Volume 57, Issue 5

The k-restricted domination number of a graph G is the minimum number d k such that for any subset U of k vertices of G, there is a dominating set in G including U and having at most d k vertices. Some new upper bounds in terms of order and degrees for this number are found.

We present here two new criteria for existence of a tame Harrison map of two formally real algebraic function fields over a fixed real closed field of constants. The first criterion (c.f. Theorem 2.5) shows that a square class group isomorphism is a tame Harrison map if it induces an isomorphism of the coproduct rings of residue Witt rings. The other result (c.f. Proposition 3.5) associates a tame Harrison map to an integral quaternion-symbol equivalence.

This paper continues the study begun in [GEROLDINGER, A.: On non-unique factorizations into irreducible elements II, Colloq. Math. Soc. János Bolyai 51 (1987), 723–757] concerning factorization properties of block monoids of the form ℬ(ℤn, S) where S = $$\{ \bar 1,\bar a\} $$ (hereafter denoted ℬa(n)). We introduce in Section 2 the notion of a Euclidean table and show in Theorem 2.8 how it can be used to identify the irreducible elements of ℬa(n). In Section 3 we use the Euclidean table to compute the elasticity of ℬa(n) (Theorem 3.4). Section 4 considers the problem, for a fixed value of n, of computing the complete set of elasticities of the ℬa(n) monoids. When n = p is a prime integer, Proposition 4.12 computes the three smallest possible elasticities of the ℬa(p).

In this paper, sufficient conditions are obtained for oscillation of all nontrivial, prepared, symmetric solutions of a class of nonlinear second order matrix differential equations of the form $$(P(t)Y')' + Q(t)F(Y) = 0, t \geqslant 0,$$ and $$Y'' + Q(t)F(Y) = 0, t \geqslant 0.$$

In this paper we introduce a new type of difference operator Δmn for fixed m, n ∈ ℕ. We define the sequence spaces ℓ∞(Δmn), c(Δmn) and c 0(Δmn) and study some topological properties of these spaces. We obtain some inclusion relations involving these sequence spaces. These notions generalize many earlier existing notions on difference sequence spaces.

In the present note we have obtained some basic results pertaining to the geometry of slant and semi-slant submanifolds of a Kenmotsu manifold.

We construct a 2-chromatic Steiner system S(2, 4, 100) in which every block contains three points of one colour and one point of the other colour. The existence of such a design has been open for over 25 years.