Estimates for the Sobolev trace constant with critical exponent and applications

In this paper we find estimates for the optimal constant in the critical Sobolev trace inequality S\|u\|^p_{L^{p_*}(\partial\Omega) \hookrightarrow \|u\|^p_{W^{1,p}(\Omega)} that are independent of $\Omega$. This estimates generalized those of [3] for general $p$. Here $p_* := p(N-1)/(N-p)$ is the critical exponent for the immersion and $N$ is the space dimension. Then we apply our results first to prove existence of positive solutions to a nonlinear elliptic problem with a nonlinear boundary condition with critical growth on the boundary, generalizing the results of [16]. Finally, we study an optimal design problem with critical exponent.Comment: 22 pages, submitte

Palladium‐Catalyzed Cross‐Dehydrogenative Coupling of <i>o</i>‐Xylene: Evidence of a New Rate‐Limiting Step in the Search for Industrially Relevant Conditions

An efficient cross‐dehydrogenative coupling of o‐xylene under neat conditions, which brings important industrial benefits towards the synthesis of a monomer used in polyimide resins, is reported. The catalyst based on the combination of Pd/N ligand/carboxylate=1:1:2 does not require a Cu cocatalyst and proceeds at 11 bar of O2 pressure. Evaluation of the deuterium kinetic isotope effect (KIE) provides evidence for three different rate‐determining steps, which depend on the reaction conditions (medium, temperature). Under the reported neat conditions, the dissociation of a carboxylate‐bridged dimer to generate a more reactive monometallic Pd species is proposed to be the rate‐limiting step

Energy optimization of supplied flows from multiple pumping stations in water distributions networks

[EN] One of the most important concerns within the field of urban hydraulic engineers is the right management of water resources. When there is more than one water source, there is a question that must be answered: How much water should be provided by each water source according to the demand curve of the network? This work proposes a methodology that solves this question. It involves an energy analysis of the water network based on the concept of the setpoint curve. The setpoint curve gives, for every supplied flow, the minimum head needed to satisfy pressure requirements in the network. In this sense, the setpoint curve of every source relates two variables: supplied flow and minimum required head. Energy consumption in every source is evaluated by means of the product of these two variables. Then flow distribution among sources is optimized and minimum heads are obtained from the setpoint curve. The optimization process has been validated in two different ways. On one hand, a discrete method has been used, where a predefined combination of flow distributions are evaluated. On the other hand, the solution is found by means of Hooke-Jeeves and Nelder-Mead optimization algorithms. To apply these methods EPANET and its Toolkit has been applied to the mathematical model of the network. The optimization process can be applied to networks models with and without leakages. Finally, the methodology is applied to two cases, one academic network and real network where maximum flow limitations of every source were also taken into account.León Celi, CF.; Iglesias Rey, PL.; Martínez-Solano, FJ. (2017). Energy optimization of supplied flows from multiple pumping stations in water distributions networks. Procedia Engineering. 186:93-100. doi:10.1016/j.proeng.2017.03.214S9310018

Maximally-localized Wannier functions for entangled energy bands

We present a method for obtaining well-localized Wannier-like functions (WFs) for energy bands that are attached to or mixed with other bands. The present scheme removes the limitation of the usual maximally-localized WFs method (N. Marzari and D. Vanderbilt, Phys. Rev. B 56, 12847 (1997)) that the bands of interest should form an isolated group, separated by gaps from higher and lower bands everywhere in the Brillouin zone. An energy window encompassing N bands of interest is specified by the user, and the algorithm then proceeds to disentangle these from the remaining bands inside the window by filtering out an optimally connected N-dimensional subspace. This is achieved by minimizing a functional that measures the subspace dispersion across the Brillouin zone. The maximally-localized WFs for the optimal subspace are then obtained via the algorithm of Marzari and Vanderbilt. The method, which functions as a postprocessing step using the output of conventional electronic-structure codes, is applied to the s and d bands of copper, and to the valence and low-lying conduction bands of silicon. For the low-lying nearly-free-electron bands of copper we find WFs which are centered at the tetrahedral interstitial sites, suggesting an alternative tight-binding parametrization.Comment: 13 pages, with 9 postscript figures embedded. Uses REVTEX and epsf macro

Epigenetic mechanisms in gastric cancer: potential new therapeutic opportunities

Gastric cancer (GC) is one of the deadliest malignancies worldwide. Complex disease heterogeneity, late diagnosis, and suboptimal therapies result in the poor prognosis of patients. Besides genetic alterations and environmental factors, it has been demonstrated that alterations of the epigenetic machinery guide cancer onset and progression, representing a hallmark of gastric malignancies. Moreover, epigenetic mechanisms undergo an intricate crosstalk, and distinct epigenomic profiles can be shaped under different microenvironmental contexts. In this scenario, targeting epigenetic mechanisms could be an interesting therapeutic strategy to overcome gastric cancer heterogeneity, and the efforts conducted to date are delivering promising results. In this review, we summarize the key epigenetic events involved in gastric cancer development. We conclude with a discussion of new promising epigenetic strategies for gastric cancer treatment

The effects of sildenafil citrate on the fetoplacental development and hemodynamics in a rabbit model of intrauterina growth restriction

