The polynomial invariants of twisted links

A twisted link is a generalization of a virtual link, which is related to a link diagram on a closed, possibly non-orientable surface. In this paper we generalize the Miyazawa polynomial invariant of a virtual link to an invariant of a twisted link in two formulae one of which is introduced by A. Ishii and the other by the author.     

The Miyazawa polynomial for long virtual knots

We introduce a two-variable polynomial invariant of a long virtual knot, which dominates the Kauffman f-polynomial and the Miyazawa polynomial of the closure. Our invariant satisfies a product formula for the concatenation product of long virtual knots. It describes a formula of the Miyazawa polynomial of a ‘connected sum’ of two virtual knots. It also gives lower bounds for the real crossing number and the virtual crossing number of a long virtual knot.     

Blocks with nonabelian defect groups which have cyclic subgroups of index p

In representation theory of finite groups, one of the most important and interesting problems is that, for a p-block A of a finite group G where p is a prime, the numbers k(A) and ℓ(A) of irreducible ordinary and Brauer characters, respectively, of G in A are p-locally determined. We calculate k(A) and ℓ(A) for the cases where A is a full defect p-block of G, namely, a defect group P of A is a Sylow p-subgroup of G and P is a nonabelian metacyclic p-group M _n+1(p) of order p ⁿ⁺¹ and exponent p ⁿ for n \geqslant 2{n \geqslant 2}, and where A is not necessarily a full defect p-block but its defect group P = M _n+1(p) is normal in G. The proof is independent of the classification of finite simple groups.     

Synthesis and development of biologically active fluorescent-labeled vitamin K analogues and monitoring of their subcellular distribution

New fluorescent analogues of menaquinone-4 and phylloquinone were prepared and their subcellular distribution monitored using a confocal laser scanning microscope. These analogues incorporate an FITC group anchored to the naphthoquinone skeleton through an amide bond expected to be resistant to metabolism. On their addition to the culture medium, fluorescence was readily observed inside a human osteosarcoma cell line. This result indicates that the fluorescent analogues penetrate into cells the same as vitamin K, and therefore, would be useful for achieving insight into the action mechanism of vitamin K.     

Convergent synthesis of the F-K ring segment of brevetoxin B

A convergent synthesis of the F-K ring segment of brevetoxin B has been achieved via the intramolecular allylation of an α-chloroacetoxy ether and subsequent ring-closing metathesis.     

Direct observation of unstable intermediate species in the reaction of trans-2-butene on ferrierite zeolite by picosecond infrared laser spectroscopy

The reaction dynamics of trans-2-butene adsorbed to acidic hydroxyl groups on the surface of ferrierite zeolite is examined by time-resolved spectroscopy using a tunable infrared picosecond pulse laser system. The transient absorption spectra measured by a two-color pump-probe technique at 188-243 K reveal bleaching and hot bands of the OD stretching mode 2 ps after excitation. This vibrationally excited state relaxes within 20 ps at 188 K, while the bleaching band includes a long-lifetime component that lasts for more than 100 ps at 243 K. Thus, the OD (isotope-exchanged hydroxy groups) stretching band does not entirely recover in this period and is mirrored by an analogous weakening of the CH bending band of the adsorbed trans-2-butene. Simultaneously, three new bands in CH stretching region were observed at 3045, 3095, and 3130 cm(-1). This result suggests the presence of a short-lived intermediate formed by reaction between the acidic hydroxyl groups and adsorbed trans-2-butene.     

New base pairing motifs. The synthesis and thermal stability of oligodeoxynucleotides containing imidazopyridopyrimidine nucleosides with the ability to form four hydrogen bonds

