Remark on weakly convergent cycles

Weakly Convergent Sequence Coefficient of Product Space

W. L. Bynum introduced the weakly convergent sequence coefficient WCS(A') of the Banach space X as WCS(Jf) = sup{M: for each weakly convergent sequence {xn} in X , there is some y e co({x«}) such that M • lim sup ||x,, y\\ < A({x„})} . We consider the weakly convergent sequence coefficient of the /^-product space Z = (fTjLi Xi)t of tne finite non-Schur space Xx, ... , X„ and show that WCS(Z) = ...

A remark on duality solutions for some weakly nonlinear scalar conservation laws

We investigate existence and uniqueness of duality solutions for a scalar conservation law with a nonlocal interaction kernel. Following [3], a notion of duality solution for such a nonlinear system is proposed, for which we do not have uniqueness. Then we prove that a natural definition of the flux allows to select a solution for which uniqueness holds.

Weakly Convergent Nonparametric Forecasting of Stationary Time Series

The conditional distribution of the next outcome given the infinite past of a stationary process can be inferred from finite but growing segments of the past. Several schemes are known for constructing pointwise consistent estimates, but they all demand prohibitive amounts of input data. In this paper we consider real-valued time series and construct conditional distribution estimates that make...

Remark on Taylor's Formula

does not contain any point of Er other than p. Cp(r]) is defined as in (5). From this it can be shown that Er has finite (n —1)-dimensional measure. Let us not assume now that r is large. We then write E = UjLxE^ where the E's are closed and their diameter is less than €. Then, by what has been shown before, if e is small enough Ef* has finite (w —1)-dimensional measure. Clearly ErCUjLxE?^'. Bu...

A Remark on a Remark by Macaulay or Enhancing Lazard Structural Theorem