Part I. Approximate Hartree-Fock wavefunctions one-electron properties and electronic structure of the water molecule. Part II. Perturbation-variational calculation of the nuclear spin-spin isotope coupling constant in HD

Part I

Several approximate Hartree-Fock SCF wavefunctions for the ground electronic state of the water molecule have been obtained using an increasing number of multicenter s, p, and d Slater-type atomic orbitals as basis sets. The predicted charge distribution has been extensively tested at each stage by calculating the electric dipole moment, molecular quadrupole moment, diamagnetic shielding, Hellmann-Feynman forces, and electric field gradients at both the hydrogen and the oxygen nuclei. It was found that a carefully optimized minimal basis set suffices to describe the electronic charge distribution adequately except in the vicinity of the oxygen nucleus. Our calculations indicate, for example, that the correct prediction of the field gradient at this nucleus requires a more flexible linear combination of p-orbitals centered on this nucleus than that in the minimal basis set. Theoretical values for the molecular octopole moment components are also reported.

Part II

The perturbation-variational theory of R. M. Pitzer for nuclear spin-spin coupling constants is applied to the HD molecule. The zero-order molecular orbital is described in terms of a single 1s Slater-type basis function centered on each nucleus. The first-order molecular orbital is expressed in terms of these two functions plus one singular basis function each of the types e^-r/r and e^-r ln r centered on one of the nuclei. The new kinds of molecular integrals were evaluated to high accuracy using numerical and analytical means. The value of the HD spin-spin coupling constant calculated with this near-minimal set of basis functions is J_HD = +96.6 cps. This represents an improvement over the previous calculated value of +120 cps obtained without using the logarithmic basis function but is still considerably off in magnitude compared with the experimental measurement of J_HD = +43 0 ± 0.5 cps.

Formal languages, part theory, and change

A general definition of interpreted formal language is presented. The notion “is a part of" is formally developed and models of the resulting part theory are used as universes of discourse of the formal languages. It is shown that certain Boolean algebras are models of part theory.

With this development, the structure imposed upon the universe of discourse by a formal language is characterized by a group of automorphisms of the model of part theory. If the model of part theory is thought of as a static world, the automorphisms become the changes which take place in the world. Using this formalism, we discuss a notion of abstraction and the concept of definability. A Galois connection between the groups characterizing formal languages and a language-like closure over the groups is determined.

It is shown that a set theory can be developed within models of part theory such that certain strong formal languages can be said to determine their own set theory. This development is such that for a given formal language whose universe of discourse is a model of part theory, a set theory can be imbedded as a submodel of part theory so that the formal language has parts which are sets as its discursive entities.

Part I. Regulation of development in the cellular slime mold Dictyostelium discoideum. Part II. Polysomes and RNA synthesis during early development of the surf clam Spisula solidissima

Part I. The cellular slime mold Dictyostelium discoideum is a simple eukaryote which undergoes a multi-cellular developmental process. Single cell myxamoebae divide vegetatively in the presence of a food source. When the food is depleted or removed, the cells aggregate, forming a migrating pseudoplasmodium which differentiates into a fruiting body containing stalk and spore cells. I have shown that during the developmental cycle glycogen phosphorylase, aminopeptidase, and alanine transaminase are developmentally regulated, that is their specific activities increased at a specific time in the developmental cycle. Phosphorylase activity is undetectable in developing cells until mid-aggregation whereupon it increases and reaches a maximum at mid-culmination. Thereafter the enzyme disappears. Actinomycin D and cycloheximide studies as well as studies with morphologically aberrant and temporally deranged mutants indicate that prior RNA and concomitant protein synthesis are necessary for the rise and decrease in activity and support the view that the appearance of the enzyme is regulated at the transcriptional level. Aminopeptidase and alanine transaminase increase 3 fold starting at starvation and reach maximum activity at 18 and 5 hours respectively.

The cellular DNA s of D. discoideum were characterized by CsC1 buoyant density gradient centrifugation and by renaturation kinetics. Whole cell DNA exhibits three bands in CsCl: ρ = 1.676 g/cc (nuclear main band), 1.687 (nuclear satellite), and 1.682 (mitochondrial). Reassociation kinetics at a criterion of Tm -23°C indicates that the nuclear reiterated sequences make up 30% of the genome (Cot_1/2 (pure) 0.28) and the single-copy DNA 70% (Cot_1/2(pure) 70). The complexity of the nuclear genome is 30 x 10⁹ daltons and that of the mitochondrial DNA is 35-40 x 10⁶ daltons (Cot_1/2 0.15). rRNA cistrons constitute 2.2% of nuclear DNA and have a ρ = 1.682.

RNA extracted from 4 stages during developmental cycle of Dictyostelium was hybridized with purified single-copy nuclear DNA. The hybrids had properties indicative of single-copy DNA-RNA hybrids. These studies indicate that there are, during development, qualitative and quantitative changes in the portion of the single-copy of the genome transcribed. Overall, 56% of the genome is represented by transcripts between the amoeba and mid-culmination stages. Some 19% are sequences which are represented at all stages while 37% of the genome consists of stage specific sequences.

