Existential monadic second order logic of undirected graphs: The Le Bars conjecture is false

In 2001, J.-M. Le Bars disproved the zero-one law (that says that every sentence from a certain logic is either true asymptotically almost surely (a.a.s.), or false a.a.s.) for existential monadic second order sentences (EMSO) on undirected graphs. He proved that there exists an EMSO sentence ? such that $\mathsf{P}(G_n??)$ does not converge as $n\to \infty$ (here, the probability distribution is uniform over the set of all graphs on the labeled set of vertices $\{1,\dots ,n\}$). In the same paper, he conjectured that, for EMSO sentences with 2 first order variables, the zero-one law holds. In this paper, we disprove this conjecture.     

Jordan operator algebras revisited

Jordan operator algebras are norm‐closed spaces of operators on a Hilbert space with for all . In two recent papers by the authors and Neal, a theory for these spaces was developed. It was shown there that much of the theory of associative operator algebras, in particular, surprisingly much of the associative theory from several recent papers of the first author and coauthors, generalizes to Jordan operator algebras. In the present paper we complete this task, giving several results which generalize the associative case in these papers, relating to unitizations, real positivity, hereditary subalgebras, and a couple of other topics. We also solve one of the three open problems stated at the end of our earlier joint paper on Jordan operator algebras.     

First and second moments for self‐similar couplings and Wasserstein distances

We study aspects of the Wasserstein distance in the context of self‐similar measures. Computing this distance between two measures involves minimising certain moment integrals over the space of couplings, which are measures on the product space with the original measures as prescribed marginals. We focus our attention on self‐similar measures associated to equicontractive iterated function systems consisting of two maps on the unit interval and satisfying the open set condition. We are particularly interested in understanding the restricted family of self‐similar couplings and our main achievement is the explicit computation of the 1st and 2nd moment integrals for such couplings. We show that this family is enough to yield an explicit formula for the 1st Wasserstein distance and provide non‐trivial upper and lower bounds for the 2nd Wasserstein distance for these self‐similar measures.     

UCT-Kirchberg algebras have nuclear dimension one

We prove that every Kirchberg algebra in the UCT class has nuclear dimension 1. We first show that Kirchberg 2-graph algebras with trivial _K0$K_0$ and finite _K1$K_1$ have nuclear dimension 1 by adapting a technique developed by Winter and Zacharias for Cuntz algebras. We then prove that every Kirchberg algebra in the UCT class is a direct limit of 2-graph algebras to obtain our main theorem.     

On mathematical problems as historically determined artifacts: Reflections inspired by sources from ancient China

Is a mathematical problem a cultural invariant, which would invariably give rise to the same practices, independent of the social groups considered? This paper discusses evidence found in the oldest Chinese mathematical text handed down by the written tradition, the canonical work The Nine Chapters on Mathematical Procedures and its commentaries, to answer this question in the negative. The Canon and its commentaries bear witness to the fact that, in the tradition for which they provide evidence, mathematical problems not only were questions to be solved, but also played a key part in conducting proofs of the correctness of algorithms.     

New large deviation results for some super-Brownian processes

We give large deviation results for the super-Brownian excursion conditioned to have unit mass or unit extinction time and for super-Brownian motion with constant non-positive drift. We use a representation of these processes by a path-valued process, the so-called Brownian snake for which we state large deviation principles.     

Transcendance de l'invariant modulaire en caractéristique finie

Transcendence of the modular invariant in finite characteristic Abstract. Let J be the Fourier expansion at infinity of the modular invariant j associated to a Drinfeld module of rank 2 defined on the algebraic closure of and t an element of the completion of . Then at least one of the two elements t, J(t) is transcendental over .

Received: October 22, 1997; in final form January 21, 1998     

Effects of Inorganic Salts on Micellization and Solubilization in an Aqueous Solution of Poly(ethylene oxide)/Poly(propylene oxide)/Poly(ethylene oxide) Triblock Copolymer

The effects of inorganic salts on micellization and solubilization of prednisolone in aqueous solution of poly(ethylene oxide)/poly(propylene oxide)/poly(ethylene oxide) triblock copolymer (Pluronic P85) were studied. The effect of inorganic salts on decrease in the cloud point and the critical micelle concentration (cmc) of Pluronic P85 was the order of Na₂HPO₄ > NaH₂PO₄ > NaCl > NaBr. Moreover, it was found that Pluronic P85 forms two kinds of micelles: monomolecular micelles and polymolecular micelles. The polymolecular micelle increased with increasing amount of added inorganic salts. Moreover, solubilization behavior is explained from the standpoint of salting out for prednisolone and association characteristics of Pluronic P85.     

Brézis-Gallouët-Wainger type inequality with a double logarithmic term in the Hölder space: Its sharp constants and extremal functions

We investigate the sharp constants in a Brézis-Gallouët-Wainger type inequality with a double logarithmic term in the Hölder space in a bounded domain in Rⁿ. Ibrahim, Majdoub and Masmoudi gave the sharp constant in the two-dimensional case. We make precise estimates to give the sharp constants, and pass to the case of higher dimensions n≥2. We can also show that the inequality with fixed constants including the sharp ones admits an extremal function under a suitable condition when the domain is a ball.     

Satisfactory graph partition,variants, and generalizations

The Satisfactory Partition problem asks for deciding if a given graph has a partition of its vertex set into two nonempty parts such that each vertex has at least as many neighbors in its part as in the other part. This problem was introduced by Gerber and Kobler [M. Gerber, D. Kobler, Algorithmic approach to the satisfactory graph partitioning problem, European Journal of Operational Research 125 (2000) 283–291] and studied further by other authors. In this paper we first review some applications and related problems. Then, we survey structural, complexity, and approximation results obtained for Satisfactory Partition and for some of its variants and generalizations. A list of open questions concludes this survey.