In this paper we prove optimal regularity for the convex envelope of supersolutions to general fully nonlinear elliptic equations with unbounded coefficients. More precisely, we deal with ...coefficients and right hand sides (RHS) in
L
q
with
q
≥
n
. This extends the result of Caffarelli on the
C
loc
1
,
1
regularity of the convex envelope of supersolutions of fully nonlinear elliptic equations with bounded RHS. Moreover, we also provide a regularity result with estimates for
ω
-semiconvex functions that are supersolutions to the same type of equations with unbounded RHS (i.e, RHS in
L
q
,
q
≥
n
). By a completely different method, our results here extend the recent regularity results obtained by Braga et al. (Adv Math 334:184–242,
2018
) for
q
>
n
, as far as fully nonlinear PDEs are concerned. These results include, in particular, the apriori estimate obtained by Caffarelli et al. (Commun Pure Appl Math 38(2):209–252,
1985
) on the modulus of continuity of the gradient of
ω
-semiconvex supersolutions (for linear equations and bounded RHS) that have a Hölder modulus of semiconvexity.
ABSTRACT
1E 1740.7−2942 is one of the strongest hard X-ray emitters in the Galactic Centre region, believed to be a black hole in a high-mass X-ray binary system. Although extensively studied in ...X-rays, many aspects about the underlying nature of the system are still unknown. For example, X-ray data analyses of 1E 1740.7−2942 to date have not yet unveiled the signature of a reflection component, whose modelling could be used to estimate parameters such as the spin of the black hole and inclination of the disc. We report here on the determination of these parameters from the analysis of the reflection component present in a public NuSTAR observation which has not been subject to any previous study. We include XMM–Newton and INTEGRAL data to build a combined spectrum, enabling a joint analysis of both the disc and comptonization components. Results point to a relatively high inclination disc ≳ 50° (3 σ) and a near-maximum speed rotating black hole. The former is in agreement with a previous radio study and the latter is reported here for the first time. Lastly, we follow the methodology of recent efforts to weigh black holes with only X-ray spectra and find results that suggest a black hole mass of about 5 M⊙ for 1E 1740.7−2942.
On 2019 April 25.346 and 26.640 UT the Laser Interferometer Gravitational-Wave Observatory (LIGO) and Virgo gravitational-wave (GW) observatory announced the detection of the first candidate events ...in Observing Run 3 that contained at least one neutron star (NS). S190425z is a likely binary neutron star (BNS) merger at dL = 156 41 Mpc, while S190426c is possibly the first NS-black hole (BH) merger ever detected, at dL = 377 100 Mpc, although with marginal statistical significance. Here we report our optical follow-up observations for both events using the MMT 6.5 m telescope, as well as our spectroscopic follow-up of candidate counterparts (which turned out to be unrelated) with the 4.1 m SOAR telescope. We compare to publicly reported searches, explore the overall areal coverage and depth, and evaluate those in relation to the optical/near-infrared (NIR) kilonova emission from the BNS merger GW170817, to theoretical kilonova models, and to short gamma-ray burst (SGRB) afterglows. We find that for a GW170817-like kilonova, the partial volume covered spans up to about 40% for S190425z and 60% for S190426c. For an on-axis jet typical of SGRBs, the search effective volume is larger, but such a configuration is expected in at most a few percent of mergers. We further find that wide-field γ-ray and X-ray limits rule out luminous on-axis SGRBs, for a large fraction of the localization regions, although these searches are not sufficiently deep in the context of the γ-ray emission from GW170817 or off-axis SGRB afterglows. The results indicate that some optical follow-up searches are sufficiently deep for counterpart identification to about 300 Mpc, but that localizations better than 1000 deg2 are likely essential.
In this paper we present a short proof of the following classification Theorem for
g
−harmonic functions in half-spaces. Assume that
u
is a nonnegative solution to Δ
g
u
= 0 in {
x
n
> 0} that ...continuously vanishes on the flat boundary {
x
n
= 0}. Then, modulo normalization,
u
(
x
) =
x
n
in {
x
n
≥ 0}. Our proof depends on a recent quantitative version of the Hopf-Oleı̆nik Lemma proven by the authors in Braga and Moreira (
Adv. Math.
