1. Lie groups and Lie algebras 2 1.1. Definition and examples of Lie groups 2 1.2. Left invariant vector fields and Lie algebras 3 1.3. The exponential map 6 2. Representations of Lie groups and Lie algebras 9 2.1. Definitions and examples 9 2.2. The adjoint representation 9 2.3. Semisimplicity and Schur’s lemma 9 2.4. Haar measure and Weyl’s trick 9 2.5. Characters 9 2.6. Examples 9 2.7. Peter...

abstract background brucellosis is endemic in iran, and is seen in all age groups, including children. its diagnosis in childhood needs a high index of suspicion. the diagnostic methods currently in use need evaluation for analytical performance. objective the present study tries to evaluate the hematological indices, serologic markers of inflammation and symptoms in patients suspected of bruce...

Khoo SB. Test Your Knowledge: A right " spider " hand and a left " eagle " hand. Malaysian Family Physician. 2009;4(2&3):100-2 CASE HISTORY Jim (not his real name) is a 68 year-old friendly and pleasant Eurasian man who has been very pleased to participate in our clinical teaching sessions for many years. To the medical students, Jim is fond of showing his hands and to test them by providing th...

Introduction: Brucellosis is one of the most common zoonotic infections worldwide. The clinical symptoms of brucellosis are similar to a wide range of diseases; hence, reliable diagnostic and laboratory methods are required to identify the causative agent. Iran is an endemic region of brucellosis, and many patients are misdiagnosed due to the nature of the infection. In this study, we aimed to ...

a new 2-[(4-substituted-phenyl-3-chloroazetidin-2-one)-5-(2'-methylamino 4-phenyl-1', 3'-thiazolyl-]-1, 3, 4-thiadiazoles, 5(a-n) were synthesized from 2-substituted-benzylideneamino-5-[2'-methylamino-4'-phenyl-1',3'-thiazolyl]-1,3, 4-thiadiazole, 4(a-n) using 2-amino-4phenyl-1, 3-thiazole as a starting material. the synthesised compounds have been screened in vitro for their antimicrobial acti...

On her way to a dreaded dental appointment to have an aching tooth pulled, Clara Spencer meets a solicitous stranger, Jim, and by the end of the story runs off with him, in many interpretations to perdition. But since 1) Shirley Jackson (who herself had much dental work and hated it) has suffered from typecasting as a horror writer, 2) dental gas anesthesia protocols of the time as Clara is ant...

‎‎in the category of mordell curves (e_d:y^2=x^3+d) with nontrivial torsion groups we find curves of the generic rank two as quadratic twists of (e_1), ‎and of the generic rank at least two and at least three as cubic twists of (e_1). ‎previous work‎, ‎in the category of mordell curves with trivial torsion groups‎, ‎has found infinitely many elliptic curves with rank at least seven as sextic tw...

Graphs and Digraphs: A graph G = (V,E) is a structure that represents a discrete set V objects, called vertices or nodes, and a set of pairwise relations E between these objects, called edges. Edges may be directed from one vertex to another or may be undirected. The term “graph” means an undirected graph, and directed graphs are often called digraphs (see Fig. 1). Graphs and digraphs provide a...