We survey some recent mathematical works we have contributed to that are related to the modeling of defects in materials science at different scales. We emphasize the similarities (need of a reference, often periodic system; renormalization procedure; etc) shared by models arising in different contexts. Our illustrative examples are taken from electronic structure models, atomistic models, homo...

Albright, Burnett, Smith, and Parson (I942) investigated a female patient of 28 years who had suffered from idiopathic epilepsy since the age of I2. Because the bones of the skull were unusually dense, hypoparathyroidism was suspected. The diagnosis was made when it was found that her Chwostek sign was positive and that her serum calcium and phosphorus levels were 6-4 and 6o mg. per I00 ml. res...

BACKGROUND & OBJECTIVES Fibrous dysplasia (FD) is a rare metabolic bone disease and information available from India is limited to only anecdotal case reports. We describe the clinical profile and therapeutic outcome of 25 patients with FD observed over a period of 14 yr in a tertiary care centre from north India. METHODS In this retrospective study patients (n = 25) with diagnosis of fibrous...

We study geometric quantization of moduli spaces of vector bundles on an algebraic curve X, and its relation to theta functions. In limits when the complex structure of X degenerates, we describe vector spaces of distributions with Verlinde dimension, associated to the quantization of some of these moduli spaces in real polarizations. We show that special bases on these spaces, defined using a ...