This article argues for the use of contrasts to test a priori interaction hypotheses in 2-way analysis of variance designs. It focuses on 3 underused types of interaction contrast tests: a "matching" pattern for cognate levels of row and column factors; the "qualitative quadratic," for monotonic profiles of means in the same direction but with opposed concavities; and a "differential curvilinea...

If E = {ei} and F = {fi} are two 1-unconditional basic sequences in L1 with E r-concave and F p-convex, for some 1 ≤ r < p ≤ 2, then the space of matrices {ai,j} with norm ∥{ai,j}∥E(F ) = ∥∥∑ k ∥ ∑ l ak,lfl∥ek ∥∥ embeds into L1. This generalizes a recent result of Prochno and Schütt.

We consider a cooperative game defined by an economic lot sizing problem with concave ordering costs over a finite time horizon, in which each player faces demand for a single product in each period and coalitions can pool orders. We show how to compute a dynamic cost allocation in the strong sequential core of this game, i.e. an allocation over time that exactly distributes costs and is stable...

Let Ωn stand for the volume of the unit ball in Rn for n ∈ N. In the present paper, we prove that the sequence Ω 1/(n lnn) n is logarithmically convex and that the sequence Ω 1/(n lnn) n Ω 1/[(n+1) ln(n+1)] n+1 is strictly decreasing for n ≥ 2. In addition, some monotonic and concave properties of several functions relating to Ωn are extended and generalized.

We define the excedence set and the excedance word on Gr,n, generalizing a work of Ehrenborg and Steingrimsson and use the inclusion-exclusion principle to calculate the number of colored permutations having a prescribed excedance word. We show some symmetric properties as Log concavity and unimodality of a specific sequence of excedance words.

Energetic proton acceleration from concave targets, the fronts of which were irradiated with 40 fs laser pulses with an intensity of 10 W/cm, has been studied as a function of the depth of the concave shape. Three kinds of targets, a triangular concave target, a circular concave target and a parabolic concave target are considered. When the depth of the concave shape was varied, the peak proton...

This article examines the relationships between interaction (product) terms and curvilinear (quadratic) terms in regression models in which the independent variables are correlated. The author uses 2 substantive examples to demonstrate the following outcomes: (a) If the appropriate quadratic terms are not added to the estimated model, then the observed interaction may indicate a synergistic (of...