Partial regularity of mass-minimizing rectifiable sections

Let B be a fiber bundle with compact fiber F over a compact Riemannian n-manifold M ⁿ. There is a natural Riemannian metric on the total space B consistent with the metric on M. With respect to that metric, the volume of a rectifiable section σ: M → B is the mass of the image σ(M) as a rectifiable n-current in B. Theorem 1. For any homology class of sections of B, there is a mass-minimizing rectifiable current T representing that homology class which is the graph of a C¹ section on an open dense subset of M. Mathematics Subject Classifications (2000): 49F20, 49F22, 49F10, 58A25, 53C42, 53C65.     

Perron's method for quasilinear hyperbolic systems, Part II

In part I (P. Smith, Perron's method for quasilinear hyperbolic systems, part I, J. Math. Anal., in press) of this paper we defined a notion of viscosity solution (sub- (super-)solution) for these systems, proved a comparison principle for viscosity sub- and supersolutions. Here, in part II, we prove existence of viscosity solutions to the Cauchy problem, using a Perron-like method, for long time, and for all time.     

Incommensurate magnetic structure of CeSi as observed by neutron diffraction

The magnetic ordering of the orthorhombic compound CeSi (Pama space group, FeB type of structure, Z = 4) T_n = 5.6 K was investigated by means of powder neutron diffraction in the temperatures 1.5 and 10 K. Our results show that the magnetic ordering is associated with a three dimensionally amplitude-modulated phase which is incommensurate with the crystal lattice with wave vector q = (q_χ,q_y,q_z). The ordered Ce³⁺ moments are confined to the plane (a,b) at an angle of 16.7° with the b direction. It follows from the present data analysis that the dominant wave vector component is q_z, which approximately corresponds to a transversal modulation, however the incommensurateness involves also the q_x and q_y components. The amplitude of the sine wave is μ⁰_j = 1.667μ_B at 1.5 K which corresponds to quite a reduced ordered moment value compared to the Ce³⁺ free ion value gJ = 2.14μ_B.     

Unilateral NMR applied to the conservation of works of art

In conventional NMR, samples from works of art in sizes above those considered acceptable in the field of art conservation would have to be removed to place them into the bore of large superconducting magnets. The portable permanent-magnet-based systems, by contrast, can be used in situ to study works of art, in a noninvasive manner. One of these portable NMR systems, NMR-MOUSE®, measures the information contained in one pixel in an NMR image from a region of about 1 cm², which can be as thin as 2–3 µm. With such a high depth resolution, profiles through the structures of art objects can be measured to characterize the materials, the artists’ techniques, and the deterioration processes. A novel application of the technique to study a deterioration process and to follow up a conservation treatment is presented in which micrometer-thick oil stains on paper are differentiated and characterized. In this example, the spin–spin relaxation T ₂ of the stain is correlated to the iodine number and to the degree of cross-linking of the oil, parameters that are crucial in choosing an appropriate conservation treatment to remove them. It is also shown that the variation of T ₂ over the course of treatments with organic solvents can be used to monitor the progress of the conservation interventions. It is expected that unilateral NMR in combination with multivariate data analysis will fill a gap within the set of high-spatial-resolution techniques currently available for the noninvasive analysis of materials in works of art, where procedures to study the inorganic components are currently far more developed than those suitable for the study of the organic components.     

Formation of thesyn-isomer of [Cp*MoO(μ−S)]2

The structure of the title compound,syn-[Cp^*MoO(μ?S)]₂,1, has been determined.1 crystallized in the monoclinic space groupC2/c with dimensionsa=11.758(2),b=12.243(2), c = 15.585(3)Å, β=104.63(3)°. The reaction of Cp^* ₂Mo₂(S₂)(S)(S₂O₃) with Me₂PhP producessyn-[Cp^*MoO(μ?S)]₂ and Me₂PhPO. The compounds [Cp′MoO(μ?S)]₂ [Cp′=Cp, CpMe, Cp^*] can exist as either thesyn- oranti-isomers. The present structure,syn-[Cp^*MoO(μ?S)]₂ is compared with the structure of theanti-isomer and with the previously determined structure ofsyn-[Cp^*MoO(μ?S)]₂ in a different space group.     

