The finite section method for Moore-Penrose inversion of Toeplitz operators

It is shown that for certain classes of infinite block Toeplitz matricesT(a)=[a _j-k ] ₀ the Moore-Penrose inverses of the finite sectionT _n (a)=[a _j-k ] ₀ ^n–1 converge to the Moore-Penrose inverse ofT(a). Furthermore the convergence for modified finite section methods and the finite section method for Wiener-Hopf integral and related operators are studied.     

Local Borel summability of Euclidean 311-1311-1311-1a simple proof via differential flow equations

It is shown how the differential flow equation (or, equivalently, the continous renormalization group) method can be employed to give an astonishingly easy proof of the local Borel summability of the renormalized perturbative Euclidean massive ₄ ⁴ .Supported by NSF grant # DMS-9100383     

Structural phase transitions in ‘hcp’ C70 single-crystals

The thermal expansion of vapor-grownC ₇₀ single crystals ahs been investigated using high-resolution capacitance dilatometry from 5–380 K. Measurements were made both parallel and perpendicular to the hexagonalc-axis. Three first-order phase transitions which we associate with the consecutive disordering of theC ₇₀ molecules are observed upon heating at 280 K (long-axis spinning), 300 K (long-axis precession) and 355 K (quasi-free rotation), respectively. The highest-temperature transition exhibits a very large (50 K) thermal hysteresis. Powder and single-crystal X-ray diffraction show that the crystals are predominantly hexagonal-close-packed (HCP) with an idealc/a1.63 above 360 K andc/a1.84 at 295 K.     

Two-photon spectroscopy of the low-lying singlet states of naphthalene and acenaphthene

Two-photon excitation spectra of naphthalene and acenaphthene have been measured up to 50000 cm^?1. In naphthalene. three two-photon allowed states are observed for which the symmetry assignment is confirmed by polarization. The corre- sponding transitions are also seen in acenaphthene. The experimental data are in excellent agreement with theoretical predictions.     

Carbon Participation in the Solvolysis of 6-exo-substituted 2-exo- and 2-endo-Norbornyl p-Toluenesulfonates. Norbornanes part 5

The solvolysis rates and products of the 6-exo-substituted 2-exo- 1a - 1u , and 2-endo-norbornyl p-toluenesulfonates 2a - 2u , have been determined. In general, the rate constants for 1 and 2 (log k) correlate well with the inductive constants σ of the substitutents at C(6); however, their sensitivity to σ is much larger in the 2-exo-series 1 than in the 2-endo-series 2 . This differential transmission of polar effects is the cause of decreasing 2-exo/2-endo rate ratios from 2388 for R = t-C₄H₉ to 0.37 for R = Br, i. e. with increasing electron attraction by the substituent. The high sensitivity of the rate constants for the 2-exo-p-toluenesulfonates 1 to σ indicates an unusually strong inductive interaction between C(6) and the incipient cationic center at C(2). This interaction is ascribed to the participation of the pentacoordinate C(6)-atom, i. e. to 1,3-bridging, a consequence of steric hindrance of nucleophilic solvent participation in norbornanes. Donor substituents enhance 1,3-bridging, lead to faster reactions and to the formation of 2-exo substitution products. Conversely, acceptor substituents reduce 1,3-bridging, decrease rates and facilitate the formation of 2-endo substitution products. Graded 1,3-bridging is discussed in the light of Winstein's nonclassical ion concept.     

pH-Dependent force spectroscopy of tri(ethylene glycol)- and methyl-terminated self-assembled monolayers adsorbed on gold

Self-assembled monolayers (SAMs) of methoxy-tri(ethylene glycol)- (EG(3)-OMe) and methyl-terminated alkanethiols (C(16)) adsorbed on polycrystalline gold were investigated by chemical force spectroscopy. Measurements were performed in aqueous electrolyte solutions depending on ionic strength and pH value. Charged and hydrophobic tips were employed as probes to mimic local patches of proteins and to study the interaction at the organic/liquid interface in detail. Force-distance curves reveal information about the origin of the observed interaction and the underlying mechanisms. The measurements confirm an effective negative surface charge to be present at the oligo(ethylene glycol) (OEG) and the methyl interface and suggest that the charges are due to the adsorption of hydroxyl ions from aqueous solution. pH-dependent measurements further support the robustness of the established charge associated with the OEG films. Its sign does not change over the whole range of investigated values between pH approximately 3.5 and approximately 10. In contrast, the hydrophobic self-assembled hexadecanethiol films on gold show an isoelectric point (IEP) around pH 4. While the mechanism of charge establishment appears to be similar for both SA films, the strength of hydrogen bonding to interfacial water, which acts as a template for hydroxyl ion adsorption, is likely to be responsible for the observed difference.     

Koordinative Verankerung von Nickelkomplexen an Hectorit-Schichtsilicaten mit Hilfe langkettiger Diphenylphosphinogruppen

Coordinative Anchoring of Nickel Complexes on Hectorite-Layer Silicates through long-chain Diphenylphosphine Groups The treatment of sodium and calcium hectorites with 2-diphenylphosphinoethyltriethoxysilane leads, by condensation of free hydroxyl groups, to functionalized layer silicates with long-chain diphenylphosphine groups onto which nickel chloride can be coordinated. In these modified hectorites the fourth coordination site of the tetrahedrally coordinated nickel is occupied by a labile solvent molecule. On the other hand, the complex bis(2-diphenylphosphinoethyltriethoxysilane)nickel(II) chloride prepared beforehand also reacts with sodium hectorite under condensation; but the square-planar coordination of the four stable ligands (two chloride and two phosphor atoms) is maintained. This finds its expression in a significant activity decrease in catalytic reactions as compared to the aforementioned products.     

Partial indices for Toeplitz-like operators

The concept of partial indices, which is usually associated with matrix-functions, is defined for operators A satisfying rank (AU-VA)< for some fixed U and V (Toeplitz-like operators). A survey of the properties of partial indices is presented, some examples, and the connection with Kronecker indices as well. An application concerning Toeplitz plus Hankel matrices is supplemented.     

Synthesis of cryptophycins via an N-acyl-beta-lactam macrolactonization

An efficient and concise approach to the synthesis of the macrolide core of the cryptophycins has been developed. A novel macrolactonization utilizing a reactive acyl-beta-lactam intermediate incorporates the beta-amino acid moiety within the 16-membered macrolide core. This modular approach, involving a cyanide-initiated acyl-beta-lactam ring opening followed by cyclization, was successfully applied to the total synthesis of cryptophycin-24. The strategy was also used in an efficient synthesis of the 6,6-dimethyl-substituted dechlorocryptophycin-52. In this case, the cyanide-initiated ring opening of the bis-substituted 2-azetidinone followed by macrolactonization was achieved through a catalytic process.     

Thermal synthesis of the optical pure pentapeptide derivative Z-(L)-Ala-(L)-Phe-Gly-(L)-Phe-Gly-OMe

The pentapeptide Z-(L)-Ala-(L)-Phe-Gly-(L)-Phe-Gly-OMe was obtained by reacting the activated dipeptide derivative Z-(L)-Ala-(L)-Phe-OPcp with the amino peptide derivative TFA·H-Gly-(L)-Phe-Gly-OMe at 100–105°C under reduced pressure (10^?2-10-^?3 Torr) without using solvents. The product obtained by bulk condensation showed no racemization, whereas the product obtained by a matrix mediated condensation contained 5,5 % diastereomer Z-(L)-Ala-(D)-Phe-Gly-(L)-Phe-Gly-OMe. Separation of diastereomers was achieved by HPLC on a silicagel column.