Explicit formulas,symmetry and symmetry breaking for Willmore surfaces of revolution

In this paper, we prove explicit formulas for all Willmore surfaces of revolution and demonstrate their use in the discussion of the associated Dirichlet boundary value problems. It is shown by an explicit example that symmetric Dirichlet boundary conditions do in general not entail the symmetry of the surface. In addition, we prove a symmetry result for a subclass of Willmore surfaces satisfying symmetric Dirichlet boundary data.     

Simultaneous single-frequency oscillations on different transitions in a laser-diode-pumped LiNdP(4)O(12) laser

Simultaneous single-mode oscillations on different transitions were observed in a laser-diode-pumped microchip LiNdP(4)O(12) laser. The unusual modal-output characteristics of the laser were reproduced by multitransition-oscillation laser model equations that include cross saturation of population inversions with a strong spatial exponential decay and transition-dependent resonant reabsorption loss.     

Orbital-Overlap control in the solid-state reactivity of beta-azido-propiophenones: selective formation of cis-azo-dimers

Solid-state photolysis of 1a,b yields selectively cis-3a,b. X-ray analysis of 1a,b reveals the molecules adopt an extended structure and as such the crystal packing arrangement consists of planar, pi-stacked molecules. The shortest intermolecular distance between adjacent N-atoms is approximately 3.76 A and would lead to formation of trans-3a,b, whereas cis-3a,b is formed by dimerization between N-atoms that are approximately 3.9 A apart. We propose that the molecular orbital alignment of the adjacent nitrenes controls the solid-state reactivity.     

On the mechanism of reaction of radicals with tirapazamine

Ketyl radicals produced by photolysis of ketones or di-tert-butyl peroxide (DTBP) in alcohol solvents react rapidly with tirapazamine (TPZ). The acetone ketyl radical (ACOH) reacts with TPZ with an absolute second-order rate constant of (9.7 +/- 0.4) x 108 M-1 s-1. The reaction kinetics can be followed by monitoring the bleaching of TPZ absorption at 475 nm or the formation of a reaction product which absorbs at 320 and 410 nm. The ACOD radical reacts with TPZ in 2-propanol-OD with an absolute rate constant of (6.7 +/- 0.5) x 108 M-1 s-1, corresponding to a kinetic isotope effect (KIE) of 1.4. Deuteration of the radical on carbon (ACOH-d6) retards the reaction of the radical with TPZ even further (absolute rate constant = (4.8 +/- 0.04) x 108 M-1 s-1). This result corresponds to a KIE of 2.0. Radicals derived from dioxane and diisopropyl ether by flash photolysis of DTBP in ethereal solvent react with TPZ more slowly than do ketyl radicals. It is concluded that ketyl radicals react, in part, with TPZ in organic solvents by transfer of a hydrogen atom from the OH and CH3 groups of the ketyl radical to the oxygen atom at the N4 position of TPZ to form acetone or acetone enol and a radical derivative of TPZ (TPZH). The latter species absorbs at 320 and 405 nm, has a lifetime of hundreds of microseconds in alcohol solvents, and decays by disproportionation to form TPZ and a reduced heterocycle. The reduced heterocycle eventually forms a desoxytirapazamine by a polar mechanism. The results are supported by density functional theory calculations. It is proposed that dioxanyl radical will also react, in part, with TPZ by transfer of a hydrogen atom from the carbon adjacent to the radical center to the oxygen atom at the N4 position of TPZ. This produces the enol ether and the previously mentioned TPZH radical. It is further posited that ether radicals react a bit more slowly than ketyl radicals because they lack the second mode of hydrogen transfer (from the OH group) that is present in the ACOH radical. Our data are permissive of the possibility that ether radicals add to TPZ at a rate that is competitive with beta-hydrogen atom transfer.     

