Let G be a finite group and Irr ( ) the set of all complex irreducible characters . The character-graph Δ associated to , is graph whose vertex primes which divide degrees some in two distinct p q are adjacent if product pq divides χ 1 for ∈ Tong-Viet posed conjecture that k -regular integer ⩾ 2 then either complete or cocktail party graph. In this paper, we show his true regular character-grap...

Calogero-Moser systems are classical and quantum integrable multi-particle dynamics defined for any root system ∆. The quantum Calogero systems having 1/q2 potential and a confining q2 potential and the Sutherland systems with 1/ sin q potentials have “integer” energy spectra characterised by the root system ∆. Various quantities of the corresponding classical systems, e.g. minimum energy, freq...

We discuss asymptotics of the number of states of Boson gas whose Hamiltonian is given by a positive elliptic pseudo-differential operator of order one on a compact manifold. We obtain an asymptotic formula for the average of the number of states. Furthermore, when the operator has integer eigenvalues and the periodic orbits of period less than 2π of the classical mechanics form clean submanifo...

Graph eigenvalues are examples of totally real algebraic integers, i.e. roots of real-rooted monic polynomials with integer coefficients. Conversely, the fact that every totally real algebraic integer occurs as an eigenvalue of some finite graph is a deep result, conjectured forty years ago by Hoffman, and proved seventeen years later by Estes. This short paper provides an independent and eleme...

We study the stability of synchronized fixed-point state for linear fractional-order coupled map lattice(CML). observe that eigenvalues connectivity matrix determine as integer-order CML. These can be determined exactly in certain cases. find exact bounds one-dimensional lattice with translationally invariant coupling using theory circulant matrices. This extended to any finite dimension. Simil...

This paper addresses the problem of generating strong convex relaxations of Mixed Integer Quadratically Constrained Programming (MIQCP) problems. MIQCP problems are very difficult because they combine two kinds of non-convexities: integer variables and non-convex quadratic constraints. To produce strong relaxations of MIQCP problems, we use techniques from disjunctive programming and the lift-a...

This paper addresses the problem of generating strong convex relaxations of Mixed Integer Quadratically Constrained Programming (MIQCP) problems. MIQCP problems are very difficult because they combine two kinds of non-convexities: integer variables and nonconvex quadratic constraints. To produce strong relaxations of MIQCP problems, we use techniques from disjunctive programming and the liftand...

A bstract In this note we study the mass spectrum of type IIB flux compactifications. We first give a general discussion matrix for F-term vacua in four-dimensional $$ \mathcal{N} N = 1 supergravity theories and then specialize to Calabi-Yau orientifold compactifications presence geometric non-geometric fluxe...

This paper is concerned with the problem of designing discrete-time control systems with closed-loop eigenvalues in a prescribed region of stability. First, we obtain a state feedback matrix which assigns all the eigenvalues to zero, and then by elementary similarity operations we find a state feedback which assigns the eigenvalues inside a circle with center   and radius. This new algorithm ca...

To every compact Riemannian manifold M there corresponds the sequence 0 = X1 < X2 < X3 .< ... of eigenvalues for the Laplace operator on M. It is not known just how much information about M can be extracted from this sequence.' This note will show that the sequence does not characterize M completely, by exhibiting two 16-dimensional toruses which are distinct as Riemannian manifolds but have th...