Toward a protecting-group-free halogen-metal exchange reaction: practical, chemoselective metalation of functionalized aromatic halides using dianion-type zincate, tBu4ZnLi2

A versatile preparation method for aromatic zincate compounds through a halogen-zinc exchange reaction using dilithium tetra-tert-butylzincate (tBu4ZnLi2) has been developed. This reagent permits efficient preparation of highly functionalized aromatic zincates, particularly, those with electrophilic functional groups, such as ester, amide, alcohol, and phenol. Halogen-zinc exchange reactions followed by electrophilic trapping (with allyl bromide or benzaldehyde) proved to be a powerful tool for C-C bond formation on functionalized aromatic rings. The functionalized aromatic zincate intermediate was also found to undergo copper- and palladium-catalyzed C-C bond-forming reactions with good yields and high chemoselectivity.     

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.