PURPOSE This study tests if running economy differs in minimal shoes versus standard running shoes with cushioned elevated heels and arch supports and in forefoot versus rearfoot strike gaits. METHODS We measured the cost of transport (mL O(2)·kg(-1)·m(-1)) in subjects who habitually run in minimal shoes or barefoot while they were running at 3.0 m·s(-1) on a treadmill during forefoot and rea...

An order bounded disjointness preserving operator T on an Archimedean vector lattice is algebraic if and only if the restriction of Tn! to the vector sublattice generated by the range of Tm is strongly diagonal, where n is the degree of the minimal polynomial of T and m is its ‘valuation’.

Let L/K be a separable field extension of degree 6. An 1867 theorem of P. Joubert asserts that if char(K) 6= 2 then L is generated over K by an element whose minimal polynomial is of the form t + at + bt + ct+ d for some a, b, c, d ∈ K. We show that this theorem fails in

where |B| is the length of second fundamental form. |B|2 = 4|H|2 − 2K, where H is the mean curvature and K is the Gauss curvature. The curvature of minimal surfaces is nonpositive. Then we exam what is still hold for some minimal surface theorems if extending the minimal condition H ≡ 0 to the surfaces with K ≤ 0 and (1). In 2001, F. Xavier [18] has the following theorem: Theorem [Xavier]. Let ...

Let G be a generalized dicyclic group with identity 1. An inverse closed subset S of G∖{1} is called minimal if 〈S〉=G and there exists some s∈S such that 〈S∖{s,s−1}〉≠G. In this paper, we characterize distance-regular Cayley graphs Cay(G,S) under the condition minimal.

This lecture introduces the Jordan canonical form of a matrix — we prove that every square matrix is equivalent to a (essentially) unique Jordan matrix and we give a method to derive the latter. We also introduce the notion of minimal polynomial and we point out how to obtain it from the Jordan canonical form. Finally, we make an encounter with companion matrices. 1 Jordan form and an applicati...