Coupled Optimal Results with an Application to Nonlinear Integral Equations

In the present work, we consider the best proximal problem related to a coupled mapping, which we define using control functions and weak inequalities. As a consequence, we obtain some results on coupled fixed points. Our results generalize some recent results in the literature. Also, as an application of the results obtained, we present the solution to a system of a coupled Fredholm nonlinear integral equation. Our work is supported by several illustrations.The authors are grateful to the Basque Government by the support of this work through Grant IT1207-19

Surface-confined core–shell structures based on gold nanoparticles and metal–organic networks

A gold nanoparticle platform enhances the optical properties and order in a metal–organic network (MON)

Observation of surface layering in a nonmetallic liquid

Oscillatory density profiles (layers) have previously been observed at the free surfaces of liquid metals, but not in other isotropic liquids. We have used x-ray reflectivity to study a molecular liquid, tetrakis(2-ethylhexoxy)silane. When cooled to T/Tc~0.25 (well above the freezing point for this liquid), density oscillations appear at the surface. Lateral order within the layers is liquid-like. Our results confirm theoretical predictions that a surface-layered state will appear even in dielectric liquids at sufficiently low temperatures, if not preempted by freezing.Comment: accepted for publication in Phys. Rev. Lett. 15 pages 4 figure

Geoeconomic variations in epidemiology, ventilation management, and outcomes in invasively ventilated intensive care unit patients without acute respiratory distress syndrome: a pooled analysis of four observational studies

Background: Geoeconomic variations in epidemiology, the practice of ventilation, and outcome in invasively ventilated intensive care unit (ICU) patients without acute respiratory distress syndrome (ARDS) remain unexplored. In this analysis we aim to address these gaps using individual patient data of four large observational studies. Methods: In this pooled analysis we harmonised individual patient data from the ERICC, LUNG SAFE, PRoVENT, and PRoVENT-iMiC prospective observational studies, which were conducted from June, 2011, to December, 2018, in 534 ICUs in 54 countries. We used the 2016 World Bank classification to define two geoeconomic regions: middle-income countries (MICs) and high-income countries (HICs). ARDS was defined according to the Berlin criteria. Descriptive statistics were used to compare patients in MICs versus HICs. The primary outcome was the use of low tidal volume ventilation (LTVV) for the first 3 days of mechanical ventilation. Secondary outcomes were key ventilation parameters (tidal volume size, positive end-expiratory pressure, fraction of inspired oxygen, peak pressure, plateau pressure, driving pressure, and respiratory rate), patient characteristics, the risk for and actual development of acute respiratory distress syndrome after the first day of ventilation, duration of ventilation, ICU length of stay, and ICU mortality. Findings: Of the 7608 patients included in the original studies, this analysis included 3852 patients without ARDS, of whom 2345 were from MICs and 1507 were from HICs. Patients in MICs were younger, shorter and with a slightly lower body-mass index, more often had diabetes and active cancer, but less often chronic obstructive pulmonary disease and heart failure than patients from HICs. Sequential organ failure assessment scores were similar in MICs and HICs. Use of LTVV in MICs and HICs was comparable (42\ub74% vs 44\ub72%; absolute difference \u20131\ub769 [\u20139\ub758 to 6\ub711] p=0\ub767; data available in 3174 [82%] of 3852 patients). The median applied positive end expiratory pressure was lower in MICs than in HICs (5 [IQR 5\u20138] vs 6 [5\u20138] cm H2O; p=0\ub70011). ICU mortality was higher in MICs than in HICs (30\ub75% vs 19\ub79%; p=0\ub70004; adjusted effect 16\ub741% [95% CI 9\ub752\u201323\ub752]; p<0\ub70001) and was inversely associated with gross domestic product (adjusted odds ratio for a US$10 000 increase per capita 0\ub780 [95% CI 0\ub775\u20130\ub786]; p<0\ub70001). Interpretation: Despite similar disease severity and ventilation management, ICU mortality in patients without ARDS is higher in MICs than in HICs, with a strong association with country-level economic status. Funding: No funding

Crowding and Anomalous Capacitance at an Electrode–Ionic Liquid Interface Observed Using Operando X‑ray Scattering

[Image: see text] Room temperature ionic liquids are widely recognized as novel electrolytes with properties very different from those of aqueous solutions, and thus with many potential applications, but observing how they actually behave at electrolytic interfaces has proved to be challenging. We have studied the voltage-dependent structure of [TDTHP](+)[NTF(2)](−) near its interface with an electrode, using in situ synchrotron X-ray reflectivity. An anion-rich layer develops at the interface above a threshold voltage of +1.75 V, and the layer thickness increases rapidly with voltage, reaching ∼6 nm (much larger that the anion dimensions) at +2.64 V. These results provide direct confirmation of the theoretical prediction of “crowding” of ions near the interface. The interfacial layer is not purely anionic but a mixture of up to ∼80% anions and the rest cations. The static differential capacitance calculated from X-ray measurements shows an increase at higher voltages, consistent with a recent zero-frequency capacitance measurement but inconsistent with ac capacitance measurements

Structure and phase transitions in Langmuir monolayers

CONTENTS I. Introduction 779 II. Phase Diagrams of Simple Amphiphiles 780 A. Molecules 780 B. Isotherms 780 C. Phase diagrams 782 D. Chain-length dependence 782 E. Head-group dependence 784 F. Mixtures 785 G. Collapse 786 H. Unresolved issues 786 III. Structure of Phases 787 A. Structure-sensitive techniques 787 B. Interpretation of the diffraction data 787 C. Structures of the phases 789 D. Local packing and crystalline structures 793 E. Peak widths and anisotropic correlations 794 IV. Computer Simulations 796 A. Simulations with atomic models of molecules 796 1. Model systems 796 2. Some results 796 B. Simulations with simplified models of molecules 798 1. Energy minimization 798 2. Models for the tilting transitions and backbone ordering 799 V. Molecular Models 799 A. Tilting transitions 799 B. Backbone ordering 800 C. Fluid-fluid transitions 801 VI. Landau Theory of Phase Transitions in Monolayers 801 A. Types of ordering 801 1. Orientational ordering 801 2. Translationa