This paper is devoted to finding out some realization of the concept of
b
-metric like space. First, we attain a fixed point for two fuzzy mappings satisfying a suitable requirement of ...contractiveness. Subsequently, we apply such a result to graphic contractions. Also, we attain a unique solution for a system of integral equations, and lastly we give an application to ensure that there exists a common bounded solution of a suitable functional equation in dynamic programming.
In this paper, inspired by Hussain
et al.
(Fixed Point Theory Appl. 2015:17,
2015
), we study a modified Mann method to approximate strongly fixed points of strict pseudo-contractive mappings. In ...(Hussain
et al.
in Fixed Point Theory Appl. 2015:17,
2015
) it is shown that the same algorithm converges strongly to a fixed point of a nonexpansive mapping under suitable hypotheses on the coefficients. Here the assumptions on the coefficients are different, as well as the techniques of the proof.
The purpose of this paper is to define generalized ( α β - ψ ) -contraction in the context of F -metric space and obtain some new fixed point results. As applications, we solve a nonlinear neutral ...differential equation with an unbounded delay ϑ / ( ι ) = − ρ 1 ( ι ) ϑ ( ι ) + ρ 2 ( ι ) L ( ϑ ( ι − ς ( ι ) ) ) + ρ 3 ( ι ) ϑ / ( ι − ς ( ι ) ) , where ρ 1 ( ι ) , ρ 2 ( ι ) are continuous, ρ 3 ( ι ) is continuously differentiable and ς ( ι ) > 0 , for all ι ∈ R and is twice continuously differentiable.
Abstract
The effect of stellar multiplicity on planetary architecture and orbital dynamics provides an important context for exoplanet demographics. We present a volume-limited catalog of up to 300 ...pc of 66 stars hosting planets and planet candidates from Kepler, K2, and TESS with significant Hipparcos-Gaia proper motion anomalies, which indicates the presence of companions. We assess the reliability of each transiting planet candidate using ground-based follow-up observations, and find that the TESS Objects of Interest (TOIs) with significant proper anomalies show nearly four times more false positives due to eclipsing binaries compared to TOIs with marginal proper anomalies. In addition, we find tentative evidence that orbital periods of planets orbiting TOIs with significant proper anomalies are shorter than those orbiting TOIs without significant proper anomalies, consistent with the scenario that stellar companions can truncate planet-forming disks. Furthermore, TOIs with significant proper anomalies exhibit lower Gaia differential velocities in comparison to field stars with significant proper anomalies, suggesting that planets are more likely to form in binary systems with low-mass substellar companions or stellar companions at wider separation. Finally, we characterize the three-dimensional architecture of LTT 1445 ABC using radial velocities, absolute astrometry from Gaia and Hipparcos, and relative astrometry from imaging. Our analysis reveals that LTT 1445 is a nearly flat system, with a mutual inclination of ∼2.°88 between the orbit of BC around A and that of C around B. This coplanarity may explain why multiple planets around LTT 1445 A survive in the dynamically hostile environments of this system.
Dielectric nanoantennas have recently emerged as an alternative solution to plasmonics for nonlinear light manipulation at the nanoscale, thanks to the magnetic and electric resonances, the strong ...nonlinearities, and the low ohmic losses characterizing high refractive-index materials in the visible/near-infrared (NIR) region of the spectrum. In this frame, AlGaAs nanoantennas demonstrated to be extremely efficient sources of second harmonic radiation. In particular, the nonlinear polarization of an optical system pumped at the anapole mode can be potentially boosted, due to both the strong dip in the scattering spectrum and the near-field enhancement, which are characteristic of this mode. Plasmonic nanostructures, on the other hand, remain the most promising solution to achieve strong local field confinement, especially in the NIR, where metals such as gold display relatively low losses.
We present a nonlinear hybrid antenna based on an AlGaAs nanopillar surrounded by a gold ring, which merges in a single platform the strong field confinement typically produced by plasmonic antennas with the high nonlinearity and low loss characteristics of dielectric nanoantennas. This platform allows enhancing the coupling of light to the nanopillar at coincidence with the anapole mode, hence boosting both second- and third-harmonic generation conversion efficiencies. More than one order of magnitude enhancement factors are measured for both processes with respect to the isolated structure.
The present results reveal the possibility to achieve tuneable metamixers and higher resolution in nonlinear sensing and spectroscopy, by means of improved both pump coupling and emission efficiency due to the excitation of the anapole mode enhanced by the plasmonic nanoantenna.
F-contractions have inspired a branch of metric fixed point theory committed to the generalization of the classical Banach contraction principle. The study of these contractions and α-fuzzy mappings ...in b-metric spaces was attempted timidly and was not successful. In this article, the main objective is to obtain common α-fuzzy fixed point results for F-contractions in b-metric spaces. Some multivalued fixed point results in the literature are derived as consequences of our main results. We also provide a non-trivial example to show the validity of our results. As applications, we investigate the solution for fuzzy initial value problems in the context of a generalized Hukuhara derivative. Our results generalize, improve and complement several developments from the existing literature.
The transient optical response of multiresonant all‐dielectric nanoantennas via a combination of broadband ultrafast reflectivity experiments and nonlinear optics nanoscale modeling is studied. ...Ultrafast all‐optical control of the reflectivity is demonstrated in variably sized Al.18Ga.82As nanoantennas over four distinct Mie resonances (including Fano‐like resonances), spanning a broad spectral range, from the red to the near‐infrared. A spatially inhomogeneous dynamical model, which accounts for diffusion of the photogenerated carriers inside the semiconductor, is introduced and exploited to isolate the physical phenomena leading to the overall transient response, namely, Drude plasma formation and Pauli blocking following band filling and thermo‐optical effect. The results pave the way to the development of multiwavelength all‐optically reconfigurable filters for next‐generation ultrafast add/drop multiplexing.
All‐dielectric nanoantennas enable to control light fields via excitation of Mie resonances inducing ultrafast all‐optical reflectivity switching. Herein, combining inhomogeneous modeling of the photoexcited charge‐carrier dynamics and ultrafast pump‐probe spectroscopy experiments, the capability of simultaneous modulation of multiple geometrically tunable resonances in the visible and near‐infrared ranges is demonstrated.
We propose a modified hybrid projection algorithm to approximate a common fixed point of a
-strict pseudocontraction and of two sequences of nonexpansive mappings. We prove a strong convergence ...theorem of the proposed method and we obtain, as a particular case, approximation of solutions of systems of two equilibrium problems.
Flat Magnetic Stimulation (FMS) is characterized by a stimulation generated by electromagnetic fields with a homogenous profile. One possible application is the treatment of stress urinary ...incontinence (SUI). We aimed to compare the objective, subjective, quality of life, and instrumental outcomes in women with SUI not eligible for surgery undergoing either FMS or pelvic floor muscle training (PFMT).
This was a prospective interventional study. After proper counseling, patients with isolated SUI were divided according to their treatment of choice into FMS and PFMT groups. At baseline and after treatment, patients completed the International Consultation on Incontinence Questionnaire-Short Form, the Female Sexual Function Index, and the Incontinence Impact Questionnaire, and volumetric measurement of the urethral rhabdosphincter (RS) was performed. The Patient Global Impression of Improvement questionnaire and stress test defined subjective and objective cure rates, respectively.
We observed improvements in urinary-related quality of life scores and an increase in RS volume after FMS compared to baseline. All these outcomes were significantly better compared to women who underwent PFMT.
Our study demonstrated that FMS is a safe and effective conservative option for SUI management in terms of objective and subjective cure rates.
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