Tripartite Ramsey numbers for paths

In this article, we study the tripartite Ramsey numbers of paths. We show that in any two‐coloring of the edges of the complete tripartite graph K(n, n, n) there is a monochromatic path of length (1 ? o(1))2n. Since R(P_2n+1,P_2n+1)=3n, this means that the length of the longest monochromatic path is about the same when two‐colorings of K_3n and K(n, n, n) are considered. © 2007 Wiley Periodicals, Inc. J Graph Theory 55: 164–174, 2007     

Convergence and nonlinear stability of the Lagrange-Galerkin method for the Navier-Stokes equations

Summary The Lagrange-Galerkin method is a numerical technique for solving convection — dominated diffusion problems, based on combining a special discretisation of the Lagrangian material derivative along particle trajectories with a Galerkin finite element method. We present optimal error estimates for the Lagrange-Galerkin mixed finite element approximation of the Navier-Stokes equations in a velocity/pressure formulation. The method is shown to be nonlinearly stable.     

Full ordering in the Shorrocks mobility sense of the semiring of monotone doubly stochastic matrices

In this paper, we investigate the ordering on a semiring of monotone doubly stochastic transition matrices in Shorrocks’ sense. We identify a class of an equilibrium index of mobility that induces the full ordering in a semiring, while this ordering is compatible with Dardanoni’s partial ordering on a set of monotone primitive irreducible doubly stochastic matrices.     

Asymmetric integral as a limit of generated Choquet integrals based on absolutely monotone real set functions

We introduce a generated Choquet integral with respect to absolutely monotone and sign stable set functions. Another type of integrals defined with respect to such a set function is obtained as a limit of an appropriate sequence of generated Choquet integrals.     

The negative cycles polyhedron and hardness of checking some polyhedral properties

Given a graph G=(V,E) and a weight function on the edges w:E→ℝ, we consider the polyhedron P(G,w) of negative-weight flows on G, and get a complete characterization of the vertices and extreme directions of P(G,w). Based on this characterization, and using a construction developed in Khachiyan et al. (Discrete Comput. Geom. 39(1–3):174–190, 2008), we show that, unless P=NP, there is no output polynomial-time algorithm to generate all the vertices of a 0/1-polyhedron. This strengthens the NP-hardness result of Khachiyan et al. (Discrete Comput. Geom. 39(1–3):174–190, 2008) for non 0/1-polyhedra, and comes in contrast with the polynomiality of vertex enumeration for 0/1-polytopes (Bussiech and Lübbecke in Comput. Geom., Theory Appl. 11(2):103–109, 1998). As further applications, we show that it is NP-hard to check if a given integral polyhedron is 0/1, or if a given polyhedron is half-integral. Finally, we also show that it is NP-hard to approximate the maximum support of a vertex of a polyhedron in ℝ ⁿ within a factor of 12/n.     

Symmetry preserving regularization with a cutoff

A Lorentz and gauge symmetry preserving regularization method is proposed in 4 dimensions based on a momentum cutoff. We use the conditions of gauge invariance or equivalently the freedom to shift the loop momentum to define the evaluation of the terms carrying even number of Lorentz indices, e.g. proportional to k _μ k _ν . The remaining scalar integrals are calculated with a four dimensional momentum cutoff. The finite terms (independent of the cutoff) are free of ambiguities coming from subtractions in non-trivial cases. Finite parts of the result are equal to that of dimensional regularization.     

Flow sharing and bankruptcy games

We discuss the relationship between bankruptcy problems and flow sharing problems, respectively, and show that the latter type of problem can be interpreted as a generalization of the former. The corresponding flow sharing game is convex, hence we can use the converse reduced game property to characterize the nucleolus and the constrained egalitarian solution. Our main contribution is thus to introduce the nucleolus as an alternative solution concept for flow sharing problems, and to offer a game-theoretic interpretation of the traditional egalitarian solution.     

How to avoid using the Regularity Lemma: Pósa’s conjecture revisited

In this paper we investigate how the use of the Regularity Lemma and the Blow-up Lemma can be avoided in certain extremal problems of dense graphs. We present the ideas for the following well-known Pósa conjecture on the square of a Hamiltonian cycle. In 1962 Pósa conjectured that any graph G of order n and minimum degree at least contains the square of a Hamiltonian cycle. In an earlier paper we proved this conjecture with the use of the Regularity Lemma-Blow-up Lemma method for n≥n₀ where n₀ is very large. Here we present another proof (and a general method) that avoids the use of the Regularity Lemma and thus the resulting n₀ is much smaller.     

Generation of a stable surface concentration of amino groups on silica coated onto titanium substrates by the plasma enhanced chemical vapour deposition method

This report describes the amino functionalisation of the surface of plasma enhanced chemically vapour deposited silica films (PECVD-SiO₂), which were coated onto titanium substrates. Amino groups were linked to PECVD-SiO₂ via 3-aminpropyl triethoxysilane (APTES). We showed that the APTES functionalised PECVD-SiO₂ surfaces contained a high packing density of amino groups (67-92 NH₂ groups per nm²), indicative of a multilayered and highly cross-linked APTES film. 65-66% of the original surface concentration of APTES was retained on the PECVD-SiO₂ surface after incubation under physiological conditions, indicating that APTES films are relatively stable on PECVD-SiO₂ in these environments. The stability of the amino groups obtained on PECVD-SiO₂ in this study is much higher compared to other hydroxyl-bearing materials, such as titanium. Therefore, PECVD-SiO₂ films may find use as functional biomaterial coatings and as intermediate adhesion layers in silanisation processes.     

Volumetric properties and electrolytic conductances of aqueous ternary mixtures of hydrogen chloride and some transition metal chlorides at 25°C

Densities and electrolytic conductances of hydrochloric acid and ternary aqueous solutions of HCl with manganese(II), copper(II), and cadmium(II) chlorides, respectively, have been measured from about 0.2 m to ternary saturation points at several constant molalities of the salt, MnCl₂, or that of HCl for the system MnCl₂–HCl–H₂O as well as at constant total molal ionic strength of I=10.0 for all the three ternary systems (Mn, Cu, Cd)Cl₂–HCl–H₂O at 25°C. The molality dependence of the calculated volume of mixing changes V _m and of the specific conductances are discussed on the basis of the different degrees of complex formation of the bivalent transition metal chlorides in the presence of excess amounts of chloride anions in the form of HCl. It was to be seen from the present results that even the manganese(II) chloride, which behaves as a fairly strong electrolyte in dilute aqueous solutions, is considerably complexed at high concentrations of HCl, with the degree of complexation of the cations increasing in the sequence Mn^2–2–2–.Part of this publication was presented at the XIX International Conference on Solution Chemistry (XIX ICSC), Lund, Sweden, August 15–18, 1988.