Tracking poles and representing Hankel operators directly from data

Summary We propose and analyse a method of estimating the poles near the unit circleT of a functionG whose values are given at a grid of points onT: we give an algorithm for performing this estimation and prove a convergence theorem. The method is to identify the phase for an estimate by considering the peaks of the absolute value ofG onT, and then to estimate the modulus by seeking a bestL ² fit toG over a small arc by a first order rational function. These pole estimates lead to the construction of a basis ofL ² which is well suited to the numerical representation of the Hankel operator with symbolG and thereby to the numerical solution of the Nehari problem (computing the bestH , analytic, approximation toG relative to theL norm), as analysed in [HY]. We present the results of numerical tests of these algorithms.Partially supported by grants from the AFOSR and NSF     

5-(2′-苯骈噻唑偶氮)-8-氨基喹啉的合成及应用——分光光度法测定钯的新试剂

本文报道了新试剂5-(2′-苯骈噻唑偶氮)-8-氨基喹啉(BTAQ)的合成。研究了在溴化十六烷基三甲铵(CTMAB)增溶下,在弱酸性介质中它与钯的显色反应。建立了分光光度法测定微量钯的高选择性新方法,用于钯催化剂中微量钯的测定,结果满意。     

(4S)-4-羧基杂氮硅三环的合成

利用L-N,N-双(β-羟乙基)丝氨酸及L-N,N-双(β-羟乙基)苏氨酸与三乙氧基硅烷或氯烷基三乙氧基硅烷反应合成了具有手性的(4S)-4-羧基杂氮硅三环(1～5),并运用IR、~1HNMR、EI-MS等手段表征了结构。证据显示存在着贯穿笼状结构的N→Si配键。     

First example of the formation of bipolar spiro σ-complexes from 6-bromo-5,7-dinitrobenzo[e]-1,2,3,4-tetrazine 1,3-di-N-oxide

The reactions of 3,5,7-trimethyltropolone and 2-(N-benzylamino)tropone with 6-bromo-5,7-dinitrobenzo[e]-1,2,3,4-tetrazine 1,3-di-N-oxide afforded novel bipolar spiro -complexes. The kinetic and activation parameters of the R,S-enantiotopomerization of a chiral spiro -complex of 2-(N-benzylamino)tropone were determined using dynamic ¹H NMR spectroscopy.     

[2+2]-Photocycloaddition von Cyclohexen an 2-Acetyl-5,5-dimethyl-1,3-cyclohexandion und 3-Acetyl-1,5,5-trimethyl-2,4-pyrrolidindion

Summary Irradiation of solutions of excess cyclohexene and 2-acetyl-5,5-dimethyl-1,3-cyclohexanedione (1), and 3-acetyl-1,5,5-trimethyl-2,4-pyrrolidinedione (4) results mainly in the formation of 1,5-diones2 and5. These originate from intermediate cycloadducts of cyclohexene and theexo-enols of the cyclic 1,3-diketones. The yields decrease with increasing polarity of the solvent. In solution2 and5 are in equilibrium with the cyclic hemiacetales3 and6.

     

Investigation of 2-[(<Emphasis Type="Italic">E</Emphasis>)-2-(4-diethylaminophenyl)-1-ethenyl]-1,3,3-trimethyl-3H-indolium as a new highly sensitive reagent for the spectrophotometric determination of nitrophenols

A new, simple, rapid, and sensitive spectrophotometric method has been developed for the determination of nitrophenols [picric acid (PA); dinitrophenols (DNP)] in wastewater samples. The method is based on the reaction of nitrophenols with 2-[(E)-2-(4-diethylaminophenyl)-1-ethenyl]-1,3,3-trimethyl-3 H-indolium chloride reagent to form the colored ion associates, which are extracted by organic solvents. The molar absorptivity of the ion associates of PA with the investigated reagent ranges from 8.3×10⁴ to 11.3×10⁴ L mol^–1 cm^–1, depending on the extractant. Because only PA is extracted in an acidic medium with the investigated reagent, but both PA and DNP are extracted in an alkaline medium, it is possible to determine both substances in a mixture. Appropriate reaction conditions have been established. The absorbance of the colored extracts obeys Beers law in the range of 0.04–4.58 mg L^–1 PA, 1.0–18.4 mg L^–1 2,4-DNP and 1.2–14.7 mg L^–1 2,6-DNP, respectively. The limit of detections, calculated from a blank test (n=10; P=0.95), are 0.05 mg L^–1 PA, 0.9 mg L^–1 (2,4-DNP), and 1.1 mg L^–1 (2,6-DNP), respectively.     

GC-MS与GC-FTIR联合测定C9烃馏分组成

混合碳九组成复杂,估计为环状烯烃、芳烃、多环烃、烷烃等,目前该产品主要用于生产石油树脂。随着我国乙烯生产能力的不断扩大,其产量也在不断增加,为充分利用碳九资源,研究开拓其新的应用领域非常必要。而此研究的首要条件在于对其组成进行较为全面、准确地分析。传统的分析方法不能对其组成提供详尽的数据资料,直接影响了对碳九进行综合利用研究。GC-MS兼有GC的高效分离能力与MS很好的定性功能,且灵敏度较高,是分析有机混合物十分有效的手段。本文将GC-MS应用于碳九组成的定性分析中。但由于碳九组分中含有较多的同分异构体如三甲苯与二甲苯等,同分异构体的质谱图几乎相同,GC-MS对其不易鉴别,而红外(FTIR)对有机物同分异构体尤其苯系物的异构体具有非常好的鉴别能力。因此本文将GC-MS与GC-FTIR联合使用,对碳九组成进行定性分析,样品定量采用色谱氢火焰检测器峰面积归一化法得到的各组分峰面积相对百分含量,较好地解决了碳九组分的定性定量问题,为开发碳九新的应用领域提供依据。     

流动注射-氢化物发生-原子吸收光谱法测定雪中的微量铅

建立了测定雪中微量铅的流动注射-氢化物发生-原子吸收光谱法。在优化条件下。测定铅的线性范围为0～52．0ng／mL，线性回归方程为A=0．018c 0．016，相关系数r=0．9995，检出限为0．2ng／mL。用于雪中微量铅的测定，加标回收率为94．2％～107．3％，相对标准偏差为1．47％～3．22％。该方法的测定结果与标准加入法基本一致。     

N,C10-Überbrückte Morphinalkaloide, 5H-10,13-Iminoethano-phenanthro[4,5-bcd]furan, 2. Mitt.

Summary Following our concept of rather new structural variations in the nitrogen region of morphine alkaloids we describe the first synthesis of N/C-10-bridged tertiary bases.