The combinatorial description via ribbon graphs of the moduli space of Riemann surfaces makes it possible to define combinatorial cycles in a natural way. Witten and Kontsevich first conjectured that these classes are polynomials in the tautological classes. We answer affirmatively to this conjecture and find recursively all the polynomials.

We affirmatively answer and generalize the question of Kubicka, Kubicki and Lehel (1999) concerning the path-pairability of high-dimensional complete grid graphs. As an intriguing by-product of our result we significantly improve the estimate of the necessary maximum degree in path-pairable graphs, a question originally raised and studied by Faudree, Gyárfás, and Lehel (1999). © 2017 Elsevier B...

Can phase separation be induced by strong electron correlations? We present a theorem that affirmatively answers this question in the Falicov-Kimball model away from half filling, for any dimension. In the ground state the itinerant electrons are spatially separated from the classical particles.

Tensions between religious freedoms and lesbian, gay, bisexual, trans queer (LGBTQ) rights have evolved from debates about sinful deviance to competing equality claims. There is a growing debate, originally in the US, but emerging UK, whether social workers, particularly those holding fundamentalist Christian beliefs, can deliver affirmative, anti-oppressive services LGBTQ people. This importan...

In this note, we give a new simple system of global parameters on the moduli space of rational functions, and clarify the relation to the parameters indicating location of fixed points and the indices at them. As a byproduct, we solve a conjecture of Milnor affirmatively.

A question of Barker and Larman asks whether convex bodies that contain a sphere of radius t in their interiors are uniquely determined by the volumes of sections by hyperplanes tangent to the sphere. We affirmatively solve this problem for convex polytopes.

An infinite word w is called self-shuffling, if w = ∏ ∞ i=0 UiVi = ∏ ∞ i=0 Ui = ∏ ∞ i=0 Vi for some finite words Ui, Vi. Harju [4] recently asked whether square-free self-shuffling words exist. We answer this question affirmatively.

Let X be a smooth, closed, oriented non-spin 4-manifold with even intersection form kE8 ⊕ nH . In this article we show that n ≥ |k| on X . Thus we confirm the 10 8 -conjecture affirmatively. As an application, we also give an estimate of intersection forms of spin coverings of non-spin 4-manifolds with even intersection forms.

Can we know that nothing is in itself both thinking and spatially extended?1 This was among the most central and divisive philosophical issues of the early modern period, one with obvious relevance not only to the theoretical understanding of mind and matter, but also to the practical prospects for immortality and, with it, divine sanctions for morality. While many important philosophers—includ...

Motivated by Kloeckner's result on the isometry group of quadratic Wasserstein space $\mathcal{W}_2\left(\mathbb{R}^n\right)$, we describe $\mathrm{Isom}\left(\mathcal{W}_p (E)\right)$ for all parameters $0 1$, solving problem affirmatively existence mass-splitting isometries.