Variable exponent Besov-Morrey spaces

In this paper we introduce Besov-Morrey spaces with all indices variable and study some fundamental properties. This includes a description in terms of Peetre maximal functions and atomic and molecular decompositions. This new scale of non-standard function spaces requires the introduction of variable exponent mixed Morrey-sequence spaces, which in turn are defined within the framework of semimodular spaces. In particular, we obtain a convolution inequality involving special radial kernels, which proves to be a key tool in this work.publishe

Interpolation in variable exponent spaces

In this paper we study both real and complex interpolation in the recently introduced scales of variable exponent Besov and Triebel–Lizorkin spaces. We also take advantage of some interpolation results to study a trace property and some pseudodifferential operators acting in the variable index Besov scale

Velocity boundary conditions for vorticity formulations of the incompressible Navier-Stokes equations

Velocity boundary conditions for the vorticity form of the incompressible, viscous fluid momentum equations are presented. Vorticity is created on boundaries to simultaneously satisfy the tangential and normal components of the velocity boundary condition. The newly created vorticity is specified by a kinematical formulation which is a generalization of Helmholtz decomposition of a vector field. Related forms of the decomposition were developed by Bykhovskiy and Smirnov in 1983, and Wu and Thompson in 1973. Though it has not been generally recognized as such, these formulations resolve the over-specification issues associated with determining a velocity field from velocity boundary conditions and a vorticity field. The generalized decomposition has not been widely used, however, apparently due to a general lack of a useful physical interpretation. An analysis is presented which shows that the generalized decomposition has a relatively simple physical interpretation which facilitates its numerical implementation. The implementation of the generalized decomposition for the normal and tangential velocity boundary conditions is discussed in detail. As an example of the use of this boundary condition, the flow in a lid-driven cavity is simulated. The solution technique is based on a Lagrangian transport algorithm in the hydrocode ALEGRE. ALEGRE`s Lagrangian transport algorithm has been modified to solve the vorticity transport equation, thus providing a new, accurate method to simulate incompressible flows. This numerical implementation and the new boundary condition formulation allow vorticity-based formulations to be used in a wider range of engineering problems

Magnetic moments of short-lived nuclei with part-per-million accuracy: Towards novel applications of β\beta-detected NMR in physics, chemistry and biology

We determine for the first time the magnetic dipole moment of a short-lived nucleus with part-per-million (ppm) accuracy. To achieve this two orders of magnitude improvement over previous studies, we implement a number of innovations into our $\beta$-detected Nuclear Magnetic Resonance ($\beta$-NMR) setup at ISOLDE/CERN. Using liquid samples as hosts we obtain narrow, sub-kHz linewidth, resonances, while a simultaneous in-situ $^1$H NMR measurement allows us to calibrate and stabilize the magnetic field to ppm precision, thus eliminating the need for additional $\beta$-NMR reference measurements. Furthermore, we use ab initio calculations of NMR shielding constants to improve the accuracy of the reference magnetic moment, thus removing a large systematic error. We demonstrate the potential of this combined approach with the 1.1 s half-life radioactive nucleus $^{26}$Na, which is relevant for biochemical studies. Our technique can be readily extended to other isotopic chains, providing accurate magnetic moments for many short-lived nuclei. Furthermore, we discuss how our approach can open the path towards a wide range of applications of the ultra-sensitive $\beta$-NMR in physics, chemistry, and biology.Comment: re-submitte

An analysis of the quality of experimental design and reliability of results in tribology research

