有理插值问题存在性的一个判别准则

１引言我们知道,多项式Ｌａｇｒａｎｇｅ插值是适定的［１,２］,但有理插值函数却未必存在［８,３］．并且到目前为止,也没有类似于多项式Ｌａｇｒａｎｇｅ插值的能够揭示插值结构的显式插值公式．不过有理插值已有许多算法,比如Ｓｔｏｅｒ算法,Ｔｈｉｅｌｅ倒差商算法,Ｓａｌｚｅｒ算法以及Ｗｕｙｔａｃｋ算法等等,见［８,４,５,６］．本文为寻求尽可能接近显式的插值公式,进而揭示有理插值问题的内在结构,得到了有理插值函数存在的一个充要条件,同时也给出了有理插值函数的一种表现形式,参见［１１］．本文约定,所有矩阵…     

Defect modes in photonic crystal slabs studied using terahertz time-domain spectroscopy

We describe broadband coherent transmission studies of two-dimensional photonic crystals consisting of a hexagonal array of air holes in a dielectric slab in a planar waveguide. By filling several of the air holes in the photonic crystal slab, we observe the signature of a defect mode within the stop band, in both the amplitude and phase spectra. The experimental results are in reasonable agreement with theoretical calculations using the transfer matrix method.     

叶绿素浓度垂直不均一分布对于分层水体表观光学特性的影响

以往大部分海洋光学和海色研究都是以海洋光学有效成分及固有光学特性垂直均一分布的假设为基础进行的,然而海洋观测表明海水成分的垂直不均一性大量存在。文章通过Hydrolight辐射传输模拟研究了叶绿素浓度垂直不均一分布对海水表观光学特性的影响。叶绿素浓度垂直不均一分布由高斯模型来近似模拟,选择成熟的一类水体生物光学模型,利用Hydrolight辐射传输代码模拟表观光学特性,将垂直不均一廓线情况下模拟的表观光学特性值与具有本底值的均一廓线情况所模拟的相应值进行了比较。结果表明,水表面以下的叶绿素浓度最大值增加了蓝光波段的遥感反射率,减小了绿光波段的遥感反射率,而且改变了水体中辐射的方向分布,在叶绿素浓度最大值处,下行辐射漫衰减系数和平均余弦廓线分别出现峰值和谷值。     

Protonated free-base corroles: acidity, electrochemistry, and spectroelectrochemistry of [(Cor)H4]+, [(Cor)H5]2+, and [(Cor)H6]3+

Protonated meso-substituted free-base macrocycles of the form [(Cor)H4]+, [(Cor)H5]2+, and [(Cor)H6]3+ where Cor is the trianion of a given corrole, were chemically generated from neutral (Cor)H3 in benzonitrile by addition of trifluoroacetic acid (TFA) and characterized as to their relative acidity, electrochemistry, and spectroelectrochemistry. Three types of protonated free-base corroles with different electron-donating or electron-withdrawing substituents at the meso positions of the macrocycle were investigated. One is protonated exclusively at the central nitrogens of the corrole forming [(Cor)H4]+ from (Cor)H3, while the second and third types of corroles undergo protonation at one or two meso pyridyl substituents prior to protonation of the central nitrogens and give as the final products [(Cor)H5]2+ and [(Cor)H6]3+, respectively. Altogether the relative deprotonation constants (pKa) for 10 different corroles were determined in benzonitrile and analyzed with respect to the molecular structure and/or type of substituents on the three meso positions of the macrocycle. Mechanisms for oxidation and reduction of the protonated corroles are proposed in light of the electrochemical and spectroelectrochemical data.     

在线热辅助甲基化-气相色谱法分析棉籽仁中的脂肪酸组成

建立了分析棉籽仁中脂肪酸组成的在线热辅助甲基化-气相色谱法。将0.3 mg棉籽仁样品与2 μ L三甲基氢氧化硫（0.2 mol/L）加入裂解器,在350℃下进行甲基化反应,通过气相色谱仪进行分离分析,共检测到8种脂肪酸甲酯成分,分别为亚油酸（C18：2）、油酸（C18：1）、棕榈酸（C16：0）、硬脂酸（C18：0）、肉豆蔻酸（C14：0）、棕榈油酸（C16：1）、花生酸（C20：0）和二十二酸（C22：0）,不饱和脂肪酸的相对含量为66.30%~72.54%,其中亚油酸的相对含量为43.20%~53.61%,相对峰面积的相对标准偏差（RSD）小于10%（n=5）。通过分析5组棉籽仁样品与3种食用油中的脂肪酸组成,结果表明不同产地的棉籽仁中的脂肪酸组成差异不明显,且棉籽仁中的脂肪酸组成与玉米油最为接近,相似度为0.960~0.992。该方法简单、快速、准确,适合分析棉籽仁中的脂肪酸组成。     

Formation and properties of cyclo[6]pyrrole and cyclo[7]pyrrole

Oxidative coupling of a tetraalkylbipyrrole under FeIII-mediated coupling conditions in the presence of HCl results in a mixture of cyclo[6]- and cyclo[7]pyrroles, as well as the known cyclo[8]pyrrole. This "matched set" of heteroannulenes was analyzed by spectroscopic, electrochemical, and X-ray diffraction methods.     

