In this paper, we show that the projection of a regular orthogonal array of strength t onto more than t factors consists of replicates of either a fractional factorial or a full factorial design of strength t, depending on the number of factors retained in the projection.

Kramers-Moyal coefficients provide a simple and easily visualized method with which to analyze nonlinear stochastic time series. One mechanism that can affect the estimation of the coefficients is geometric projection effects. For some biologically inspired examples, these effects are predicted and explored with a nonstochastic projection operator method and compared with direct numerical simul...

This article adds to the growing literature describing correlations between children's educational outcomes and family structure. Popular discussions have focused on the distinction between two-parent families and single-parent families. This article shows that educational outcomes for both types of children in blended families--stepchildren and their half-siblings who are the joint children of...

We propose a method of synthesizing computer-generated holograms of real-life three-dimensional (3-D) objects. An ordinary digital camera illuminated by incoherent white light records several projections of the 3-D object from different points of view. The recorded data are numerically processed to yield a two-dimensional complex function, which is then encoded as a computer-generated hologram....

We study L bounds on spectral projections for the Laplace operator on compact Riemannian manifolds, restricted to small frequency dependent neighborhoods of submanifolds. In particular, if λ is a frequency and the size of the neigborhood is O(λ−δ), then new sharp estimates are established when δ ≥ 1, while for 0 ≤ δ ≤ 1/2, Sogge’s estimates [17] turn out to be optimal. In the intermediate regio...

In the scattering theory framework, we point out a connection between the spectrum of the scattering matrix of two operators and the spectrum of the difference of spectral projections of these operators.

FINDING OPTIMIZED BOUNDING BOXES OF POLYTOPES IN D-DIMENSIONAL SPACE AND THEIR PROPERTIES IN K-DIMENSIONAL PROJECTIONS

The peaks that were reached in various equity markets by mid-July followed a sequence of gains dating back to the early 1980s, in most cases broken only by shortlived setbacks. While there were sound reasons to believe that these longer-term trends in various markets represented a response to improved fundamentals, for example, the drop in inflation (Blanchard, 1993), by the late 1990s many of ...

Let X be a simplicial complex on the vertex set V . The rational Leray number L(X) of X is the minimal d such that H̃i(Y ;Q) = 0 for all induced subcomplexes Y ⊂ X and i ≥ d. Suppose V = ⋃m i=1 Vi is a partition of V such that the induced subcomplexes X[Vi] are all 0-dimensional. Let π denote the projection of X into the (m − 1)-simplex on the vertex set {1, . . . ,m} given by π(v) = i if v ∈ Vi...

Given a finite set X ⊆ R we characterize the diagonals of self-adjoint operators with spectrum X. Our result extends the SchurHorn theorem from a finite dimensional setting to an infinite dimensional Hilbert space analogous to Kadison’s theorem for orthogonal projections [8, 9] and the second author’s result for operators with three point spectrum [7].