Barr KP, Griggs M, Cadby T: Lumbar stabilization: Core concepts and current literature, part 1. Am J Phys Med Rehabil 2005;84:473–480. The factors that affect lumbar stability have been an area of extensive research. The clinical application of this research in the form of lumbar stabilization exercise programs has become a common treatment of low back pain and is also increasingly used by athl...

If d(x, y) denotes the distance between vertices x and y in a graph G, then an L(2, 1)-labeling of a graph G is a function f from vertices of G to nonnegative integers such that |f(x)−f(y)| ≥ 2 if d(x, y) = 1, and |f(x)−f(y)| ≥ 1 if d(x, y) = 2. Griggs and Yeh conjectured that for any graph with maximum degree ∆ ≥ 2, there is an L(2, 1)-labeling with all labels not greater than ∆. We prove that...

We are interested in maximizing the number of pairwise unrelated copies of a poset P in the family of all subsets of [n]. For instance, Sperner showed that when P is one element, ( n bn2 c ) is the maximum number of copies of P . Griggs, Stahl, and Trotter have shown that when P is a chain on k elements, 1 2k−1 ( n bn2 c ) is asymptotically the maximum number of copies of P . We prove that for ...

The four-card selection task (Wason, 1966) has been one of the most well-known tasks used in the literature on human reasoning. This article aimed to analyze this selection task by item response theory (Lord & Novick, 1968). Japanese undergraduates (N = 327 and 277 in Studies 1 and 2, respectively) responded to up to 10 types of representative Wason selection tasks, including the indicative tas...

Given a properly face two-coloured triangulation of the graph Kn in a surface, a Steiner triple system can be constructed from each of the colour classes. The two Steiner triple systems obtained in this manner are said to form a biembedding. If the systems are isomorphic to each other it is a self-embedding. In the following, for each k ≥ 2, we construct a self-embedding of the doubled affine S...

Motivated by the conjecture on the L(2, 1)-labelling number λ(G) of a graph G by Griggs and Yeh [2] and the question: “Is the upper bound (∆+3)/4 for λ(G) for chordal graphs with maximum degree ∆ is sharp?”, posed by Sakai [3], we study the bounds for λ(G) for chordal graphs in this paper. Let G be a chordal graph on n vertices with maximum degree ∆ and maximum clique number ω. We improve the u...

We conducted general shear experiments on synthetic mixtures of quartz and muscovite aggregates at 800 °C 1.5 GPa with 0.1 wt% H2O added in the Griggs apparatus to investigate role content microstructural evolution rheological properties aggregates. Muscovite varied between 0, 5, 10 25% muscovite. Mechanically, sample strengths decrease an increase content. At high strains grains align sub-para...

Shear deformation of a solid-fluid, two-phase material induces fluid segregation process that produces fluid-enriched bands and fluid-depleted regions, crystallographic preferred orientation (CPO) characterized by girdles [100] [001] axes sub-parallel to the shear plane cluster [010] sub-normal plane, namely AG-type fabric. Based on experiments aggregates olivine + basalt, flow theory CPO forma...

Increasing attention is being paid to the study of families of subsets of an nset that contain no subposet P . Especially, we are interested in such families of maximum size given P and n. For certain P this problem is solved for general n, while for other P it is extremely challenging to find even an approximate solution for large n. It is conjectured that for any P , the maximum size is asymp...