We consider the optimal scheduling problem for a single-server queue without arrivals. We allow preemptions, and our purpose is to minimize the expected flow time. The optimal non-anticipating discipline is known to be the Gittins index policy, which, however, is defined in an implicit way. Until now, its general behaviour in this specific problem has been characterized only in a few special ca...

Let q (G) denote the spectral radius of the signless Laplacian matrix of a graph G, also known as the Q-index of G. The aim of this note is to study a general extremal problem: How large can q (G) be when G belongs to an abstract graph property? Even knowing very little about the graph property, this paper shows that useful conclusions about the asymptotics of q (G) can be made, which turn out ...

There is a growing literature on implied volatility indices in developed markets. However, no similar research has been conducted in the context of emerging markets. In this paper, an implied volatility index (GVIX) is constructed for the fast developing Greek derivatives market. Next, the properties of GVIX are explored. In line with earlier results, GVIX can be interpreted as a gauge of the i...

This paper considers the Euler tour of an uncertain random graph, in which some edges exist with some degrees in uncertain measure and others exist with some degrees in probability measure. The concept of Euler index of an uncertain random graph is proposed first, and then a method to calculate the Euler index of an uncertain random graph is given. In addition, some properties of the Euler inde...

A new topological index Xu based on the adjacency matrix A and the distance matrix D is derived in this paper. The index, which is very simple to calculate and also has good discrimination of alkane isomers, is used to correlate with the selected physicochemical properties of a wide range of alkanes. The comprehensive studies show that the proposed index correlates highly both with the normal b...

thyme essential oils (eo) with antimicrobial and antioxidant properties are widely used in pharmaceutical, cosmetic, and perfume industry. it is also used for flavoring and preservation of several foods. nowadays, packaging research is receiving a considerable attention due to the development of eco-friendly materials made from natural polymers such as starch and chitosan. in this study thymus ...

Let An denote the n-th cycle index polynomial, in the variables Xj , for the symmetric group on n letters. We show that if the variables Xj are assigned nonnegative real values which are logconcave, then the resulting quantities An satisfy the two inequalities An−1An+1 ≤ An ≤ ( n+1 n ) An−1An+1. This implies that the coefficients of the formal power series exp(g(u)) are log-concave whenever tho...

We study the bandgap properties of twodimensional photonic crystals created by a lattice of rods or holes conformed in a symmetric or asymmetric triangular structure. Using the plane-wave analysis, we calculate a minimum value of the refractive index contrast for opening both partial and full two-dimensional spectral gaps for both TM and TE polarized waves. We also analyze the effect of ellipti...

Gradient-index (GRIN) lenses have been widely used as collimators in various fiber-optic sensors and as optical coupling devices in components designed for optical communication systems. However, relatively little attention has been paid to the birefringent properties of GRIN lenses and the potential for using them as photoelastic sensing elements in optical transducers. Analytical and experime...