Multilevel augmentation methods for eigen-problems of compact integral operators

Numerical Algorithms - In this paper, we combine the ideas of multilevel augmentation methods for solving integral equations and the shifted-inverse power method to develop a new multilevel...     

基于级联PPMgLN晶体的双倍/三倍频双波长激光器

本文演示了紧凑的绿色和近红外双色连续波激光光源,其发射波长分别为516 nm和775 nm。设计并制造了级联的周期性极化掺镁铌酸锂晶体,用于同时转换通信波长的二次谐波(SHG)和三次谐波(THG),可以在相同温度下获得绿色和近红外激光的输出。通过建立一个单程激光测量系统,在2 W泵浦功率下获得516 nm的0.15 mW绿光和775 nm的1.19 mW的光,晶体温度控制在30.8 ℃。实验结果将为单激光器泵浦的紧凑型双波长共线激光器提供重要的案例。     

Comparison of different methodologies for the computation of damped nonlinear normal modes and resonance prediction of systems with non-conservative nonlinearities

Nonlinear Dynamics - The nonlinear modes of a non-conservative nonlinear system are sometimes referred to as damped nonlinear normal modes (dNNMs). Because of the non-conservative...     

Gold-Catalyzed Divergent Ring-Opening Rearrangement of Cyclopropenes Enabled by Dichotomous Gold−Carbenes

The gold-catalyzed ring-opening rearrangement of cyclopropenes affords an efficient route to either polysubstituted naphthols or aryl-substituted furans. Owing to the unique dichotomy of gold−carbenes, this protocol provides a switchable reaction selectivity between naphthols and furans enabled by the use of TFP−Au(MeCN)SbF₆ (tri(2-furyl) phosphine) or PNP(AuNTf₂)₂ (bis(diphenylphosphino)(isopropyl) amine) as catalysts respectively. It is proposed that the gold−carbene intermediate might be involved in the cyclopropene→naphthol rearrangement while the gold-carbocation is more likely to be involved in the cyclopropene→furan rearrangement.     

Auto-deposition of 210Bi and 210Po on nickel discs and their application in the analysis of natural waters

Journal of Radioanalytical and Nuclear Chemistry - This study presents a time-efficient method of analysing 210Pb, 210Bi, and 210Po in natural waters. The optimum pH (1.00), temperature...     

Enantioselective Synthesis of Acyclic Stereotriads Featuring Fluorinated Tetrasubstituted Stereocenters

Elaboration of enantioenriched complex acyclic stereotriads represents a challenge for modern synthesis even more when fluorinated tetrasubstituted stereocenters are targeted. We have been able to develop a simple strategy in a sequence of two unprecedented steps combining a diastereoselective aldol-Tishchenko reaction and an enantioselective organocatalyzed kinetic resolution. The aldol-Tishchenko reaction directly generates a large panel of acyclic 1,3-diols possessing a fluorinated tetrasubstituted stereocenter by condensation of fluorinated ketones with aldehydes under very mild basic conditions. The anti 1,3-diols featuring three contiguous stereogenic centers are generated with excellent diastereocontrol (typically >99 : 1 dr). Depending upon the precursors both diastereomers of stereotriads are accessible through this flexible reaction. Furthermore, from the obtained racemic scaffolds, development of an organocatalyzed kinetic resolution enabled to generate the desired enantioenriched stereotriads with excellent selectivity (typically er >95 : 5).     

Finding any given 2‐factor in sparse pseudorandom graphs efficiently

Given an $n$‐vertex pseudorandom graph $G$ and an $n$‐vertex graph $H$ with maximum degree at most two, we wish to find a copy of $H$ in $G$, that is, an embedding $\phi :V\left(H\right)\to V\left(G\right)$ so that $\phi \left(u\right)\phi \left(v\right)\in E\left(G\right)$ for all $uv\in E\left(H\right)$. Particular instances of this problem include finding a triangle‐factor and finding a Hamilton cycle in $G$. Here, we provide a deterministic polynomial time algorithm that finds a given $H$ in any suitably pseudorandom graph $G$. The pseudorandom graphs we consider are $\left(p,\lambda \right)$‐bijumbled graphs of minimum degree which is a constant proportion of the average degree, that is, $\mathrm{\Omega }\left(pn\right)$. A $\left(p,\lambda \right)$‐bijumbled graph is characterised through the discrepancy property: $|e\left(A,B\right)?p|A||B||<\lambda \sqrt{|A||B|}$ for any two sets of vertices $A$ and $B$. Our condition $\lambda =O(p^{2}n/\log n)$ on bijumbledness is within a log factor from being tight and provides a positive answer to a recent question of Nenadov. We combine novel variants of the absorption‐reservoir method, a powerful tool from extremal graph theory and random graphs. Our approach builds on our previous work, incorporating the work of Nenadov, together with additional ideas and simplifications.