The lightlike flat geometry on spacelike submanifolds of codimension two in Minkowski space

We introduce the notion of the lightcone Gauss–Kronecker curvature for a spacelike submanifold of codimension two in Minkowski space, which is a generalization of the ordinary notion of Gauss curvature of hypersurfaces in Euclidean space. In the local sense, this curvature describes the contact of such submanifolds with lightlike hyperplanes. We study geometric properties of such curvatures and show a Gauss–Bonnet type theorem. As examples we have hypersurfaces in hyperbolic space, spacelike hypersurfaces in the lightcone and spacelike hypersurfaces in de Sitter space.     

Singularities of Solution Surfaces for Quasilinear First-Order Partial Differential Equations

For a closed curve in a CAT(K) space with given circumradius and upper bound on curvature, a basic lower bound on the length is established. The inequality is sharp, assumed only when the curve is the boundary of an isometric copy of a racetrack (the convex hull of two congruent circles) from a plane of constant curvature K. Previously such a theorem was proved for Euclidean plane curves by G.D.Chakerian, H.H. Johnson, and A. Vogt, and for curves in higher dimensional Euclidean spaces by A.D. Milka. A similar theorem is proved for nonclosed curves, with a notion of breadth replacing circumradius. Thus we illustrate how singular methods can extend classical Euclidean theorems to a large class of new spaces (including Riemannian manifolds of curvature bounded above) and also give significant strengthenings even in Euclidean space.     

1H-NMR study on acylamino acids. Relationship between the chemical shift of amide protons and electronegativity of acyl groups

The chemical shift of amide protons of acylamine acids showed a linear relation with electronegativity of the acyl groups. Prediction of the carbonyl group participated in intramolecular hydrogen bonding was discussed, gramiciding S being used as an example.     

Energy-saving seawater electrolysis for hydrogen production

The change in the polarization potentials of anode and cathode due to pH change on electrode surfaces during galvanostatic polarization was examined in 0.5 M NaCl solutions of different pH. On the basis of these results, feeding of the anolyte after oxygen evolution to the cathode compartment for hydrogen production was examined for energy-saving seawater electrolysis. This was assumed to prevent the occurrence of a large pH difference on cathode and anode in electrolysis of neutral solution if sufficient H⁺ is permeated through the membrane. The cell performance was examined using Nafion 115 or Selemion HSF membranes for separation of anode and cathode compartments. The permeation fraction of H⁺ with Nafion 115 was 45–65% in 0.5 M NaCl and was about 90% in 0.25 M Na₂SO₄. These values were smaller than 97% necessary for prevention of the occurrence of pH difference on cathode and anode. The permeation fraction of H⁺ with Selemion HSF became more than 97% during electrolysis of 0.025 M Na₂SO₄, and the cell voltage was kept at low values. These results indicate the effectiveness of our seawater feeding system if the 97% H⁺ permeation fraction through the membrane is attained. Contribution to the Fall Meeting of the European Materials Research Society, Symposium D: 9th International Symposium on Electrochemical/Chemical Reactivity of Metastable, Warsaw, 17th-21st September, 2007.     

Myostatin preferentially down-regulates the expression of fast 2x myosin heavy chain in cattle

Myostatin is involved in an inhibitor of muscular growth and differentiation. Myoblasts derived from double-muscled Japanese shorthorn cattle (DM myoblasts) with absence of functional myostatin had higher abilities to proliferate and differentiate than myoblasts derived from normal-muscled cattle (NM myoblasts). In DM myoblasts, mRNA expressions of fetal myosin heavy chain (MyHC) in growth medium and of fast 2a and 2x MyHC in fusion medium were significantly greater than that in NM myoblasts. No significant difference existed in expressions of embryonic and slow MyHC mRNA between DM and NM myoblasts. The expression of MyoD mRNA was suppressed in myoblasts by administration of myostatin. Two cloned DM myoblast strains (DMc) were established. Addition of myostatin for DMc resulted in less myotube formation and suppression of mRNA expression of fast 2x MyHC. These findings suggest that the endogenous myostatin preferentially down-regulates the expression of the fast 2x MyHC and participates in differentiation of myofiber types during early bovine myogenesis.     

Evolutes of Hyperbolic Plane Curves

Abstract We define the notion of evolutes of curves in a hyperbolic plane and establish the relationships between singularities of these subjects and geometric invariants of curves under the action of the Lorentz group. We also describe how we can draw the picture of an evolute of a hyperbolic plane curve in the Poincaré disk.     

The Horospherical Geometry of Submanifolds in Hyperbolic Space

Some geometrical properties associated to the contact of submanifoldswith hyperhorospheres in hyperbolic n-space are studied as anapplication of the theory of Legendrian singularities.     

Vector fields near a generic submanifold

We give a classification of generic vector fields near a generic submanifold. The normal forms are linear vector fields near the local model of the submanifold. Similar results are obtained for vector fields near a hypersurface with boundary and near a piecewise-smooth hypersurface.     

Syntheses of AM-toxin III and its analogs using the Hofmann degradation

Syntheses of cyclotetradepsipeptides, AM-toxin III and two analogs, were achieved, in which the Hofmann degradation method was used in order to derive a dehydroalanine residue from a 2,3-diaminopropionic acid residue in cyclodepsipeptide precursors.