Lucas' theorem refined ∗

We prove a refined version of the classical Lucas' theorem: if p is a polynomial with zeros a ₁,…,a _n+1 all having modulus one and φis the Blaschke product whose zeros are those of the derivative p ¹, then the compression of the shift S(φ) has its numerical range circumscribed about by the (n+ l)-gon a ₁…a _n+1 with tangent points the midpoints of then+ l sides of the polygon. This is proved via a special matrix representation of S(φ) and is a generalization of the known case for n= 2.     

A new strategy for designing non-C2-symmetric monometallic bifunctional catalysts and their application in enantioselective cyanation of aldehydes

A monometallic bifunctional catalyst, in which only one imidazolyl moiety is directly attached at the 3-position of a binaphthol moiety, has been developed. The ligand (R)-1, which lacks C2-symmetry and flexible linkers, in combination with Ti(OiPr)4, has been demonstrated to promote the enantioselective cyanation of aldehydes with trimethylsilylcyanide (TMSCN), giving excellent enantioselectivities of up to 98 % ee and high yields of up to 99 %. The use of this bifunctional catalytic system obviates the need for additives and is extremely simple as the reagents are added in one portion at the beginning of the reaction. The protocol has been found to tolerate a relatively wide range of aldehydes when 10 mol % of the (R)-1/Ti(OiPr)4 complex is deployed in CH2Cl2 at -40 degrees C, the conditions which proved most practical and effective. The asymmetric cyanations also proceeded with lower catalyst loadings (5 mol %, or even 2 mol %), still giving satisfactory enantiomeric excesses and yields. Interestingly, the use of freshly distilled TMSCN dried over CaH2 gave a low enantioselectivity and only a moderate yield of the adduct as compared with direct use of the commercial reagent. The results of 13C NMR spectroscopic studies implicate HCN as the actual reactive nucleophile.     

Differentiable Distance Spaces

The distance function \({\varrho(p, q) ({\rm or} d(p, q))}\) of a distance space (general metric space) is not differentiable in general. We investigate such distance spaces over \({\mathbb{R}^n}\), whose distance functions are differentiable like in case of Finsler spaces. These spaces have several good properties, yet they are not Finsler spaces (which are special distance spaces). They are situated between general metric spaces (distance spaces) and Finsler spaces. We will investigate such curves of differentiable distance spaces, which possess the same properties as geodesics do in Finsler spaces. So these curves can be considered as forerunners of Finsler geodesics. They are in greater plenitude than Finsler geodesics, but they become geodesics in a Finsler space. We show some properties of these curves, as well as some relations between differentiable distance spaces and Finsler spaces. We arrive to these curves and to our results by using distance spheres, and using no variational calculus. We often apply direct geometric considerations.     

Surface functionalization of polymer latex particles. II. Catalytic oxidation of poly(methylstyrene) latexes in the presence of cetyltrimethylammonium bromide

Surface-functionalized cationic poly(methylstyrene) (PMS) latex particles containing aldehyde and carboxylic acid groups were successfully achieved via an emulsion polymerization of 3(4)-methylstyrene in the presence of cetyltrimethylammonium bromide, followed by an in-situ oxidation catalyzed by copper chloride and tert-butyl hydroperoxide (t-BuOOH). Factors such as the type of metal catalyst, oxidant, and their concentration strongly affected the rate of oxidation. Step addition of t-BuOOH resulted in both a higher degree of oxidation and a more uniform distribution of particle size of the functionalized PMS as compared to the batch addition method. The effect of organic solvent was found to be insignificant, and the oxidation could still proceed in its absence. The particle sizes increased significantly during the oxidation but could be controlled by using crosslinked PMS latexes. Finally, the versatility of this oxidation process was demonstrated by oxidation of the polymer with a solid loading as high as 28%. © 1997 John Wiley & Sons, Inc. J Polym Sci A: Polym Chem 35 : 3585–3593, 1997     

Crystal structure and ionic conductivity of the soft solid crystal: isoquinoline<Subscript>3</Subscript>•(LiCl)<Subscript>2</Subscript>

A soft solid crystal composed of isoquinoline (IQ) and LiCl was prepared based on the concept of Pearson’s hard-soft acid-base (HSAB) theory. Single-crystal X-ray diffraction best described the isoquinoline₃?(LiCl)₂ as consisting of molecular Li₄Cl₄(isoquinoline)₆ units, where the LiCl cluster is an array of edge-fused Li₂Cl₂ rhombs. Electrochemical impedance measurements on pressed pellets showed that conductivity occurs mainly through the bulk via a hopping mechanism, with a calculated activation energy of E_a = 67 kJ/mol. The high value of the activation energy was due to Li₄Cl₄ clusters that were well separated by intervening IQ ligands in the crystal structure, requiring large hops for ions to migrate through the lattice.     

Tantalum,easy as Pi: understanding differences in metal–imido bonding towards improving Ta/Nb separations

The separation and purification of niobium and tantalum, which co-occur in natural sources, is difficult due to their similar physical and chemical properties. The current industrial method for separating Ta/Nb mixtures uses an energy-intensive process with caustic and toxic conditions. It is of interest to develop alternative, fundamental methodologies for the purification of these technologically important metals that improve upon their environmental impact. Herein, we introduce new Ta/Nb imido compounds: M(^tBuN)(TriNOx) (1-M) bound by the TriNOx³⁻ ligand and demonstrate a fundamental, proof-of-concept Ta/Nb separation based on differences in the imido reactivities. Despite the nearly identical structures of 1-M, density functional theory (DFT)-computed electronic structures of 1-M indicate enhanced basic character of the imido group in 1-Ta as compared to 1-Nb. Accordingly, the rate of CO₂ insertion into the M N_imido bond of 1-Ta to form a carbamate complex (2-Ta) was selective compared to the analogous, unobserved reaction with 1-Nb. Differences in solubility between the imido and carbamate complexes allowed for separation of the carbamate complex, and led to an efficient Ta/Nb separation (S_Ta/Nb = 404 ± 150) dependent on the kinetic differences in nucleophilicities between the imido moieties in 1-Ta and 1-Nb.

A selective separation of the critical metals tantalum and niobium was accomplished from π-bonding-based reactivity differences of imido complexes. New insights into Ta/Nb separations were gained through detailed kinetic and computational studies.     

ICP－AES法测定栽培灵芝中9种微量元素

本文报导了采用美国ＬｅｅｍａｎＬａｂｓ公司生产的ＰＳ－Ⅰ型中阶梯光栅光谱仪，对栽培灵芝中Ｇｅ、Ｃａ、Ｍｇ、Ｚｎ、Ｃｕ、Ｍｎ、Ｆｅ、Ｋ、Ｎａ等元素进行了测定。为防止Ｇｅ的挥发损失，采用了ＨＮＯ３－ＨＣｌＯ４低温湿法消化的前处理方法。相对标准偏差为１．３１％－９．１１％，回收率为９１．０％－１１０．０％，结果令人满意。     

Constituents of Ilex Species I. On the Leaves of Ilex Cornuta Lindl

Phytochemical examination on the leaves of Ilex cornuta Lindl. (Aquifoliaceae) resulted in the isolation and identification of lupeol (I), 3β-hydroxylup-20(29)-en-30-al (II), oleanolic acid (III), and β-sitosterol-β-D-glucoside (IV).