Optical reference geometry for stationary and static dynamics

Attention is drawn to the advantages of representing dynamical behavior in a stationary or static background spacetime in terms of a fixed reference 3-geometry that differs from the usual one by a certain conformal rescaling factor. The resulting Riemannian metric may be appropriately described as the optical geometry in recognition of the fact that line-of-sight trajectories are faithfully represented within it as geodesic, at least in the strictly static case for which such lines-of-sight are unambiguously defined. (In more general stationary examples the geodesies represent what amounts to the result of a cancellation between the Coriolis-type effects that would cause a physical light path to deviate to one side or the other depending on the sense of propagation.) The application to the particular case of the Schwarzschild solution is discussed: In this example the optical 3-geometry has a throat that occurs not on the horizon (as in the directly projected 3-geometry) but at the radius of the circular null geodesic orbit.     

Noise-induced global asymptotic stability

We prove analytically that additive and parametric (multiplicative) Gaussian distributed white noise, interpreted in either the Itô or Stratonovich formalism, induces global asymptotic stability in two prototypical dynamical systems designated as supercritical (the Landau equation) and subcritical, respectively. In both systems without noise, variation of a parameter leads to a switching between a single, globally stable steady state and multiple, locally stable steady states. With additive noise this switching is mirrored in the behavior of the extrema of probability densities at the same value of the parameter. However, parametric noise causes a noise-amplitude-dependent shift (postponement) in the parameter value at which the switching occurs. It is shown analytically that the density converges to a Dirac delta function when the solution of the Fokker-Planck equation is no longer normalizable.     

直接键连原子间的NMR偶合常数的自然杂化轨道研究V.~(13)C-~(13)C和~(13)C-~(31)P核自旋偶合常数~1J_(CC)和~1J_(CP)

在前文工作的基础上，结合ＭＮＤＯ／ＥＨＭＯ分子轨道方法和自然杂化轨道方法，具体计算了ＣＣ键和ＣＰ键的核自旋偶合常数．计算结果表明，１ＪＣＣ和１ＪＣＰ主要由成键原子的轨道杂化作用和键极性这两种结构因素所决定．为从简单价键理论角度解释和计算１ＪＣＣ和１ＪＣＰ值提供了简便直观的方法．     

On fitting rotating bodies to exterior gravitational fields

Some inequalities have to be satisfied if there is to exist a fluid source for a given exterior gravitational field. In the case of the Kerr solution one of the inequalities presented here is much more restrictive than those obtained by Boyer [1]. However, our conditions do not exclude the possibility of a fluid source for the Kerr spacetimes.     

Electrical coupling effects in an ultrasonic transducer array

Ultrasonic imaging devices often use transducer arrays for sampling the incoming acoustic field and converting it into electrical signals. After some convenient processing (amplification, dephasing, summing, etc), the electrical signals are used to modulate the brightness of a cathode ray tube (crt) monitor on which the ultrasonic image becomes visible. The quality of the imaging apparatus depends critically on the transducer array design and implementation.

Each individual transducer would, ideally, produce an electrical signal related exclusively to the ultrasonic field arriving at its surface; the reciprocal would also be true for transmission. In all practical cases, however, numerous effects lead to some coupling between nearby transducers, especially for very narrow transducers. The subsequent perturbations may be described as a narrowing of the radiation (or reception) pattern of the individual transducers, with respect to the theoretical predictions. To understand the mechanism for these couplings and to minimize them, their possible origins have been systematically studied. One of the most important sources of coupling is electrical leakage, which is reported here. Since no simple analytical calculation can be performed, diagrams have been established that enable evaluation of the electrical coupling against the dimensional characteristics of the array. Some means for reducing this coupling are suggested and comparative experimental results are given.     

Self-reported fatigue and health complaints of refuse collectors

Central European Journal of Operations Research - Working as a refuse collector is a physically strenuous activity. The aim of the investigations in this work was to evaluate the fatigue and...     

Properties of stationary solutions of a generalized Tjon-Wu equation

A generalized version of the Tjon-Wu equation is considered. Solutions of this equation are functions with values in the space of probability measures on [0,∞). We prove that the stationary solution μ_∗ of the equation has the following property: Either μ_∗ is supported at one point or suppμ_∗=[0,∞). Moreover we show that in the second case the distribution function of μ_∗ is continuous. Some open questions are discussed.