A generalization of a theorem of Turán

AbstractA set of points Y ⊂ X of an n-graph G = (X, Γ) is s-complete, s ≤ n, if each subset Z ⊂ Y with ∣ Z ∣ = s is contained in some edge of Γ.f(n, m, k, s) is the maximal number of edges of a graph G ∈ M(n, m, k, s), where M(n, m, k, s) is the family of all n-graphs on m points which contain no s-complete set of cardinality k.Turán [1] determined the function f(2, m, k, 2) and the structure of the corresponding maximal graphs. T. S. Motzkin and E. G. Straus [2] gave a different proof of Turán's result. J. W. Moon and L. Moser [3] settled the question for f(3, m, 4, 2).In this paper the function f(n, m, k, 2) and the structure of the corresponding maximal graphs are determined

Assessing servant leadership in athletic training clinical education

The purpose of this study was to examine 1) if students felt servant leadership was present within the Approved Clinical Instructors (ACI\u27s) of the programs surveyed; and 2) if those students who perceived their ACI\u27s to be servant leaders also had more student satisfaction, and greater student success. Based on the literature search conducted, there was little to no research found on servant leadership in athletic training clinical education, especially from the athletic training students\u27 perspective. Responses were obtained from 11 of the 27 Athletic Training Education Programs that were randomly selected for participation. Bivariate correlations were run on the thirty five student surveys that were collected and deemed complete. Regression analyses were run if a strong correlation was identified among any of the variables. Servant leadership had a strong influence on satisfaction in student athletic trainers whether from the ACI or the clinical site (n= 35, r=.877, p=.000; n= 35, r=.601, p=.000). Regression analysis was run showing that 83.4% of variance in student satisfaction is accounted for by variation in servant leadership qualities of approved clinical instructors (Y=--2.53+.583x). Student success, as defined in this study, was not influenced by servant leadership qualities regardless of the ACI or clinical affiliation (p\u3e.05) --document

Catalytic reactor and organometallic model studies of the mechanism of thiophene hydrodesulfurization

The reactivity of transition metal complexes of thiophene (Th) and 2,3- and 2,5-dihydrothiophenes (DHT) and catalytic reactor studies of thiophene and the dihydrothiophenes have been used to examine the mechanism for the hydrodesulfurization (HDS) of thiophene;Catalytic deuterium exchange of thiophene over HDS catalysts was modeled by the reaction of (pi)-thiophene complexes, CpRu(Th)(\u27+) (where Th = thiophene, 2, or 3 methylthiophene or 2,5-dimethylthiophene) in CD(,3)OD with OH(\u27-). The exchanges follow a rate law Rate = k CpRu(Th)(\u27+) OH(\u27-) which suggests a mechanism involving rate determining proton abstraction from the thiophene by OH(\u27-) followed by deuteration by the solvent. Rates of exchange for the different hydrogens in the complexes follow the trend H(,2,5) \u3e\u3e H(,3,4) \u3e methyl; the same order of reactivity which is observed over HDS catalysts;Reactor studies with thiophene and 2,3- and 2,5-DHT were done at 300(DEGREES) and 400(DEGREES)C over a Re/(gamma)-Al(,2)O(,3) HDS catalyst. At 400(DEGREES)C, the distributions of butane and 1 and 2-butenes were very similar. At 300(DEGREES) however, both 2,3- and 2,5-DHT gave butadiene as the major desulfurized product. Formation of thiophene and tetrahydrothiophene and the interconversion of the dihydrothiophenes was also observed over the catalysts. Deuterodesulfurization studies established that 2,5-DHT directly eliminates butadiene while butadiene formation from 2,3-DHT must involve several surface steps over the catalyst;Several reactions of the dihydrothiophenes over HDS catalysts were modeled using transition metal complexes of 2,3 and 2,5-DHT. The S-bound 2,3-DHT in W(CO)(,5)(2,3-DHT) is converted to tetrohydrothiophene upon treatment with HCl. When Fe(,2)(CO)(,9)2 is reacted in THF with 2,3-DHT though, no isolable Fe(CO)(,4)(2,3-DHT) complex is obtained, but small amounts of 2,5-DHT are observed by (\u271)H NMR. Reaction of 2,5-DHT with Fe(,2)(CO)(,9) does result in the formation of Fe(CO)(,4)(2,5-DHT), which readily eliminates butadiene

Endocrinological effects of high-dose Hypericum perforatum extract WS 5570 in healthy subjects

In this single-blind study, the effects of acute oral administration of high-dose Hypericum perforatum extract WS 5570 on the cortisol ( COR), adrenocorticotropic hormone ( ACTH), growth hormone (GH), and prolactin (PRL) secretions were examined in 12 healthy male volunteers. In a randomized order, the subjects received placebo or WS 5570 at several dosages (600, 900, and 1,200 mg) at 08.00 h on 4 different days. After insertion of an intravenous catheter, blood samples were drawn 1 h prior to administration of placebo or WS 5570 ( 600, 900, or 1,200 mg), at the time of administration, and during 5 h thereafter at intervals of 30 min. The serum concentrations of COR, GH, and PRL as well as the plasma levels of ACTH were determined in each blood sample by means of double antibody radioimmunoassay, fluoroimmunoassay, and chemiluminescence immunometric assay methods. The area under the curve value was used as parameter for COR, ACTH, GH, and PRL responses. Repeated-measures Anova revealed a significant stimulatory effect of WS 5570 on the ACTH secretion, whereas COR and PRL secretions were not significantly influenced. Moreover, there was a stimulatory peak of GH release 240 min after challenge with WS 5570 in some but not all volunteers, without reaching statistical significance in comparison with placebo. Mean arterial blood pressure and heart rate remained unchanged after administration of WS 5570. Apparently, WS 5570 at the dosages given in this study inconsistently causes endocrinological effects in healthy subjects by influencing central neurotransmitters. Copyright (C) 2004 S. Karger AG, Basel

Betaine, organic acids and inulin do not affect ileal and total tract nutrient digestibility or microbial fermentation in piglets

The study was conducted to investigate the effects of betaine alone or combined with organic acids and inulin on ileal and total tract nutrient digestibilities and intestinal microbial fermentation characteristics in piglets. In total, 24 four-week-old barrows with an average initial body weight of 6.7 kg were used in two consecutive experiments with 12 piglets each. Betaine, organic acids and inulin at a level of 0.2, 0.4 and 0.2%, respectively, or combinations of these supplements were added to the basal diet. The supplementation of betaine, organic acids and inulin or any of their combinations did not affect ileal and total tract nutrient digestibilities. The microbial fermentation products both at the ileal and faecal level were not affected by any of the treatments. In conclusion, combining betaine with organic acids and inulin did not have any associated effects on the variables that were measured