Search results for " Fixed"
showing 10 items of 248 documents
An Integral Version of Ćirić’s Fixed Point Theorem
2011
We establish a new fixed point theorem for mappings satisfying a general contractive condition of integral type. The presented theorem generalizes the well known Ciric's fixed point theorem [Lj. B. Ciric, Generalized contractions and fixed point theorems, Publ. Inst. Math. 12 (26) (1971) 19-26]. Some examples and applications are given.
Fixed point theorems on ordered metric spaces and applications to nonlinear elastic beam equations
2012
In this paper, we establish certain fixed point theorems in metric spaces with a partial ordering. Presented theorems extend and generalize several existing results in the literature. As application, we use the fixed point theorems obtained in this paper to study existence and uniqueness of solutions for fourth-order two-point boundary value problems for elastic beam equations.
Normal forms of hyperbolic logarithmic transseries
2021
We find the normal forms of hyperbolic logarithmic transseries with respect to parabolic logarithmic normalizing changes of variables. We provide a necessary and sufficient condition on such transseries for the normal form to be linear. The normalizing transformations are obtained via fixed point theorems, and are given algorithmically, as limits of Picard sequences in appropriate topologies.
Attractors/Basin of Attraction
2020
It is a controversial issue to decide who first coined the term “attractor”. According to Peter Tsatsanis, the editor of the English version of Prédire n’est pas expliquer, it was René Thom who first introduced such a term. It is necessary, however, to remember that Thom thought that it was first introduced by the American mathe- matician Steven Smale, “although Smale says it was Thom that coined the neolo- gism “attractor”“(Tsatsanis 2010: 63–64 n. 20). From this point of view, Bob Williams expressed a more cautious opinion by saying that “the word “attractor” was invented by these guys, Thom and Smale” (Cucker and Wong 2000: 183). But other mathematicians are of the opinion that the term …
Fluorescence In Situ Hybridization (FISH) on Formalin-Fixed Paraffin-Embedded (FFPE) Tissue Sections
2011
Fluorescence In Situ Hybridization (FISH) is a powerful technique for localizing specific DNA targets directly in the fixed tissue or cells. Bacterial artificial chromosome (BAC) as well as commercial probes, which could be supplied ready for use or concentrated and must be diluted following the manufacturers instructions, can be used. The technique requires 2 days, as an overnight incubation of the FISH probes is needed for optimal hybridization. The critical steps include deparaffinization of tissue sections, optimal pretreatment (target retrieval and protein digestion), and probe hybridization. In this chapter, the described FISH protocol provides a methodology for analyzing the cytogene…
MR3098564 Reviewed Al-Thagafi, M. A.; Shahzad, Naseer Krasnosel'skii-type fixed-point results. J. Nonlinear Convex Anal. 14 (2013), no. 3, 483–491. (…
2014
The Krasnosel'skii fixed-point theorem is a powerful tool in dealing with various types of integro-differential equations. The initial motivation of this theorem is the fact that the inversion of a perturbed differential operator may yield the sum of a continuous compact mapping and a contraction mapping. Following and improving this idea, many fixed-point results were proved.\\ The authors present significant and interesting contributions in this direction. In particular, they give the following main theorem: \begin{theorem} Let $M$ be a nonempty bounded closed convex subset of a Banach space $E$, $S:M \to E$ and $T:M \to E$. Suppose that \begin{itemize} \item[(a)] $S$ is 1-set-contractive…
Stochastic sensitivity of bull and bear states
2021
We study the price dynamics generated by a stochastic version of a Day–Huang type asset market model with heterogenous, interacting market participants. To facilitate the analysis, we introduce a methodology that allows us to assess the consequences of changes in uncertainty on the dynamics of an asset price process close to stable equilibria. In particular, we focus on noise-induced transitions between bull and bear states of the market under additive as well as parametric noise. Our results are obtained by combining the stochastic sensitivity function (SSF) approach, a mixture of analytical and numerical techniques, due to Mil’shtein and Ryashko (1995) with concepts and techniques from th…
Rotation correlation time as a measure of microviscosity of excited state isomerization reactions of three cyanine dyes in n-alcohol solutions
1994
Abstract Rotation correlation times of three chemically similar cyanine dyes of different sizes in n -alcohol solutions have been recorded at several temperatures by using polarized picosecond spectroscopy. For all three dyes the linear temperature dependencies of τ or on η/ T were observed to be independent of solvent up to viscosities of about 60 cP. The rotational motion of the dyes proceeds at much slower rates than the excited state isomerization in viscous solutions of the same fluidity. Isomerization seems to depend on special solvent-induced changes of the force field of the reactant and clearly proceeds faster, especially for the two larger dyes, than predicted by Kramers' theory a…
Translational and rotational molecular motion in supercooled liquids studied by NMR and forced Rayleigh scattering
1994
It has been shown that translational diffusion coefficients, Dt, in the supercooled van der Waals liquids, orthoterphenyl, phenolphthaleindimethylether, and salol, have a weaker temperature dependence than the shear viscosity, η, at T ≲ 1.2Tg and can be described by Dt ∼ η−χ with χ < 1 whereas Dr ∼ η−1 applies for the mean rotational diffusion coefficients, Dr, down to the glass transition temperature, Tg. This apparent decoupling of translational and rotational motion has been discussed in relation with possible anomalous short time diffusion, spatial heterogeneity, and cooperative molecular motions close to Tg.
Process-independent strong running coupling
2016
We unify two widely different approaches to understanding the infrared behaviour of quantum chromodynamics (QCD), one essentially phenomenological, based on data, and the other computational, realised via quantum field equations in the continuum theory. Using the latter, we explain and calculate a process-independent running-coupling for QCD, a new type of effective charge that is an analogue of the Gell-Mann--Low effective coupling in quantum electrodynamics. The result is almost identical to the process-dependent effective charge defined via the Bjorken sum rule, which provides one of the most basic constraints on our knowledge of nucleon spin structure. This reveals the Bjorken sum to be…