Projective structure in 4-dimensional manifolds with positive definite metrics

This paper considers the situation on a 4-dimensional manifold admitting two metric connections, one of which is compatible with a positive definite metric, and which have the same unparametrised geodesics. It shows how, in many cases, the relationship between these connections and metrics can be found. In many of these cases, the connections are found to be necessarily equal. The general technique used is that based on a certain classification of the curvature tensor together with holonomy theory.     

A note on a Wiener process with measurement error

In this paper we give a closed form for the determinant and the inverse matrix of the covariance matrix of a Wiener process with measurement error. We will discuss its application in the analysis of degradation data for highly-reliable products.     

Some remarks on Kong-Liu’s conjecture on Lorentzian metrics

For a(1+3)-dimensional Lorentzian manifold(M,g),the general form of solutions of the Einstein field equations takes that of type I,II,or III.For type I,there is a known result in Gu(2007).In this paper,we try to find the necessary and sufficient conditions for the Lorentzian metric to take the form of types II and III,and we show how to construct the new coordinate system.     

The Completeness of the Bergman Distance of Planar Domains has a Local Character

It is shown that the property of completeness of the Bergman metric of a planar domain whose complement is not a polar set, is a local one.     

Cooperative Effects of Noise and Coupling on Stochastic Dynamics of a Membrane-Bulk Coupling Model

Based on a membrane-bulk coupling cell model proposed by Gomez-Marin et al. [ Phys. Rev. Lett. 98 （2007） 168303], the cooperative effects of noise and coupling on the stochastic dynamical behavior are investigated. For parameters in a certain region, the oscillation can be induced by the cooperative effect of noise and coupling. Whether considering the coupling or not, corresponding coherence resonance phenomena are observed. Furthermore, the effects of two coupling parameters, cell size L and coupling intensity k, on the noise-induced oscillation of membranes are studied. Contrary effects of noise are found in and out of the deterministic oscillatory regions.     

Stochastic averaging of n-dimensional non-linear dynamical systems subject to non-Gaussian wide-band random excitations

The averaged generalized Fokker-Planck-Kolmogorov (GFPK) equation for response of n-dimensional (n-d) non-linear dynamical systems to non-Gaussian wide-band stationary random excitation is derived from the standard form of equation of motion. The explicit expressions for coefficients of the fourth-order approximation of the averaged GFPK equation are given in series form. Conditions for convergences of these series are pointed out. The averaged GFPK equation is then reduced to that for 1-d dynamical systems derived by Stratonovich and compared with the closed form of GFPK equation for n-d dynamical systems subject to Poisson white noise derived by Di Paola and Falsone. Finally, this averaged GFPK equation is further reduced to that for quasi linear system subject to non-Gaussian wide-band stationary random excitation. Stationary probability density for quasi linear system subject to filtered Poisson white noise is obtained. Theoretical results for an example are confirmed by using Monte-Carlo simulation for different parameter values.     

Phenomenon of Resonance in a Two-Mode Laser with an Input Additive Signal

Exact formulas for the power spectrum and signal-to-noise ratio (SNR) with periodic additive signal are calculated in the linear system. Then the phenomenon of resonance is studied in detail. We show that resonance peak and suppressed valley exist in the curves of the SNR versus the coefficient of self-saturation, the net gain and the cross-coupling coefficient of the laser system.     

Metric Expansion from Microscopic Dynamics in an Inhomogeneous Universe

Theories with ingredients like the Higgs mechanism, gravitons, and inflatonfields rejuvenate the idea that relativistic kinematics is dynamicallyemergent. Eternal inflation treats the Hubble constant H as depending onlocation. Microscopic dynamics implies that H is over much smaller lengthsthan pocket universes to be understood as a local space reproduction rate.We illustrate this via discussing that even exponential inflation inTeV-gravity is slow on the relevant time scale. In our on small scalesinhomogeneous cosmos, a reproduction rate H depends on position. We therefore discuss Einstein-Strauss vacuoles and a Lindquist-Wheeler like lattice to connect the local rate properly with the scaling of an expanding cosmos. Consistency allows H to locally depend on Weyl curvature similar to vacuum polarization. We derive a proportionality constant known from Kepler's third law and discuss the implications for the finiteness of the cosmological constant.     

False Euro (FEUR) exchange rate correlated behaviors and investment strategy

We have searched for correlations and anticorrelations with respect to currencies as CHF, DKK, JPY, and USD in order to understand the EUR behavior. In order to do so we have invented a false euro (FEUR) dating back to 1993 and have derived simulated exchange rates of the FEUR. Within the Detrended Fluctuation Analysis (DFA) statistical method we have obtained the power law behavior describing the rms. deviation of the fluctuations as a function of time. We have compared the time-dependent exponent for these four exchange rates, and observe the role of the DEM, and the other currencies forming the EUR. A simple investment strategy based on the local DFA technique shows one can obtain appreciable gains, even taking into account some modest transaction fee. We compare the time dependent α exponent of the DFA for various exchange rates as in a correlation matrix for estimating respective influences. Received 31 August 2000