Descriptions of strongly multiplicity free representations for simple Lie algebras

Let $\mathfrak{g}$ be a simple Lie algebra over the complex numbers $\mathbb{C}$. Let $Z(\mathfrak{g})$ be the center of the universal enveloping algebra $U(\mathfrak{g})$. Denote by $V_\lambda$ the finite-dimensional simple $\mathfrak{g}$-module with highest weight $\lambda$. Lehrer and Zhang defined the notion of strongly multiplicity free representations for simple Lie algebras motivited by studying the structure of the endomorphism algebras $End _{ U(\mathfrak{g})}(V_\lambda^{\otimes r})$in terms of the quotients of Kohno's infinitesimal braid algebra. Kostant introduced the $\mathfrak{g}$ -invariant endomorphism algebras $R_\lambda= (End V_\lambda\otimes U(\mathfrak{g}))^\mathfrak{g}$ and $R_{\lambda,\pi}=(End V_\lambda\otimes \pi[U(\mathfrak{g})])^\mathfrak{g}.$ In this paper, we give some other criterion for a multiplicity free representation to be a strongly multiplicity free representation for simple Lie algebras by classifing the pairs $(\mathfrak{g}, V_\lambda)$, which are multiplicity free irreducible modules and for such pairs, $R_\lambda$ and $R_{\lambda,\pi}$ are generated by generalizations of the quadratic Casimimir elements of $Z(\mathfrak{g})$

Learning Micromanipulation, Part 1: An Approach Based on Multidimensional Ability Inventories and Text Mining.

In the last decades, an effort has been made to improve the efficiency of high-level and academic education players. Nowadays, students’ preferences and habits are continuously evolving and so the educational institutions deal with important challenges, such as not losing attractiveness or preventing early abandonment during the programs. In many countries, some important universities are public, and so they receive national grants that are based on a variety of factors, on which the teaching efficiency has a great impact. This contribution presents a method to improve students commitment during traditional lessons and laboratory tests. The idea consists in planning some activities according to the students’ learning preferences, which were studied by means of two different approaches. The first one was based on Gardner’s multiple intelligence inventory, which is useful to highlight some peculiar characteristics of the students on the specific educational field. In the second method, direct interviews, voice recognition, and text mining were used to extract some interesting characteristics of the group of students who participated in the projects. The methods were applied in May 2018 to the students attending the course of Micro-Nano Sensors and Actuators for the postgraduate academic program dedicated to Industrial Nanotechnologies Engineering of the University of Rome La Sapienza. The present paper represents the first part of the investigation and it is dedicated essentially to the adopted methods. The second part of the work is presented in the companion paper dedicated to the presentation of the practical project that the students completed before the exam

Quasi-normal modes of a black hole localized on a codimension-two brane of finite tension

We calculate the quasi-normal modes of black holes localized on a 3-brane of finite tension embedded in six-dimensional flat spacetime. Using the WKB approximation, we obtain the frequencies of various types of perturbation both analytically and numerically for arbitrary brane tension. We thus extend earlier analytical results which were derived for a brane of small tension.Comment: 17 pages, uses bibTeX, 5 figure

A rare case of broad ligament hematoma masquerading ovarian malignancy in a post-menopausal woman: a case report

Spontaneous broad ligament hematomas are relatively rare in non- pregnant state. We hereby present a case report of a 73 year old post-menopausal female, who initially presented with complain of postmenopausal bleeding since 4 month. Patient had underwent a diagnostic endometrial curettage in an another hospital, prior to presenting to our institution. On imaging, she was found to have a right sided complex adenexal mass (about 5cm in size) suspicious of ovarian malignancy. Patient was taken up for exploratory laparotomy and per-operatively found to have a broad ligament hematoma, which was further confirmed on histopathological examination

Transition Metal Oxide Nanostructures: Shape Controlled Synthesis, Characterizations and Studies of Physical Properties

Ph.DDOCTOR OF PHILOSOPH

Restaurant Revenue Prediction and Recommendation System

There are thousands of quick service restaurants over the globe,and many others. Deciding when and where to setup a restaurant is largely a tedious process which requires a lot of experience and judgment. For launching a new restaurant a large investment of time and capital is needed. Therefore, wrong location for a restaurant if chosen, leads to a heavy amount of loss. Also, for a customer to decide which restaurant to visit according to a budget and location preference is again a tedious job. Therefore, restaurant revenue prediction and recommendation system can be a promising solution for the problem mentioned above. Using Hadoop and big data, evaluation will be done using different aspects taken from the customers and hoteliers

Severe morbidity with sublingual misoprostol in a post-partum patient: a case report

Misoprostol is highly useful in preventing and treating postpartum hemorrhage. However, it may be associated with side effects like fever, chills and vomiting. Rarely may it cause severe morbidity and even death. We witnessed a case of 30 year old female, who developed postpartum hemorrhage immediately after her delivery. Patient was administered various uterotonics including 800 mcg sublingual misoprostol, with which her PPH was finally controlled. However, she developed hyperthermia, hypotension, tachycardia and fall in saturation of O2, after few hours of misoprostol administration. Patient was managed by strict monitoring in ICU setting and mechanical ventilation. She gradually recovered over a period of 48 hours and was discharged in stable condition. Misoprostol should be carefully used as it has a potential to cause serious adverse effects in pregnant and postpartum phase