Singly Periodic Solutions of the Allen-Cahn Equation and the Toda Lattice

The Allen-Cahn equation ? Δu = u ? u ³ in ?² has family of trivial singly periodic solutions that come from the one dimensional periodic solutions of the problem ?u″ =u ? u ³. In this paper we construct a non-trivial family of singly periodic solutions to the Allen-Cahn equation. Our construction relies on the connection between this equation and the infinite Toda lattice. We show that for each one-soliton solution to the infinite Toda lattice we can find a singly periodic solution to the Allen-Cahn equation, such that its level set is close to the scaled one-soliton. The solutions we construct are analogues of the family of Riemann minimal surfaces in ?³.     

Physicochemical and Graph Theoretical Descriptors in Developmental Toxicity SAR: A Comparative Study

Abstract

Chemical insults to the developing fetus can lead to growth retardation, malformation, death, and functional deficits. The present study seeks to determine if physicochemical and/or graph theoretical parameters can be used to determine a structure-activity relationship (SAR) for developmental toxicity, and if consistency is observed among the selected features. The biological data utilized consists of a diverse series of compounds evaluated within the Chernoff-Kavlock in vivo mouse assay. Physicochemical parameters calculated correspond to electronic, steric, and transport properties. Graph theoretical parameters calculated include the simple, valence, and kappa indices. Both sets of parameters were independently applied to derive SARs in order to compare the quality of the respective models. Multiple random sampling, without replacement, was utilized to obtain ten training/test partitions. Models were built by linear discriminant analysis, decision trees, and neural networks respectively. Comparisons on identical sets of data were carried out to determine if any of the model building procedures had a significant advantage in terms of predictive performance. Furthermore, comparison of the features selected within and across the model building processes led to the determination of model consistency. Our results indicate that consistent features related to developmental toxicity are observed and that both physicochemical and graph theoretical parameters have equal utility.     

Enantioseparation of chiral aromatic acids by multiple dual mode counter‐current chromatography using hydroxypropyl‐β‐cyclodextrin as chiral selector

This work concentrates on extending the utilization of multiple dual mode (MDM) counter‐current chromatography in chiral separations. Two aromatic acids, 2‐(6‐methoxy‐2‐naphthyl)propionic acid (NAP) and 2‐phenylpropionic acid (2‐PPA), were enantioseparated by MDM counter‐current chromatography using hydroxypropyl‐β‐cyclodextrin (HP‐β‐CD) as chiral selector. The two‐phase solvent systems consisting of n‐hexane/ethyl acetate 0.1 mol/L phosphate buffer pH 2.67 containing 0.1 mol/L HP‐β‐CD (7.5:2.5:10 for NAP and 7:3:10 for 2‐PPA, v/v/v) were used. Conventional MDM and modified MDM were compared according to peak resolution under current separation mechanism. The influence of elution time after the first‐phase inversion and number of cycles for MDM were investigated. Peak resolution of NAP and 2‐PPA increased from 0.62 to 1.05 and 0.72 to 0.84, respectively, using optimized MDM conditions. Being an alternative elution method for counter‐current chromatography, MDM elution greatly improved peak resolution in chiral separations.     

Quantitative fingerprinting by headspace—Two-dimensional comprehensive gas chromatography–mass spectrometry of solid matrices: Some challenging aspects of the exhaustive assessment of food volatiles

The study proposes an investigation strategy that simultaneously provides detailed profiling and quantitative fingerprinting of food volatiles, through a “comprehensive” analytical platform that includes sample preparation by Headspace Solid Phase Microextraction (HS-SPME), separation by two-dimensional comprehensive gas chromatography coupled with mass spectrometry detection (GC × GC–MS) and data processing using advanced fingerprinting approaches.     

ADSORPTION OF SURFACE-ACTIVE AGENTS FROM AQUEOUS SOLUTION: HYDROPHOBIC SUBSTRATES∗

Isotherms for the adsorption of sodium dodecyl benzene sulfonate, sodium POE (4) nonyl phenol sulfate, and POE (25) nonyl phenol, on the hydrophobic crystalline herbicides atrazine and cyanazine were determined. Anionic surfactants were measured at 5°, 25°, and 50° C; the nonionic surfactant at 25° C only. Low degrees of surface coverage were observed; in only one case (atra-zine/NaDBS) was monolayer coverage approached. On the other hand, adsorption was accompanied by a significant increase in negative zeta potential. Although DLVO calculations suggest that this adsorption should lead to stable aggregates, these are of such size that gravitational effects overpower the DLVO terms.     

Cooperative spectrum sharing MIMO systems with successive decoding

A spectrum sharing system with primary and secondary nodes, each equipped with an arbitrary number of antennas, is investigated. Particularly, the outage performance of an underlay cognitive system is analytically studied, in the case when the end-to-end ($e2e$) communication is established via an intermediate relay node. To better enhance the $e2e$ communication, successive interference cancellation (SIC) is adopted, which compensates for both the transmission power constraint and the presence of interference from primary nodes. Both the relay and secondary receiver perform unordered SIC to successively decode the multiple streams, whereas the decode-and-forward relaying protocol is used for the $e2e$ communication. New closed-form expressions for the $e2e$ outage performance of each transmitted stream are derived in terms of finite sum series of the Tricomi confluent hypergeometric function. In addition, simplified yet tight approximations for the asymptotic outage performance are obtained. Useful engineering insights are manifested, such as the diversity order of the considered system and the impact of interference from the primary nodes in conjunction with the constrained transmission power of the secondary nodes.     

