Quantum measurements are inherently probabilistic and quantum theory often forbids to precisely predict the outcomes of simultaneous measurements. This phenomenon is captured quantified through uncertainty relations. Although studied since inception theory, problem determining possible expectation values a collection remains, in general, unsolved. By constructing close connection between observ...

In this article, some interesting applications of generalized inverses in the graph theory are revisited. Interesting properties employed to make proof several known results simpler, and techniques such as bordering method inverse complemented matrix methods used obtain simple expressions for Moore-Penrose incidence Laplacian matrix. Some simpler obtained special cases tree graph, complete bipa...

Effective-field-theory methods are used to separate the free energy for a nonabelian gauge theory at high temperature T into the contributions from the momentum scales T , gT , and g2T , where g is the coupling constant at the scale 2πT . The effects of the scale T enter through the coefficients in the effective lagrangian for the 3-dimensional effective theory obtained by dimensional reduction...

The concept of geometric-arithmetic indices was introduced in the chemical graph theory. These indices are defined by the following general formula:     ( ) 2 ( ) uv E G u v u v Q Q Q Q GA G , where Qu is some quantity that in a unique manner can be associated with the vertex u of graph G. In this paper the exact formula for two types of geometric-arithmetic index of Vphenylenic nanotube ar...

This book is based on Graph Theory courses taught by P.A. Petrosyan, V.V. Mkrtchyan and R.R. Kamalian at Yerevan State University.

Graphs may be classified in many ways apart from their order. A complete graph has each distinct pair of vertices connected by an edge. Many interesting problems arise in looking at complete graphs, several of which have to do with determining whether or not it is possible to pass through every vertex and edge once and only once (a Peterson cycle). A connected graph allows movement from any ver...

Course number: 0366.3267. When and where: Wednesdays 15-18, Ornstein 111. Prospective audience: the course is intended for second and third year undergraduate students in Mathematics or Computer Science. Prerequisites: first year courses in mathematics, most notably Discrete Mathematics or Introduction to Combinatorics. Requirements and grade: Homeworks will be given once every two-three weeks;...