Generalized projections, decompositions, and the Pythagorean-type theorem in Banach spaces

In this paper, we investigate new properties of the generalized projection operators on convex closed cones in uniformly convex and uniformly smooth Banach spaces; establish decompositions theorems for arbitrary elements both in primary and dual spaces; and prove the Banach space analogue of the Pythagorean-type theorem. Earlier, all these results were known only in Hilbert spaces.     

The interaction of shockwaves with a vapour bubble in boiling histotripsy: The shock scattering effect

Boiling histotripsy is a High Intensity Focused Ultrasound (HIFU) technique which uses a number of short pulses with high acoustic pressures at the HIFU focus to induce mechanical tissue fractionation. In boiling histotripsy, two different types of acoustic cavitation contribute towards mechanical tissue destruction: a boiling vapour bubble and cavitation clouds. An understanding of the mechanisms underpinning these phenomena and their dynamics is therefore paramount to predicting and controlling the overall size of a lesion produced for a given boiling histotripsy exposure condition. A number of studies have shown the effects of shockwave heating in generating a boiling bubble at the HIFU focus and have studied its dynamics under boiling histotripsy insonation. However, not much is known about the subsequent production of cavitation clouds that form between the HIFU transducer and the boiling bubble. The main objective of the present study is to examine what causes this bubble cluster formation after the generation of a boiling vapour bubble. A numerical simulation of 2D nonlinear wave propagation with the presence of a bubble at the focus of a HIFU field was performed using the k-Wave MATLAB toolbox for time domain ultrasound simulations, which numerically solves the generalised Westervelt equation. The numerical results clearly demonstrate the appearance of the constructive interference of a backscattered shockwave by a bubble with incoming incident shockwaves. This interaction (i.e., the reflected and inverted peak positive phase from the bubble with the incoming incident rarefactional phase) can eventually induce a greater peak negative pressure field compared to that without the bubble at the HIFU focus. In addition, the backscattered peak negative pressure magnitude gradually increased from 17.4 MPa to 31.6 MPa when increasing the bubble size from 0.2 mm to 1.5 mm. The latter value is above the intrinsic cavitation threshold of –28 MPa in soft tissue. Our results suggest that the formation of a cavitation cloud in boiling histotripsy is a threshold effect which primarily depends (a) the size and location of a boiling bubble, and (b) the sum of the incident field and that scattered by a bubble.     

On progressive functions

Progressive functions at time t involve only the progressive functions at time before t and some nice compactly supported function at time t. We give sufficient conditions and explicit formulas to construct progressive functions with exponential decay and characterize the conditions on which the positive integer translates of a progressive function are orthonormal or a Riesz sequence. We provide explicit ways for construction of orthonormal progressive functions and for construction of the biorthogonal functions of nonorthogonal progressive functions. Such progressive functions can be used to construct wavelets with arbitrary smoothness on the half line if they are generated by a smooth refinable compactly supported function.     

On the Dual Orlicz Mixed Volumes

In this paper, the authors define a harmonic Orlicz combination and a dual Orlicz mixed volume of star bodies, and then establish the dual Orlicz-Minkowski mixed-volume inequality and the dual Orlicz-Brunn-Minkowksi inequality.     

Non-linear normal modes and their bifurcation of a class of systems with three double of pure imaginary roots and dual internal resonances

The method of multiple scales is used to construct non-linear normal modes (NNMs) of a class of systems with three double of pure imaginary roots and 1:2:5 dual internal resonance. It is found that the three NNMs associated with dual internal resonances include two uncoupled NNMs as well as a coupled NNM. And the bifurcation problem of the coupled NNM is in two variables, which is greatly different from the bifurcation of the NNMs of systems with single internal resonance. Because no results in singularities can be straightly applied, a practical way is proposed to do singularity analysis for bifurcation of two dimensions. It is also noted that with the variation of the bifurcation parameters, the modes may convert to each other or suddenly emerge and disappear, which give rise to the number of the NNMs more or fewer than the number of the degrees of freedom.     

Dual gradient LC method for the determination of pharmaceutical residues in environmental samples using a monolithic silica reversed phase column

Detailed below is a simple reversed-phase liquid chromatography (RP-LC) method for the simultaneous separation of up to 21 acidic, basic, and neutral pharmaceuticals using Merck Chromolith Performance RP-C18e monolithic columns with direct ultraviolet (UV) absorption detection. By simultaneously applying a solvent elution gradient program with a mobile phase flow gradient, both a decrease in the overall analysis time and a general increase in peak efficiencies were observed. Mobile phase pH and buffer concentration were optimised using the overall resolution product under applied gradient conditions. Under optimised conditions peak area reproducibility (n?=?6) ranged between 0.4 and 9.3%, determined at the method LOQ level. For real sample analysis pharmaceutical residues were extracted using an optimised solid phase extraction (SPE) procedure, utilising Strata-X extraction cartridges, which overall provided the highest relative recovery data in comparison with four other commercially available SPE sorbents (17 out of 20 residues investigated had recoveries over 70%). Complete method precision, including all sample pre-treatment and LC analysis for six spiked river water samples at the 1 and 2?µg?L^?1 level was between 10 and 29%. Using 1?L volumes of 1?µg?L^?1 spiked estuarine water samples, the majority of detection limits were found to be in the 10–50?ng?L^?1 range.     