The present study evaluated the effectiveness of sildenafil citrate (SC) to improve placental and fetal growth in a diet-induced rabbit model of intrauterine growth restriction (IUGR). Pregnant rabbits were fed either ad libitum (Group C) or restricted to 50% of dietary requirements (Group R) or restricted and treated with SC (Group SC). The treatment with SC improved placental development by increasing vascularity and vessel hypertrophy in the decidua. The assessment of feto–placental haemodynamics showed higher resistance and pulsatility indices at the middle cerebral artery (MCA) in fetuses treated with SC when compared with Group R, which had increased systolic peak and time-averaged mean velocities at the MCA. Furthermore, fetuses in the SC group had significantly higher biparietal and thoracic diameters and longer crown–rump lengths than fetuses in Group R. Hence, the SC group had a reduced IUGR rate and a higher kit size at birth compared with Group R. In conclusion, SC may provide potential benefits in pregnancies with placental insufficiency and IUGR, partially counteracting the negative effects of food restriction on placental development and fetal growth. However, the present study also found evidence of a possible blood overflow in the brain that warrants further investigation

Multiparametric renal magnetic resonance imaging: A reproducibility study in renal allografts with stable function

Monitoring renal allograft function after transplantation is key for the early detection of allograft impairment, which in turn can contribute to preventing the loss of the allograft. Multiparametric renal MRI (mpMRI) is a promising noninvasive technique to assess and characterize renal physiopathology; however, few studies have employed mpMRI in renal allografts with stable function (maintained function over a long time period). The purposes of the current study were to evaluate the reproducibility of mpMRI in transplant patients and to characterize normal values of the measured parameters, and to estimate the labeling efficiency of Pseudo-Continuous Arterial Spin Labeling (PCASL) in the infrarenal aorta using numerical simulations considering experimental measurements of aortic blood flow profiles. The subjects were 20 transplant patients with stable kidney function, maintained over 1 year. The MRI protocol consisted of PCASL, intravoxel incoherent motion, and T1 inversion recovery. Phase contrast was used to measure aortic blood flow. Renal blood flow (RBF), diffusion coefficient (D), pseudo-diffusion coefficient (D*), flowing fraction ( f ), and T1 maps were calculated and mean values were measured in the cortex and medulla. The labeling efficiency of PCASL was estimated from simulation of Bloch equations. Reproducibility was assessed with the within-subject coefficient of variation, intraclass correlation coefficient, and Bland-Altman analysis. Correlations were evaluated using the Pearson correlation coefficient. The significance level was p less than 0.05. Cortical reproducibility was very good for T1, D, and RBF, moderate for f , and low for D*, while medullary reproducibility was good for T1 and D. Significant correlations in the cortex between RBF and f (r = 0.66), RBF and eGFR (r = 0.64), and D* and eGFR (r = -0.57) were found. Normal values of the measured parameters employing the mpMRI protocol in kidney transplant patients with stable function were characterized and the results showed good reproducibility of the techniques

Cosmological distance indicators

We review three distance measurement techniques beyond the local universe: (1) gravitational lens time delays, (2) baryon acoustic oscillation (BAO), and (3) HI intensity mapping. We describe the principles and theory behind each method, the ingredients needed for measuring such distances, the current observational results, and future prospects. Time delays from strongly lensed quasars currently provide constraints on $H_0$ with < 4% uncertainty, and with 1% within reach from ongoing surveys and efforts. Recent exciting discoveries of strongly lensed supernovae hold great promise for time-delay cosmography. BAO features have been detected in redshift surveys up to z <~ 0.8 with galaxies and z ~ 2 with Ly-$\alpha$ forest, providing precise distance measurements and $H_0$ with < 2% uncertainty in flat $\Lambda$CDM. Future BAO surveys will probe the distance scale with percent-level precision. HI intensity mapping has great potential to map BAO distances at z ~ 0.8 and beyond with precisions of a few percent. The next years ahead will be exciting as various cosmological probes reach 1% uncertainty in determining $H_0$, to assess the current tension in $H_0$ measurements that could indicate new physics.Comment: Review article accepted for publication in Space Science Reviews (Springer), 45 pages, 10 figures. Chapter of a special collection resulting from the May 2016 ISSI-BJ workshop on Astronomical Distance Determination in the Space Ag

Evolution of composition of dairy manure supernatant in a controlled dung pit

Anaerobic conversion of dairy manure into biogas is an attractive way of managing this waste. It is well known that the hydrolysis of large molecules into small, directly biodegradable ones is the rate limiting step of the overall anaerobic process. The present work studies the development of the hydrolytic and acidogenic stages of dairy manure with different solid concentrations (40, 60 and 80 g VS/L) at ambient temperature (20 ° C). The purpose was to determine the operational conditions that provide a liquid fraction with a high soluble chemical oxygen demand (COD) and a high volatile fatty acids (VFA) content in manure before the methanogenic stage starts up. At 20 ° C, the evolution of the studied parameters showed that, in a controlled plug-flow dung pit, the hydrolytic and acidogenic stages progressed moderately in a continuous way during the 25 days that the experimentation lasted, whereas no methanization was observed. Supernatant COD and VFA concentrations increased 30% and 107%, respectively, for the 60 g VS/L samples. Manure was also operated at 35 ° C with a similar increase in supernatant COD but a higher increase in VFA, 154%. For both operational temperatures, the predominant VFAs were, in this order, acetic, propionic and butyric acids. During the operation at 35 ° C, the methanogenic stage started between days 20 and 25 for the samples with lower solids content, i.e. 40 and 60 g VS/L