Triplet-sensitized photolysis of alkoxycarbonyl azides in solution and matrices

Photolysis of azides 1–4 in methanol, which have a built-in intramolecular triplet sensitizer, yields mainly carbamates 5–8. Laser flash photolysis of 1–4 shows formation of their triplet-excited ketone, which decays by intramolecular energy transfer to form triplet nitrenes 1n–4n. Irradiating 1–3 in matrices yields isocyanic acid, whereas photolysis of 4 forms isocyanate 4i. The depletion rate of the azide bands between 2100 and 2200 cm^?1 is different than the rate of formation for the isocyanic acid bands at ～2265 cm^?1; thus, the formation of isocyanic acid is a stepwise process. Irradiating 1 in matrices produces an absorption band due to nitrene 1n (λ_max ～ 343 nm), which is depleted upon further irradiation, whereas the absorption due to 4-acetyl benzaldehyde (λ_max ～ 280 nm) increases with prolonged irradiation. We propose that formation of isocyanic acid in matrices must come from secondary photolysis of nitrenes 1n–3n. This mechanism is further supported by calculation, which show that the estimated transition state for 1n–4n to fall apart to yield alkoxy and cyanato radicals is only ～34 kcal/mol above the ground state of the triplet nitrenes and thus the cleavage can take place photochemically. Thus, nitrenes 1n–4n can be formed selectively, but these intermediates are highly photosensitive and undergo secondary photolysis in matrices.     

Laryngeal Myasthenia Gravis: Report of 40 Cases

Myasthenia gravis, an autoimmune disorder of the neuromuscular junction, is usually recognized because of ocular complaints or generalized weakness. We report a series of 40 patients who presented with dysphonia as their initial and primary complaint. Diagnostic testing included strobovideolaryngoscopy, electromyography (EMG) with repetitive stimulation and Tensilon testing, and laboratory and radiographic evaluation. Strobovideolaryngoscopy most commonly revealed fluctuating impairment of vocal fold mobility, either unilateral or bilateral. EMG detected evidence of neuromuscular junction abnormalities in all patients. Only one patient had evidence of antiacetylcholine receptor (ACh-R) antibodies, but many other abnormalities suggestive of autoimmune dysfunction were present. Pyridostigmine therapy was initiated in 34 patients but was not tolerated in 4. Of the remaining 30 patients, 23 reported improvement of symptoms. We conclude that myasthenia gravis can present with symptoms confined primarily to the larynx and should be included in the differential diagnosis of dysphonia.     

On the convergence of a dual-primal substructuring method

Summary.   In the Dual-Primal FETI method, introduced by Farhat et al. [5], the domain is decomposed into non-overlapping subdomains, but the degrees of freedom on crosspoints remain common to all subdomains adjacent to the crosspoint. The continuity of the remaining degrees of freedom on subdomain interfaces is enforced by Lagrange multipliers and all degrees of freedom are eliminated. The resulting dual problem is solved by preconditioned conjugate gradients. We give an algebraic bound on the condition number, assuming only a single inequality in discrete norms, and use the algebraic bound to show that the condition number is bounded by for both second and fourth order elliptic selfadjoint problems discretized by conforming finite elements, as well as for a wide class of finite elements for the Reissner-Mindlin plate model. Received January 20, 2000 / Revised version received April 25, 2000 / Published online December 19, 2000     

Pulsed laser photothermal displacement spectroscopy for surface studies

The feasibility of pulsed laser photothermal displacement spectroscopy for surface studies is demonstrated. With this method transient heating phenomena can be investigated. The technique provides a real-time, non-contact and non-destructive probe of the surface temperature and can be used to study thermal properties and their changes, e.g. during pulsed laser annealing. Possible applications also include investigations of thin films and adsorbates in ultrahigh vacuum as well as in other environments.First results of these experiments have been reported at the Spring Meeting on Surface Physics of the German Physical Society in Bayreuth, March 25–29, 1985     

Slowing down of gamma photons

Hyperfine Interactions - By a transformation to a rotating reference system, a nuclear level mixing scheme is equivalent to a scheme with pure quadrupole splitting and a strong RF-drive between...