Porphyrazines with annulated diazepine rings. 2. Alternative synthetic route to tetrakis-2,3-(5,7-diphenyl-1,4-diazepino)porphyrazines: new metal complexes, general physicochemical data, ultraviolet-visible linear and optical limiting behavior, and electrochemical and spectroelectrochemical properties

Following a previous report on the synthesis and physicochemical characterization of a novel class of porphyrazines carrying peripherally annulated seven-membered rings, i.e., tetrakis-2,3-(5,7-diphenyl-1,4-diazepino)porphyrazine [Ph(8)DzPzH(2)].4H(2)O and its metal derivatives [Ph(8)DzPzM].xH(2)O (x = 2-7, M = Mg(II)(H(2)O), Cu(II), and Zn(II)), a new more convenient procedure is reported here, allowing the preparation in high yields of the Li(I) and Na(I) derivatives of formulas [Ph(8)DzPzLi(2)].5H(2)O and [Ph(8)DzPzNa(2)].6H(2)O, which can be directly converted into other metal derivatives under mild conditions (room temperature) and in good yields. The series studied has been extended to include the Mn(II) and Co(II) complexes also reported here for the first time. Physicochemical characterization of the new "diazepinoporphyrazines" was based on fast atom bombardment (FAB) mass spectrometry and X-ray powder patterns, infrared (IR), electron paramagnetic resonance (EPR), and room-temperature magnetic susceptibility measurements. A detailed discussion of the UV-vis spectra emphasizes the role played by the external diazepine rings in electron delocalization through their tautomeric or protonated forms present in neutral, basic, and acidic media. The nonlinear optical effect of optical limiting for the different species [M = 2H, Mg(II)(H(2)O), Mn(II), Co(II), Cu(II), and Zn(II)] has also been measured. It has been observed that the extent of the optical limiting depends on the specific M center. The observed nonlinear optical features are analyzed and discussed in terms of the electronic and magnetic properties exhibited by some of the metal ions and taking into account the model of the excited-state absorption in which the nature of M determines the kinetics of formation of the highly absorbing state of the specific complex examined. As evidenced by the detailed electrochemical and spectroelectrochemical study carried out on this new class of macrocycles, one of the most important aspects is the facilitated electron delocalization for the oxidized and reduced species allowed by a 1H-6Htautomerism taking place on the peripheral diazepine rings.     

Substituent effects on the site of electron transfer during the first reduction for gold(III) porphyrins

Gold(III) porphyrins of the type (P-R)AuPF(6), where P = 5,10,15,20-tetrakis(3,5-di-tert-butylphenyl)porphyrin and R is equal to H (1), NO(2) (2), or NH(2) (3) which is substituted at one of the eight beta-pyrrolic positions of the macrocycle, were investigated as to their electrochemistry and spectroelectrochemistry in nonaqueous media. Each compound undergoes three reductions, the first of which involves the central metal ion to give a Au(II) porphyrin or a Au(III) porphyrin pi-anion radical depending upon the nature of the porphyrin ring substituent. A similar metal-centered reduction also occurs for compounds 1, 3, and Au(III) quinoxalinoporphyrin, (PQ)AuPF(6) (4), where PQ = 5,10,15,20-tetrakis(3,5-di-tert-butylphenyl)quinoxalino[2,3-b]porphyrin, and these results on the three Au(III) porphyrins overturn the long held assumption that reductions of such complexes only occur at the macrocycle. In contrast, when a NO(2) group is introduced on the porphyrin ring to give (P-NO(2))AuPF(6) (2), the site of electron transfer is changed from the gold metal to the macrocycle to give a porphyrin pi-anion radical in the first reduction step. This change in the site of electron transfer was examined by electrochemistry combined with thin-layer UV-vis spectroelectrochemistry and ESR spectroscopy of the singly reduced compound produced by chemical reduction. The reorganization energy (lambda) of the metal-centered electron transfer reduction for (P-H)AuPF(6) (1) in benzonitrile was determined as lambda = 1.23 eV by analyzing the rates of photoinduced electron transfer from the triplet excited states of an organic electron donor to 1 in light of the Marcus theory of electron transfer. The lambda value of the metal-centered electron transfer of gold porphyrin (1) is significantly larger than lambda values of ligand-centered electron transfer reactions of metalloporphyrins.     

Vertex Correction at Finite Temperature and Decoupling Transition in (2+1) Dimensional Chiral Gross-Neveu Model

With the aid of imaginary time temperature field theory and fermion mass spectrum derived from Ward-Takahashi identities with composite fields,the vertex correction among fermions and σ meson is calculated beyond the leading order in 1/N expansion,and the change of vertex function with temperature and decoupling transition are discussed in (2+1) dimensional chiral Gross-Neveu model.It turns out that the critical temperature of decoupling transitionarises with increasing fermion mass and π meson mass at zero temperature;the vertex correction resulting from thermal fluctuation will affect the fermion dynamical mass and cannot be ignored at finite temperature.     

Electroanalytical Behaviour of a Nanoarray Self-Assembled Thiocholesterol Gold Electrode

Thiocholesterol forms a self-assembled monolayer (SAM) on polycrystalline gold, offering a defect-rich hydrophobic surface. This SAM gold electrode has been exploited in batch and flow injection analysis (FIA) as it allows selective detection of hydrophobic analytes such as phenothiazines in presence of potentially interfering species such as ascorbic acid. Several phenothiazines have been investigated. Quantification has been achieved in FIA, in a broad linear concentration range: 0.5–100?μM. The stability of the modified electrode allows more than 500 sample injections in FIA.