MR diffusion - "diffraction" phenomenon in multi-pulse-field-gradient experiments

Using pulsed-field-gradient (PFG) experiments, the sizes of the pores in ordered porous media can be estimated from the "diffraction" pattern that the signal attenuation curves exhibit. A different diffraction pattern is observed when the experiment is extended to a larger number (N) of diffusion gradient pulse pairs. Simulations to calculate signal values from arbitrary gradient waveforms are performed for diffusion in restricted geometries using a matrix operator formalism. The simulations suggest that the differences in the characteristics of the attenuation curves are expected to make it possible to measure smaller pore sizes, to improve the accuracy of pore size measurements and potentially to distinguish different pore shapes using the N-PFG technique. Moreover, when an even number of PFG pairs is used, it is possible to observe the diffraction pattern at shorter diffusion times and measure an approximation to the average pore size even when the sample contains pores with a broad distribution of sizes.     

酰胺连接的共价有机骨架的制备及其在水中高效光催化性能

光催化是将太阳能转换为化学能的绿色可持续发展途径,有望解决日益严重的能源危机和环境污染问题.在光催化过程中,半导体材料作为光催化剂,负责可见光的捕获、光生载流子的生成和传输以及氧化还原反应,在整个光催化系统中起着决定性的作用.共价有机骨架材料(COFs)是一类新兴的半导体光催化剂,已被证明在可见光诱导的水分解、二氧化碳还原、有机转化反应和水中污染物降解方面具有应用前景.然而,大部分COFs是通过可逆反应构筑的,在水中及苛刻条件下的稳定性差.因此,提升基于COFs的光催化剂在水相中的光催化活性和循环稳定性仍然面临巨大挑战.本文提出了一种新策略,即通过实现多重协同效应,设计和开发2D-COFs作为在水中的高效非均相光催化剂.通过后合成策略将亚胺键连接的2D-COFs氧化,制备了两种具有丰富三嗪结构单元的以酰胺键连接的2D-COFs(命名为COF-JLU18和COF-JLU19).结果表明,COF-JLU18和COF-JLU19具有高比表面积和孔体积,其比表面积分别为1156和541 m2/g;COF-JLU19具有比相似拓扑结构的亚胺COF-JLU17更好的水蒸气吸附性能.此外,COF-JLU19表现出了极高的化学稳定性,在水中、盐酸和氢氧化钠溶液中浸泡两天,其结构和结晶性均没有发生明显变化.由此可见,酰胺键不仅可以增加材料骨架的亲水性,还能够提高COFs对水的稳定性.本文制备的酰胺键连接的COF-JLU19材料,在光降解罗丹明B水溶液(RhB)反应中可以获得高达0.69 min?1的光降解速率常数,活性明显优于其他光催化剂,如C3N4等.COF-JLU19具有较好的催化活性主要归因于以下两方面:一方面,良好的亲水性和固有孔隙率之间的协同效应可以增强COFs在水中对染料的吸附能力,使其光催化活性得到有效提升;另一方面,高的结晶度和优秀的稳定性使酰胺键连接的COFs在多相光催化中实现稳定循环利用.为了扩展COFs的应用前景,本文还制备了一种基于酰胺键连接COFs的静电纺丝膜,在以太阳光为光源的光降解罗丹明B水溶液实验中表现出较高的光催化活性和重复使用性.综上,本文提出的多重协同效应为基于COFs的高效光催化剂的设计提供了一种有效策略.     

Simultaneous photoelectrochemical detection of dual microRNAs by capturing CdS quantum dots and methylene blue based on target-initiated strand displaced amplification

Herein,we propose a novel photoelectrochemical(PEC) biosensor for dual microRNAs(miRNAs) highly sensitive and simultaneous biosensing based on strand displaced amplification(SDA) reaction.The recognition of H_(miR-21) and H_(let-7 a) by microRNA-21 and let-7 a leads to their change in hairpin structures,subsequently initiating the immobilization of abundant CdS quantum dots(CdS QD s) and methylene blue(MB) based on SDA reaction.The immobilized CdS QDs and MB produce both high PEC currents under430 nm light and 627 nm light illumination,respectively,and the generated PEC currents are closely relied on target miRNAs amounts.Thus,highly sensitive and simultaneous detection of microRNA-21 and let-7 a was readily achieved with detection limit at 6.6 fmol/L and 15.4 fmol/L based on 3σ,respectively.Further,this PEC biosensor was applied in simultaneous analysis of miRNA-21 and let-7 a in breast cancer patient's serum with acceptable results.We expect this biosensor will find more useful application in diagnosis of miRNA-related diseases.