Several investigators have reported that commercial L-proline is contaminated with small amounts of hydroxy-n-proline (l-3). During the course of investigations in this laboratory all of five commercial samples proved to contain up to 3.5 per cent hydroxyproline when tested by the method of Neuman and Logan (1). The preparation of n-proline from gelatin by the formation of complex salts is tedi...

The index bundle of the Overlap lattice Dirac operator over the orbit space of lattice gauge fields is introduced and studied. Obstructions to the vanishing of gauge anomalies in the Overlap formulation of lattice chiral gauge theory have a natural description in this context. Our main result is a formula for the topological charge (integrated Chern character) of the index bundle over evendimen...

We show that the percentage of primitive forms level one and weight $4k\rightarrow \infty$ for which associated $L$-function at central point is no less than $(\log{k})^{-2}$ least 20%. The key ingredients our proof are Kuznetsov convolution formula Liouville-Green method.

We propose a novel finite element formulation that significantly reduces the number of degrees of freedom necessary to obtain reasonably accurate approximations of the low-frequency component of the deformation in boundary-value problems. In contrast to the standard Ritz–Galerkin approach, the shape functions are defined on a Lie algebra—the logarithmic space—of the deformation function. We con...