Hessian sufficiency for bordered Hessian

We show that the second–order condition for strict local extrema in both constrained and unconstrained optimization problems can be expressed solely in terms of principal minors of the (Lagrengean) [sic] Hessian. This approach unifies the determinantal tests in the sense that the second-order condition can be always given solely in terms of Hessian matrix

Optical-Near Infrared Color Gradients of Elliptical Galaxies and Their Environmental Dependence

We have studied the environmental effect on optical-NIR color gradients of 273 nearby elliptical galaxies. Color gradient is a good tool to study the evolutionary history of elliptical galaxies, since the steepness of the color gradient reflects merging history of early types. When an elliptical galaxy goes through many merging events, the color gradient can be get less steep or reversed due to mixing of stars. One simple way to measure color gradient is to compare half-light radii in different bands. We have compared the optical and near infrared half-light radii of 273 early-type galaxies from Pahre(1999). Not surprisingly, we find that r$_{e}$(V)s (half-light radii measured in V-band) are in general larger than r$_{e}$(K)s (half-light radii measured in K-band). However, when divided into different environments, we find that elliptical galaxies in the denser environment have gentler color gradients than those in the less dense environment. Our finding suggests that elliptical galaxies in the dense environment have undergone many merging events and the mixing of stars through the merging have created the gentle color gradients.Comment: 3 pages, 2 figures. Proceedings of the 6th East Asian Meeting of Astronomy, held at Seoul National University, Korea, from October 18-22, 200

Deal Making in Whitehall: competing and complementary motivations behind the Review of Sub-national Economic Development and Regeneration'

Purpose – The aim of this paper is to explore Whitehall motivations underpinning the Sub-national Review of Economic Development and Regeneration. Design/methodology/approach – The paper is based on interviews conducted with senior Whitehall officials involved in regional working. Findings – The Sub-national Review seeks to streamline regional structures and provide regions with enhanced autonomy. However, findings indicate that there are distinct differences of opinion across Whitehall departments regarding the future trajectory of English regionalism and what powers and functions regional bodies should acquire. These contradictory positions raise questions about the implementation and effectiveness of the proposals. Originality/value – An examination of these phenomena is intended to provide greater clarity regarding the opportunities and constraints presented by the latest phase of regional restructuring