Transcendence Criterion for Values of Certain Functions of Several Variables

Let ${\Phi_0(\boldmath{z})}$ be the function defined by $$\Phi_0({\boldmath z}) = \Phi _{0}(z_1,\ldots, z_m)=\sum_{k\geq 0}\frac{E_k(z_1^{r^k},\ldots,z_m^{r^k})}{F_k(z_1^{r^k},\ldots,z_m^{r^k})},$$ where ${E_k(\boldmath{z})}$ and ${F_k(\boldmath{z})}$ are polynomials in m variables ${\boldmath{z} = (z_1,\ldots, z_m)}$ with coefficients satisfying a weak growth condition and r ≥ 2 a fixed integer. For an algebraic point ${\boldmath{\alpha}}$ satisfying some conditions, we prove that ${\Phi_{0}(\boldmath{\alpha})}$ is algebraic if and only if ${\Phi_{0}(\boldmath{z})}$ is a rational function. This is a generalization of the transcendence criterion of Duverney and Nishioka in one variable case. As applications, we give some examples of transcendental numbers.     

Fermi-arc superconductivity, pseudogap and charge order in Bi2Sr2CaCu2O8+δ

We report STM/STS observations on the 4a×4a charge order in the pseudogap (PG) and superconducting (SC) states of Bi₂Sr₂CaCu₂O_8+δ, and suggest that the charge order is associated with incoherent quasiparticle or pair states around the antinodal fermi surface (FS), which are also responsible for the PG, and it can coexist with the superconductivity caused by the pairing of coherent quasiparticles on the nodal fermi arc. We also suggest that the nanometer-scale gap inhomogeneity in the SC state, reported previously [Pan, et al., Nature 413 (2001) 282; Mommo, et al., J. Phys. Soc. Jpn. 74 (2005) 2400; Hashimoto, et al., Phys. Rev. B74 (2006) 064508] arises from that in the PG state, which occurs around the antinodal FS.     

Syntheses of thallusin analogues and their algal morphogenesis-inducing activities

Thallusin is the only known natural product that induces cell differentiation followed by formation of a thallus during the growth of green macroalgae such as Monostroma and Ulva. Herein, various thallusin analogues based on the terpen skeleton were synthesized to study the structure?activity relationships of thallusin. The potency of the synthetic analogues was investigated in an experimental assay, which demonstrated that the 19-methyl group in thallusin is essential for potent morphogenesis-inducing activity.     

Near‐Infrared Light‐Driven Hydrogen Evolution from Water Using a Polypyridyl Triruthenium Photosensitizer

In order to realize artificial photosynthetic devices for splitting water to H₂ and O₂ (2 H₂O+hν→2 H₂+O₂), it is desirable to use a wider wavelength range of light that extends to a lower energy region of the solar spectrum. Here we report a triruthenium photosensitizer [Ru₃(dmbpy)₆(μ‐HAT)]⁶⁺ (dmbpy=4,4′‐dimethyl‐2,2′‐bipyridine, HAT=1,4,5,8,9,12‐hexaazatriphenylene), which absorbs near‐infrared light up to 800 nm based on its metal‐to‐ligand charge transfer (¹MLCT) transition. Importantly, [Ru₃(dmbpy)₆(μ‐HAT)]⁶⁺ is found to be the first example of a photosensitizer which can drive H₂ evolution under the illumination of near‐infrared light above 700 nm. The electrochemical and photochemical studies reveal that the reductive quenching within the ion‐pair adducts of [Ru₃(dmbpy)₆(μ‐HAT)]⁶⁺ and ascorbate anions affords a singly reduced form of [Ru₃(dmbpy)₆(μ‐HAT)]⁶⁺, which is used as a reducing equivalent in the subsequent water reduction process.     

Nickeladihydrofuran. Key intermediate for nickel-catalyzed reaction of alkyne and aldehyde

The formation of a nickeladihydrofuran by oxidative cyclization of an alkyne and an aldehyde with nickel(0) has been demonstrated; the transformation of the nickeladihydrofuran into an enone by decomposition, a lactone by carbonylation and an allylic alcohol by treatment with ZnMe(2) suggests that nickeladihydrofuran is an important key intermediate in a variety of catalytic reactions.     

