Here we develop a minimal model of the cell actomyosin cortex by forming a quasi-2D cross-linked filamentous actin (F-actin) network adhered to a model cell membrane and contracted by myosin thick filaments. Myosin motors generate both compressive and tensile stresses on F-actin and consequently induce large bending fluctuations, which reduces their effective persistence length to <1 μm. Over a...

*Correspondence: [email protected] Department of Mathematics and Applied Physics, Rzeszów University of Technology, P.O. Box 85, Rzeszów, 35-959, Poland Abstract Recently, Wardowski (Fixed Point Theory Appl. 2012:94, 2012) introduced a new concept of F-contraction and proved a fixed point theorem which generalizes the Banach contraction principle. Following this direction of research, in this...

The purpose of this paper is to present a new approach to study the existence of fixed points for multivalued F-contraction in the setting of modular metric spaces. In establishing this connection, we introduce the notion of multivalued F-contraction and prove corresponding fixed point theorems in complete modular metric space with some specific assumption on the modular. Then we apply our resu...

Let H be a real Hilbert space, C a nonempty closed convex subset of H , and T : C → C a mapping. Recall that T is nonexpansive if ‖Tx−Ty‖ ≤ ‖x− y‖ for all x, y ∈ C. A point x ∈ C is called a fixed point of T provided Tx = x. Denote by F(T) the set of fixed points of T , that is, F(T) = {x ∈ C : Tx = x}. Recall that a self-mapping f : C → C is a contraction on C, if there exists a constant α∈ (0...

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...

(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 ...

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...

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...