334
, 184–242,
2018
). Moreover, in this paper, we show how to adapt the proofs in the literature to extend Carleson Estimate, Boundary Harnack Inequality and Schwartz Reflection Principle to the context of nonnegative
g
−harmonic functions. These results are also ingredients for the proof of the main result.
Abstract
STUDY QUESTION
What are the effects of endocannabinoid anandamide (AEA) in uterine natural killer (unK) cells from miscarriage decidua, regarding their cytokine profile and endometrial ...stromal cell (ESC) crosstalk?
SUMMARY ANSWER
uNK-conditioned media from miscarriage samples present high TNF-α levels which inhibit ESC decidualisation.
WHAT IS KNOWN ALREADY
AEA plasma levels are higher in women who have suffered a miscarriage. Moreover, AEA inhibits ESC proliferation and differentiation, although the levels and impact on the uNK cell cytokine profile at the feto-maternal interface remain elusive.
STUDY DESIGN, SIZE, DURATION
This laboratory-based study used human primary uNK cells which were isolated from first-trimester decidua (gestational age, 5–12 weeks) derived from 8 women with elective pregnancy termination and 18 women who suffered a miscarriage.
PARTICIPANTS/MATERIALS, SETTING, METHODS
The first-trimester placental tissues were assayed for AEA levels by UPLC-MS/MS and respective enzymatic profile by western blot. The uNK cells were isolated and maintained in culture. The expression of angiogenic markers in uNK cells was examined by quantitative PCR (qPCR). The uNK-conditioned medium was analysed for IFN-γ, TNF-α and IL-10 production by enzyme-linked immunosorbent assay, and the impact on ESC differentiation was assessed by measuring decidual markers Prl, Igfbp-1 and Fox01 mRNA expression using qPCR.
MAIN RESULTS AND THE ROLE OF CHANCE
AEA levels were higher in miscarriage decidua compared with decidua from elective terminations. The uNK cell-conditioned medium from the miscarriage samples exhibited high TNF-α levels and interfered with the decidualisation of ESCs. Exacerbated inflammation and elevated TNF-α levels at the feto-maternal interface may trigger AEA signalling pathways that, in turn, may impact decidualisation and the angiogenic ability of uNK cells.
LARGE-SCALE DATA
N/A.
LIMITATIONS, REASONS FOR CAUTION
Primary uNK cell responses are based on a simple in vitro model. Thus, in complex microenvironments, such as the feto-maternal interface, the mechanisms may not be exactly the same. Also, the inflammatory events of miscarriage that, in this study, have happened prior to processing of the samples may cause different responses to that observed. In addition, the magnitude of the inflammatory response, required to trigger the AEA pathways that impact decidualisation and the uNK angiogenic ability in vivo, is still unclear.
WIDER IMPLICATIONS OF THE FINDINGS
The endocannabinoid AEA is a modulator of reproductive competence. AEA not only may contribute to neuroendocrine homeostasis but also can take part in uterine changes occurring during early pregnancy.
STUDY FUNDING/COMPETING INTEREST(S)
The work was supported by UID/MULTI/04378/2019 with funding from Fundação para a Ciência e a Tecnologia (FCT)/MCTES through national funds and PORTUGAL 2020 Partnership Agreement, NORTE-01-0145-FEDER-000024. S.C. Cunha acknowledges FCT for the IF/01616/2015 contract. There are no conflicts of interest.
Hopfield neural network was used to retrieve liquid gallium radial distribution function from an experimental structure factor, obtained at 959 K. The inversion framework was carried out under two ...initial conditions: (a) a constant radial distribution function corresponding to an ideal gas and (b) a step function, simulating a gas with square well potential of interaction. Both situations lead to accurate inverse results if compared with the radial distribution function obtained by Bellisent-Funel et al., using the Fourier transform method and Monte Carlo simulation. The Hopfield neural network has shown to be a powerful strategy to calculate the radial distribution function from experimental data.
