On the existence of certain SOLS with Holes

Existence of an Algebra Norm on Certain Subalgebras of C(X)

ON THE EXISTENCE OF PERIODIC SOLUTIONS FOR CERTAIN NON-LINEAR DIFFERENTIAL EQUATIONS

Here we consider some non-autonomous ordinary differential equations of order n and present some results and theorems on the existence of periodic solutions for them, which are sufficient conditions, section 1. Also we include generalizations of these results to vector differential equations and examinations of some practical examples by numerical simulation, section 2. For some special cases t...

On frame self-orthogonal Latin squares of type hm1n

An SOLS (self orthogonal Latin square) of order v with ni missing subSOLS (holes) of order hi (1 ≤ i ≤ k), which are disjoint and spanning (i.e. ∑k i=1 nihi = v), is called a frame SOLS and denoted by FSOLS(h n1 1 h n2 2 · · ·hk k ). In this paper, we prove that: if h ≥ 7, m ≥ 4, n ≥ 4 and n = 6, then there exists an FSOLS(h1); an FSOLS(h1) exists if h ≥ 7, h = 8, 12, 28 and m ≥ 17.

M ar 2 00 3 Non - Existence of Black Holes in Certain Λ < 0 Spacetimes

Assuming certain asymptotic conditions, we prove a general theorem on the non-existence of static regular black holes in spacetimes with a negative cosmological constant, given that the fundamental group of space is infinite. We use this to rule out the existence of regular negative mass AdS black holes with Ricci flat scri. For any mass, we also rule out a class of conformally compactifiable s...

2 00 2 Non - Existence of Black Holes in Certain Λ < 0 Spacetimes

Assuming certain asymptotic conditions, we prove a general theorem on the non-existence of static regular black holes in spacetimes with a negative cosmological constant, given that the fundamental group of space is infinite. We use this to rule out the existence of regular negative mass AdS black holes with Ricci flat scri. For any mass, we also rule out a class of conformally compactifiable s...