二维连续信号的近似采样定理

利用加细方程的面具,给出该方程的一个近似解,并根据这个近似解构造出二维连续信号的近似采样定理.其近似采样函数是所求加细方程的近似解,它是由加细方程的面具唯一确定的逐段线性函数,且有显示的计算公式.因此可以根据需要选择加细方程的面具,从而达到控制近似采样函数的衰减速度.     

微流控芯片用于单细胞分析

微流控芯片通道内径一般约10~50 μm.典型哺乳类动物细胞直径一般为8~30 μm,体积为87 fL~4 pL.     

三维Ising模型的蒙特卡罗模拟

采用蒙特卡罗(Monte Carlo)重点抽样法对三维Ising模型进行计算机模拟,测量无外磁场时三维Ising模型中自旋键链的能量、磁化强度、比热及磁化率的统计平均值与标准误差(不确定度).结果表明,三维Ising模型在无外磁场时存在自发磁化现象,铁磁→非铁磁相变临界点在J/(k_BT_C)=0.222 0,或居里温度T_C=4.500 0处.并研究存在外磁场时上述物理量随温度与外磁场的变化规律,给出物理解释.     

一种用于蠕变损伤失效概率计算的分层抽样方法

根据蠕变损伤试验和相关的研究资料,确定出影响材料蠕变损伤的随机参数;建立了蠕变损伤失效的概率模型.其次根据分层抽样法的基本思想,建立了一种考虑对蠕变损伤失效概率区间分情况抽样的蒙特卡洛分层抽样方法.并且在蠕变损伤模型中选择等效应力作为一个分层抽样变量.随后根据工程实际情况,提出了一种在统计意义下确定抽样变量的安全区域和失效区域的分层抽样的策略,以减少抽样次数.并推导出确定分层抽样区间的计算方法.然后对选择区间大小进行了讨论,可知如果所选择的分层抽样区间太小,会漏掉许多导致蠕变损伤失效的等效应力抽样值,从而使计算结果误差增大;但是如果分层抽样区间选择太大,会增加无效抽样次数,因而降低抽样效率.最后的算例表明了该方法在同样的计算精度下,其计算效率比直接抽样法的效率要高.     

An Instrumental Correction for the Determination of Mercury in Biological and Sediment Samples Using Cold Vapor Atomic Absorption Spectrophotometry

Low recovery rate and inconsistent measurements were found in the determination of mercury by method of cold vapor atomic absorption spectrophotometry using the hydride formation system (Hitachi HFS-2, Hitachi Ltd., Tokyo). To overcome this problem of insufficient reaction time we developed a simple T-joint device attaching to the commercial HFS-2 system for the determination of mercury in various biological tissues and sediment samples. The T-joint device was designed to combine sample and reductant injection which increased the reaction time of the sample allowing a complete formation of mercury vapor and speeding up the analysis process in comparison to the traditional cold vapor atomic absorption spectrometric method. Recoveries of mercury were in the range 95% - 100%. The corrected procedure gave precise and accurate readings with several certified reference materials: NIES No. 2 from the Japan Environment Agency; IAEA-356 from the International Atomic Energy Association, and DOLT-2, DORM-2, TORT-2, PACS-1 and MESS-2 from the National Research Council of Canada. Simple acid digestion methods were developed based on the sample Hg level and the nature of the sample. The sample detection limits were 0.0125 μg g⁻¹ fresh weight and 0.0625 μg g⁻¹ dry weight for biological samples, and as low as 0.0125 μg g⁻¹ dry weight for sediment samples. These analytical protocols we established met the general requirements in environmental research and monitoring of mercury pollution.     

悬浮体进样/氟化电热蒸发(ETV)/ICP-AES直接测定二氧化钛粉末中痕量钇

以聚四氟乙烯(PTFE)悬浮体为氟化剂,悬浮体制样/氟化辅助电热蒸发(ETV)/ICP-AES直接测定TiO₂陶瓷粉末中痕量杂质钇;考察了影响基体和待测元素的蒸发过程的各种因素;对比研究了待测元素和基体的氟化蒸发行为;实现了基体和待测元素的预分离,显着降低了基体效应。本法的检出限为0.26μg/L,相对偏差为3.8%(n=5,c=0.5mg/L).     

Truncation Error on Wavelet Sampling Expansions

We estimate the truncation error of sampling expansions on translationinvariant spaces, generated by integer translations of a single functionand on wavelet subspaces of L ₂(R). As a byproduct of themain result, we get the classical Jagerman's bound for Shannon's samplingexpansions. We also examine this error on certain wavelet sampling expansions.     

Scenarios for Multistage Stochastic Programs

A major issue in any application of multistage stochastic programming is the representation of the underlying random data process. We discuss the case when enough data paths can be generated according to an accepted parametric or nonparametric stochastic model. No assumptions on convexity with respect to the random parameters are required. We emphasize the notion of representative scenarios (or a representative scenario tree) relative to the problem being modeled.     

Accelerated Nuclear Magnetic Resonance Spectroscopy with Deep Learning

Nuclear magnetic resonance (NMR) spectroscopy serves as an indispensable tool in chemistry and biology but often suffers from long experimental times. We present a proof-of-concept of the application of deep learning and neural networks for high-quality, reliable, and very fast NMR spectra reconstruction from limited experimental data. We show that the neural network training can be achieved using solely synthetic NMR signals, which lifts the prohibiting demand for a large volume of realistic training data usually required for a deep learning approach.