Active‐Set Newton Methods and Partial Smoothness

Diverse optimization algorithms correctly identify, in finite time, intrinsic constraints that must be active at optimality. Analogous behavior extends beyond optimization to systems involving partly smooth operators, and in particular to variational inequalities over partly smooth sets. As in classical nonlinear programming, such active‐set structure underlies the design of accelerated local algorithms of Newton type. We formalize this idea in broad generality as a simple linearization scheme for two intersecting manifolds.

Spectral Distribution of Transport Operator Arising in Growing Cell Populations

Transport equation with partly smooth boundary conditions arising in growing cell populations is studied inLp (1<p<+∞)space. It is to prove that the transport operatorAHgenerates aC0semigroup and the ninth-order remainder termR9(t)of the Dyson-Phillips expansion of the semigroup is compact, and the spectrum of transport operatorAHconsists of only finite isolated eigenvalues with finite algebraic multiplicities in a tripΓω. The main methods rely on theory of linear operators, comparison operators, and resolvent operators approach.

SITES OF GLYCOGEN SYNTHESIS IN RAT LIVER CELLS AS SHOWN BY ELECTRON MICROSCOPE RADIOAUTOGRAPHY AFTER ADMINISTRATION OF GLUCOSE-H3

Glycogen synthesis was investigated by giving tritium (H3)-labeled glucose with carrier to fasted rats in vivo or incubating liver slices from fasted rats in vitro using a glucose-H3-containing medium. After 15 min or 1 hr, pieces of liver were fixed and radioautographed for light and electron microscopy. In vivo and in vitro, radioautographic reactions appeared over "glycogen areas" and over zones transitional between these areas and ergastoplasm. Treatment of sections by alpha amylase removed all but about 5% of the radioactivity, so that about 95% of it consisted of glycogen (synthesized during the 15 min or 1 hr elapsing after administration of glucose-H3). Within glycogen areas and transitional zones, most silver grains were over or very close to glycogen granules and smooth (or partly smooth) vesicles. Presumably, much of the label was added onto growing glycogen granules, in accord with the biochemical view that glycogen may serve as substrate for further glycogen synthesis. The few silver grains located far from glycogen granules—15% at the 15 min interval in vivo—approximated smooth (or partly smooth) vesicles of endoplasmic reticulum. This observation raised the possibility that smooth membranes play a role in glucose uptake at an early stage in de novo formation of glycogen granules.