Whittaker functions for generalized principal series representations of GSp(2,R)

We study Whittaker functions for generalized principal series representations of $\mathrm{GSp}(2,\mathbf{R})$ induced from Siegel parabolic subgroup. We give Mellin–Barnes type integral representations of Whittaker functions belonging to certain K-types. As an application of our explicit formulas, we compute the archimedean parts of Novodvorsky's zeta integrals. As a consequence we can show the entireness of the spinor L-functions for generic cusp forms on $\mathrm{GSp}(2)$.     

Critical energy for direct initiation of detonation induced by laser ablation

This study describes experimental work examining the critical energy for direct initiation of detonation by laser ablation in a stoichiometric acetylene–oxygen mixture. The amount of input energy, the target material, and the surface roughness of the target were varied to study their effects on shock wave generation. Aluminum and stainless steel were used as target materials. The propagating shock wave induced by laser ablation was observed using high-speed shadow imaging. The critical energy for direct initiation of detonation was calculated using the strong blast wave theory. The critical input energy for aluminum was found to be lower than that for stainless steel. Because the thermodynamic critical temperature of aluminum is lower than that of stainless steel, aluminum caused a phase explosion more easily than stainless steel, thus resulting in direct initiation of detonation with a lower amount of input energy. The effects of surface roughness on critical input energy and shock wave generation were negligibly small. The critical initiation energy was estimated to be \(10.3 \pm 0.2\) mJ, which is in agreement with the experimental data obtained in previous work. The estimated critical initiation energy was independent of the target material. However, other predictions of the critical initiation energy by using the cell size overestimated this value because of the scatter in cell size data of an unstable cellular structure. Furthermore, interaction between plasma plumes formed by laser ablation and those formed by breakdown near the target surface might have contributed to requiring a lower amount of energy for initiating detonation.     

On the Large Time Behavior of Solutions of Hamilton–Jacobi Equations Associated with Nonlinear Boundary Conditions

In this article, we study the large time behavior of solutions of first-order Hamilton–Jacobi Equations set in a bounded domain with nonlinear Neumann boundary conditions, including the case of dynamical boundary conditions. We establish general convergence results for viscosity solutions of these Cauchy–Neumann problems by using two fairly different methods: the first one relies only on partial differential equations methods, which provides results even when the Hamiltonians are not convex, and the second one is an optimal control/dynamical system approach, named the “weak KAM approach”, which requires the convexity of Hamiltonians and gives formulas for asymptotic solutions based on Aubry–Mather sets.     

Optically Active Oxo(phthalocyaninato)vanadium(IV) with Geometric Asymmetry: Synthesis and Correlation between the Circular Dichroism Sign and Conformation

Oxovanadium(IV) phthalocyanines (VOPcs) with a single‐handed rotation have been prepared, and their right‐ and left‐handed enantiomers resolved on a chiral HPLC column. These enantiomers gave circular dichroism (CD) spectra of opposite signs; the correlation between the CD sign and conformation was obtained by time‐dependent density functional theory (TDDFT) calculations: an enantiomer showing a negative sign in the Q band was suggested to be the right‐handed conformer viewing from the axial oxygen side, whereas that giving a positive CD sign was assigned to the left‐handed conformer. Although silicon phthalocyanines (SiPcs) with two different alkoxy axial ligands have been resolved similarly, the absence of a meaningful CD difference probably reflects the flat character of the SiPc plane compared to the VOPc plane. Changes in the Q‐band CD, depending on the relative orientation of the peripheral substituents, have been worked out theoretically and the origin of the chiroptical properties is discussed.     

A family of degenerate elliptic operators: Maximum principle and its consequences

In this paper we investigate the validity and the consequences of the maximum principle for degenerate elliptic operators whose higher order term is the sum of k eigenvalues of the Hessian. In particular we shed some light on some very unusual phenomena due to the degeneracy of the operator. We prove moreover Lipschitz regularity results and boundary estimates under convexity assumptions on the domain. As a consequence we obtain the existence of solutions of the Dirichlet problem and of principal eigenfunctions.     

Studies on two different diastereoselective reaction pathways from a serinol derivative to 4-hydroxymethyl-2-oxazolidinones using 2-chloroethyl chloroformate and N,N′-disuccinimidyl carbonate

Two reaction pathways and their diastereoselectivity-determining steps of the asymmetric desymmetrization of (R)-2-(α-methylbenzyl)amino-1,3-propanediol 1 with 2-chloroethyl chloroformate (CCF) and with N,N′-disuccinimidyl carbonate giving (4S,αR)-4-hydroxymethyl-3-α-methylbenzyl-2-oxazolidinones (4S)-3 and its (4R,αR)-diastereomer (4R)-3 were investigated. The reaction of serinol 1 and CCF to give the corresponding carbonates was not a diastereoselectivity-determining step. The carbonates gave (R)-5-(α-methylbenzyl)amino-1,3-dioxan-2-one 4 after addition of DBU, and an intramolecular acyl transfer of 4 was found to be a diastereoselectivity-determining step to give (4S)-3. Conversely, the reaction of serinol 1 and N,N′-disuccinimidyl carbonate afforded directly the opposite diastereomer (4R)-3 but not via the intermediate 4. Thus, their diastereoselectivities depended on the acylating reagent.     

Observation of hydrogen in deuterated methane hydrate by maximum entropy method with neutron powder diffraction

The crystal structure of deuterated methane hydrate (structure I, space group: Pm(-)3n) was investigated by neutron powder diffraction at temperatures of 7.7-185 K. The scattering amplitude density distribution was examined by a combination of Rietveld method and maximum entropy method (MEM). The distribution of the D atoms in both D(2)O and CD(4) molecules was clarified from three-dimensional graphic images of the scattering amplitude density. The MEM results showed that there were low-density sites for the D atom of D(2)O in a particular location within the D(2)O cage at low temperatures. The MEM provided more reasonable results because of the decrease in the R factor that is attainable by this method. Accordingly, the low-density sites for the D atom of D(2)O probably exist within the D(2)O cage. This suggests that a spatial disorder of the D atom of D(2)O occurs at these sites and that hydrogen bonds between D(2)O molecules become partially weakened. With regard to the CD(4) molecules, there were high-density sites for the D atom of CD(4), and the density distribution of the C and D atoms was observed separately in the scattering amplitude density image. Consequently, the C-D bonds of CD(4) were not observed clearly because the CD(4) molecules had an orientational disorder. The D atoms of CD(4) were displaced from the line between the C and O atoms, and were located near the face center of the polygon in the cage. Accordingly, the D atoms of CD(4) were not bonded to specific O atoms. This result is consistent with the hydrophobicity of the CD(4) molecule. We also report the difference between the small and the large cages in the density distribution map and the temperature dependence of the scattering amplitude density.     

Ruthenium-catalyzed cycloaddition of 1,6-diynes and nitriles under mild conditions: role of the coordinating group of nitriles

In the presence of a catalytic amount of [Cp*RuCl(cod)] (Cp*=pentamethylcyclopentadienyl, cod=1,5-cyclooctadiene), 1,6-diynes were allowed to react chemo- and regioselectively with nitriles bearing a coordinating group, such as dicyanides or alpha-halonitriles, at ambient temperature to afford bicyclic pyridines. Careful screening of nitrile components revealed that a C[triple chemical bond]C triple bond or heteroatom substituents, such as methoxy and methylthio groups, proved to act as the coordinating groups, whereas C==C or C==O double bonds and amino groups failed to promote cycloaddition. This suggests that coordinating groups with multiple pi-bonds or lone pairs are essential for the nitrile components.