A note on Fukuyama (2000)

This brief note discusses Fukuyama’s paper [Fukuyama, H., 2000. Returns to scale and scale elasticity in data envelopment analysis. European Journal of Operational Research 125, 93–112]. We prove that the Proof of Lemma 1 by Fukuyama (2000) is incorrect due to incorrect substitution. In addition, we exemplify our conclusion by a counterexample taken from Fukuyama (2000). Thus all conclusions, based on Lemma 1, of Fukuyama (2000) cannot be reached and are left for further research.     

Topological Homology Semi-Biplanes

 Coherent, topological, tactical semi-biplanes are homology semi-biplanes. In particular, semi-biplanes constructed from pairs of non-collinear points in compact antiregular quadrangles are homology semi-biplanes. (Received 7 March 2000; in final form 12 October 2000)     

Minimal bases of matrix pencils and coprime matrix fraction descriptions

Two new methods for the construction of coprime MFDs are proposedstarting from a minimal state space realization of a transferfunction matrix. The approaches are based on the constructionof minimal bases for the kernels of the state-space-based pencils[s I – A, – B], [s I – A^t, –C^t]. Thelatter problem is explicitly solved using the Toeplitz matrixconstruction of minimal bases of matrix pencils. The numericalalgorithms of the methods are presented and some examples demonstratingthe implementation of the algorithms are also given. Received 18 May 2000. Revised 5 September 2000. Accepted 5 September 2000.     

The Simultaneous Approximation Order by Hermite Interpolation in a Smooth Domain

Let D be a smooth domain in the complex plane. In D consider the simultaneous approximation to a function and its ith (0 ≤i≤q) derivatives by Hermite interpolation. The orders of uniform approximation and approximation in the mean, are obtained under some domain boundary conditions. Some known results are included as particular cases of the theorems of this paper. Received May 25, 2000, Revised November 3, 2000, Accepted December 7, 2000     

Light paths in 4‐connected graphs in the plane and other surfaces

Several results concerning existence of k‐paths, for which the sum of their vertex degrees is small, are presented. © 2000 John Wiley & Sons, Inc. J Graph Theory 34: 170–179, 2000     

Stable and Unstable Solitary-Wave Solutions of the Generalized Regularized Long-Wave Equation

Summary. Investigated here are interesting aspects of the solitary-wave solutions of the generalized Regularized Long-Wave equation For p>5 , the equation has both stable and unstable solitary-wave solutions, according to the theory of Souganidis and Strauss. Using a high-order accurate numerical scheme for the approximation of solutions of the equation, the dynamics of suitably perturbed solitary waves are examined. Among other conclusions, we find that unstable solitary waves may evolve into several, stable solitary waves and that positive initial data need not feature solitary waves at all in its long-time asymptotics. Received March 28, 2000; accepted August 24, 2000 %%Online publication November 15, 2000 Communicated by Thanasis Fokas     

Upper bounds on the height difference of the Gaussian random field and the range of random graph homomorphisms into ℤ

Bounds on the range of random graph homomorphism into ℤ, and the maximal height difference of the Gaussian random field, are presented. © 2000 John Wiley & Sons, Inc. Random Struct. Alg., 17: 20–25, 2000     

Miscellaneous problems on infinite graphs

A collection of open problems on infinite graphs is presented, divided into twelve sections which are largely independent of each other. © 2000 John Wiley & Sons, Inc. J Graph Theory 35: 128–151, 2000     

Reply to comments by Soleimani-damaneh and Mostafaee (2006) and Zhang (2006)

In Fukuyama [Fukuyama, H., 2000. Returns to scale and scale elasticity in data envelopment analysis. European Journal of Operational Research 125, 93–112], I investigated some mathematical structure on scale elasticity and returns to scale. Soleimani-damaneh and Mostafaee [Soleimani-damaneh, M., Mostafaee, A., in press. A comment on “Returns to scale and scale elasticity in data envelopment analysis”. European Journal of Operational Research. doi:10.1016/j.ejor.2006.11.042] and Zhang [Zhang, B., in press. A Note on Fukuyama (2000). European Journal of Operational Research. doi:10.1016/j.ejor.2006.11.040] claim that some results, which are related to homogeneity, are incorrect. This note replies to their comments by demonstrating that Fukuyama (2000) results are still valid.     

