Let λ denote a singular cardinal. Zeman, improving a previous result of Shelah, proved that together with 2λ = λ+ implies ⋄S for every S ⊆ λ+ that reflects stationarily often.

In this paper, for a set S ⊆ λ+, a normal subideal of the weak approachability ideal is introduced, and denoted by I[S; λ]. We say that the ideal is fat if it contains a stationary set. It is proved:

1. if I[S; λ] is fat, then NSλ + ∣ S is non-saturated;

2. if I[S; λ] is fat and 2λ = λ+, then ⋄S holds;

3. implies that I[S; λ] is fat for every S ⊆ λ+ that reflects stationarily often;

4. it is relatively consistent with the existence of a supercompact cardinal that fails, while I[S; λ] is fat for every stationary S ⊆ λ+ that reflects stationarily often.

The stronger principle is studied as well.

The sap of Acer mono has been called ‘bone-benefit-water’ in Korea because of its mineral and sugar content. In particular, the calcium concentration of the sap of A. mono is 37·5 times higher than commercial spring water. In the current study, we examined whether A. mono sap could improve or prevent osteoporosis-like symptoms in a mouse model. Male mice (3 weeks old) were fed a low-calcium diet supplemented with 25, 50 or 100 % A. mono sap, commercial spring water or a high calcium-containing solution as a beverage for 7 weeks. There were no differences in weekly weight gain and food intake among all the groups. Mice that were given a low-calcium diet supplemented with commercial spring water developed osteoporosis-like symptoms. To assess the effect of sap on osteoporosis-like symptoms, we examined serum calcium concentration, and femur density and length, and carried out a histological examination. Serum calcium levels were significantly lower in mice that received a low-calcium diet supplemented with commercial spring water (the negative control group), and in the 25 % sap group compared to mice fed a normal diet, but were normal in the 50 and 100 % sap and high-calcium solution groups. Femur density and length were significantly reduced in the negative control and 25 % sap groups. These results indicate that a 50 % sap solution can mitigate osteoporosis-like symptoms induced by a low-calcium diet. We also examined the regulation of expression of calcium-processing genes in the duodenum and kidney. Duodenal TRPV6 and renal calbindin-D9k were up-regulated dose-dependently by sap, and the levels of these factors were higher than those attained in the spring water-treated control. The results demonstrate that the sap of A. mono ameliorates the low bone density induced by a low-calcium diet, most likely by increasing calcium ion absorption.

Semi-quantitative biochemical analyses by paper chromatography–densitometry and pH determinations of honeydew excreted by Nephotettix virescens (Distant) feeding on rice plants revealed higher free amino compound and sugar concentrations in honeydew excreted on the susceptible variety TN1 than on resistant ASD7 or P203. Furthermore, sap exudates from these three varieties, presumed to be mainly from xylem, as well as honeydew excreted on the resistant varieties were acidic, whereas honeydew from TN1 was predominantly basic. Since phloem sap in herbaceous plants usually gives an alkaline reaction whereas xylem sap is acidic, and because the former contains much higher concentrations of sugars and free amino acids than the latter, the biochemical evidence strongly suggests that Nephotettix virescens is primarily a xylem feeder on the resistant plants tested, but feeds predominantly on phloem sap in susceptible TNI.