To establish the incidence of acute intraoperative suprachoroidal haemorrhage (AISH) during cataract surgery and identify the risk factors for this complication.
Data from the Royal College of ...Ophthalmologists' National Ophthalmology Database was analysed. During the 11-year study period, from 01/04/2010 to 31/03/2021, 709 083 operations performed on 498 170 patients from 65 centres were eligible for inclusion.
AISH occurred in 0.03% (204/709 083, approximately 1 in 3 500) of eligible cataract operations performed during the study period. Posterior capsule rupture was the risk factor most strongly associated with AISH (OR: 17.6, 95% CI: 12.4-24.9, p < 0.001). Other ocular risk factors identified were raised intraocular pressure (IOP) preoperatively (OR: 3.7, 95% CI: 2.5-5.5, p < 0.001), glaucoma (OR: 1.7, 95% CI: 1.2-2.4, p = 0.004). Risk increased with age and patients aged over 90 years were at greatest risk (OR: 6.7, 95% CI: 3.5-12.8, p < 0.001). The addition of intracameral anaesthetic when performing surgery under topical anaesthetic appears to be protective (OR: 0.5, 95% CI: 0.3-0.8, p = 0.003), compared to topical anaesthetic alone. There was a 16-fold increase in the incidence of vision loss when AISH occurred.
The risk of AISH during modern cataract surgery is approximately 1 in 3 500 and is associated with a significant increase in the risk of vision loss should it occur. Posterior capsule rupture is the risk factor most strongly associated with AISH. Preoperative IOP control is a modifiable risk factor. The use of intracameral anaesthesia may reduce the risk of AISH.
The predicted rate constants for C + NO and O + CN collisions in three potential energy surfaces (PESs) for the 2A′ state of the CNO molecule are compared using quasiclassical trajectories. Different ...temperature dependencies are obtained for the C + NO reaction, which are explained in terms of the long-range properties of the PESs. Recommended values and mechanistic details are also reported. For O + CN collisions, a better agreement between the theoretical results is found, except for temperatures below 100 K.
Research findings are particularly important for medication choice for first-episode patients as individual prior medication response to guide treatment decisions is unavailable. We describe the ...first large-scale double-masked randomized comparison with first-episode patients of aripiprazole and risperidone, 2 commonly used first-episode treatment agents. One hundred ninety-eight participants aged 15-40 years with schizophrenia, schizophreniform disorder, schizoaffective disorder or psychotic disorder Not Otherwise Specified, and who had been treated in their lifetime with antipsychotics for 2 weeks or less were randomly assigned to double-masked aripiprazole (5-30 mg/d) or risperidone (1-6 mg/d) and followed for 12 weeks. Positive symptom response rates did not differ (62.8% vs 56.8%) nor did time to response. Aripiprazole-treated participants had better negative symptom outcomes but experienced more akathisia. Body mass index change did not differ between treatments but advantages were found for aripiprazole treatment for total and low-density lipoprotein cholesterol, fasting glucose, and prolactin levels. Post hoc analyses suggested advantages for aripiprazole on depressed mood. Overall, if the potential for akathisia is a concern, low-dose risperidone as used in this trial maybe a preferred choice over aripiprazole. Otherwise, aripiprazole would be the preferred choice over risperidone in most situations based upon metabolic outcome advantages and some symptom advantages within the context of similar positive symptom response between medications.
This paper presents an aerial manipulator consisting of a multirotor equipped with a robotic multi-link arm attached to the top of the multirotor body. This setup has strong potentialities for ...inspection of structures, since the arm is able to safely touching the structure surface with a sensor while flying, taking measurements from the underside for example in bridges. The paper presents the dynamic model of the system and the derivation of a nonlinear controller, which is tested in simulation. First flight experiments with prototype of the system are also presented.
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