The Penrose Polynomial of Binary Matroids

 A polynomial, called the Penrose polynomial, is studied for binary matroids, generalizing previous work on plane graphs. In particular, several formulae of Penrose are extended via the theory of isotropic systems. (Received 9 February, 2000; in revised form 26 June 2000)     

The Gray graph revisited

Certain graph‐theoretic properties and alternative definitions of the Gray graph, the smallest known cubic edge‐ but not vertex‐transitive graph, are discussed in detail. © 2000 John Wiley & Sons, Inc. J Graph Theory 35: 1–7, 2000     

A Hierarchy of Models for Two-Phase Flows

Summary. We derive a hierarchy of models for gas-liquid two-phase flows in the limit of infinite density ratio, when the liquid is assumed to be incompressible. The starting model is a system of nonconservative conservation laws with relaxation. At first order in the density ratio, we get a simplified system with viscosity, while at the limit we obtain a system of two conservation laws, the system of pressureless gases with constraint and undetermined pressure. Formal properties of this constraint model are provided, and sticky blocks solutions are introduced. We propose numerical methods for this last model, and the results are compared with the two previous models. Received April 20, 2000; accepted September 12, 2000 %%Online publication November 15, 2000 Communicated by Gérard Iooss     

Strong duality of the Monge–Kantorovich mass transfer problem in metric spaces

This paper studies the Monge–Kantorovich mass transfer (MT) problem on metric spaces and with an unbounded cost function. Conditions are given under which the strong duality condition holds; that is, MT and its dual MT are both solvable and their optimal values coincide. Received: 21 July 2000; in final form: 4 December 2000 / Published online: 18 January 2002     

Laufer's vanishing theorem for embedded CR manifolds

Let D be a sufficiently small open subset of a generic CR manifold in . We show that the cohomology groups are either zero or infinite dimensional. Received: 2 May 2000; in final form: 6 September 2000 / Published online: 28 February 2002     

A characterization of (γ, i)‐trees

We characterize trees with equal domination and independent domination numbers in terms of the sets of vertices of the tree which are contained in all its minimum dominating and minimum independent dominating sets. © 2000 John Wiley & Sons, Inc. J Graph Theory 34: 277–292, 2000     

Discontinuous Galerkin approximations for elliptic problems

In this article, we analyze a discontinuous finite element method recently introduced by Bassi and Rebay for the approximation of elliptic problems. Stability and error estimates in various norms are proven. © 2000 John Wiley & Sons, Inc. Numer Methods Partial Differential Eq 16: 365–378, 2000     

Smooth macro-elements based on Clough-Tocher triangle splits

Summary. Macro-elements of smoothness on Clough-Tocher triangle splits are constructed for all . These new elements are improvements on elements constructed in [11] in that (disproving a conjecture made there) certain unneeded degrees of freedom have been removed. Numerical experiments on Hermite interpolation with the new elements are included. Received September 6, 2000 / Revised version received November 15, 2000 / Published online July 25, 2001     

Families of Ternary -Nets Related to BCH-Codes

 A link between the theory of error-correcting codes and -nets leads to the efficient construction of two families of very good ternary nets. These have parameters (for all ) and (for all odd ). The underlying codes are cyclic codes. (Received 26 June 2000; in revised form 2 October 2000)     

The universality of equivariant complex bordism

We show that if A is an abelian compact Lie group, all A-equivariant complex vector bundles are orientable over a complex orientable equivariant cohomology theory. In the process, we calculate the complex orientable homology and cohomology of all complex Grassmannians. Received: 14 February 2000; in final form: 4 August 2000 / Published online: 19 October 2001