Nonlinear dynamics of the heartbeat: I. The AV junction: Passive conduit or active oscillator?

Under physiologic conditions, the AV junction is traditionally regarded as a passive conduit for the conduction of impulses from the atria to the ventricles. An alternative view, namely that subsidiary pacemakers play an active role in normal electrophysiologic dynamics during sinus rhythm, has been suggested based on nonlinear models of cardiac oscillators. A central problem has been the development of a simple but explicit mathematical model for coupled nonlinear oscillators relevant both to stable and perturbed cardiac dynamics. We use equations describing an analog electrical circuit with an external d.c. voltage source (V₀) and two nonlinear oscillators with intrinsic frequencies in the ratio of 3:2, comparable to the SA node and AV junction rates. The oscillators are coupled by means of a resistor. 1:1 (SA:AV) phase-locking of the oscillators occurs over a critical range of V₀. Externally driving the SA oscillator at increasing rates results in 3:2 AV Wenckebach periodicity and a 2:1 AV block. These findings appear with no assumptions about conduction time or refractoriness. This dynamical model is consistent with the new interpretation that normal sinus rhythm may represent 1:1 coupling of two or more active nonlinear oscillators and also accounts for the appearance of an AV block with critical changes in a single parameter such as the pacing rate.     

125m Te (109.3 keV) stimulated emission and gamma lasers

Summary Proceeding from the drastic discrepancy between experimental data and theory, we show (contrary to other authors) that the relations between the Einstein's coefficients are true for transitions from any of the excited levels and theground state of the quantum system only. The relations connecting those coefficients are derived for transitions betweenany two states; the corresponding cross-sections are calculated and it is shown (contrary to other authors) that the stimulated emission cross-section may be large enough for the creation of gamma lasers. The new relation for Einstein's coefficients (and the corresponding cross-sections) are fundamentally different from those known so far (74 years after Einstein). The results are compared with experiment and the coincidence is very good. These investigations can lead to progress in the study of physical processes in star atmospheres. The author of this paper has agreed to not receive the proofs for correction.     

Convergence rates for the approximations of the solutions to algebraic Riccati Equations with unbounded coefficients: case of analytic semigroups

Summary Approximations schemes for the solutions of the Algebraic Riccati Equations will be considered. We shall concentrate on the case when the input operator is unbounded and the dynamics of the system is described by an analytic semigroup. The main goal of the paper is to establish the optimal rates of convergence of the underlying approximations. By optimal, we mean such approximations which would reconstruct the optimal regularity of the original solutions as well as the best approximation properties of the finite-dimensional subspaces. It turns out that, if one aims to obtain the optimal rates in the case of unbounded input operators, the choice of the approximations to the generator, as well as to the control operator, is very critical. While the convergence results hold with any consistent approximations, the optimal rates require a careful selection of the approximating schemes. Our theoretical results will be illustrated by several examples of boundary/point control problems where the optimal rates of convergence are achieved with the appropriate numerical algorithms.Research partially supported by the NSF Grant DMS-8301668 and by the AFOSR Grant AFOSR 89-0511     

中国股票市场风险的实证分析研究

本文从实证角度说明了上证指数和深证成份指数存在着GARCH现象 ,并建立了沪、深两市股指波动率的IGARCH(1,1) M模型与EGARCH(1,1) M模型。将估计的IGARCH(1,1) M模型与EGARCH(1,1) M模型比较得出 ,对上证指数的波动率 ,IGARCH(1,1) M模型与EGARCH(1,1) M模型的模拟效果基本相同 ,而对深证成份指数的波动率 ,IGARCH M模型要略优于EGARCH M模型。同时还对两市的股指收益的波动率进行了预测分析     

随机市场系数的M-V最优投资组合选择:一个鞅方法

通过引进凹函数U(x)以及等价鞅测度p^-，应用鞅的性质得到了随机市场系数情形下的M—V模型的最优投资策略以及有效前沿．     

Antiferromagnetism in double-layered perowskitic oxides SrLa2Fe2O7 and BaLa2Fe2O7

Il Nuovo Cimento D - Two double-layered perowskitic compounds have been investigated by XRD analysis and Mössbauer spectroscopy. The experimental data allow the conclusion that magnetization...     

The analytic continuation and the asymptotic behaviour of certain multiple zeta-functions I

We consider general multiple zeta-functions of multi-variables, including both Barnes multiple zeta-functions and Euler-Zagier sums as special cases. We prove the meromorphic continuation to the whole space, asymptotic expansions, and upper bound estimates. These results are expected to have applications to some arithmetical L-functions (such as of Hecke and of Shintani). The method is based on the classical Mellin-Barnes integral formula.     

Relationship between tetrahedron shape measures

Tetrahedron shape measures are used for evaluating the quality of tetrahedra in finite element meshes. Three shape measures, theminimum solid angle _min theradius ratio , and themean ratio , are discussed in this paper. A new formula for the computation of a solid angle of tetrahedron is derived. For different shape measures andv (with values 1), we establish a relationship between andv of the form wherec ₀,c ₁,e ₀, ande ₁ are positive constants. This means that if one measure approaches zero for a poorly-shaped tetrahedron, so does the other. Combined with the property that each measure attains a maximum value only for the regular tetrahedron, this means that the shape measures are equivalent.This work was partially supported by a grant from the Natural Sciences and Engineering Research Council of Canada.     

Mossbauer study of ferrite systems Co x Mn1−x Fe2O4 and Ni x Mn1−x Fe2O4

Mössbauer spectra of Co _x Mn_1?x Fe₂O₄ and Ni _x Mn_1?x Fe₂O₄ ferrites withx values ranging from 0·1 to 0·8 in steps of 0·1 have been recorded at room temperature. All spectra exhibit well-defined Zeeman hyperfine patterns. It has been observed that hyperfine field at Fe³⁺ nucleus increases more rapidly by nickel substitution than by cobalt substitution. This has been explained in terms of exchange interactions and cation distribution in the spinels. Hyperfine fields, isomer shifts and quadrupole splittings have been determined.