Dynamics of heart rate

Heart rate oscillates on several different time scales and has long-term variability in the form of 1/f noise. The physiological control of heart rate is briefly reviewed, and several typical patterns of heart rate variability, in health and sickness, are described. Considered briefly are some possible dynamical mechanisms for heart rate variability.     

Measurement of frequency differences between visible laser lines up to 170GHz using metal-insulator-metal point contact diodes

Frequency differences of up to 170 GHz between a cw dye laser and a krypton laser at 568 nm were measured by mixing laser and microware radiation with a metalinsulator-metal point contact diode. Beat signals are well above noise and there is still great potential for improvement when better microwave oscillators are used. From the measurements reported it follows that the diode can be used for determining still higher frequency differences of visible laser radiation.     

Local convergence of the (exact and inexact) iterative aggregation method for linear systems and Markov operators

Summary. The iterative aggregation method for the solution of linear systems is extended in several directions: to operators on Banach spaces; to the method with inexact correction, i.e., to methods where the (inner) linear system is in turn solved iteratively; and to the problem of finding stationary distributions of Markov operators. Local convergence is shown in all cases. Convergence results apply to the particular case of stochastic matrices. Moreover, an argument is given which suggests why the iterative aggregation method works so well for nearly uncoupled Markov chains, as well as for Markov chains with other zero-nonzero structures. Received May 25, 1991/Revised version received February 23, 1994     

Equivalence of conditions for convergence of iterative methods for singular equations

Equivalence is shown between different conditions for convergence of iterative methods for consistent singular systems of linear equations on Banach spaces. These systems appear in many applications, such as Markov chains and Markov processes. The conditions considered relate the range and null spaces of different operators.     

Stark broadening of visible neutral helium lines in a plasma

Side-on observations of the visible spectrum emitted by a helium plasma generated in a wall-stabilized arc are reported. Electron densities range from 0.2 to 1.3 × 10²²m^-3 and electron temperatures vary from 10,000 to 20,000 K. Most of the seventeen measured lines are “isolated” at the conditions of the experiment. Here, “isolated” refers to quantum levels which are non-degenerate even in the presence of perturbing fields. Electron densities derived from the Stark-widths of the isolated lines agree to within 15% of the values determined from Hβ and from the quasi-degenerate He(I) lines at 4471 and 4921 Å. Similar agreement is observed for the static-ion Stark broadening parameters. However, at the conditions of this experiment, the static-ion approximation is not valid near the center of some of the isolated lines. The observation of ion-dynamic effects in neutral isolated lines is reported here for the first time. In the isolated lines, the measured ion-dynamic effects are reasonably consistent with calculations based on an adiabatic “unified” theory for the ion perturbers. A simple parametric expression closely approximates the ion-dynamic contribution to the half-width of isolated lines. Hydrogenic (non-isolated) neutral helium lines exhibit a large discrepancy with theoretical profiles near the line center, where ion-dynamic effects are important.     

Morera and mean-value type theorems in the hyperbolic disk

Some Morera and mean-value type theorems are proved in the hyperbolic disk. Partially supported by NSF grants DMS-9000619 and CDR-8803012. Partially supported by NSF grants DMS-8703072 and DMS-9000619, and DGI-CYT grant PB 89-0311.     

An experimental investigation of the pressure and concentration dependence of muonic Coulomb capture and cascade in gases

Muonic Coulomb capture ratios and x-ray intensity patterns in four binary mixtures of the gases N₂, Ne, Ar, Kr, and Xe have been measured at three atomic ratios. An influence of the concentration has been established. The Lyman series intensity patterns of pure N₂, Ne, Ar, Kr, and Xe were measured at pressures between 0.4 and 51 bar and found to depend on the pressure. Possible explanations are discussed.     

Properties of the skeleton of aggregates grown on a Cayley tree

We discuss and analyze a family of trees grown on a Cayley tree, that allows for a variable exponent in the expression for the mass as a function of chemical distance, M(l)l ^dl . For the suggested model, the corresponding exponent for the mass of the skeleton,d _l ^s , can be expressed in terms ofd _l asd _l ^s = 1,d _l d _l ^c = 2;d _l ^s = d _l –1,d ₁ d _l ^c = 2, which implies that the tree is finitely ramified ford _l 2 and infinitely ramified whend _l 2. Our results are derived using a recursion relation that takes advantage of the one-dimensional nature of the problem. We also present results for the diffusion exponents and probability of return to the origin of a random walk on these trees.