Zur Theorie der Gammafunction

Ohne Zusammenfassung Vergl. meine Abhandlung:Om en ny klass af transcendenta functioner, hvilka ?ro n?ra besl?gtade med gammafunktionen, Acta soc. scient. Fennic?, Tom. XIV, XV; 1885, 1886.     

A nanoscale field effect data storage of bipolar endo-fullerenes shuttle device

We investigated the internal dynamics of an electro-fluid shuttle memory element, consisting of K⁺@C₆₀ and F⁻@C₆₀ encapsulated in a C₆₄₀ nanocapsule. Energetics and operating responses of bipolar endo-fullerenes shuttle memory device, (K⁺@C₆₀–F⁻@C₆₀)@C₆₄₀, were examined by classical molecular dynamics simulations under the external force fields.     

On the Automorphism Group of the Kohn-Nirenberg Domain

In this paper, we prove that there are no automorphism orbits of the Kohn-Nirenberg domain accumulating at the origin.     

A Family of Molecular Sieves Containing Framework‐Bound Organic Structure‐Directing Agents

Organic structure‐directing agents (OSDAs), such as quaternary ammonium cations and amines, used in the synthesis of zeolites and related crystalline microporous oxides usually end up entrapped inside the void spaces of the crystallized inorganic host lattice. But none of them is known to form direct chemical bonds to the framework of these industrially important catalysts and adsorbents. We demonstrate that ECR‐40, currently regarded as a typical silicoaluminophosphate molecular sieve, constitutes instead a new family of inorganic‐organic hybrid networks in which the OSDAs are covalently bonded to the inorganic framework. ECR‐40 crystallization begins with the formation of an Al–OSDA complex in the liquid phase in which the Al is octahedrally coordinated. This unit is incorporated in the crystallizing ECR‐40. Subsequent removal of framework‐bound OSDAs generates Al‐O‐Al linkages in a fully tetrahedrally coordinated framework.     

Global gradient estimates for non-uniformly elliptic equations

We consider a nonlinear and non-uniformly elliptic problem in divergence form on a bounded domain. The problem under consideration is characterized by the fact that its ellipticity rate and growth radically change with the position, which provides a model for describing a feature of strongly anisotropic materials. We establish the global Calderón–Zygmund type estimates for the distributional solution in the case that the boundary of the domain is of class \(C^{1,\beta }\) for some \(\beta >0\).     

Total synthesis of α-1C-galactosylceramide, an immunostimulatory C-glycosphingolipid, and confirmation of the stereochemistry in the first-generation synthesis

A nonisosteric α-C-glycoside analogue of KRN7000 (α-1C-GalCer, 1) was reported to induce a selective type of cytokine release in human invariant natural killer cells in vitro. We report here a very concise synthetic route to 1 and its analogue 1'. The key steps include olefin cross-metathesis, Sharpless asymmetric epoxidation, and epoxide opening by NaN(3)/NH(4)Cl. Inversion of configuration at the amide-bearing carbon in the phytosphingosine backbone constructed by epoxide opening in our previous synthesis of 1 was verified, indicating that remote group participation is not involved during the epoxide-opening reaction.     

Progressive formation of fine and coarse ripples on SiC surface by repeated irradiation of femtosecond laser pulses

In this work, we report the progressive formation of first nanoparticles, next fine ripples, and eventually coarse ripples during the irradiation of single-crystal 6H-SiC surfaces with increasing number of femtosecond laser pulses (λ = 515 nm, τ = 250 fs, repetition rate = 100 kHz). At laser fluences greater than the single-pulse ablation threshold, nanoparticles were produced on the surface by the first few pulses over which fine ripple patterns overlapped at increased pulse numbers. As the pulse number was further increased over ten, the surface was gradually transformed into a coarse ripple–covered one. At laser fluence below the threshold, however, only fine ripples were formed nonuniformly.     

Beam Recombination Characteristics in Array Laser Amplification Using Stimulated Brillouin Scattering Phase Conjugation

Beam recombination characteristics were numerically investigated in array laser amplification using stimulated Brillouin scattering phase conjugation. To clarify the effect of piston errors due to imperfect phase locking, spatial intensity profiles of the beam recombination output were calculated in both the near and the far field on the basis of Rayleigh-Sommerfeld diffraction theory. The analyses indicate that piston errors are seriously detrimental to the quality of a beam recombination output and should be eliminated by a proper phase locking. It is also found that the gap between the beam splitting-combining wedges has a negligible effect.Presented at 1996 International Workshop on Interferometry (IWI ‘96), August 27-29, Saitama, Japan.     

Combined study of X-ray reflectivity and atomic force microscopy on a surface-grafted phospholipid monolayer on a solid

We investigated the detailed structure of a surface-grafted phospholipid monolayer, which was polymerized in situ onto a methacryloyl-silanized solid surface. By the combined study of X-ray reflectivity and atomic force microscopy, the in situ polymerization step of the lipid molecules are sufficiently detailed to reveal the molecular structure of lipid molecules before and after in situ polymerization. From the data of the X-ray reflectivity, we confirmed that the in situ polymerization process produces a flat lipid monolayer structure and that the lipid monolayer is substantially grafted on a silanized surface by chemical bonding. After the polymerization and washing processes, the thickness of the head group was 9 angstroms and the thickness of the tail group was 21 angstroms. The surface morphology of the polymerized phospholipid monolayer obtained by the measurements of atomic force microscopy was consistent with the results of the X-ray reflectivity. The cross-sectional analysis shows that the surface coverage of lipid molecules, which are chemically grafted onto a silanized surface, is approximately 89%.