Fixed point results using Ft-contractions in ordered metric spaces having t-property

In this paper, we prove the existence of fixed points of Ft-contraction mappings in partially ordered metric spaces not necessarily complete. We require that the ordered metric space has the t-property, which is a new concept introduced recently by Rashid et.al. We also give some examples to illustrate the new concepts and obtained results.The publication of this article was funded by the Qatar National Library

Ginzburg-Landau model with small pinning domains

We consider a Ginzburg-Landau type energy with a piecewise constant pinning term $a$ in the potential $(a^2 - |u|^2)^2$. The function $a$ is different from 1 only on finitely many disjoint domains, called the {\it pinning domains}. These pinning domains model small impurities in a homogeneous superconductor and shrink to single points in the limit $\v\to0$; here, \v is the inverse of the Ginzburg-Landau parameter. We study the energy minimization in a smooth simply connected domain $\Omega \subset \mathbb{C}$ with Dirichlet boundary condition $g$ on \d \O, with topological degree {\rm deg}_{\d \O} (g) = d >0. Our main result is that, for small \v, minimizers have $d$ distinct zeros (vortices) which are inside the pinning domains and they have a degree equal to 1. The question of finding the locations of the pinning domains with vortices is reduced to a discrete minimization problem for a finite-dimensional functional of renormalized energy. We also find the position of the vortices inside the pinning domains and show that, asymptotically, this position is determined by {\it local renormalized energy} which does not depend on the external boundary conditions.Comment: 39 page

Shocks and dust formation in nova V809 Cep

The discovery that many classical novae produce detectable GeV $\gamma$-ray emission has raised the question of the role of shocks in nova eruptions. Here we use radio observations of nova V809 Cep (Nova Cep 2013) with the Jansky Very Large Array to show that it produced non-thermal emission indicative of particle acceleration in strong shocks for more than a month starting about six weeks into the eruption, quasi-simultaneous with the production of dust. Broadly speaking, the radio emission at late times -- more than a six months or so into the eruption -- is consistent with thermal emission from $10^{-4} M_\odot$ of freely expanding, $10^4$~K ejecta. At 4.6 and 7.4 GHz, however, the radio light-curves display an initial early-time peak 76 days after the discovery of the eruption in the optical ($t_0$). The brightness temperature at 4.6 GHz on day 76 was greater than $10^5 K$, an order of magnitude above what is expected for thermal emission. We argue that the brightness temperature is the result of synchrotron emission due to internal shocks within the ejecta. The evolution of the radio spectrum was consistent with synchrotron emission that peaked at high frequencies before low frequencies, suggesting that the synchrotron from the shock was initially subject to free-free absorption by optically thick ionized material in front of the shock. Dust formation began around day 37, and we suggest that internal shocks in the ejecta were established prior to dust formation and caused the nucleation of dust

Multi-Wavelength Observations Of A New Redback Millisecond Pulsar 4FGL J1910.7-5320

We present the study of multi-wavelength observations of an unidentified Fermi Large Area Telescope (LAT) source, 4FGL J1910.7-5320, a new candidate redback millisecond pulsar binary. In the 4FGL 95% error region of 4FGL J1910.7-5320, we find a possible binary with a 8.36-hr orbital period from the Catalina Real-Time Transient Survey (CRTS), confirmed by optical spectroscopy using the SOAR telescope. This optical source was recently independently discovered as a redback pulsar by the TRAPUM project, confirming our prediction. We fit the optical spectral energy distributions of 4FGL J1910.7-5320 with a blackbody model, inferring a maximum distance of 4.1 kpc by assuming that the companion fills its Roche-lobe with a radius of R = 0.7R_sun. Using a 12.6 ks Chandra X-ray observation, we identified an X-ray counterpart for 4FGL J1910.7-5320, with a spectrum that can be described by an absorbed power-law with a photon index of 1.0+/-0.4. The spectrally hard X-ray emission shows tentative evidence for orbital variability. Using more than 12 years of Fermi-LAT data, we refined the position of the {\gamma}-ray source, and the optical candidate still lies within the 68% positional error circle. In addition to 4FGL J1910.7-5320, we find a variable optical source with a periodic signal of 4.28-hr inside the 4FGL catalog 95% error region of another unidentified Fermi source, 4FGL J2029.5-4237. However, the {\gamma}-ray source does not have a significant X-ray counterpart in a 11.7 ks Chandra observation, with a 3-{\sigma} flux upper limit of 2.4*10^-14 erg cm^-2 s^-1 (0.3-7 keV). Moreover, the optical source is outside our updated Fermi-LAT 95% error circle. These observational facts all suggest that this new redback millisecond pulsar powers the {\gamma}-ray source 4FGL J1910.7-5320 while 4FGL J2029.5-4237 is unlikely the {\gamma}-ray counterpart to the 4.28-hr variable.Comment: Accepted for publication in Ap