We are concerned with the first-order differential system of form $$\left\{ \begin{array}{ll} u'(t)+a(t)u(t)=\lambda b(t) f(v(t-\tau(t))), &t\in\mathbb{R},\\ v'(t)+a(t)v(t)=\lambda b(t)g(u(t-\tau(t))), \end{array} \right. $$ where $\lambda\in\mathbb{R}$~is a parameter. $a,b\in C(\mathbb{R},[0,+\infty))$ two $\omega$-periodic functions such that $\int_0^\omega a(t)\text{d}t>0$,~$\int_0^\omega b(...

Most noninvasive measures of diastolic function are made during left ventricular (LV) filling and are therefore subject to "pseudonormalization," because variation in left atrial (LA) pressure may confound the estimation of relaxation rate. Counterclockwise twist of the LV develops during ejection, but untwisting occurs rapidly during isovolumic relaxation, before mitral opening. We hypothesize...

This clinical investigation was designed to determine the effect of changes in loading patterns on left ventricular (LV) relaxation when heart rate was maintained constant. Not only were changes noted in total load or time in which load is changed, but also the contour of the ascending aortic systolic pressure wave. Twenty patients were studied. LV and ascending aortic pressure were measured by...

The influence of timing and magnitude of arterial wave reflection (WR) on afterload-dependent relaxation was evaluated in patients with a variety of heart diseases (group 1, age < 30 yr; group 2, age > 40 yr) and in dogs. While both femoral arteries were compressed (FC), WR returned just after the dicrotic notch (early diastole) in group 1 but before the dicrotic notch (late systole) in group 2...

Let $H$ be a bialgebra. $\sigma: H\otimes H\to A$ linear map, where $A$ is left $H$-comodule coalgebra, and an algebra with $H$-weak action $\triangleright$. $\tau: B$ $B$ right $\triangleleft$. In this paper, we improve the necessary conditions for two-sided crossed product $A\#^{\sigma} H~{^{\tau}\#} smash coproduct coalgebra $A\times H\times to form bialgebra (called double biproduct) such t...

‎We determine the‎ ‎form of polynomially bounded solutions to the Loewner differential ‎equation that is satisfied by univalent subordination chains of the‎ ‎form $f(z,t)=e^{int_0^t A(tau){rm d}tau}z+cdots$‎, ‎where‎ ‎$A:[0,infty]rightarrow L(mathbb{C}^n,mathbb{C}^n)$ is a locally‎ ‎Lebesgue integrable mapping and satisfying the condition‎ ‎$$sup_{sgeq0}int_0^inftyleft|expleft{int_s^t‎ ‎[A(tau)...

Let x ∈ (0, 1) be a real number with continued fraction expansion [a1 (x),a2 (x), a3(x), ⋯]. This paper is concerned the multifractal spectrum of convergence exponent {an (x)}n≥1 defined by $$\tau (x): = \inf \left\{{s \ge 0:\sum\limits_{n 1} {a_n^{- s}(x) < \infty}} \right\}.$$

Although present in many patients with heart failure and a normal ejection fraction, the role of isolated impairments in active myocardial relaxation in the genesis of elevated filling pressures is not well characterized. Because of difficulties in determining the effect of prolonged myocardial relaxation in vivo, we used a cardiovascular simulated computer model. The effect of myocardial relax...