Assessing performance factors in the UK banking sector: A multicriteria methodology

Further consolidation takes place not only among UK banks but also across borders, since some banks see size as a key factor in remaining competitive in international markets. Therefore, it is interesting to investigate the effectiveness and performance of UK banks. Based on their assets, banks are distinguished into small and large ones and a classification of UK banks in a multivariate environment for the period 1998211;2002 takes place. The PAIRCLAS multicriteria methodology is employed to investigate the performance of UK small and large banks over multiple criteria, such as asset quality, capital adequacy, liquidity and efficiency/profitability. A comparison with discriminant analysis (DA) and logistic regression (LR) facilitates the investigation of the relative performance of PAIRCLAS against them. The results of the study determine the key factors that specify the classification of a bank as small or large and provide us with the responsible banking decision makers for future readjustments.     

Aldo Cossu’s Work in Finite Geometry

A survey of the contributions of Aldo Cossu in finite geometry is given. Dedicated to the memory of Professor Aldo Cossu     

On constant mean curvature hypersurfaces with finite index

We discuss the non-existence of complete noncompact constant mean curvature hypersurfaces with finite index in a 4- or 5-dimensional manifold. As a consequence, we obtain that a complete noncompact constant mean curvature hypersurface in with finite index must be minimal. Received: 30 May 2005     

The logarithmic entropy formula for the linear heat equation on Riemannian manifolds

In this paper we introduce a new logarithmic entropy functional for the linear heat equation on complete Riemannian manifolds and prove that it is monotone decreasing on complete Riemannian manifolds with nonnegative Ricci curvature. Our results are simpler version, without Ricci flow, of R.-G. Ye’s recent result (arXiv:math.DG/0708.2008). As an application, we apply the monotonicity of the logarithmic entropy functional of heat kernels to characterize Euclidean space.     

Almost isometries and orthogonality

Given any two almost orthonormal systems A and 2123605000273-si1.gif"> of unit vectors in a Hilbert space X of the same cardinality, there exists a norm preserving almost isometry F of X so that 21" border="0" style="vertical-align:bottom" width="77" alt="View the MathML source" title="View the MathML source" src="http://ars.els-cdn.com/content/image/1-s2.0-S0022123605000273-si2.gif">. It follows that to every almost orthonormal system there corresponds a system of almost coefficient functionals.     

Dubins’ problem on surfaces. I. nonnegative curvature

Let M be a complete, connected, two-dimensional Riemannian manifold. Consider the following question: Given any (p₁,v₁) and (p₂, v₂) in T M, is it possible to connect p₁ to P₂ by a curve y in M with arbitrary small geodesic curvature such that, for i = 1, 2, y is equal to v_i at p_i? In this article, we bring a positive answer to the question if M verifies one of the following three conditions: (a) M is compact, (b) M is asymptotically flat, and (c) M has bounded nonnegative curvature outside a compact subset.     

The modified Yamabe problem and geometry of modified scalar curvatures

Study of modified scalar curvatures and the modified Yamabe problem is given. An existence theorem of type of Trudinger and Aubin is obtained. Interpreting Isotropic curvature as a certain modified scalar curvature we can extend the four-dimensional sphere theorem of [23]. Another modified scalar curvature is used in solving open problems concerning the conjecture of self-dual Einstein 4-manifold and the Goldberg conjecture, both being under negative Ricci condition.     

Examples of scalar-flat hypersurfaces in $${\mathbb{R}^{n+1}}$$

Given a hypersurface M of null scalar curvature in the unit sphere 215728/229_2008_247_Article_IEq2.gif" alt="$${\mathbb{S}^n}$$" align="middle" border="0"> , n ≥ 4, such that its second fundamental form has rank greater than 2, we construct a singular scalar-flat hypersurface in 215728/229_2008_247_Article_IEq3.gif" alt="$${\mathbb{R}^{n+1}}$$" align="middle" border="0"> as a normal graph over a truncated cone generated by M. Furthermore, this graph is 1-stable if the cone is strictly 1-stable.