Study on the Ring Eulargment Reaction: Synthesis of 7,8,13, 13a-tetrahydroisoindolo[1,2-b][3]benzazepine and 5,6,8,9,14,14a-hexahydroisoquino[1,2-b][3]benzazepine

In our research on the ring enlargement of certain N-heterocycles, a general procedure for the ring enlargement with the insertion of an extra -CH2- was improved and shown in Scheme I1.Scheme IThe procedure had been carried out with such N-heterocycles as 2-methyl-1,2,3,4-tetrahydroisoquinoline2, tetrahydroberberine and strychnine3 with expected results. Thus, the procedure shown in Scheme I provides a new approach to the synthesis of larger N-heterocycles.Isoindolo[1,2-b][3]benzazepines a…     

The equation of the p-adic closed strings for the scalar tachyon field

We investigate the structure of solutions of boundary value problems for a non-linear pseudodifferential equation describing the dynamics(rolling)of p-adic closed strings for a scalar tachyon field.     

Improved Generalization via Tolerant Training

Theoretical and computational justification is given for improved generalization when the training set is learned with less accuracy. The model used for this investigation is a simple linear one. It is shown that learning a training set with a tolerance improves generalization, over zero-tolerance training, for any testing set satisfying a certain closeness condition to the training set. These results, obtained via a mathematical programming formulation, are placed in the context of some well-known machine learning results. Computational confirmation of improved generalization is given for linear systems (including nine of the twelve real-world data sets tested), as well as for nonlinear systems such as neural networks for which no theoretical results are available at present. In particular, the tolerant training method improves generalization on noisy, sparse, and overparameterized problems.     

Galois theory in variable categories

The order-reversing bijection between field extensions and subgroups of the Galois group G follows from the equivalence between the opposite of the category of étale algebras and the category of discrete G-spaces [2]. We show that the basic ingredient for this equivalence of categories, and for various known generalizations, is a factorization system for variable categories.     

Designing protein beta-sheet surfaces by Z-score optimization

Studies of lattice models of proteins have suggested that the appropriate energy expression for protein design may include nonthermodynamic terms to accommodate negative design concerns. One method, developed in lattice model studies, maximizes a quantity known as the " Z-score," which compares the lowest energy sequence whose ground state structure is the target structure to an ensemble of random sequences. Here we show that, in certain circumstances, the technique can be applied to real proteins. The resulting energy expression is used to design the beta-sheet surfaces of two real proteins. We find experimentally that the designed proteins are stable and well folded, and in one case is even more thermostable than the wild type.     

New compounds in the Mn-X-Bi system where X = Ni, Cu, RhorPd

A new class of magnetic compounds has been discovered in the temary system Mn-X-Bi where X is Ni, Cu, Rh or Pd. The approximate compositions of these compounds are Mn₅Ni₂Bi₄, Mn₃Cu₄Bi₄, Mn₅Rh₂Bi₄, and Mn₅Pd₂Bi₄. The Bravais lattice is face-centered cubic, and the lattice constants are 12.16 Å (X = Ni), 12.18 Å (X = Cu), 12.31 Å (X = Rh) and 12.44 Å (X = Pd). These compounds are probably ferromagnetic and have Curie temperatures in the range -7°C to 183°C. A crystal structure is proposed for these compounds which contains 88 atoms/unit cell.     

Conductivity and Hall effect measurements in doped polyacetylene

Conductivity and Hall effect measurements are reported for polyacetylene films heavily doped with AsF₅. The Hall coefficient is anomalously small, however, it is p-type and relatively temperature insensitive in the range 4–300 K indicative of metallic conduction. The effects of film degration by heating and air exposure are also investigated.