Curves on threefolds and a conjecture of Griffiths-Harris

We prove that any arithmetically Gorenstein curve on a smooth, general hypersurface of degree at least 6, is a complete intersection. This gives a characterisation of complete intersection curves on general type hypersurfaces in . We also verify that certain 1-cycles on a general quintic hypersurface are non-trivial elements of the Griffiths group.

Plastic response of orthotropic spherical shells under blast loading

The plastic response of a segment of a simply supported orthotropic spherical shell under a uniform blast loading applied on the convex surface of the shell is presented. The blast is assumed to impart a uniform velocity to the shell surface initially. The material of the shell is orthotropic obeying a modified Tresca yield hypersurface conditions and the associated flow rules. The deformation of the shell is determined during all phases of its motion by considering the motion of plastic hinges in different regimes of flow. Numerical results presented include the permanent deformed configuration of the shell and the total time of shell response for different degrees of orthotropy. Conclusions regarding the plastic behaviour of spherical shells with circumferential and meridional stiffening under uniform blast load are presented.

The Noether-Lefschetz theorem for the divisor class group

Let X be a normal projective threefold over a field of characteristic zero and vertical bar L vertical bar be a base-point free, ample linear system on X. Under suitable hypotheses on (X, vertical bar L vertical bar), we prove that for a very general member Y is an element of vertical bar L vertical bar, the restriction map on divisor class groups Cl(X) -> Cl(Y) is an isomorphism. In particular, we are able to recover the classical Noether-Lefschetz theorem, that a very general hypersurface X subset of P-C(3) of degree >= 4 has Pic(X) congruent to Z.

Arithmetically Cohen-Macaulay bundles on complete intersection varieties of sufficiently high multidegree

Recently it has been proved that any arithmetically Cohen-Macaulay (ACM) bundle of rank two on a general, smooth hypersurface of degree at least three and dimension at least four is a sum of line bundles. When the dimension of the hypersurface is three, a similar result is true provided the degree of the hypersurface is at least six. We extend these results to complete intersection subvarieties by proving that any ACM bundle of rank two on a general, smooth complete intersection subvariety of sufficiently high multi-degree and dimension at least four splits. We also obtain partial results in the case of threefolds.

Plastic response of orthotropic spherical shells under blast loading

The plastic response of a segment of a simply supported orthotropic spherical shell under a uniform blast loading applied on the convex surface of the shell is presented. The blast is assumed to impart a uniform velocity to the shell surface initially. The material of the shell is orthotropic obeying a modified Tresca yield hypersurface conditions and the associated flow rules. The deformation of the shell is determined during all phases of its motion by considering the motion of plastic hinges in different regimes of flow. Numerical results presented include the permanent deformed configuration of the shell and the total time of shell response for different degrees of orthotropy. Conclusions regarding the plastic behaviour of spherical shells with circumferential and meridional stiffening under uniform blast load are presented.

Some regularity theorems for CR mappings

The purpose of this article is to study Lipschitz CR mappings from an h-extendible (or semi-regular) hypersurface in . Under various assumptions on the target hypersurface, it is shown that such mappings must be smooth. A rigidity result for proper holomorphic mappings from strongly pseudoconvex domains is also proved.

Microwave spectroscopic and theoretical investigations of the strongly hydrogen bonded hexafluoroisopropanol...water complex

This paper reports microwave spectroscopic and theoretical investigations on the interaction of water with hexafluoroisopropanol (HFIP). The HFIP monomer can exist in two conformations, antiperiplanar (AP) and synclinical (SC). The former is about 5 kJ mol(-1) more stable than the latter. Theoretical calculations predicted three potential minima for the complex, two having AP and one having SC conformations. Though, the binding energy for the HFIP(SC)...H2O turned out to be larger than that for the other two conformers having HFIP in the AP form, the global minimum for the complex in the potential energy hypersurface had HFIP in the AP form. Experimental rotational constants for four isotopologues measured using a pulsed nozzle Fourier transform microwave spectrometer, correspond to the global minimum in the potential energy hypersurface. The structural parameters and the internal dynamics of the complex could be determined from the rotational spectra of the four isotopologues. The global minimum has the HFIP(AP) as a hydrogen bond donor forming a strong hydrogen bond with H2O. To characterize the strength of the bonding and to probe the other interactions within the complex, atoms in molecules, non-covalent interaction index and natural bond orbital theoretical analyses have been performed.