How Fast can a Subharmonic Function Decay Along a Ray?

Much is known about the connection between the growth and decayof subharmonic functions. The results indicate that there isa general principle: asubharmonic function cannot decay ‘toofast’ relative to its growth.Three theorems are provedwhich, together with work previously published elsewhere, givea fairly complete account of how this principle works out fora subharmonic function having extremal decay along a ray. 1991Mathematics Subject Classification: 30D20, 31A05.     

Analysis of the healthy rabbit lens surface using MAC Mode atomic force microscopy

In this investigation healthy rabbit crystalline lenses were characterized by atomic force microscopy (AFM). The lenses were cut in slices with thickness with 1mm and thus, put after cortex distinct regions of nucleus and cortex for AFM examination. AFM analysis were carried out using a PicoSPM I operating in Mac Mode. We obtained topographic images of rabbit lenses and a quantitative analysis of the width and height of fibers for nucleus and cortex regions. The longitudinal section analysis of fibers in the nucleus region indicated structures with an average width of 200nm and average height of 200nm. The intershells distance was determined as 4microm. Fiber cell cross-section dimensions, longitudinal and transverse widths, could be estimated in these regions from the AFM images. Structures with average widths as small as 1.0microm are observed in the nucleus; the intershell distance is 4.0microm. In cortical regions, hexagonal structures with average longitudinal and transverse widths of 5.0mum and 3.0mum, respectively, were identified. Three-dimensional images of tissue sections with resolution on a nanometer scale were obtained. The potential of AFM analysis for characterizing healthy and pathologic lens tissues is discussed.