Formation of acylruthenium promoted by coordination of AlMe(3) to (eta(4)-cyclopentadienone)Ru(CO)(3)

The reaction of AlMe(3) with (eta(4)-tetraphenylcyclopentadienone)Ru(CO)(3) leads to rapid and quantitative formation of an adduct arising from coordination of the enone oxygen to aluminium, which undergoes alkylation at the Ru(CO)(3) moiety to give (eta(5)-C(4)Ph(4)C(OAlMe(2)))Ru(CO)(2)(COMe) concomitant with a change of hapticity of the dienone ligand.     

Efficient Rabin-type Digital Signature Scheme

Rabin's cryptosystem was proved to be as hard as factorization. However, Rabin's digital signature schemes is probabilistic. This paper shows two efficient Rabin type digital signature schemes, a basic scheme and an improved scheme. Both schemes run much faster than Rabin's scheme. They are deterministic and the size of a signature is much smaller than that of a signature in Rabin's scheme. Furthermore, it is proved that, by applying the technique of Bellare and Rogaway, the proposed scheme is secure against chosen plaintext attack. More precisely, breaking the proposed digital signature scheme by chosen plaintext attack is as hard as factoring N.     

Formation of nickeladihydropyran by oxidative addition of cyclopropyl ketone. Key intermediate in nickel-catalyzed cycloaddition

Cyclopropyl phenyl ketone underwent oxidative addition to Ni(PCy3) generated from Ni(cod)2 and PCy3 to give a nickeladihydropyran, which is a key intermediate for the Ni(0)-catalyzed homo- or heterocycloaddition to give cyclopentane compounds having two carbonyl substituents at the 1,3-position.     

Structure-activity relationships of neuromedin U. V. study on the stability of porcine neuromedin U-8 at the C-terminal asparagine amide under mild alkaline and acidic conditions

Porcine neuromedin U-8 (X-Asn-NH(2), X=H-Tyr-Phe-Leu-Phe-Arg-Pro-Arg) is occasionally unstable in the biological fluids used for bioassay as well as in the acidic solutions used for purification of synthetic peptides. In this study, HPLC examination of an incubate solution of X-Asn-NH(2) revealed that the main decomposition products in Tyrode's solution (pH 7.4) were either alpha- or beta-monocarboxylic acid analogs (X-Asn-OH or X-Asp-NH(2)), and that no dicarboxylic acid analog (X-Asp-OH) was produced. Further investigation, employing a model peptide (Y-Asn-NH(2), Y=Benzoyl-Pro-Arg) incubated in a 0.1 M sodium bicarbonate solution at 60 degrees C, revealed that the decomposition of C-terminal Asn-NH(2) occurred through the formation of an aminosuccinimide intermediate (Y-Asu), at a rate faster than that of Y-Asn-Ser peptide but slower than that of Y-Asn-Gly peptide. Mild acid hydrolysis of X-Asn-NH(2) examined in a 1 M HCl solution at 60 degrees C yielded X-Asn-OH and X-Asp-NH(2), which further decomposed to yield X-Asp-OH. The C-terminal degradation of X-Asn-NH(2) resulted in reduced biological and immunochemical binding activities.     

Piezoelectric immunosensor for bisphenol A based on signal enhancing step with 2-methacrolyloxyethyl phosphorylcholine polymeric nanoparticle

An immunoassay in which BPA competed with a BPA-horseradish peroxidase conjugate for binding to anti-BPA antibodies, coupled to a piezoelectric (PZ) immunosensor, was able to detect 0.1 ng mL(-1) BPA. To enhance the sensitivity of the assay, we tested nanoparticles approximately 200 nm in diameter, coupled to anti-BPA antibodies, to increase the mass change on the surface of the immunosensor and thereby increase the frequency shift detected. This second step, using nanoparticles coated with anti-BPA antibodies, improved the sensitivity of the assay by approximately eight times at BPA concentrations below 10 ng mL(-1). Field emission-scanning electron microscopy (FE-SEM) showed that polymeric 2-methacrolyloxyethyl phosphorylcholine (MPC) nanoparticles coupled to antibodies remained monodisperse on the surface of the immunosensor and therefore produced stable signals in the immunosensors. Since the frequency shift detected in the assay mainly originated from the mass change on the surface of the PZ crystal, the colloidal stability of the antibody-conjugated particles used in the enhancement step played an extremely important role in achieving a stable and highly sensitive signal.