstract

Simple Analytical Particle and Kinetic Energy Densities for a Dilute Fermionic Gas in a d-Dimensional Harmonic Trap

We derive simple analytical expressions for the particle density $\rho(r)$ and the kinetic energy density $\tau(r)$ for a system of noninteracting fermions in a $d-$dimensional isotropic harmonic oscillator potential. We test the Thomas-Fermi (TF, or local-density) approximation for the functional relation $\tau[\rho]$ using the exact $\rho(r)$ and show that it locally reproduces the exact kinetic energy density $\tau(r)$, {\it including the shell oscillations,} surprisingly well everywhere except near the classical turning point. For the special case of two dimensions (2D), we obtain the unexpected analytical result that the integral of $\tau_{TF}[\rho(r)]$ yields the {\it exact} total kinetic energy.Comment: 4 pages, 4 figures; corrected versio

Role of color doppler in the diagnosis of intra uterine growth restriction (IUGR)

Background: The purpose of our study was to evaluate the diagnostic efficacy of the pulsatility index (PI) and resistive index (RI) in uterine artery, umbilical artery and middle cerebral artery in the diagnosis of IUGR and prediction of adverse perinatal outcome.Methods: A total of 100 clinically suspected IUGR cases were enrolled in the study. A detailed history and examination was done, color doppler carried out serially every three weeks starting from 30 weeks till delivery, subsequently confirmation of fetal growth restriction (FGR) was done by assessing the newborn parameters for growth restriction.Results: Doppler measurement for uterine artery showed higher efficacy as compared to umbilical artery and middle cerebral artery findings. The uterine artery RI was found to be 84.6% sensitive and 82.9% specific even at 30 weeks. Uterine artery PI too showed a good diagnostic efficacy with an accuracy of 79%, a sensitivity of 76.9%, a specificity of 82.9%.Both PI and RI for uterine artery showed a relatively higher specificity.Conclusion: Here we concluded that once IUGR is suspected, Doppler velocimetry may be useful as a part of evaluation and uterine artery analysis identifies a subgroup with an increased risk for developing IUGR.