We study the stability of a-Browder-type theorems for orthogonal direct sums of operators. We give counterexamples which show that in general the properties (SBaw), (SBab), (SBw) and (SBb) are not preserved under direct sums of operators. However, we prove that if S and T are bounded linear operators acting on Banach spaces and having the property (SBab), then S ⊕ T has the property (SBab) if and only if σSBF− + (S ⊕ T ) = σSBF− + (S) ∪ σSBF− + (T ), where σSBF− + (T ) is the upper semi-B-Weyl spectrum of T . We obtain analogous preservation results for the properties (SBaw), (SBb) and (SBw) with extra assumptions.
Rice (Oryza sativa L.) plants were grown in nutríent solutíon containing concentrations of Cu vaiying from deficiency to toxicity [0.002-6.25 g(Cu) m"^]. Shoot contents of Cu, Mn and Fe were measured as well as the concentrations of plastocyanin (PC), plastoquinone (PQ) and cytochromes (cyt) f, 6553, 6-559up, and b- 559hp. While Cu concentration increased wilh increasing levels of metal in the solutíon, Mn and Fe concentrations progressively decreased after Cu treatments higher than 0.05 g m‘3. On a chlorophyll basis, the contents of PC and cyt/decreased after the 0.01 g(Cu) m'^ Cu treatonent, while the contents of cyt f>-559Lp and b- 559hp did not show any apparent conelatíon, and the PQ concentration sharply increased with increasing Cu toxicity. Membrane permeability and acid RNAse activity were enhanced with increasing Cu concentration.
This paper reviews past, current and likely future research on the fish haemogregarine, Haemogregarina bigemina Laveran et Mesnil, 1901. Recorded from 96 species of fishes, across 70 genera and 34 families, this broad distribution for H. bigemina is questioned. In its type hosts and other fishes, the parasite undergoes intraerythrocytic binary fission, finally forming mature paired gamonts. An intraleukocytic phase is also reported, but not from the type hosts. This paper asks whether stages from the white cell series are truly H. bigemina. A future aim should be to compare the molecular constitution of so-called H. bigemina from a number of locations to determine whether all represent the same species. The transmission of H. bigemina between fishes is also considered. Past studies show that young fish acquire the haemogregarine when close to metamorphosis, but vertical and faecal-oral transmission seem unlikely. Some fish haemogregarines are leech-transmitted, but where fish populations with H. bigemina have been studied, these annelids are largely absent. However, haematophagous larval gnathiid isopods occur on such fishes and may be readily eaten by them. Sequential squashes of gnathiids from fishes with H. bigemina have demonstrated development of the haemogregarine in these isopods. Examination of histological sections through gnathiids is now underway to determine the precise development sites of the haemogregarine, particularly whether merozoites finally invade the salivary glands. To assist in this procedure and to clarify the internal anatomy of gnathiids, 3D visualisation of stacked, serial histological sections is being undertaken. Biological transmission experiments should follow these processes.
High (HI, 200 W m'^) and low (LI, 30 W m"^) irradiance treatments on the cells of cyanobactenum Synechococcus elongatus Nfig., var. thermalis Geitl. strain KOVROV 1972/8 were perfonned in the presence of chloramphenicol (CAP), and with addition of DCMU and hydroxylamine (HA), respectively, at growth (56 °C) and low (20 °C) temperatures, to distínguish allegedly different mechanisms of PS 2 photoinactivation (PS 2 PI). At both temperatures HI caused a decline of Fy and Hill reaction activity (HRA) followed by degradation of Dl and to a lesser extent also D2 protein. Fq increased slowly during irradiance at 56 while at 20 ®C it quickly rose to constant level. Degradation of proteins was slowed at a lower temperature. The presence of DCMU during photoinhibition significantly blocked the Fq rise and also prevented PS 2 protein degradation at both temperatures. The course of PS 2 PI under LI resembled tlmt, observed at HI, but changes were much slower. During irradiation of the cells, in which oxygen evolving complex (OEC) was impaired by HA, we observed: (/) at least a ten-fold faster decline of PS 2 electron transport activity than in the cells vňth fimctional OEC under the same conditions; (2) an extensive degradation not only of Dl and D2, but also of the apoprotein of chlorophyll-protein CP43 {ACP43y, (3) almost complete inhibition of PS 2 protein degradation in the presence of DCMU. Thus under all conditions tested in vivo which do not affect the fimction of OEC, the fimction of OEC, PS 2 PI proceeds via the acceptor side and a fimctional impairment of OEC is necessary for induction of the donor side mechanism. When OEC is impaired (e.g. by HA) this mechanism can come in action.
In this paper we extend the notion of weak degree domination in graphs to hypergraphs and find relationships among the domination number, the weak edge-degree domination number, the independent domination number and the independence number of a given hypergraph.