双原子催化剂:制备、表征和应用

发展可持续和清洁的电化学能源转化技术是应对能源短缺和环境污染挑战的关键一步,燃料电池、电解电池和金属空气电池作为清洁能源储存和转换装置目前得到广泛应用推广,这些装置依靠电催化反应以及电极材料上发生的电荷转移过程来转换电能和化学能.而电催化剂是该类装置电极材料的核心部件,电催化反应的热力学和动力学过程与电催化剂的物理性质和化学状态密切相关.因此探索和开发性能优良、成本低廉的新型电催化剂,将进一步促进这些能源转化技术的商业化应用.单原子催化剂(SACs)以其暴露的活性位点、高选择性和最大限度地原子利用率而受到人们的广泛关注.然而,随着单原子表面自由能的增加,粒子在制备和催化过程中的聚集,催化活性位点的降低和催化剂负荷的相对较低,严重制约了SACs的发展和应用.考虑到SACs的缺点,为了进一步增加单原子活性位点的数量和负载,双原子催化剂(DACs)作为SACs家族成员的扩展近年来逐渐兴起,且两种金属原子(同核/异核)在DACs中的协同作用显著提高了催化剂的催化活性.本文基于当前最新的研究工作对比了同核/异核DACs的不同优势,列举了一系列包括原子层沉积法、湿化学吸附法以及高温热处理法等方法用于制备性能优异的DACs,其中高温热处理法因应用广泛被重点强调.同时,本文也对DACs的表征和识别手段进行了重点概括,包含XANES, EXAFS, IR, DFT等;详细概括和对比了当前DACs在电化学方面的主要应用,如氧还原反应(ORR)和二氧化碳还原反应.目前, DACs作为一个新兴的研究领域,由于其金属原子负载量高、活性位点比SACs更为灵活,已经在电催化领域取得了快速的发展.相对于同核DACs,原则上不同的两个金属原子会组成更多的异核DACs,因此,对于性能优异的异核DACs还有更多的可能性值得深入探索.可以预见, DACs的发展将弥补SACs的不足,在电化学能源的转换和储存方面发挥全面的优势;借助于异核DACs中不同的两个金属原子的多样性,探索以过渡金属为主的DACs,将会为节约贵金属资源及环境保护带来巨大贡献,进一步设计和优化DACs,有利于燃料电池和金属-空气电池创造出更大的经济效益和社会效益.因此,我们相信DACs的发展将成为材料研究的一个新前沿,并为合成更多的高效应用催化剂开辟一条新的途径.     

Ultrasound-assisted tandem synthesis of tri- and tetra-substituted pyrrole-2-carbonitriles from alkenes,TMSCN and N,N-disubstituted formamides

An energy-saving and eco-friendly method for the efficient construction of various tri- and tetra-substituted pyrrolecarbonitriles through ultrasound-assisted multicomponent tandem reaction of readily available alkenes, TMSCN and N,N-disubstituted formamides within 40 min under metal-, solvent-free and mild conditions was developed. The dual role of iodine (catalyst and oxidant) notably simplified the reaction conditions and reduced the chemical waste generated     

Synthesis of a series of novel dihydro-[1,2,4]triazolo [1,5-a]pyrimidine scaffolds: Dual solvent-catalyst activity of a low viscous and acid-functionalized ionic liquid

Abstract

The viscosity of neat ionic liquids is very important for their application in organic synthesis as a solvent because most of the neat ionic liquids are very viscous, which would result in the less efficient mass transfer of reactants. In the present study, a series of novel dihydro-[1,2,4]triazolo[1,5-a]pyrimidines were prepared using a low viscous and acid-functionalized ionic liquid. Our results showed that new ionic liquid can act as a green solvent and acid catalyst due to low viscosity and acid functionality. The products were simply extracted and the ionic liquid was retrieved several times without reducing its catalytic efficiency. The current application of TMDPS in the one-pot multicomponent reactions as dual solvent-catalyst highlights the importance of low viscous acid-functionalized ionic liquids in organic synthesis, and we hope that further research will be conducted in the future to finding other applications of TMDPS with promising results.     

双波长高效液相色谱法同时测定对二甲苯及其氧化产物

采用双波长高效液相色谱法同时测定对二甲苯及其氧化产物的含量。通过二极管阵列检测器进行光谱扫描,选择在210nm下检测对甲基苯甲醇和对二甲苯,在254nm检测其余物质。优化了流动相及其梯度洗脱程序,将流动相乙腈比例降至20%~30%,各色谱峰能实现较好的分离。采用液相色谱法和气相色谱-质谱法研究了溶剂对对羧基苯甲醛和对甲基苯甲醛的影响。对羧基苯甲醛和对甲基苯甲醛可与溶剂甲醇反应生成缩醛。方法的检出限(3S/N)为0.07~0.8mg·L-1。各物质的回收率在99.2%~100%之间,相对标准偏差(n=6)小于2.5%。