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

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

Nicholson’s blowflies equation with a distributed delay

on the occasion of their retirement ABSTRACT. For the Nicholson’s blowflies equation with a distributed delay Z t N(t) ˙ = −δN(t) + p N(s)e h(t) −aN(s) dsR(t, s), t ≥ 0, we obtain existence, positiveness and permanence results for solutions with positive initial conditions. We prove that all nonoscillatory about the positive equilibrium N ∗ solutions tend to N ∗. In the case δ < p < δe there are no slowly oscillating solutions and the positive equilibrium is globally asymptotically stable. Some generalizations to other nonlinear models of population dynamics with a distributed delay in the recruitment term and a nondelayed linear death term are considered

Blood Pressure Management in Afferent Baroreflex Failure JACC Review Topic of the Week

Afferent baroreflex failure is most often due to damage of the carotid sinus nerve because of neck surgery or radiation. The clinical picture is characterized by extreme blood pressure lability with severe hypertensive crises, hypotensive episodes, and orthostatic hypotension, making it the most difficult form of hypertension to manage. There is little evidence-based data to guide treatment. Recommendations rely on understanding the underlying pathophysiology, relevant clinical pharmacology, and anecdotal experience. The goal of treatment should be improving quality of life rather than normalization of blood pressure, which is rarely achievable. Long-acting central sympatholytic drugs are the mainstay of treatment, used at the lowest doses that prevent the largest hypertensive surges. Short-acting clonidine should be avoided because of rebound hypertension, but can be added to control residual hypertensive episodes, often triggered by mental stress or exertion. Hypotensive episodes can be managed with countermeasures and short-acting pressor agents if necessary. (C) 2019 by the American College of Cardiology Foundation

Orthostatic Hypotension : Management of a Complex, But Common, Medical Problem

Orthostatic hypotension (OH), a common, often overlooked, disorder with many causes, is associated with debilitating symptoms, falls, syncope, cognitive impairment, and risk of death. Chronic OH, a cardinal sign of autonomic dysfunction, increases with advancing age and is commonly associated with neurodegenerative and autoimmune diseases, diabetes, hypertension, heart failure, and kidney failure. Management typically involves a multidisciplinary, patient-centered, approach to arrive at an appropriate underlying diagnosis that is causing OH, treating accompanying conditions, and providing individually tailored pharmacological and nonpharmacological treatment. We (1) propose a novel streamlined pathophysiological classification of OH; (2) review the relationship between the cardiovascular disease continuum and OH; (3) discuss OH-mediated end-organ damage; (4) provide diagnostic and therapeutic algorithms to guide clinical decision making and patient care; (5) identify current gaps in knowledge and try to define future research directions. Using a case-based learning approach, specific clinical scenarios are presented highlighting various presentations of OH to provide a practical guide to evaluate and manage patients who have OH

A Phase I, Single Ascending Dose Study of Cimaglermin Alfa (Neuregulin 1β3) in Patients With Systolic Dysfunction and Heart Failure.

A first-in-human, phase 1, double blind, placebo-controlled, single ascending dose study examined the safety, tolerability, and exploratory efficacy of intravenous infusion of a recombinant growth factor, cimaglermin alfa, in patients with heart failure and left ventricular systolic dysfunction (LVSD). In these patients on optimal guideline-directed medical therapy, cimaglermin treatment was generally tolerated except for transient nausea and headache and a dose-limiting toxicity was noted at the highest planned dose. There was a dose-dependent improvement in left ventricular ejection fraction lasting 90 days following infusion. Thus, cimaglermin is a potential therapy to enhance cardiac function in LVSD and warrants further investigation