F responses were recorded from the surface of the tibialis muscle and medial aspect of the soleus muscle in 14 normal subjects. The persistence (that is the fraction of measurable F responses found with a series of supramaximal stimuli) and average F amplitudes (measured peak-to-peak and based on at least five F responses) were determined both at rest and with isometric contraction with the ank...

The study of fixed points of single-valued self-mappings or multivalued self-mappings satisfying certain contraction conditions has a great majority of results inmetric fixed point theory. All these results are mainly generalizations of Banach contraction principle. The Banach contraction principle guarantees the existence and uniqueness of fixed points of certain self-maps in complete metric s...

(5.1) The contraction mapping principle Let 0 ≤ r < 1. Let (X, d) be a nonempty metric space and f : X → X be a function that is a strict contraction, that is, for all x, y ∈ X, d(f(x), f(y)) ≤ rd(x, y). Then f has a unique fixed point. proof Existence of a fixed point: Let x0 ∈ X, and define the sequence (xn)n by: for all n ∈ N, xn+1 = f(xn). Then (xn)n is a Cauchy sequence: first, we have by ...

During sustained maximal voluntary contractions (MVCs), most fatigue occurs within the muscle, but some occurs because voluntary activation of the muscle declines (central fatigue), and some of this reflects suboptimal output from the motor cortex (supraspinal fatigue). This study examines whether supraspinal fatigue occurs during a sustained submaximal contraction of 5% MVC. Eight subjects sus...

We prove a type of converse of the Banach contraction mapping theorem for metric spaces: if X is a T 1 topological space and f : X ! X is a function with unique xed point a such that f n (x) converges to a for each x 2 X , then there exists a distance function d on X such that f is a contraction on the complete ultrametric space (X; d) with contractivity factor 1 2. We explore properties of the...

The annular scram combustor is a popular configuration for combined engines owing to its compatibility with both turbines and rockets ability withstand high flame temperatures. However, significant challenge associated this design the large width of combustor, which can make it difficult establish stabilize flames at supersonic speeds. To address issue, under conditions Tt = 1680 K, Pt 1.64 MPa...

Fibroplasia and angiogenesis are essential components of tissue repair when substantial tissue has been lost at a site of injury. Platelets and monocyte/macrophages accumulate at these sites and release a variety of growth factors that are thought to initiate and sustain the repair. Often the involved tissue contracts, a process that can markedly reduce the amount of fibroplasia and angiogenesi...

In this paper we introduce the notion of the fractional weak discrepancy of a poset, building on previous work on weak discrepancy in [5, 8, 9]. The fractional weak discrepancy wdF (P ) of a poset P = (V,≺) is the minimum nonnegative k for which there exists a function f : V → R satisfying (1) if a ≺ b then f(a) + 1 ≤ f(b) and (2) if a ‖ b then |f(a)− f(b)| ≤ k. We formulate the fractional weak...

In the last few years a large number of papers have appeared in the literature dealing with the weak convergence of iterates of contractions and strong convergence of their averages. The trend started with the Blum-Hanson Theorem [3]. The latest result in this direction is due to Akcoglu and Sucheston [ 1 ], [2]. The purpose of this paper is to give a simple, straightforward proof of the Adcogl...