ABSTRACT
We present a theorem that allows one to simplify the linear stability analysis of periodic and quasiperiodic nonlinear regimes in N-particle mechanical systems with different kinds of discrete symmetry. This theorem suggests a decomposition of the linearized system arising in the standard stability analysis into a number of subsystems whose dimensions can be considerably less than the dimension of the full system. As an example of such a simplification, we discuss the stability of bushes of modes (invariant manifolds) for the Fermi-Pasta-Ulam chains and prove another theorem about the maximal dimension of the above-mentioned subsystems.
ABSTRACT
The diastolic function of left and right parts of the heart using left and right mechanocardiogram method was investigated in 69 male patients with coronary artery disease and preceding myocardial infarction and in 18 normal patients. Nine patients were in angina class I, 28 were in class II, 32 were in class III. Forty-seven patients were in heart failure class II and 22 were in class III. The duration of isometric relaxation and atrium wave in left and right mechanocardiograms was more, and rapid filling wave was less in patients after myocardial infarction than in the control group. The duration of isometric relaxation and of atrium wave in left mechanocardiogram was more, and the duration of rapid filling wave was less in patients with heart failure class III than in patients in class II. The duration of isometric relaxation was more and the duration of rapid filling wave was less in right mechanocardiogram in patients with heart failure class III than in patients in class II. The diastolic abnormalities correlate more with the severity of heart failure than the angina severity. The diastolic abnormalities in right mechanocardiogram were found in patients without clinical manifestations of right ventricle failure.