Part II. RNA and protein synthesis and polysome formation were studied during early development of the surf clam Spisula solidissima embryos. The oocyte has a small number of polysomes and a low but measurable rate of protein synthesis (leucine-³H incorporation). After fertilization, there is a continual increase in the percentage of ribosomes sedimenting in the polysome region. Newly synthesized RNA (uridine-5-³H incorporation) was found in polysomes as early as the 2-cell stage. During cleavage, the newly formed RNA is associated mainly with the light polysomes.

RNA extracted from polysomes labeled at the 4-cell stage is polydisperse, nonribosomal, and non-4 S. Actinomycin D causes a reduction of about 30% of the polysomes formed between fertilization and the 16-cell stage.

In the early cleavage stages the light polysomes are mostly affected by actinomycin.

Matrices whose hermitian part is positive definite

We are concerned with the class ∏_n of nxn complex matrices A for which the Hermitian part H(A) = A+A*/2 is positive definite.

Various connections are established with other classes such as the stable, D-stable and dominant diagonal matrices. For instance it is proved that if there exist positive diagonal matrices D, E such that DAE is either row dominant or column dominant and has positive diagonal entries, then there is a positive diagonal F such that FA ϵ ∏_n.

Powers are investigated and it is found that the only matrices A for which A^m ϵ ∏_n for all integers m are the Hermitian elements of ∏_n. Products and sums are considered and criteria are developed for AB to be in ∏_n.

Since ∏_n n is closed under inversion, relations between H(A)^-1 and H(A^-1) are studied and a dichotomy observed between the real and complex cases. In the real case more can be said and the initial result is that for A ϵ ∏_n, the difference H(adjA) - adjH(A) ≥ 0 always and is ˃ 0 if and only if S(A) = A-A*/2 has more than one pair of conjugate non-zero characteristic roots. This is refined to characterize real c for which cH(A^-1) - H(A)^-1 is positive definite.

The cramped (characteristic roots on an arc of less than 180°) unitary matrices are linked to ∏_n and characterized in several ways via products of the form A ^-1A*.

Classical inequalities for Hermitian positive definite matrices are studied in ∏_n and for Hadamard's inequality two types of generalizations are given. In the first a large subclass of ∏_n in which the precise statement of Hadamardis inequality holds is isolated while in another large subclass its reverse is shown to hold. In the second Hadamard's inequality is weakened in such a way that it holds throughout ∏_n. Both approaches contain the original Hadamard inequality as a special case.

Part I: Total yield measurements for the ^(21)Ne(α,n)^)(24)Mg reaction. Part II: A study of the ^(12)C(He,p)^(14)N reaction

PART I

The total cross-section for the reaction ²¹Ne(α, n)²⁴Mg has been measured in the energy range 1.49 Mev ≤ E_cm ≤ 2.6 Mev. The cross-section factor, S(O), for this reaction has been determined, by means of an optical model calculation, to be in the range 1.52 x 10¹² mb-Mev to 2.67 x 10¹² mb-Mev, for interaction radii in the range 5.0 fm to 6.6 fm. With S(O) ≈ 2 x 10¹² mb-Mev, the reaction ²¹Ne(α, n)²⁴Mg can produce a large enough neutron flux to be a significant astrophysical source of neutrons.

PART II

The reaction¹²C(³He, p)¹⁴N has been studied over the energy range 12 Mev ≤ E_lab ≤ 18 Mev. Angular distributions of the proton groups leading to the lowest seven levels in ¹⁴N were obtained.

Distorted wave calculations, based on two-nucleon transfer theory, were performed, and were found to be reliable for obtaining the value of the orbital angular momentum transferred. The present work shows that such calculations do not yield unambiguous values for the spectroscopic factors.

Linefish resources annual report for the year 2000. Part 1: fisheries assessment

This work reflects the activities of line and trap fishing in Southern Mozambique in 2000. The catch in line fishing has been estimated at 441 mt, according to the DNAP records. The same sources indicated that 1767 days were spent at sea and the estimated catch rate was 250 Kg per boaticlay. Most of the line fishing effort shifted away from Maputo and moved to Inhambane region. The monthly analysis of fishing vessels, stricter controls over catch and effort data submission, development of long-term research programme and the continuation of the on board sampling to improve the data collection are the recommendation for line fishing. The catch of trap vessels increases from 30mt in 1997 to 172 mt in 2000, during which the total number of traps increased from 25 to 300. During this time the number of fishing days has remained relatively constant, as well the soak time. These data sets are thus not compatible with each other, reflecting an increase in daily catch from 243 Kg to 791 kg. The species composition is mainly dominated by P. coeruleopunctatus, C. puniceus, C. nufar and E. andersoni.