We establish a general counting theory for nonattacking placements of chess pieces with unbounded straight-line moves, such as the queen, and we apply the theory to square boards. We show that the number of ways to place q nonattacking queens on a chessboard of variable size n but fixed shape is a quasipolynomial function of n. The period of the quasipolynomial is bounded by a function of the q...

Jeřábek showed that analytic propositional-logic deep-inference proofs can be constructed in quasipolynomial time from nonanalytic proofs. In this work, we improve on that as follows: 1) we significantly simplify the technique; 2) our normalisation procedure is direct, i.e., it is internal to deep inference. The paper is self-contained, and provides a starting point and a good deal of informati...

We rigorously justify the so-called one and one-half layer quasi-geostrophic model from the two layer model as the ratio of the depth of the bottom layer over that of the top layer approaches infinity. The effective dynamics is given by the classical barotropic quasi-geostrophic dynamics for the bottom layer without topography, and the one layer quasi-geostrophic dynamics with the stream functi...

Two properties concerning the space of differences of sublinear functions D(X) for a real Banach space X are proved. First, we show that for a real separable Banach space (X, ‖ · ‖) there exists a countable family of seminorms such that D(X) becomes a Fréchet space. For X = R this construction yields a norm such that D(R) becomes a Banach space. Furthermore, we show that for a real Banach space...

Since 2013 there have been several developments in algorithms for computing discrete logarithms in small-characteristic finite fields, culminating in a quasipolynomial algorithm. In this paper, we report on our successful computation of discrete logarithms in the cryptographically-interesting characteristic-three finite field F36·509 using these new algorithms; prior to 2013, it was believed th...

The present paper is devoted to the problem of (local) geodesic equivalence of Riemannian metrics and sub-Riemannian metrics on generic corank 1 distributions. Using Pontryagin Maximum Principle, we treat Riemannian and sub-Riemannian cases in an unified way and obtain some algebraic necessary conditions for the geodesic equivalence of (sub-)Riemannian metrics. In this way first we obtain a new...

A locally free resolution of a subscheme is by definition an exact sequence consisting of locally free sheaves (except the ideal sheaf) which has uniqueness properties like a free resolution. The purpose of this paper is to characterize certain locally Cohen-Macaulay subschemes by means of locally free resolutions. First we achieve this for arithmetically Buchsbaum subschemes. This leads to the...

In this paper, we consider the modified quasi-geostrophic equation ∂tθ + (u · ∇) θ + κΛ θ = 0 u = ΛRθ. with κ > 0, α ∈ (0, 1] and θ0 ∈ L(R). We remark that the extra Λ is introduced in order to make the scaling invariance of this system similar to the scaling invariance of the critical quasi-geostrophic equations. In this paper, we use Besov space techniques to prove global existence and regula...

Topological structure of fuzzy soft sets has been recently introduced by Tanay and Kandemir in [23]. In this paper, we introduce the notion of soft quasi-coincidence for fuzzy soft sets and we use this notion to characterize fundamental concepts of fuzzy soft topological spaces such as fuzzy soft closures, fuzzy soft bases and fuzzy soft continuity. Some basic properties of this concept are als...

We say that the quasi-norm Φ of a symmetric sequence space E has property P if, for all x, y ∈ E with 0 ≤ xn ≤ yn for all n, and xN < yN for some N , we have Φ (xn) < Φ (yn) . Simon [6] proved that if the Banach norm Φ has property P , then whenever An → A in the weak operator topology on the unitary matrix space CE and Φ(An)→ Φ(A), then An → A in the strong operator topology on CE . In this no...