The Hellmann-Feynman theorem applied to long-range forces

The relations between the Hellmann-Feynman forces in laboratory fixed (L-) and relative (R-) coordinate systems are clarified. In the usualL-coordinate system, the force is interpreted as force on nucleus, while in theR-coordinate system, it means force on whole particles consisting of the electrons and nuclei of each interacting subsystem. From a perturbation theoretical viewpoint, the concept of the force on whole particles correctly corresponds to the perturbation energy and is superior to the force on the nucleus.     

13C-NMR studies on the cevanine alkaloids : the application of 13C-NMR spectrum for structure elucidation of new alkaloids,baimonidine and isoverticine

The ¹³C-NMR spectra of seven cavanine alkaloids isolated from Veratrum and Fritillaria plants were measured and their signals were assigned, and these results were applicated for structure elucidation of two new cevanine alkaloids, baimonidine and isoverticine, isolated from mature Fritillaria verticillata.     

Stereoselective ring-opening polymerization of racemic lactide using aluminum-achiral ligand complexes: exploration of a chain-end control mechanism

Stereoselective polymerization of racemic lactide (rac-LA) was examined using Al-achiral ligand complexes. By introduction of substituents in aromatic rings of Schiff base ligands, a higher selectivity was obtained without any chiral auxiliaries in the catalyst via a chain-end control mechanism. The T(m) values (T(m) 170-192 degrees C) were comparable to or higher than that of homochiral polymer, poly(L-LA) (T(m) 162 degrees C), and a thermally more stable polylactide than poly(L-LA) was prepared from rac-LA.     

Magnetic structure of Fe−Si−Al films implanted with Al and N ions

Changes in the magnetic structure of Fe–Si–Al films due to Al and N ion implantation were studied by⁵⁷Fe Conversion Electron Mössbauer Spectrometry (CEMS). The peaks of the magnetic sextets due to the crystalline films became broader by implantation with 5×10¹⁶ Al/cm², suggesting the formation of amorphous phases. In the CEM spectrum of one sample with large grains implanted with 1×10¹⁷ Al/cm² a crystalline -Fe phase appeared. N implantation with the same dose did not amorphize the sample but the components with high magnetic hyperfine fields were enhanced.     

A remark on bipartite distance-regular graphs of even valency

Let be a bipartite distance-regular graph of even valencyk. Let us consider the intersection array modulo 2, which would become Lett be the length of any series of (1, 0, 1)'s witht > 1. Thent + 1|r ₁ + 1, withr ₁ the length of the first series.     

Grassmann manifold of aJH-algebra

We study the set of rankp idempotents in a topologically simple Hilbert Jordan algebra (JH-algebra for short). To produce the differential geometric structure on, we establish Jordan algebraic results concerning the structure of some two-generator subalgebras. We identify geodesics, the Riemannian distance and the sectional curvature of by using the Jordan algebraic structure.     

Mechanical properties of twist grain boundaries in Cu

In a previous paper we studied the Young's and shear modulus of a high-angle twist grain boundary (5) in Cu, using the EAM, and related it to the uniaxial strain derivatives of single crystals. In this paper, we discuss elastic properties of ten additional twist grain boundaries, from 8.8–43.6°. The monolayer Young's modulus at each boundary was calculated and found to be 20–50% higher than the bulk value for all eleven boundaries for both csl and type1 structures. The monolayer shear modulus at each boundary was calculated and found to be 93–98% lower than the bulk value for six grain boundaries with csl structure and found to decrease with increasing twist angle. The critical shear stress was also calculated for eleven boundaries with csl structure and found to roughly decrease with increasing twist angle.     

Non-linear structures in the non-critical NSR string

We investigate the Ward identities of theW symmetry in the super-Liouville theory coupled to the super-conformal matter of central charge . The theory is classified into two chiralities. For the positive chirality, all gravitationally dressed scaling operators are generated from theq–1 gravitational primaries by one of the ring generators in the R-sector acting on them repeatedly. After fixing the normalizations of the dressed scaling operators, we find that the Ward identities are expressed in the form of theusual W _q algebra constraints as in the bosonic case:W _n ^(k+1) ,=0, (k=1,...,q–1;nZ1–k), where the equations for even and oddn come from the currents in the NS- and the R-sector respectively. The non-linear terms come from the anomalous contributions at the boundaries of moduli space. The negative chirality is defined by interchanging the roles ofp andq. Then we get theW _p algebra constraints.     

On the class numbers of certain Hilbert class fields

LetL/k be a finite Galois extension with Galois groupG, and a group extension. We study the existence of the Galois extensionM/L/k such that the canonical projection Gal(M/k)→Gal(L/k) coincides with the given homomorphismj:E→G and thatM/L is unramified.