On the factor-thickness of regular graphs

For eachr-regular graphG, define a binary sequence(G) = ( ₁, ₂,..., _r-1) by _k = 0 ifG has ak-factor, and _k = 1 otherwise. A binary sequence = ( _i |i = 1, 2,...,r – 1) is said to be realizable if there exists anr-regular graphG such that(G) = . In this paper we characterize all binary sequences which are realizable.     

The asymptotic properties of the multichannel autoregressive spectral estimates

If we fit a-vector stationary time series using observationsx(1), ...,x(T) with AR models , then the spectral densityf() of {x(t)} can be estimated byf _k ^(T) ()=(2)^– A _k ^(T) (e ^–)^–1 _k ^(T) A _k ^(T) (e ^–i)^–, where are estimates of the variance matrix of(t), the residuals of the best linear prediction. By extending some results for the scalar case, this paper treats the asymptotic properties of the estimates in the multichannel case.     

Polarization density matrix forZ decay intoWff' with generalZWW couplings

We give the polarization density matrix ofZ andW for the decay processZ ⁰→Wff' with generalZWW couplings. The matrix elements are expressed in terms of kinematical invariants so that they can be readily used in \(p\bar p \to Z^0 W\) as well. Using these formulas, we analyze the possibilities of probing theZWW couplings through the decay of polarizedZ ⁰.     

Convergence of the fractional step Lax-Friedrichs scheme and Godunov scheme for the isentropic system of gas dynamics

A convergence theorem of the fractional step Lax-Friedrichs scheme and Godunov scheme for an inhomogeneous system of isentropic gas dynamics (1<5/3) is established by using the framework of compensated compactness. Meanwhile, a corresponding existence theorem of global solutions with large data containing the vacuum is obtained.Partially supported by U.S. NSF Grant # DMS-850403