Diameters of 3-sphere quotients

Let G⊂O(4) act isometrically on S³. In this article we calculate a lower bound for the diameter of the quotient spaces S³/G. We find it to be , which is exactly the value of the lower bound for diameters of the spherical space forms. In the process, we are also able to find a lower bound for diameters for the spherical Aleksandrov spaces, Sn/G, of cohomogeneities 1 and 2, as well as for cohomogeneity 3 (with some restrictions on the group type). This leads us to conjecture that the diameter of Sn/G is increasing as the cohomogeneity of the group G increases.     

Strichartz Estimates for the Schrödinger Equation on Polygonal Domains

We prove Strichartz estimates with a loss of derivatives for the Schrödinger equation on polygonal domains with either Dirichlet or Neumann homogeneous boundary conditions. Using a standard doubling procedure, estimates on the polygon follow from those on Euclidean surfaces with conical singularities. We develop a Littlewood-Paley squarefunction estimate with respect to the spectrum of the Laplacian on these spaces. This allows us to reduce matters to proving estimates at each frequency scale. The problem can be localized in space provided the time intervals are sufficiently small. Strichartz estimates then follow from a recent result of the second author regarding the Schrödinger equation on the Euclidean cone.     

Revisiting the Solubility Concept of Pharmaceutical Compounds

Summary.  The kinetic and thermodynamic solubilities of Roche (Ro) pharmaceutical compounds were determined by HPLC, titrimetry, and UV/Vis spectroscopy in aqueous buffers and in non-buffered systems. For kinetic solubility, a turbidimetric method that allows the rapid determination of solubilities using small amounts of compounds (5–50 mg) was used. Two types of precipitation were observed during the kinetic solubility determinations: i) a disperse precipitation where the solution became foggy with very small particles uniformly distributed in the solution, and ii) discrete precipitation characterized by formation of crystals that rapidly sediment. The thermodynamic solubility was determined by shake flask and titrimetrically using a pH-STAT. The pH-STAT titrimetric method for the pH-thermodynamic solubility profile determination eliminates the buffer species and represents a new way to approach the solubility characterization of pharmaceutical compounds. The strengths of the turbidimetric method for determining the kinetic solubility are its rapidity, minimal compound requirements, and suitability for high throughput screening. The limitations are that the maximum solubility is limited to less than 100 mg · cm⁻³, and the precipitation of trace impurities cannot be distinguished from precipitation of the analyte. The pH-STAT titrimetric approach for the thermodynamic solubility has a lower throughput and is suitable for the characterization of the lead candidate. It is not limited in its solubility range and provides a common basis for the comparison of the solubility values at different pH values in contrast to traditional buffered systems. Received August 21, 2000. Accepted (revised) February 5, 2001     

Intermediate Q from soluble methane monooxygenase hydroxylates the mechanistic substrate probe norcarane: evidence for a stepwise reaction.

Norcarane is a valuable mechanistic probe for enzyme-catalyzed hydrocarbon oxidation reactions because different products or product distributions result from concerted, radical, and cation based reactions. Soluble methane monooxygenase (sMMO) from Methylosinus trichosporium OB3b catalyzes the oxidation of norcarane to afford 3-hydroxymethylcyclohexene and 3-cycloheptenol, compounds characteristic of radical and cationic intermediates, respectively, in addition to 2- and 3-norcaranols. Past single turnover transient kinetic studies have identified several optically distinct intermediates from the catalytic cycle of the hydroxylase component of sMMO. Thus, the reaction between norcarane and key reaction intermediates can be directly monitored. The presence of norcarane increases the rate of decay of only one intermediate, the high-valent bis-mu-oxo Fe(IV)(2) cluster-containing species compound Q, showing that it is responsible for the majority of the oxidation chemistry. The observation of products from both radical and cationic intermediates from norcarane oxidation catalyzed by sMMO is consistent with a mechanism in which an initial substrate radical intermediate is formed by hydrogen atom abstraction. This intermediate then undergoes either oxygen rebound, intramolecular rearrangement followed by oxygen rebound, or loss of a second electron to yield a cationic intermediate to which OH(-) is transferred. The estimated lower limit of 20 ps for the lifetime of the putative radical intermediate is in accord with values determined from previous studies of sterically hindered sMMO probes.     

Preparation and characterization of superionic materials in a new mixed system (Cu(1−x)AgxI)–(Ag2O)–(P2O5), (0.05≤x≤0.25)

In this paper attempts have been made to prepare superionic glassy electrolytes in the mixed system 30(Cu_(1−x)Ag_xI)–46.66(Ag₂O)–23.33(P₂O₅), where x=0.05, 0.1, 0.15, 0.2 and 0.25, respectively, using the melt quenching process. The solid samples were characterized by X-ray diffraction (XRD), differential scanning calorimetry (DSC), Fourier transform infrared (FT-IR) spectroscopy and silver ionic transport number studies. XRD analysis and FT-IR spectroscopic results have provided details regarding the various phases present in the new system and also indicated the formation of composite materials consisting of glassy and crystalline phases. The transport number measurements have indicated the formation of superionic solids having Ag⁺ ions as the mobile species in the present system.     