The synthesis and thermal stability of oligodeoxynucleotides (ODNs) containing imidazo[5',4':4,5]pyrido[2,3-d]pyrimidine nucleosides 1-4 (N(N), O(O), N(O), and O(N), respectively) with the aim of developing two sets of new base pairing motifs consisting of four hydrogen bonds (H-bonds) is described. The proposed four tricyclic nucleosides 1-4 were synthesized through the Stille coupling reaction of a 5-iodoimidazole nucleoside with an appropriate 5-stannylpyrimidine derivative, followed by an intramolecular cyclization. These nucleosides were incorporated into ODNs to investigate the H-bonding ability. When one molecule of the tricyclic nucleosides was incorporated into the center of each ODN (ODN I and II, each 17mer), no apparent specificity of base pairing was observed, and all duplexes were less stable than the duplexes containing natural G:C and A:T pairs. On the other hand, when three molecules of the tricyclic nucleosides were consecutively incorporated into the center of each ODN (ODN III and IV, each 17mer), thermal and thermodynamic stabilization of the duplexes due to the specific base pairings was observed. The melting temperature (T(m)) of the duplex containing the N(O):O(N) pairs showed the highest T(m) of 84.0 degrees C, which was 18.2 and 23.5 degrees C higher than that of the duplexes containing G:C and A:T pairs, respectively. This result implies that N(O)and O(N) form base pairs with four H-bonds when they are incorporated into ODNs. The duplex containing N(O):O(N) pairs was markedly stabilized by the assistance of the stacking ability of the imidazopyridopyrimidine bases. Thus, we developed a thermally stable new base pairing motif, which should be useful for the stabilization and regulation of a variety of DNA structures.     

Synthesis and characterization of trimetallic complexes with a borazine core

Treatment of [Cp*Ru(dppe)]⁺ with B-triethynyl-N-trimethylborazine and piperidine produces the trimetallic complex [Cp*Ru(dppe)(CC)]₃B₃N₃Me₃, the structure of which has been confirmed by X-ray diffraction. Reaction of RuHCl(CO)(PPh₃)₃ with B-triethynyl-N-trimethylborazine produces the trimetallic complex [RuCl(CO)(PPh₃)₂(CH=CH)]₃B₃N₃Me₃.     

Visible light photoelectrochemical activity of K4Nb6O17 intercalated with photoactive complexes by electrostatic self-assembly deposition

Electrostatic self-assembly deposition (ESD) results in the intercalation of Ru(bpy)₃²⁺ or methylene blue (MB) into the niobate layered oxide right after the cations come into contact with [Nb₆O₁₇]⁴⁻ nanosheets. Monolayers can be obtained by the exfoliation of proton exchanged K₄Nb₆O₁₇ (KNbO) in an aqueous tetrabutylammonium (TBA) solution as revealed by the atomic force microscopy micrographs. UV-vis spectra show that intercalated films are able to absorb in the visible light range. Heat-treatment of Ru(bpy)₃²⁺ resulted in the red-shift in the absorption spectra, which was assigned to the enhancement in the interaction between the complex molecules and [Nb₆O₁₇]⁴⁻ host layer. Intercalated niobate layered oxides are able to produce photocurrent as a result of the electron transfer from the excited guest molecule to the host layer under visible light illumination. Ru(bpy)₃²⁺ intercalated niobate layered oxide shows photocatalytic activity under visible light illumination to produce H₂ from water-methanol solution.     

An analytical method for irinotecan (CPT-11) and its metabolites using a high-performance liquid chromatography: parallel detection with fluorescence and mass spectrometry

Irinotecan or 7-ethyl-10-[4-(1-piperidino)-1-piperidino]carbonyloxycamptothecin (CPT-11) is an anticancer pro-drug used in the treatment of many types of cancer. We describe here the validation of an analytical method for CPT-11 and its metabolites, including an active metabolite, 7-ethyl-10-hydroxycamptothecin (SN-38), its glucuronidated form, SN-38G, and several cytochrome P450 3A-mediated products such as 7-ethyl-10-[4-N-(5-aminopentanoic acid)-1-piperidino]carbonyloxycamptothecin (APC) using a high-performance liquid chromatography connected to parallel fluorescence and mass spectrometry detection systems. This method is characterized as follows: (1) simple extraction of the analytes from biomaterials with perchloric acid/methanol; (2) sensitive quantitation of major metabolites (SN-38G, SN-38 and APC) with a fluorescence detector (FLD), where the limits of quantitation by FLD were 2.5 ng/mL for SN-38G and APC, 5 ng/mL for CPT-11 and 1 ng/mL for SN-38, respectively; (3) parallel selective monitoring of the metabolites including minor metabolites with a mass selected detector (MSD). There was no observed interference by other drugs expected to be co-administered. This method showed its usefulness by identifying a novel metabolite produced in human hepatic microsomes. The results indicate that this combination of FLD and MSD enables a highly selective analysis of CPT-11 and its metabolites, and is useful for studies both in vivo and in vitro.