Lower bounds for the centered Hardy-Littlewood maximal operator on the real line

Let $10$ such that for each $f\in L^p(\mathbb{R})$, the centered Hardy-Littlewood maximal operator $M$ on $\mathbb{R}$ satisfies the lower bound $\|Mf\|_{L^p(\mathbb{R})}\ge (1+\varepsilon_p)\|f\|_{L^p(\mathbb{R})}$.Comment: accepted manuscrip

Kinetics and mechanism of gas-phase thermolysis using headspace-gas chromatographic analysis

Headspace gas chromatography is employed in order to study the thermal decomposition reaction of gaseous di-tert-butyl peroxide (DTBP) in the 130°C to 160°C temperature range and in the presence of n-hexane as the internal standard and nitrogen as the carrier gas. The reaction exclusively yields acetone and ethane as products. First-order kinetics are observed, including when the surface-to-volume ratio (S/V) of the Pyrex 20-mL vial employed as the reactor is increased by packing it with silanized glass wool. However, a small increase in the rate constant values is observed at each temperature, which supports a heterogeneous surface process in DTBP decomposition. The rate constant's dependence on the homogeneous unimolecular decomposition reaction corresponds to the O-O bond rupture of the DTBP molecule in a stepwise three-stage mechanism. Thus, the relevant question of the participation of a surface catalytic effect in the DTBP gas-phase thermolysis can easily be assessed through the procedure described in this work. In general, this is advantageous for the rapid investigation of the reaction kinetics of volatile compounds at different temperatures.Laboratorio de Estudio de Compuestos Orgánico

No two without three: Modelling dynamics of the trio RNA virus-defective interfering genomes-RNA satellite

Almost all viruses, regardless of their genomic material, produce defective viral genomes (DVG) as an unavoidable byproduct of their error-prone replication. Defective interfering (DI) elements are a subgroup of DVGs that have been shown to interfere with the replication of the wild-type (WT) virus. Along with DIs, other genetic elements known as satellite RNAs (satRNAs), that show no genetic relatedness with the WT virus, can co-infect cells with WT helper viruses and take advantage of viral proteins for their own benefit. These satRNAs have effects that range from reduced symptom severity to enhanced virulence. The interference dynamics of DIs over WT viruses has been thoroughly modelled at within-cell, within-host, and population levels. However, nothing is known about the dynamics resulting from the nonlinear interactions between WT viruses and DIs in the presence of satellites, a process that is frequently seen in plant RNA viruses and in biomedically relevant pathosystems like hepatitis B virus and its $\delta$ satellite. Here, we look into a phenomenological mathematical model that describes how a WT virus replicates and produces DIs in presence of a satRNA at the intra-host level. The WT virus is subject to mechanisms of complementation, competition, and various levels of interference from DIs and the satRNA. Examining the dynamics analytically and numerically reveals three possible stable states: (i) full extinction, (ii) satellite extinction and virus-DIs coexistence and (iii) full coexistence. Assuming DIs replicate faster than the satRNA owed to their smaller size drives to scenario (ii), which implies that DIs could wipe out the satRNA. In addition, a small region of the parameter space exists wherein the system is bistable (either scenarios (ii) or (iii) are concurrently stable).Comment: 22 pages, 9 figure

Comparison of thermistor linearization techniques for accurate temperature measurement in phase change materials

Alternate energy technologies are developing rapidly in the recent years. A significant part of this trend is the development of different phase change materials (PCMs). Proper utilization of PCMs requires accurate thermal characterization. There are several methodologies used in this field. This paper stresses the importance of accurate temperature measurements during the implementation of T-history method. Since the temperature sensor size is also important thermistors have been selected as the sensing modality. Two thermistor linearization techniques, one based on Wheatstone bridge and the other based on simple serial-parallel resistor connection, are compared in terms of achievable temperature accuracy through consideration of both, nonlinearity and self-heating errors. Proper calibration was performed before T-history measurement of RT21 (RUBITHERM® GmbH) PCM. Measurement results suggest that the utilization of serial-parallel resistor connection gives better accuracy (less than ±0.1°C) in comparison with the Wheatstone bridge based configuration (up to ±1.5°C)

Kinetics and mechanism of gas-phase thermolysis using headspace-gas chromatographic analysis

Headspace gas chromatography is employed in order to study the thermal decomposition reaction of gaseous di-tert-butyl peroxide (DTBP) in the 130°C to 160°C temperature range and in the presence of n-hexane as the internal standard and nitrogen as the carrier gas. The reaction exclusively yields acetone and ethane as products. First-order kinetics are observed, including when the surface-to-volume ratio (S/V) of the Pyrex 20-mL vial employed as the reactor is increased by packing it with silanized glass wool. However, a small increase in the rate constant values is observed at each temperature, which supports a heterogeneous surface process in DTBP decomposition. The rate constant's dependence on the homogeneous unimolecular decomposition reaction corresponds to the O-O bond rupture of the DTBP molecule in a stepwise three-stage mechanism. Thus, the relevant question of the participation of a surface catalytic effect in the DTBP gas-phase thermolysis can easily be assessed through the procedure described in this work. In general, this is advantageous for the rapid investigation of the reaction kinetics of volatile compounds at different temperatures.Laboratorio de Estudio de Compuestos Orgánico

Geometric analysis of noisy perturbations to nonholonomic constraints

We propose two types of stochastic extensions of nonholonomic constraints for mechanical systems. Our approach relies on a stochastic extension of the Lagrange-d'Alembert framework. We consider in details the case of invariant nonholonomic systems on the group of rotations and on the special Euclidean group. Based on this, we then develop two types of stochastic deformations of the Suslov problem and study the possibility of extending to the stochastic case the preservation of some of its integrals of motion such as the Kharlamova or Clebsch-Tisserand integrals

Increased Amoxicillin–Clavulanic Acid Resistance in Escherichia coli Blood Isolates, Spain

To determine the evolution and trends of amoxicillin–clavulanic acid resistance among Escherichia coli isolates in Spain, we tested 9,090 blood isolates from 42 Spanish hospitals and compared resistance with trends in outpatient consumption. These isolates were collected by Spanish hospitals that participated in the European Antimicrobial Resistance Surveillance System network from April 2003 through December 2006

Proof-of-concept trial of the combination of lactitol with Bifidobacterium bifidum and Lactobacillus acidophilus for the eradication of intestinal OXA-48-producing Enterobacteriaceae

Background: The major reservoir of carbapenemase-producing Enterobacteriaceae (CPE) is the gastrointestinal tract of colonized patients. Colonization is silent and may last for months, but the risk of infection by CPE in colonized patients is significant. Methods: Eight long-Term intestinal carriers of OXA-48-producing Enterobacteriaceae (OXA-PE) were treated during 3 weeks with daily oral lactitol (Emportal®), Bifidobacterium bifidum and Lactobacillus acidophilus (Infloran®). Weekly stool samples were collected during the treatment period and 6 weeks later. The presence of OXA-PE was investigated by microbiological cultures and qPCR. Results: At the end of treatment (EoT, secondary endpoint 1), four of the subjects had negative OXA-PE cultures. Three weeks later (secondary endpoint 2), six subjects were negative. Six weeks after the EoT (primary endpoint), three subjects had negative OXA-PE cultures. The relative intestinal load of OXA-PE decreased in all the patients during treatment. Conclusions: The combination of prebiotics and probiotics was well tolerated. A rapid reduction on the OXA-PE intestinal loads was observed. At the EoT, decolonization was achieved in three patients