Loss of stability in the magnetic Bénard problem

Received January 1999; Revised April 1999     

On the Blow-Up of Solutions of a Periodic Shallow Water Equation

Received April 28, 1999; accepted December 10, 1999     

A note on economic equilibrium and financial networks

Nagurney （1999） used variational inequalities to study economic equilibrium and financial networks and applied the modified projection method to solve the problem. In this paper, we formulate the problem as a nonlinear complementarity problem. The complementarity model is just the KKT condition for the model of Nagurney （1999）. It is a simpler model than that of Nagurney （1999）. We also establish sufficient conditions for existence and uniqueness of the equilibrium pattern, which are weaker than those in Nagurney （]999）. Finally, we apply a smoothing Newton-type algorithm to solve the problem and report some numerical results.     

Very ample line bundles on quasi-abelian varieties

Received January 27, 1999; in final form May 31, 1999 / Published online October 30, 2000     

On Kodaira singularities defined by $z^n=f(x,y)$

Received May 29, 1999 / in final form June 1, 1999 / Published online October 30, 2000     

Characteristic space-time estimates for the wave equation

Received August 16, 1999; in final form November 25, 1999 / Published online December 8, 2000     

Reine oder Angewandte Mathematik?

Ohne Zusammenfassung Eingegangen am 30. April 1999 / Angenommen am 20. Juli 1999     

Abundant Semigroups with a Multiplicative Adequate Transversal

The aim of this paper is to investigate abundant semigroups with a multiplicative adequate transversal. Some properties and characterizations for such semigroups are obtained. In particular, we establish the structure of this class of abundant semigroups in terms of left normal bands, right normal bands and adequate semigroups with some simple compatibility conditions. Finally, we apply this structure to some special cases. Received February 25, 1999, Revised November 22, 1999, Accepted December 9, 1999     

Surfaces elliptiques réelles et inégalité de Ragsdale-Viro

Sans résumé Received February 1, 1999; in final form August 16, 1999 / Published online July 3, 2000     

Dependence Relations Among the Shifts of a Multivariate Refinable Distribution

Refinable functions are an intrinsic part of subdivision schemes and wavelet constructions. The relevant properties of such functions must usually be determined from their refinement masks. In this paper, we provide a characterization of linear independence for the shifts of a multivariate refinable vector of distributions in terms of its (finitely supported) refinement mask. March 14, 1998. Dates revised: February 3, 1999 and August 6, 1999. Date accepted: November 16, 1999.     

Endodualisable and endoprimal finite double Stone algebras

The finite endodualisable double Stone algebras are characterised, and every finite endoprimal double Stone algebra is shown to be endodualisable. Received February 24, 1999; accepted in final form May 10, 1999.     

The Euler Characteristic Is the Unique Locally Determined Numerical Invariant of Finite Simplicial Complexes which Assigns the Same Number to Every Cone

We show that a proof given by Levitt in [L] suffices to prove the stronger theorem stated in the title. Received April 2, 1999, and in revised form October 6, 1999.     

On the truncated conjugate gradient method

In this paper, we consider the truncated conjugate gradient method for minimizing a convex quadratic function subject to a ball trust region constraint. It is shown that the reduction in the objective function by the solution obtained by the truncated CG method is at least half of the reduction by the global minimizer in the trust region. Received January 19, 1999 / Revised version received October 1, 1999?Published online November 30, 1999     

Existence and Multiplicity of Periodic Solutions of the Second-Order Differential Equations with Jumping Nonlinearities

We provide sufficient conditions for the existence and multiplicity of periodic solutions for Duffing's equations with jumping nonlinearities under resonance conditions. Received March 1, 1999, Revised September 16, 1999, Accepted February 1, 2000     

Normal functions and α-Normal Functions

This paper has studied two open questions about normal functions due to Lappan, and obtained two corresponding results for α-normal functions. Received April 5, 1999, Accepted June 9, 1999     

The list colouring constants

We present a conjecture concerning list colourings and prove a weakened form of it. © 1999 John Wiley & Sons, Inc. J Graph Theory 31: 149–153, 1999     

Variante molle du complexe cotangent

Sans résumé Received: 1 September 1999; in final form: 10 December 1999 / Published online: 29 April 2002     

Nontrivial solutions of elliptic semilinear equations¶at resonance

We find nontrivial solutions for semilinear boundary value problems having resonance both at zero and at infinity. Received: 14 January 1999 / Revised version: 17 May 1999     

Graphs of degree 4 are 5-edge-choosable

It is shown that every simple graph with maximal degree 4 is 5-edge-choosable. © 1999 John Wiley & Sons, Inc. J Graph Theory 32: 250–264, 1999     

On Rectifiable Curves in the Plane

This paper gives a formula of integral for the rectifiable curves in the plane by the Hausdorff fractional derivation and integral. Received August 10, 1999, Revised December 27, 1999, Accepted January 14, 2000