Tetrahedral Pegs in Square Holes: Stereochemistry of Diboron Porphyrazines and Phthalocyanines

The first examples of diboron complexes of the tetrapyrroles octaethylporphyrazine (OEPz) and 2,9,16,23‐tetra‐t‐butyl‐phthalocyanine (Pc) are reported, counterpoints to the better known monoboron tripyrroles, subporphyrazine and subphthalocyanine. Two stereochemical possibilities are observed, with cisoid‐B₂OF₂(OEPz), both cisoid‐B₂OPh₂(OEPz) and transoid‐B₂OPh₂(OEPz), transoid‐B₂OF₂(Pc) and cisoid‐B₂OPh₂(Pc) having been isolated and characterised, including structure determinations for the OEPz complexes. This variation in stereochemistry, which can be extended to include the previously reported transoid‐B₂OF₂(porphyrin), cisoid‐[B₂OF₂(corrole)]^?, and both transoid‐ and cisoid‐B₂OF₂(calixphyrin), prompted a wider DFT study to elucidate the factors influencing the stereochemical preferences. This shows that the cisoid/transoid preference is correlated to the ease with which the macrocycle accommodates a rectangularly distorted N₄ cavity.     

Boron complexes of pyrrolyl ligands

Complexes of boron with ligands containing pyrrolyl motifs are surveyed. The ligands range from simple pyrrolyl groups to dipyrroles and linear terpyrroles. Macrocyclic ligands include tripyrroles, which encompass subphthalocyanines, subporphyrins, subtriazaporphyrins, and subtribenzoporphyins, the familiar tetrapyrroles porphyrin and corrole but also N-confused and -fused porphyrins, and expanded porphyrins containing up to eight pyrroles. The role of boron in these compounds depends on the nature of the ligand. Boron acts as a Lewis acid center in simple boron pyrrolyl compounds, and as a structure-directing and templating agent in the cyclic terpyrroles and some of the expanded porphyrins. The difluorboron dipyrrins are well-known as fluorescent dyes. Boron porphyrins and corroles are unusual in containing two coordinated boron atoms rather than the single coordinated atom usually occurring in these ligands, and the proximity of two boron atoms at close quarters in the ligand cavities gives rise to some unusual reaction and redox chemistry. The survey is organized by the number of pyrrole moieties occurring in the ligand and focuses on new and unique chemistry observed for the complexes.     

Rapid analysis of genetically modified organisms by in-house developed capillary electrophoresis chip and laser-induced fluorescence system

A microfabricated, inexpensive, reusable glass capillary electrophoresis chip and a laser-induced fluorescence system were developed in-house for the rapid DNA-based analysis of genetically modified organisms (GMOs). The 35S promoter sequence of cauliflower mosaic virus and the terminator of the nopaline synthase (NOS) gene from Agrobacterium tumefaciens were both detected since they are present in most genetically modified organisms. The detection of genetically modified soybean in the presence of unaltered soybean was chosen as a model. Lectin, a plant-specific gene, was also detected for confirmation of the integrity of extracted DNA. The chip was composed of two glass plates, each 25 x 76 mm, thermally bonded together to form a closed structure. Photomasks with cross-topology were prepared rapidly by using polymeric material instead of chrome plates. The widths of the injection and separation channels were 30 and 70 microm, respectively, the effective separation length 4.5 cm. The glass slide was etched to a depth of 30 microm for both the injection and separation channel. The cost of the chip was less than 1 $ and required 2 days for photomask preparation and microfabrication. The separation and detection of polymerase chain reaction-amplified NOS, 35S, and lectin sequences (180, 195, and 181 bp, respectively) was completed in less than 60 s. As low as 0.1% GMO content was detectable by the proposed system after 35 and 40 amplification cycles for 35S and NOS, respectively, using 25 ng of extracted DNA as starting material. This corresponds to only 20 genome copies of genetically modified soybean.     

Electron Spin Resonance Study of γ-Irradiated Morpholinium Hexafluorophosphate

γ-Irradiation of solid ammonium compounds at low temperatures nay lead to the formation and trapping of radicals generated from the parent ammonium ions. Thus, NH₃+ was observed in NH₄PF₆ ¹ and N(CH₃)₃,⁺ was found in tetramethyl ammonium halides². Recently it has been shown that γ-irradiation of tetraalkylammonium iodides at 77 °K leads to the breaking of a C-C bond next to the nitrogen atom³ in agreement with the mass spectrometrlc studies of amines which show the fission of the α, β-C-C bond as the primary process upon electron impact⁴.