Repeat space theory applied to carbon nanotubes and related molecular networks. III

The present article is part III of a series devoted to extending the Repeat Space Theory (RST) to apply to carbon nanotubes and related molecular networks. In this part III, four problems concerning the above-mentioned extension of the RST have been formulated. Affirmative solutions of these problems imply (i) asymptotic analysis of carbon nanotubes (CNTs) via the new techniques of normed repeat space, Banach algebra, and C*-algebra becomes possible; (ii) a new linkage is formed between the investigations of CNTs and those of ‘spectral symmetry’. In the present paper, we give affirmative solutions to all of the four problems, together with (a) estimates of the norms of matrix sequences representing CNTs, (b) Challenging Problem A^#, which complements Problems A, (c) several pictures of ‘CNT Matrix Art’ which has heuristic power to lead one to get the affirmative answers to the problems formulated in an abstract algebraic manner.     

Governing equations of envelopes created by nearly bichromatic waves and relation to the nonlinear Schrödinger equation

In this paper, we derive the governing equations of the envelope created by nearly bichromatic waves defined as the waves with wavenumber spectrum has two closely approaching peaks and spreads over around two peaks. The obtained governing equation has higher-order terms related to the distinctive quantities of nearly bichromatic waves. We show a nonlinear Schrödinger type equation governs the envelope created by nearly bichromatic waves, up to third order, under some conditions.     

Determination of lidocaine in human serum by capillary gas chromatography with surface ionization detection

A novel analytical method has been developed for the determination of lidocaine (2-(diethylamino)-N-(2,6-dimethyl)phenylacetamide) in human serum. After solvent extraction from serum the extract was analyzed by gas chromatography employing a van den Berg type solventless injector, a new sensitive and selective detector, the surface ionization detector, and a bonded phase flexible fused silica capillary column. The detection limit was ca. 30–50 ng/ml.     

Aspects of form and general topology: Alpha Space Asymptotic Linearity Theorem and the spectral symmetry of alternants

A theoretical device and a technique have been developed by which one can study, in a unifying manner, additive properties of hydrocarbons and the symmetric property of the spectrum of alternants. By using functionals introduced in the approach via the aspects of form and general topology, a special version of the Asymptotic Linearity Theorem (for the study of additivity problems of the zero-point vibrational energy of hydrocarbons and the total pi-electron energy of alternants) has been obtained in parallel with a derivation of the spectral symmetry of alternants.On leave from: Institute for Fundamental Chemistry, 34-4 Nishihiraki-cho, Takano, Sakyo-ku, Kyoto 606, Japan.     

Relative strength of cation-pi vs salt-bridge interactions: the Gtalpha(340-350) peptide/rhodopsin system

Interactions between cationic and aromatic side chains of amino acid residues, the so-called cation-pi interaction, are thought to contribute to the overall stability of the folded structure of peptides and proteins. The transferred NOE NMR structure of the G(t)alpha(340-350) peptide bound to photoactivated rhodopsin (R*) geometrically suggests a cation-pi interaction stabilizing the structure between the epsilon-amine of Lys341 and the aromatic ring of the C-terminal residue, Phe350. This interaction has been explored by varying substituents on the phenyl ring to alter the electron density of the aromatic ring of Phe350 and observing the impact on binding of the peptide to R*. The results suggest that while a cation-pi interaction geometrically exists in the G(t)alpha(340-350) peptide when bound to R*, its energetic contribution to the stability of the receptor-bound structure is relatively insignificant, as it was not observed experimentally. The presence of an adjacent and competing salt-bridge interaction between the epsilon-amine of Lys341 and the C-terminal carboxylate of Phe350 effectively shields the charge of the ammonium group. Experimental data supporting a significant cation-pi interaction can be regained through a series of Phe350 analogues where the C-terminal carboxyl has been converted to the neutral carboxamide, thus eliminating the shielding salt-bridge. TrNOE NMR experiments confirmed the existence of the cation-pi interaction in the carboxamide analogues. Various literature estimates of the strength of cation-pi interactions, including some that estimate strengths in excess of salt-bridges, are compromised by omission of the relevant anion in the calculations.     

Synthetic approach to kendomycin: preparation of the C-glycosidic core

Synthesis of the C13-C19 C-glycoside portion of kendomycin was achieved via oxidative pyran cyclization and Claisen rearrangement to construct the fully functionalized aromatic ring.     

Synthetic studies on sugar-fused erinacines

Samarium-mediated 7-endo-trig radical cyclization afforded excellent stereocontrol of the four contiguous asymmetric centers present in the 6-7-6 tricyclic cores of the (sugar-fused) erinacines E, F, and G.     

Ustalic acid as a toxin and related compounds from the mushroom Tricholoma ustale

A toxin and related compounds were isolated from a poisonous mushroom Tricholoma ustale. Their structures were determined by analyses of the spectral data and synthesis.