Existence and uniqueness of viscosity solutions for a degenerate parabolic equation associated with the infinity-Laplacian

The existence, uniqueness and regularity of viscosity solutions to the Cauchy–Dirichlet problem are proved for a degenerate nonlinear parabolic equation of the form , where denotes the so-called infinity-Laplacian given by . To do so, a coercive regularization of the equation is introduced and barrier function arguments are also employed to verify the equi-continuity of approximate solutions. Furthermore, the Cauchy problem is also studied by using the preceding results on the Cauchy–Dirichlet problem. Dedicated to the memory of our friend Kyoji Takaichi. The research of the first author was partially supported by Waseda University Grant for Special Research Projects, #2004A-366.     

Glycine cleavage system: reaction mechanism, physiological significance, and hyperglycinemia

The glycine cleavage system catalyzes the following reversible reaction: Glycine + H(4)folate + NAD(+) <==> 5,10-methylene-H(4)folate + CO(2) + NH(3) + NADH + H(+)The glycine cleavage system is widely distributed in animals, plants and bacteria and consists of three intrinsic and one common components: those are i) P-protein, a pyridoxal phosphate-containing protein, ii) T-protein, a protein required for the tetrahydrofolate-dependent reaction, iii) H-protein, a protein that carries the aminomethyl intermediate and then hydrogen through the prosthetic lipoyl moiety, and iv) L-protein, a common lipoamide dehydrogenase. In animals and plants, the proteins form an enzyme complex loosely associating with the mitochondrial inner membrane. In the enzymatic reaction, H-protein converts P-protein, which is by itself a potential alpha-amino acid decarboxylase, to an active enzyme, and also forms a complex with T-protein. In both glycine cleavage and synthesis, aminomethyl moiety bound to lipoic acid of H-protein represents the intermediate that is degraded to or can be formed from N(5),N(10)-methylene-H(4)folate and ammonia by the action of T-protein. N(5),N(10)-Methylene-H(4)folate is used for the biosynthesis of various cellular substances such as purines, thymidylate and methionine that is the major methyl group donor through S-adenosyl-methionine. This accounts for the physiological importance of the glycine cleavage system as the most prominent pathway in serine and glycine catabolism in various vertebrates including humans. Nonketotic hyperglycinemia, a congenital metabolic disorder in human infants, results from defective glycine cleavage activity. The majority of patients with nonketotic hyperglycinemia had lesions in the P-protein gene, whereas some had mutant T-protein genes. The only patient classified into the degenerative type of nonketotic hyperglycinemia had an H-protein devoid of the prosthetic lipoyl residue. The crystallography of normal T-protein as well as biochemical characterization of recombinants of the normal and mutant T-proteins confirmed why the mutant T-proteins had lost enzyme activity. Putative mechanisms of cellular injuries including those in the central nervous system of patients with nonketotic hyperglycinemia are discussed.     

Rotational anisotropy in second harmonic intensity from Cu nanowire arrays on the NaCl (1 1 0) substrates

We have measured the azimuthal angle dependence of the second harmonic (SH) intensity from Cu nanowires on the faceted NaCl (1 1 0) substrates in air at the fundamental photon energy of 1.17 eV. The SH intensity patterns showed two main lobes for p-in/p-out, s-in/p-out, and s-in/s-out polarization configurations. From the results of the experiment and the pattern analysis we have found that the observed SH light is enhanced by the electric field components along the substrate normal.     

Measurements of localized-state density in chemically vapour deposited amorphous silicon by the field-effect method

New techniques to determined the localized-state density in chemically vapour deposited amorphous silicon over a wide energy range by the field-effect method are presented. The density is measured for the first time as 10¹⁸ ～ 10²⁰ cm^?3 eV^?1 in the range ±0.4～±0.5 eV around the Fermi level. From the results it is suggested that the silicon atom network of CVD a-Si has a similar randomness to that of glow discharge a-Si, providing a density of tail states of about 10¹⁹ ～ 10²⁰ cm^?3 eV^?1 and native defect states of about 10¹⁸ cm^?3 eV^?1.     

Modified Babington nebulizer for inductively coupled plasma atomic emission spectrometry.

A PTFE Babingtonnebulizer equipped with a hood was investigated for inductively coupled plasma atomicemission spectrometry in conjunction with a PTFE cyclone chamber, in order to nebulize various sample solutions containing high salts, hydrofluoric acid and/or suspended solid. A hood of 3 mmphi (nozzle side) - 5 mmphi (outlet side) and 6 mm in length gave a comparable or higher sensitivity compared to a system with a commercially available concentric nebulizer and a glass cyclone chamber. Moreover, the present nebulizer was fully interchangeable with a concentric one at normal argon pressure, attaining sufficient stability, a short wash-out time and good nebulizing of high matrices solutions. The present system was successfully applied to the determination of trace impurities in highly pure silica powders.     

A new scheme of the time-domain fluorescence tomography for a semi-infinite turbid medium

Optical Review - A new scheme for reconstruction of a fluorophore target embedded in a semi-infinite medium was proposed and evaluated. In this scheme, we neglected the presence of the fluorophore...     

A study on the optical nonlinearity due to the Z3 and Z1,2 excitons of CuCl by the reflected four-wave mixed light generation

We have demonstrated the generation of the reflected four-wave mixed light in the energy region from 3.185 eV to 3.320 eV including the highly absorptive region due to the Z₃ and Z_1,2 exciton bands of CuCl at 1.6 K. The mixed light signal is concluded to be due to the one-photon resonant contribution of the respective exciton level, from its polarization characteristics. The corresponding third order non-linear susceptibility is estimated from the data by the correction with the Fresnel factors which are calculated on the basis of the Pekar's Additional Boundary Condition.