A Measure of Simultaneous Approximation for Quasi-Modular Functions

We improve on a recent result of Saradha giving a transcendence measure for the quotient of a period of an elliptic curve defined over by its associated quasi-period. In an (almost successful) attempt to include in a single measure both this result and that obtained by Reyssat in 1980, we blend into the modular method ideas related to modular but also hypergeometric functions, as appearing e.g. in André's work, as well as some Galois considerations.     

Surface modification by oil jet peening in Al alloys, AA6063-T6 and AA6061-T4: Part 2: Surface morphology, erosion, and mass loss

Oil jet peening is a new surface treatment technique that can be potentially applied to impart compressive residual stresses in metal parts. The effect of oil jet pressure on the surface integrity and texture of metals are discussed. The surface morphology, mass loss rate, indentation, and erosion are reported. With increasing stand-off distance, the size of indents significantly decreases and reduces the average roughness in the both specimens. Results are also compared with other mechanical surface treatment process such as shot peening, laser shock peening, and water jet peening.     

Surface modification by oil jet peening in Al alloys, AA6063-T6 and AA6061-T4: Residual stress and hardness

The life of structural members that experience cyclic loading is improved by the introduction of surface compressive residual stresses. A high-pressure oil jet is used for the introduction of surface compressive residual stresses in aluminum alloys, AA6063-T6 and AA6061-T4. The peening machine designed and developed in the laboratory is capable of generating high pressures using hydraulic oil. The magnitude of residual stress developed depends upon the stand-off distance and yield strength of the material. A hardened layer up to a depth of about 350 μm was developed in the materials investigated. The residual stresses and surface hardening induced are comparable to that produced by other peening processes. An analytical model is proposed to predict the impact pressure.     

Measures of Simultaneous Approximation for Quasi-Periods of Abelian Varieties

We examine various extensions of a series of theorems proved by Chudnovsky in the 1980s on the algebraic independence (transcendence degree 2) of certain quantities involving integrals of the first and second kind on elliptic curves; these extensions include generalizations to abelian varieties of arbitrary dimensions, quantitative refinements in terms of measures of simultaneous approximation, as well as some attempt at unifying the aforementioned theorems. In the process we develop tools that might prove useful in other contexts, revolving around explicit “algebraic” theta functions on the one hand, and Eisenstein's theorem and G-functions on the other hand.