We investigate the collapse of nonrotating gas sp~eres with a polytropic.equ~tion of state.: n = 3, corresponding toy = 4/3. Such polytropes provide~ re~sonable approximatiOn t<? collapsmg stellar cores during the early phase before nuclear density IS reached. W~ find a.famtl~ of ~xact homologously collapsing configurations. Homologous collapse of the enti~e core Is possib~e If the pressure at ...

Introduction New characterization Recognizing collapsing words Mono and stereo automata Questions Definitions We will consider finite deterministic automata with a total transition function: Remark Each element of Σ induces via δ a transformation of Q. We will view an automaton as a set of such transformations. Introduction New characterization Recognizing collapsing words Mono and stereo autom...

Liberati, Rothman and Sonego have recently showed that objects collapsing into extremal Reissner-Nordström black holes do not behave as thermal objects at any time in their history. In particular, a temperature, and hence thermodynamic entropy, are undefined for them. I demonstrate that the analysis goes through essentially unchanged for bodies collapsing into extremal Kerr black holes. PACS: 0...

A new notion of relativization—stringent relativization—has been proposed recently [CW06] for discussing collapsing relations of complexity classes, with which we hope to open a new approach for studying complexity classes. Starting with the motivation of this notion, we discuss the meaning and implication of collapsing relations under the stringent relativization.

The histopathologic diagnosis of primary focal segmental glomerulosclerosis (FSGS) has come to include a number of histologic lesions (variants), but the prognostic significance of these discrete lesions is controversial because published information regarding the presentation, course, and response to treatment is limited. A retrospective analysis was conducted of 87 nephrotic adult patients wi...