To approach experimentally the problem of contractility, stellate cells from rats were isolated and grown on a flexible silicone rubber substrate. Increases or decreases in the number of wrinkles of the silicone membrane beneath the cells that were easily observable by microscopy was employed as semi-quantitative measure of stellate cell motility. Contraction of stellate cells accompanied by di...

A graph H is a cover of a graph G if there exists a mapping φ from V (H) onto V (G) such that for every vertex v of G, φ maps the neighbours of v in H bijectively onto the neighbours of φ(v) in G. Negami conjectured in 1987 that a connected graph has a finite planar cover if and only if it embeds in the projective plane. This conjecture is not completely solved yet, but partial results due to A...

in this paper, we have dened and studied a generalized form of topological vectorspaces called s-topological vector spaces. s-topological vector spaces are dened by using semi-open sets and semi-continuity in the sense of levine. along with other results, it is provedthat every s-topological vector space is generalized homogeneous space. every open subspaceof an s-topological vector space is ...

Recently, Cho et al. [Y. J. Cho, R. Saadati, S. H. Wang, Common xed point theorems on generalized distance in ordered cone metric spaces, Comput. Math. Appl. 61 (2011) 1254-1260] dened the concept of the c-distance in a cone metric space and proved some xed point theorems on c-distance. In this paper, we prove some new xed point and common xed point theorems by using the distance in ordered con...

A very engrossing technique in theory of contractive mapping fixed point. number authors have defined type mappings on a cone metric spaces X which are generalization the well -known Banach contraction, and property that each such has unique The point can always be found by using Picard Iteration, opening with initial choice x0∈X. In this manuscript, we generalize, extend improve res...

In this paper, new concepts of monotonicity, namely (Φ, ρ)-monotonicity, (Φ, ρ)-pseudo-monotonicity and (Φ, ρ)-quasi-monotonicityare introduced for functions defined in Banach spaces. Series of necessary conditions are also given that relate (Φ, ρ)-invexity and generalized (Φ, ρ)-invexity of the function with (Φ, ρ)monotonicity and generalized (Φ, ρ)-monotonicity of its gradient.

Our theorems are on ordered cone metric spaces which are not necessarily normal. In the end, we describe the application of the main results in the integral equation.Although Du in [W‎. ‎S‎. ‎Du‎, ‎A note on cone metric fixed point theory and its equivalence‎, ‎Nonlinear Analysis‎, ‎72(2010) 2259-2261.]‎, ‎showed that the fixed point results in the setting of cone...

The well-known Banach’s fixed point theorem asserts that ifD X, f is contractive and X, d is complete, then f has a unique fixed point inX. It is well known that the Banach contraction principle 1 is a very useful and classical tool in nonlinear analysis. In 1969, Boyd and Wong 2 introduced the notion ofΦ-contraction. A mapping f : X → X on a metric space is called Φ-contraction if there exists...

Graph pyramids are often used for representing irregular image pyramids. For the 2D case, combinatorial pyramids have been recently defined in order to explicitly represent more topological information than graph pyramids. The main contribution of this work is the definition of pyramids of n-dimensional generalized maps. This extends the previous works to any dimension, and generalizes them in ...

Proof. First note that the map φ is uniquely determined by its components φ11, φ12, φ21, φ22. Indeed, by the universal property of the coproduct M1 ⊕ M2 we see that φ is uniquely determined by the maps φ∗1 := φ◦ι1 and φ∗2 := φ◦ι2. Then from the universal property of the product N1⊕N2 we see that the map φ∗1 is uniquely determined by the maps φ11 = π1 ◦φ∗1 and φ21 = π2 ◦ φ∗1. Similarly, φ∗2 is u...