Structure and reaction pathway of TMP-Zincate: amido base or alkyl base?

The novel directed ortho metalation (DoM) reagents for functionalized aromatic rings, TMP-Zn-ates (R2Zn(TMP)Li (R = Me, 1; tBu, 2)), have been reported to be synthetically useful for the chemo- and regioselective construction of multi-functionalized aromatic compounds. Here, we present the first comprehensive structural and mechanistic investigation by means of X-ray, NMR, and DFT studies on the DoM reaction employing our original TMP-Zn-ate base. The structures of TMP-Zn-ates in solution and in the solid state were determined. The DFT study strongly suggested that the deprotonation involving the TMP ligand on the TMP-Zn-ate is kinetically more favorable than that involving the alkyl ligand, and this view was supported by monitoring of the 13C NMR spectrum of the reaction mixture.     

Subadditivity of eigenvalue sums

Let be a nonnegative concave function on with , and let be matrices. Then it is known that , where is the trace norm. We extend this result to all unitarily invariant norms and prove some inequalities of eigenvalue sums.

     

A new majorization between functions, polynomials, and operator inequalities

Let P₊ be the set of all non-negative operator monotone functions defined on [0,∞), and put . Then and . For a function and a strictly increasing function h we write if is operator monotone. If and and if and , then . We will apply this result to polynomials and operator inequalities. Let and be non-increasing sequences, and put for t≧a₁ and for t≧b₁. Then v₊?u₊ if m≦n and : in particular, for a sequence of orthonormal polynomials, (p_n-1)₊?(p_n)₊. Suppose 0<r,p and s=0 or 1≦s≦1+p/r. Then 0≦A≦B implies for 0<α≦r/(p+r).     

Ubiquitous V-shape density of states in a mixed state of clean limit type II superconductors

It is demonstrated theoretically and experimentally that the low energy density of states N(E) is described by a singular V-shape form N(E)=N(0)(H)+alpha|E|+O(E2) for all clean superconductors in a vortex state, irrespective of the underlying gap structure. The linear term alpha|E| which has not been recognized so far is obtained by exactly evaluating the vortex contribution. Based on microscopic Eilenberger theory N(E) is evaluated for the isotropic gap, line, and point-node gaps to yield a V-shape N(E). Scanning tunneling spectroscopy-STM experiments on NbSe2 and YNi2B2C give direct evidence for this. We provide arguments on the significance of this finding and on the relevance to other experiments.     

Eicosapentaenoic acid release from the red alga Pachymeniopsis lanceolata by enzymatic degradation

Forty-eight species of seaweeds from Japanese waters were screened for the valuable polyunsaturated fatty acids eicosapentaenoic acid (EPA). The eight species that contained the highest levels of these compounds were analyzed in detail. Of all species tested the red alga Pachymeniopsis lanceolata contained the highest EPA concentration, and it was present as both the free and bound forms. EPA constituted 38.7% of total fatty acids, and polar lipids were the main constituent of the total lipids in P. lanceolata. EPA was obtained from the marine algae P. lanceolata by enzymatic hydrolysis of the total lipids extract using phospholipase A₂(PLA₂). The release of EPA reached a plateau after 10 min of enzymatic treatment. These results suggest that P. lanceolata is a useful natural source of EPA and that PLA₂ treatment is a convenient method for obtaining EPA from the red alga.     

Berger-Shaw's theorem forp-hyponormal operators

For an-multicyclicp-hyponormal operatorT, we shall show that |T|^2p –|T ^*|^2p belongs to the Schatten and that tr Area ((T)).     

On Schwarz type inequalities

We show Schwarz type inequalities and consider their converses. A continuous function is said to be semi-operator monotone on if is operator monotone on . Let be a bounded linear operator on a complex Hilbert space and be the polar decomposition of . Let and for . (1) If a non-zero function is semi-operator monotone on , then for , where . (2) If are semi-operator monotone on , then for . Also, we show converses of these inequalities, which imply that semi-operator monotonicity is necessary.

     

Inverse functions of polynomials and orthogonal polynomials as operator monotone functions

We study the operator monotonicity of the inverse of every polynomial with a positive leading coefficient. Let be a sequence of orthonormal polynomials and the restriction of to , where is the maximum zero of . Then and the composite are operator monotone on . Furthermore, for every polynomial with a positive leading coefficient there is a real number so that the inverse function of defined on is semi-operator monotone, that is, for matrices , implies

     

Helical structures of N-alkylated poly(p-benzamide)s

Poly(p-benzamide)s 1 bearing a chiral side chain on the nitrogen atom were synthesized by chain-growth polycondensation methodology. The polyamides exhibited well-defined molecular weights with narrow polydispersities. Solutions of the polyamides in several organic solvents (CH(3)CN, CHCl(3), and CH(3)OH) showed dispersion type CD signals characteristic of coupled-oscillator and much larger as compared with the corresponding monomer. The CD signals were dependent on the temperature and molecular weight of the polyamides but independent of the solvent, as far as examined. An exciton model analysis of the absorption and CD spectra provided a clear-cut picture for the secondary structure of these polyamides in solution that the N-alkylated poly(p-benzamide)s possess a right-handed helical conformation ((P)-helix). In the solid states, the results of X-ray crystallographic analysis of 4-(methylamino)benzoic acid oligomers substantiated that they have a helical conformation with three monomer units per turn.