On the Ellipticity of the Middle Surface of a Shell and its Application to the Asymptotic Analysis of ‘Membrane’ Shells

We consider a surface S = (), where ² is a bounded, connected, open set with a smooth boundary and : ³ is a smooth map; let () denote the components of the two-dimensional linearized strain tensor of S and let 0 with length 0 > 0. We assume the the norm ,|| ()||0, in the space V0() = { H¹() × H¹() × L²(); = 0 on 0 } is equivalent to the usual product norm on this space. We then establish that this assumption implies that the surface S is uniformly elliptic and that we necessarily have 0 = .     

On rationality of moduli spaces of vector bundles on real Hirzebruch surfaces

Let X be a real form of a Hirzebruch surface. Let M _H (r,c ₁, c ₂) be the moduli space of vector bundles on X. Under some numerical conditions on r, c ₁ and c ₂, we identify those M _H (r,c ₁,c ₂) that are rational.     

Modified function projective combination synchronization of hyperchaotic systems

In this work, a novel combination synchronization scheme in which synchronization of a new combination hyperchaotic drive system formed by combining state variables of the original drive system with appropriate scaling factors with a response hyperchaotic system is considered. A self-combination system is constructed from hyperchaotic Lorenz system by combining state variables of the Lorenz system with appropriate scaling factors. Modified function projective synchronization between the newly constructed combination hyperchaotic Lorenz system and hyperchaotic Lu system is investigated using adaptive method. By Lyapunov stability theory, the adaptive control law and the parameter update law are derived to make the state of two systems as modified function projective synchronized. Numerical simulations are done to show the validity and effectiveness of the proposed synchronization scheme.     

A General Existence Principle for Fixed Point Theorems in One Parameter Case of Soft $D_{a}$-Metric Space

In this paper, we take the case of soft points into consideration and propose a new metric structure called soft D_a-metric space for a specific orbit defined with soft points. In order to establish fixed point results in the modified metric space, we modify a few existing definitions in the sense of soft points.     

A RATIONALIZATION OF UPS AND DOWNS OF OIL PRICES BY SLUGGISH DEMAND,UNCERTAINTY, AND NONCONCAVITY

Motivated by the recent switching between “low” oil prices and “high” oil prices, this paper provides an economic explanation for oil price volatility. Given the characteristics of the oil market—sluggish, concave, and uncertain demand, as well as noncompetitive players—the corresponding profit maximizing strategy is to switch between a low price and a high price depending on whether the current demand is below or above a certain threshold. This provides an economic rationalization of oil price volatility (including the low prices) as alternative, or at least as complement, to the typically offered political explanations.