Existence and embeddings of partial Steiner triple systems of order ten with cubic leaves

Denote the set of 21 non-isomorphic cubic graphs of order 10 by L. We first determine precisely which L is an element of L occur as the leave of a partial Steiner triple system, thus settling the existence problem for partial Steiner triple systems of order 10 with cubic leaves. Then we settle the embedding problem for partial Steiner triple systems with leaves L is an element of L. This second result is obtained as a corollary of a more general result which gives, for each integer v greater than or equal to 10 and each L is an element of L, necessary and sufficient conditions for the existence of a partial Steiner triple system of order v with leave consisting of the complement of L and v - 10 isolated vertices. (C) 2004 Elsevier B.V. All rights reserved.

Existence and uniqueness of Q-processes with a given finite μ-invariant measure

Let Q be a stable and conservative Q-matrix over a countable state space S consisting of an irreducible class C and a single absorbing state 0 that is accessible from C. Suppose that Q admits a finite mu-subinvariant measure in on C. We derive necessary and sufficient conditions for there to exist a Q-process for which m is mu-invariant on C, as well as a necessary condition for the uniqueness of such a process.

On the existence of solutions to boundary value problems on time scales

This work formulates existence theorems for solutions to two-point boundary value problems on time scales. The methods used include maximum principles, a priori bounds and topological degree theory.

Existence of solutions to some equilibrium problems

The concept of a monotone family of functions, which need not be countable, and the solution of an equilibrium problem associated with the family are introduced. A fixed-point theorem is applied to prove the existence of solutions to the problem.

Existence and multiplicity results for quasilinear elliptic equations

The goal of this paper is to study the multiplicity of positive solutions of a class of quasilinear elliptic equations. Based on the mountain pass theorems and sub-and supersolutions argument for p-Laplacian operators, under suitable conditions on nonlinearity f (x, s), we show the following problem: -Delta(p)u = lambda f(x,u) in Omega, u/(partial derivative Omega) = 0, where Omega is a bounded open subset of R-N, N >= 2, with smooth boundary, lambda is a positive parameter and Delta(p) is the p-Laplacian operator with p > 1, possesses at least two positive solutions for large lambda.

On the existence of uni-instantaneous Q-processes with a given finite mu-invariant measure

Let S be a countable set and let Q = (q(ij), i, j is an element of S) be a conservative q-matrix over S with a single instantaneous state b. Suppose that we are given a real number mu >= 0 and a strictly positive probability measure m = (m(j), j is an element of S) such that Sigma(i is an element of S) m(i)q(ij) = -mu m(j), j 0 b. We prove that there exists a Q-process P(t) = (p(ij) (t), i, j E S) for which m is a mu-invariant measure, that is Sigma(i is an element of s) m(i)p(ij)(t) = e(-mu t)m(j), j is an element of S. We illustrate our results with reference to the Kolmogorov 'K 1' chain and a birth-death process with catastrophes and instantaneous resurrection.

Existence of complementary pairs of proportionally balanced designs

Proportionally balanced designs (pi BDs) were introduced by Gray and Matters in response to a need for the allocation of markers of the Queensland Core Skills Test to have a certain property. Subsequent papers extended the theoretical results relating to such designs and provided further instances and general constructions. This work focused on designs comprising blocks of precisely two sizes, and when each variety occurs with one of precisely two possible frequencies. Two designs based on the set V of varieties are complementary if, whenever B is a block of one, then its complement with regard to the set V is a block of the other. Here we present necessary conditions for the existence of complementary pairs of such pi BDs and provide lists of some restricted parameter sets satisfying these necessary conditions. The lists are arranged according to the number of blocks. We demonstrate that not all of these parameter sets give rise to designs. However we establish by construction of the sets of blocks that, for every feasible number of blocks less than or equal to 100, with the possible exception of 63, there exists at least one pair of complementary pi BDs. We also investigate the conditions under which the complementary design can be isomorphic to the original design, and again provide a list of feasible parameters for pairs of such designs with at most 400 blocks.

Existence of solutions for p(x)-Laplacian problems on a bounded domain

In this paper we study the following p(x)-Laplacian problem: -div(a(x)&VERBAR;&DEL; u&VERBAR;(p(x)-2)&DEL; u)+b(x)&VERBAR; u&VERBAR;(p(x)-2)u = f(x, u), x ε &UOmega;, u = 0, on &PARTIAL; &UOmega;, where 1< p(1) &LE; p(x) &LE; p(2) < n, &UOmega; &SUB; R-n is a bounded domain and applying the mountain pass theorem we obtain the existence of solutions in W-0(1,p(x)) for the p(x)-Laplacian problems in the superlinear and sublinear cases. © 2004 Elsevier Inc. All rights reserved.

Moreton Bay, Queensland, Australia: An example of the co-existence of significant marine mammal populations and large-scale coastal development

Recent analyses assert that large marine vertebrates such as marine mammals are now 'functionally or entirely extinct in most coastal ecosystems'. Moreton Bay is a large diverse marine ecosystem bordering the fastest growing area in Australia. The human population is over 1.6 million and increasing yearly by between 10% and 13% with resultant impacts upon the adjoining marine environment. Nonetheless, significant populations of three species of marine mammals are resident within Moreton Bay and a further 14 species are seasonal or occasional visitors. This paper reviews the current and historical distributions and abundance of these species in the context of the current management regime and suggests initiatives to increase the resilience of marine mammal populations to the changes wrought by the burgeoning human population in coastal environments. (C) 2004 Elsevier Ltd. All rights reserved.

Confirmation of the existence of alloparasitoids in nature - host relationships of an Australian Coccophagus species that parasitizes mealy bugs

Heteronomous hyperparasitoids are parasitic wasps with sex-related host relationships that are unique to a group of genera in the chalcidoid family Aphelinidae. Females are primary parasitoids of various sedentary bugs (mainly, scale insects, mealy bugs, and whiteflies). Males, in contrast, are hyperparasitic, and they frequently develop at the expense of female conspecifics. Alloparasitoids constitute a special category of heteronomous hyperparasitoids, for their males never develop through female conspecifics. The existence of alloparasitic host relationships and the utility of the category 'alloparasitoid' have both been questioned. Here, we present results that confirm the existence of the alloparasitic way of life among heteronomous aphelinids. We investigated an undescribed species of Coccophagus (Hymenoptera: Aphelinidae), an Australian parasitoid that attacks the introduced lantana mealy bug, Phenacoccus parvus Morrison (Homoptera: Pseudococcidae), in Queensland. A year-long field survey regularly returned large numbers of female Coccophagus spec. near gurneyi individuals from P. parvus (total n = 4212), but only few males (n = 11). Males emerged from samples only when the encyrtid parasitoid Anagyrus diversicornis (Howard) (Hymenoptera: Encyrtidae) was present in samples in relatively high numbers. Laboratory oviposition tests confirmed that A. diversicornis is a male host and showed that males do not develop at the expense of conspecific females. Other studies show that males are attracted in numbers to virgin females held in cages above mealy bug-infested Lantana montevidensis (Spreng.) Briq. (Verbenaceae) in the field, demonstrating that they are common in the population as a whole. This confirms that the males need hosts other than conspecific females and that their usual hosts are present outside of the lantana/P. parvus system. The implications of these results for developing a realistic classification of heteronomous host relationships are discussed.