Stability Implications of Bendixson’s Criterion

This note presents a proof that the omega limit set of a solution to a planar system satisfying the Bendixson criterion is either empty or is a single equilibrium. The proof involves elementary techniques which should be accessible to senior undergraduates and graduate students

Role of Histone Acetylation in the Stimulatory Effect of Valproic Acid on Vascular Endothelial Tissue-Type Plasminogen Activator Expression

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Impaired distal nephron acidification in chronically phosphate depleted rats

Renal tubular bicarbonate reabsorption and acidification were evaluated in phosphate depleted rats (PD) and controls. After 33 days of phosphate depletion, urine pH of PD rats ( N =5, 6.36±0.15) was significantly higher than control ( N =5, 5.64±0.09, P <0.005) following an NH 4 Cl load. Urinary titratable acid of PD rats (9.6±1.8) was significantly reduced compared to control (117.2±19.7 μEq/3 h, P <0.001), whereas NH 4 + excretion was not different. The plasma HCO 3 − thresholds at which bicarbonaturia occurred (approximately 25 mEq/l) were identical in controls and phosphate depleted rats during isotonic bicarbonate infusion. The higher urine pH of phosphate depleted rats following NH 4 Cl administration was not due to low urinary phosphate as 3-day phosphate depleted rats could normally acidify urine after NH 4 Cl (pH=5.86±0.09, N =6 vs. control 5.87±0.08, N =6, P =N.S.) despite urinary phosphate excretion as low as in 33-day PD rats. These data indicate the presence of impaired distal tubular acidification in chronically phosphate depleted rats.Peer Reviewedhttp://deepblue.lib.umich.edu/bitstream/2027.42/47445/1/424_2004_Article_BF00584277.pd

Phase Asymptotic Semiflows, Poincaré's Condition, and the Existence of Stable Limit Cycles

AbstractA concept of phase asymptotic semiflow is defined. It is shown that any Lagrange stable orbit at which the semiflow is phase asymptotic limits to a stable periodic orbit. A Lagrange stable solution of aC1differential equation is considered. When the second compound of the variational equation with respect to this solution is uniformly asymptotically stable and the omega limit set contains no equilibrium, then the semiflow is phase asymptotic at the orbit of the solution and the omega limit set is a stable periodic orbit. Analogous results are obtained for discrete semiflows and periodic differential equations

On existence and completeness of conservation laws associated with elementary beam theory

SIGLETIB: RN 1909 (1985,3) / FIZ - Fachinformationszzentrum Karlsruhe / TIB - Technische InformationsbibliothekDEGerman

Asymmetric synthesis of corsifuran a by an enantioselective oxazaborolidine reduction

Corsifuran A has been prepared in an enantiomerically pure form for the first time by an asymmetric reduction procedure, allowing confirmation of the absolute stereochemistry of the natural product as (R)