For a convex body B in R which is invariant under rotations around one coordinate axis and has a smooth boundary of bounded nonzero curvature, the lattice point discrepancy PB(t) (number of integer points minus volume) of a linearly dilated copy √ tB is estimated from below. On the basis of a recent method of K. Soundararajan [16] an Ω-bound is obtained that improves upon all earlier results of...

In this paper, we prove that directed cyclic hamiltonian cycle systems of the complete symmetric digraph, K∗ n, exist if and only if n ≡ 2 (mod 4) and n 6= 2p with p prime and α ≥ 1. We also show that directed cyclic hamiltonian cycle systems of the complete symmetric digraph minus a set of n/2 vertex-independent digons, (Kn− I)∗, exist if and only if n ≡ 0 (mod 4).

We introduce one of many classes of problems which can be defined in terms of 3-valued functions on the vertices of a graph G = (V, E) of the form f : V + { 1, 0, l}. Such a fknction is said to be a minus dominating function if the sum of its function values over any closed neighborhood is at least one. That is, for every t’ E V, ,f(N[r~])> 1, where N[a] consists of 1: and every vertex adjacent...

Bovine, human and rat serum albumins were defatted and palmitic acid, oleic acid and lauric acid added in various molar ratios. The binding of L-tryptophan to these albumins was measured at 20 degrees C in a 0.138 M salt solution at pH 7.4, by using an ultrafiltration technique, and analysed in terms of n, the number of available tryptophan-binding sites per albumin molecule, with apparent asso...

We have studied spacetime structures of static solutions in the n-dimensional Einstein-GaussBonnet-Maxwell-Λ system. Especially we focus on effects of the Maxwell charge. We assume that the Gauss-Bonnet coefficient α is non-negative and 4α̃/l ≤ 1 in order to define the relevant vacuum state. Solutions have the (n− 2)-dimensional Euclidean sub-manifold whose curvature is k = 1, 0, or −1. In Gauss...

We give many equivalent statements of Mahler’s generalization of the fundamental theorem of Thue. In particular, we show that the theorem of Thue–Mahler for degree 3 implies the theorem of Thue for arbitrary degree ≥ 3, and we relate it with a theorem of Siegel on the rational integral points on the projective line P(K) minus 3 points. Classification MSC 2010: 11D59; 11J87; 11D25

We show for every k ≥ 1 that the binomial tree of order 3k has a vertex-coloring with 2k+1 colors such that every path contains some color odd number of times. This disproves a conjecture from [1] asserting that for every tree T the minimal number of colors in a such coloring of T is at least the vertex ranking number of T minus one.

Suppose that (X, g) is a conformally compact (n+1)-dimensional manifold that is hyperbolic near infinity in the sense that the sectional curvatures of g are identically equal to minus one outside of a compact set K ⊂ X. We prove that the counting function for the resolvent resonances has maximal order of growth (n + 1) generically for such manifolds. This is achieved by constructing explicit ex...