In recent years several high profile projects have questioned the repeatability and validity of scientific research in the fields of psychology and medicine. In general, these studies have shown or estimated that less than 50% of published research findings are true or replicable even when no breaches of ethics are made. This high percentage stems from widespread poor study design; either through the use of underpowered studies or designs that allow the introduction of bias into the results. In this work, we have aimed to assess, for the first time, the prevalence of good study design in the field of tribology. A set of simple criteria for factors such as randomisation, blinding, use of control and repeated tests has been made. These criteria have been used in a mass review of the output of five highly regarded tribology journals for the year 2017. In total 379 papers were reviewed by 26 reviewers, 28% of the total output of the journals selected for 2017. Our results show that the prevalence of these simple aspects of study design is poor. Out of 290 experimental studies, 2.2% used any form of blinding, 3.2% used randomisation of either the tests or the test samples, while none randomised both. 30% repeated experiments 3 or more times and 86% of those who repeated tests used single batches of test materials. 4.4% completed statistical tests on their data. Due to the low prevalence of repeated tests and statistical analysis it is impossible to give a realistic indication of the percentage of the published works that are likely to be false positives, however these results compare poorly to other more well studied fields. Finally, recommendations for improved study design for researchers and group design for research group leaders are given

Microencapsulated herbal components in the diet of Lacaune ewes: impacts on physiology and milk production and quality

Abstract This study aimed to determine whether the addition of a microencapsulated herbal blend (MHB) based on thymol, carvacrol, and cinnamaldehyde in dairy sheep feed would improve production efficiency, milk quality, and animal health. Thirty lactating Lacaune ewes were divided into three groups: Control (T0), 150 mg blend/kg of feed (T150), and 250 mg blend/kg of feed (T250). Milk was measured before the beginning of the experiment (d 0), at the end of the adaptation period (d 15), and during the experiment (d 20). In milk samples, was measured the composition, somatic cell count (SCC), reactive oxygen species (ROS), lipoperoxidation (LPO), and total antioxidant capacity. The MHB improved the milk production (only T150 vs. T0 sheep on d 20), productive efficiency and feed efficiency, and reduced the milk SCC (only T250 vs. T0 sheep, on d 20), ROS and tended to reduce the milk levels of LPO (only T250 vs. T0 sheep on d 20). Also, MHB reduced the blood levels of neutrophils and ROS (only T250 vs. T0 sheep on d 20) and increased total protein and globulin levels. Thus, a microencapsulated blend of thymol, carvacrol, and cinnamaldehyde improved the productive performance and milk quality of sheep

How to Circumvent the Two-Ciphertext Lower Bound for Linear Garbling Schemes

At EUROCRYPT 2015, Zahur et al.\ argued that all linear, and thus, efficient, garbling schemes need at least two $k$-bit elements to garble an AND gate with security parameter $k$. We show how to circumvent this lower bound, and propose an efficient garbling scheme which requires less than two $k$-bit elements per AND gate for most circuit layouts. Our construction slightly deviates from the linear garbling model, and constitutes no contradiction to any claims in the lower-bound proof. With our proof of concept construction, we hope to spur new ideas for more practical garbling schemes. Our construction can directly be applied to semi-private function evaluation by garbling XOR, XNOR, NAND, OR, NOR and AND gates in the same way, and keeping the evaluator oblivious of the gate function

Computational Methods for Protein Identification from Mass Spectrometry Data

Protein identification using mass spectrometry is an indispensable computational tool in the life sciences. A dramatic increase in the use of proteomic strategies to understand the biology of living systems generates an ongoing need for more effective, efficient, and accurate computational methods for protein identification. A wide range of computational methods, each with various implementations, are available to complement different proteomic approaches. A solid knowledge of the range of algorithms available and, more critically, the accuracy and effectiveness of these techniques is essential to ensure as many of the proteins as possible, within any particular experiment, are correctly identified. Here, we undertake a systematic review of the currently available methods and algorithms for interpreting, managing, and analyzing biological data associated with protein identification. We summarize the advances in computational solutions as they have responded to corresponding advances in mass spectrometry hardware. The evolution of scoring algorithms and metrics for automated protein identification are also discussed with a focus on the relative performance of different techniques. We also consider the relative advantages and limitations of different techniques in particular biological contexts. Finally, we present our perspective on future developments in the area of computational protein identification by considering the most recent literature on new and promising approaches to the problem as well as identifying areas yet to be explored and the potential application of methods from other areas of computational biology