A satellite of the grand Furuta inequality and its application

The grand Furuta inequality has the following satellite (SGF;$t\in [0\text{,}1]$), given as a mean theoretic expression:$A?B>0\text{,}t\in [0\text{,}1]?A^{-r+t}{\#}_{\frac{1-t+r}{(p-t)s+r}}(A^t{?}_s{B}^p)?B\text{for}r?t\text{;}p\text{,}s?1\text{,}$where ${\#}_{\alpha }$ is the $\alpha$-geometric mean and ${?}_s$ ($s?[0\text{,}1]$) is a formal extension of ${\#}_{\alpha }$. It is shown that (SGF; $t\in [0\text{,}1]$) has the Löwner–Heinz property, i.e. (SGF; $t=1$) implies (SGF;t) for every $t\in [0\text{,}1]$. Furthermore, we show that a recent further extension of (GFI) by Furuta himself has also the Löwner–Heinz property.     

The Total Squared Curvature of Curves and Approximation by Piecewise Circular Curves

For a smooth curve in the Euclidean spaces, the total squared curvature is defined as the integral of the square of the curvature. If one takes three points on the curve which are close to one another, the reciprocal of the radius of the circle passing through those points approximates the curvature. We use this to approximate the total squared curvature and study its convergence rate.     

Disulfide‐Unit Conjugation Enables Ultrafast Cytosolic Internalization of Antisense DNA and siRNA

Development of intracellular delivery methods for antisense DNA and siRNA is important. Previously reported methods using liposomes or receptor‐ligands take several hours or more to deliver oligonucleotides to the cytoplasm due to their retention in endosomes. Oligonucleotides modified with low molecular weight disulfide units at a terminus reach the cytoplasm 10 minutes after administration to cultured cells. This rapid cytoplasmic internalization of disulfide‐modified oligonucleotides suggests the existence of an uptake pathway other than endocytosis. Mechanistic analysis revealed that the modified oligonucleotides are efficiently internalized into the cytoplasm through disulfide exchange reactions with the thiol groups on the cellular surface. This approach solves several critical problems with the currently available methods for enhancing cellular uptake of oligonucleotides and may be an effective approach in the medicinal application of antisense DNA and siRNA.     

Crystal structures of calcium IV and V under high pressure

High-pressure phases IV and V of calcium discovered in 2005 have the highest superconducting transition temperature of 25 K among all the elements; however, their crystal structures have not been determined. From the x-ray powder diffraction data, both Ca IV and V have been found to form unique and complex structures with a coordination number of 7. They were confirmed to be identical to the theoretical models that were recently predicted [Ishikawa, Phys. Rev. B 77 020101(R) (2008)].     

Metal‐Free Enantioselective Oxidative Arylation of Alkenes: Hypervalent‐Iodine‐Promoted Oxidative C−C Bond Formation

The enantioselective oxyarylation of (E)‐6‐aryl‐1‐silyloxylhex‐3‐ene was achieved using a lactate‐based chiral hypervalent iodine(III) reagent in the presence of boron trifluoride diethyl etherate. The silyl ether promotes the oxidative cyclization, and enhances the enantioselectivity. In addition, the corresponding aminoarylation was achieved.     

Atoms-in-molecules analysis of extended hypervalent five-center, six-electron (5c-6e) C(2)Z(2)O interactions at the 1,8,9-positions of anthraquinone and 9-methoxyanthracene systems

To clarify the nature of five-center, six-electron (5c-6e) C(2)Z(2)O interactions, atoms-in-molecules (AIM) analysis has been applied to an anthraquinone, 1,8-(MeZ)(2)ATQ (1 (Z=Se), 2 (Z=S), and 3 (Z=O)), and a 9-methoxyanthracene system, 9-MeO-1,8-(MeZ)(2)ATC (4 (Z=Se), 5 (Z=S), and 6 (Z=O)), as well as 1-(MeZ)ATQ (7 (Z=Se), 8 (Z=S), and 9 (Z=O)) and 9-MeO-1-(MeZ)ATC (10 (Z=Se), 11 (Z=S), and 12 (Z=O)). The total electronic energy density (H(b)(r(c))) at the bond critical points (BCPs), an appropriate index for weak interactions, has been examined for 5c-6e C(2)Z(2)O and 3c-4e CZO interactions of the n(p)(O)sigma*(Z--C) type in 1-12. Some hydrogen-bonded adducts were also re-examined for convenience of comparison. The total electronic energy densities varied in the following order: OO (3: H(b)(r(c))=0.0028 au)=OO (6: 0.0028 au)>OO (9: 0.0025 au)> or =NNHF (0.0024 au)> or =OO (12: 0.0023 au)>H(2)OHOH (0.0015 au)>SO (8: 0.0013 au)=SO (2: 0.0013 au)> or =SO (11: 0.0012 au)=SO (5: 0.0012 au)>HFHF (0.0008 au)=SeO (10: 0.0008 au)=SeO (4: 0.0008 au)> or =SeO (1: 0.0007 au)> or =SeO (7: 0.0006 au)>HCNHF (-0.0013 au). H(b)(r(c)) values for SO were predicted to be smaller than the hydrogen bond of H(2)OHOH and H(b)(r(c)) values for SeO are very close to or slightly smaller than that for HFHF in both the ATQ and 9-MeOATC systems. In the case of Z=Se and S, H(b)(r(c)) values for 5c-6e C(2)Z(2)O interactions are essentially equal to those for 3c-4e CZO if Z is the same. The results demonstrate that two n(p)(O)sigma*(Z--C) 3c-4e interactions effectively connect through the central n(p)(O) orbital to form the extended hypervalent 5c-6e system of the sigma*(C--Z)n(p)(O)sigma*(Z--C) type for Z=Se and S in both systems. Natural bond orbital (NBO) analysis revealed that n(s)(O) also contributes to some extent. The electron charge densities at the BCPs, NBO analysis, and the total energies calculated for 1-12, together with the structural changes in the PhSe derivatives, support the above discussion.     

Organic hybrid of chlorinated polyethylene and hindered phenol. II. Influence of the chemical structure of small molecules on viscoelastic properties

The viscoelastic properties and stabilities of those properties of organic hybrids consisting of chlorinated polyethylene (CPE) and tetrakis[methylene‐3‐(3‐5‐di‐tert‐butyl‐4‐hydroxy phenyl)propionyloxy]methane (AO‐60) and triethylene glycol bis[3‐(3‐tert‐butyl‐4‐hydroxy‐5‐methyl phenyl)propionyloxy] (AO‐70) were investigated. The CPE/AO‐70 hybrids show only one transition, whereas for the CPE/AO‐60 hybrids, one novel relaxation appears above the glass‐transition temperature of CPE. This relaxation on the higher temperature side in the mechanical spectrum for CPE/AO‐60 is associated with the appearance of the AO‐60‐rich phase. Furthermore, the stabilities of the viscoelastic properties and microstructures of the organic hybrids consisting of CPE and multifunctional hindered phenols are dominated by the strength of the intermolecular interaction between CPE and phenols and the conformations of the middle skeletal parts of hindered phenols. © 2000 John Wiley & Sons, Inc. J Polym Sci B: Polym Phys 38: 1496–1503, 2000