Minimal conditions on Clifford semigroup congruences

A known result in groups concerning the inheritance of minimal conditions on normal subgroups by subgroups with finite indexes is extended to semilattices of groups [E(S),Se,ϕe,f] with identities in which all ϕe,f are epimorphisms (called q partial groups). Formulation of this result in terms of q congruences is also obtained

MINIMAL CONDITIONS ON CLIFFORD SEMIGROUP CONGRUENCES

A known result in groups concerning the inheritance of minimal conditions on normal subgroups by subgroups with finite indexes is extended to semilattices of groups [E(S), S e , ϕ e, f ] with identities in which all ϕ e, f are epimorphisms (called q partial groups). Formulation of this result in terms of q congruences is also obtained

Global Diversity of Ascidiacea

The class Ascidiacea presents fundamental opportunities for research in the fields of development, evolution, ecology, natural products and more. This review provides a comprehensive overview of the current knowledge regarding the global biodiversity of the class Ascidiacea, focusing in their taxonomy, main regions of biodiversity, and distribution patterns. Based on analysis of the literature and the species registered in the online World Register of Marine Species, we assembled a list of 2815 described species. The highest number of species and families is found in the order Aplousobranchia. Didemnidae and Styelidae families have the highest number of species with more than 500 within each group. Sixty percent of described species are colonial. Species richness is highest in tropical regions, where colonial species predominate. In higher latitudes solitary species gradually contribute more to the total species richness. We emphasize the strong association between species richness and sampling efforts, and discuss the risks of invasive species. Our inventory is certainly incomplete as the ascidian fauna in many areas around the world is relatively poorly known, and many new species continue to be discovered and described each year

On semilattices of groups whose arrows are epimorphisms

A q partial group is defined to be a partial group, that is, a strong semilattice of groups S=[E(S);Se,ϕe,f] such that S has an identity 1 and ϕ1,e is an epimorphism for all e∈E(S). Every partial group S with identity contains a unique maximal q partial group Q(S) such that (Q(S))1=S1. This Q operation is proved to commute with Cartesian products and preserve normality. With Q extended to idempotent separating congruences on S, it is proved that Q(ρK)=ρQ(K) for every normal K in S. Proper q partial groups are defined in such a way that associated to any group G, there is a proper q partial group P(G) with (P(G))1=G. It is proved that a q partial group S is proper if and only if S≅P(S1) and hence that if S is any partial group, there exists a group M such that S is embedded in P(M). P epimorphisms of proper q partial groups are defined with which the category of proper q partial groups is proved to be equivalent to the category of groups and epimorphisms of groups

Maturation in the female eastern king prawn Penaeus plebejus from coastal waters of eastern Australia, and considerations for quantifying egg production in penaeid prawns

The trawl fishery for eastern king prawns, Penaeus plebejus, is of major commercial significance on the east coast of Australia. This paper describes the reproductive biology of female P. plebejus and presents new information relevant to quantifying egg production in penaeid prawn populations. The study concluded that the gonosomatic index (GSI) covaried with prawn size and was, therefore, likely to be a poor indicator of reproductive activity for penaeid prawn populations. GSI was also found to be not independent of ovary histological stage, moult stage, insemination status and parasitisation by bopyrid isopods. An histological description of ovarian development and the incidence of each stage of development is provided. This includes a description of the ovulation stage, which has not been previously recorded in naturally-occurring populations. Fifty percent of female P. plebejus were classed as mature at 42mm CL. The relationships between GSI, percent mature, and percent inseminated with size suggest that there is a decline in the capacity of large (> 60 mm CL) females to produce and fertilise eggs. The declines in both GSI and percent mature is indicative of ovarian senescence in large(o1d) females, which has not been recorded previously in penaeid prawns. An index which considers the relationships between the percent mature, fecundity and the percent inseminated with size, as well as the influence of mortality on the population, is put forward to determine the relative contribution of different size classes of females to egg production. The index suggests that females >50 mm CL contribute little to egg production, and that the bulk of eggs are produced by 35 to 48 mm CL females