Spectroscopic diagnostics of chemical processes: applications of tunable optical parametric oscillators

Optical parametric oscillator (OPO) and amplifier (OPA) devices are useful for spectroscopic sensing of chemical processes in laboratory, industrial, and environmental settings. This is particularly true of nanosecond-pulsed, continuously tunable OPO/OPA systems, for which we survey a variety of instrumental strategies, together with actual spectroscopic measurements. The relative merits of OPO wavelength control by intracavity gratings and by injection seeding are considered. A major innovation comprises an OPO with a ring cavity based on periodically poled lithium niobate (PPLN) and injection-seeded by a single-mode tunable diode laser (TDL). Active cavity control by an ‘intensity dip’ method yields an optical bandwidth ≤0.005 cm^-1 (150 MHz), which compares favourably with the performance of advanced grating-tuned OPO/OPA systems. A novel adaptation of this TDL-seeded PPLN OPO employs a compact, inexpensive multimode pump laser, with which it is still possible to obtain continuously tunable single-mode signal output. Cavity ringdown (CRD) spectroscopy also figures prominently, with infrared (IR) CRD spectra from both grating-scanned and TDL-seeded OPOs reported. Finally, a tunable ultraviolet (UV) source, combining a TDL-seeded passive-cavity OPO and a sum-frequency generation stage, is developed for measurements of time-resolved IR-UV double resonance spectra of acetylene and UV laser-induced fluorescence spectra of nitric oxide. Received: 28 March 2000 / Published online: 13 September 2000     

Role of the Immune System in Mediating the Antitumor Effect of Benzophenothiazine Photodynamic Therapy

The role of the host immune system in contributing to tumor regression following benzophenothiazine photodynamic therapy (PDT) was examined. Photodynamic therapy with 2-iodo-5-ethylamino-9-diethylaminobenzo[a]-phenothiazinium chloride (2I-EtNBS) eradicated EMT-6 mammary fibrosarcomas in 75-100% of treated mice. In contrast, PDT failed to inhibit tumor growth in T-cell-deficient nude mice. Furthermore, T-cell depletion studies with anti-CD8 antibody revealed that the CD8+ T-cell population was critical for an effective PDT response (tumor volume 14 days post-PDT: 262 mm3 vs 59 mm3 in controls; P < 0.01). Because anti-CD4 antibody inhibited tumor growth in the absence of PDT, the role of CD4+ T cells remains unclear. Depletion of natural killer (NK) cells in vivo with anti-asialo-GM1 antibody significantly reduced a suboptimal PDT effect relative to vehicle controls (tumor volume 13 days post-PDT: 513 mm3 vs 85 mm3, respectively; P < 0.001). However, splenic NK cells obtained from PDT-treated tumor-bearing mice were not cytotoxic in vitro against EMT-6 cells, suggesting that NK cells contribute to the PDT effect in vivo by an indirect mechanism. In addition, when mice with complete tumor regression following PDT were rechallenged 28 days later with 5 x 10(5) EMT-6 cells, tumor growth was significantly inhibited as compared to controls (tumor volume 40 days postrechallenge: 137 mm3 vs 833 mm3 in controls; P < 0.03; percent animals without tumor in five experiments: 67% vs 8% in controls). Collectively, these results demonstrate that CD8+ T cells are required to prevent tumor regrowth after 2I-EtNBS-PDT, NK cells contribute to this response and such PDT can elicit protective antitumor immunity.     

On k‐ordered graphs

Ng and Schultz [J Graph Theory 1 ( 6 ), 45–57] introduced the idea of cycle orderability. For a positive integer k, a graph G is k‐ordered if for every ordered sequence of k vertices, there is a cycle that encounters the vertices of the sequence in the given order. If the cycle is also a Hamiltonian cycle, then G is said to be k‐ordered Hamiltonian. We give sum of degree conditions for nonadjacent vertices and neighborhood union conditions that imply a graph is k‐ordered Hamiltonian. © 2000 John Wiley & Sons, Inc. J Graph Theory 35: 69–82, 2000     

Coupled semiempirical quantum mechanics and molecular mechanics (QM/MM) calculations on the aqueous solvation free energies of ionized molecules

The aqueous solvation free energies of ionized molecules were computed using a coupled quantum mechanical and molecular mechanical (QM/MM) model based on the AM1, MNDO, and PM3 semiempirical molecular orbital methods for the solute molecule and the TIP3P molecular mechanics model for liquid water. The present work is an extension of our model for neutral solutes where we assumed that the total free energy is the sum of components derived from the electrostatic/polarization terms in the Hamiltonian plus an empirical “nonpolar” term. The electrostatic/polarization contributions to the solvation free energies were computed using molecular dynamics (MD) simulation and thermodynamic integration techniques, while the nonpolar contributions were taken from the literature. The contribution to the electrostatic/polarization component of the free energy due to nonbonded interactions outside the cutoff radii used in the MD simulations was approximated by a Born solvation term. The experimental free energies were reproduced satisfactorily using variational parameters from the vdW terms as in the original model, in addition to a parameter from the one-electron integral terms. The new one-electron parameter was required to account for the short-range effects of overlapping atomic charge densities. The radial distribution functions obtained from the MD simulations showed the expected H-bonded structures between the ionized solute molecule and solvent molecules. We also obtained satisfactory results by neglecting both the empirical nonpolar term and the electronic polarization of the solute, i.e., by implementing a nonpolarization model. ©1999 John Wiley & Sons, Inc. J Comput Chem 20: 1028–1038, 1999     

Metal-Organic Frameworks for Efficient Electrochemical Reduction of Carbon Dioxide

The large concentration of carbon dioxide (CO₂) in the atmosphere can be utilized in industrial production using effective electrocatalysts such as metal-organic frameworks (MOFs). Due to good properties such as high surface area, designable functionality, and uniform constitution, MOFs are regarded as promising electrocatalysts for the carbon dioxide electrochemical reduction reaction (eCO₂RR). This review covers the importance, challenges, and mechanism of eCO₂RR, and simply discusses the progress in the synthesis methods and characterization of MOFs. The review also thoroughly discusses the advances of single metal-based MOFs, mixed metal-based MOFs, and MOF derivatives as electrocatalysts for efficient eCO₂RR.