On the varieties defined by Riemann-Mumford's relations

In this paper we consider varieties defined by Riemann-Mumford's relations. An irreducible component of these varieties is related to Siegel modular varieties. We prove that in most cases Riemann-Mumford varieties are not irreducible.

     

The coevolution theory of the origin of the genetic code

A review of the coevolution theory of the origin of the genetic code is presented. This theory maintains that the origin of the code should be sought in the biosynthetic relationships between amino acids. In particular, some amino acids, the precursors, occupied the structure of the genetic code early on. As the product amino acids developed from these precursors, part or all of the codon domain of the precursor amino acid was ceded to the product amino acids, which resulted in the structuring of the genetic code. This paper therefore reviews the evidence in favour of this theory. The existence of some molecular fossils representing the biosynthetic pathways on which the coevolution theory suggests biosynthetic transformations took place (precursor amino acid → product amino acid) seems to be a strong corroboration of this theory. A generalisation imposed by this theory on the ancestral metabolic state is then discussed and, finally, the main prospects that seem to stem from the coevolution theory are presented.     

Enclosing a Set of Objects by Two Minimum Area Rectangles

In this paper, we face the problem of computing an enclosing pair of axis-parallel rectangles of a set of polygonal objects in the plane, serving as a simple container. We propose anO(nα(n)log n) worst-case time algorithm, where α( ) is the inverse Ackermann's function, for finding, given a setMof points, segments and polygons defined bynvertices, a pair of axis-parallel rectangles (s, t) such thats∪tencloses all objects inMand area(s)+area(t) is minimum. The algorithm works inO(nα(n) log log n) worst-case space. Moreover, we prove an Ω(n log n) lower bound for the one-dimensional version of the problem. We also show that for the special case of enclosing a set of polygons with axis-parallel sides, our algorithm runs in optimal worst-case timeO(n log n), using worst-case spaceO(n log log n).     

Testing thermodynamic constitutive equations for polymers by adiabatic deformation experiments

During adiabatic deformation experiments on polyisobutylene of various molecular weights and on polyvinylacetate, the temperature change was measured. The thermal effects occurring during the subsequent stress relaxation were also recorded. From all data, the conclusion was drawn that the entropic elasticity theory is obeyed for temperatures sufficiently above the glass transition temperature. When the value of T_g is approached, some interesting energy effects become appreciable.     

AN ULTRASTRUCTURAL COMPARATIVE EVALUATION OF TUMORS PHOTOSENSITIZED BY PORPHYRINS ADMINISTERED IN AQUEOUS SOLUTION, BOUND TO LIPOSOMES OR TO LIPOPROTEINS

Abstract— Balb/c mice bearing a transplantedMS–2 fibrosarcoma have been injected with 2 mg kg^-1 hematoporphyrin either dissolved in phosphate-buffered saline (Hp-aq), or incorporated into unilamellar liposomes of dipalmitoyl-phosphatidylcholine (Hp-lip), or precomplexed with low density lipoproteins (Hp-LDL). At 24 h after injection, the mice received 150 J cm^-2 of600–680 nm light irradiation. Electron microscopic studies performed on tumor tissues taken from mice sacrificed at different times after the phototreatment showed that, in the presence of Hp-aq. tumor necrosis is largely the consequence of vascular damage. On the other hand, in the presence of Hp-lip and Hp-LDL, the response of the tumor to the phototreatment occurs at a faster rate and is mainly determined by direct damage of neoplastic cells. These findings are correlated with the different distribution of the various hematoporphyrin forms (Hp-aq, Hp-lip, Hp-LDL) among the serum proteins and the modalities of hematoporphyrin delivery to tissues by the possible carriers.