Complex Numbers, Quantum Mechanics and the Beginning of Time

A basic problem in quantizing a field in curved space is the decomposition of the classical modes in positive and negative frequency. The decomposition is equivalent to a choice of a complex structure in the space of classical solutions. In our construction the real tunneling geometries provide the link between the this complex structure and analytic properties of the classical solutions in a Riemannian section of space. This is related to the Osterwalder- Schrader approach to Euclidean field theory.Comment: 27 pages LATEX, UCSBTH-93-0

The relation of a particular chromosomal element to the development of the nucleoli in Zea mays

1.The nucleolus is organized in the telophase through the activity of a distinct deep-staining body having a definite position in one chromosome (the satellited chromosome) of the monoploid complement. Correlated with the number of satellited chromosomes present, the telophases of somatic tissue of haploids show one nucleolus, diploids, two nucleoli and triploids, three nucleoli. That the nucleolus develops through the activity of this body (refered to as the nucleolar-organizing body or element) was obtained from a reciprocal translocation which broke this body into two parts. Both interchanged chromosomes possessed a section. Nucleoli developed from each of these two segments. Thus, plants homozygous for the interchange developed four nucleoli in their somatic telophases; plants heterozygous for the interchange developed three nucleoli in their somatic telophases. Similarly, the telophase nucleoli resulting from the first division within the monoploid microspore of normal diploids show only one nucleolus, whereas, those of plants homozygous for the interchange are characterized by the development of two nucleoli. 2.The functional capacity to develop a nucleolus is not the same for both segments of the severed nucleolar-organizing body. This is evident when the two interchanged chromosomes are present in the same nucleus. The segment of the nucleolar-organizing body possessed by one interchanged chromosome produced a large nucleolus, whereas, the segment of the nucleolar-organizing body possessed by the other interchanged chromosome produced a small nucleolus. When this latter chromosome, with the nucleolar-organizing element of slower rate of functional capacity is present without the former (i. e. without a competing nucleolarorganizing element) it produces, in contrast, a large nucleolus. 3.The activity of the nucleolar-organizing element is hindered by certain genomic deficiencies. When this occurs, many small nucleolarlike bodies are produced and remain associated with the other chromosomes of the complement. These small nucleoli appear to develop from a swelling and later collection into droplets of the matrix substance of the chromosome