Contributions to the biology of the panga Pterogymnus laniarus (Pisces : Sparidae): age, growth and reproduction

All the fish used in this investigation were caught by commercial side trawlers along the eastern Cape coast of South Africa. Age and growth of P. laniarius was determined from otoliths collected monthly from April 1974 to September 1975. The validity of annuli was proved by monthly edge examination of the otoliths. There is no difference in growth between the sexes. The Von Bertalanffy equation Lt = 48,1 (l-e-0,10(e + 0.22)) was found to describe the growth of the panga in length. Some fish become sexually mature at a total length of 26 cm. Fifty percent maturity is attained at a length of 28 cm, between the ages of 4 and 5 years. All fish are sexually mature at a total length of 32 cm, at an age of 6 years. The spawning season of the panga extends from mid-September to May

Branching rules for the subgroups of the unitary group

Expressions are given in terms of simple matrices d for the reduction of the Kronecker (outer) product of two or more irreducible representations which can be characterized by Young patterns. These are then used to obtain practical formulas for branching rules. The needed matrices d can be constructed by a very efficient recursive process.Peer Reviewedhttp://deepblue.lib.umich.edu/bitstream/2027.42/69691/2/JMAPAQ-19-3-720-1.pd

Construction of SU(3) irreps in canonical SO(3)-coupled bases

Alternative canonical methods for defining canonical SO(3)-coupled bases for SU(3) irreps are considered and compared. It is shown that a basis that diagonalizes a particular linear combination of SO(3) invariants in the SU(3) universal enveloping algebra gives basis states that have good $K$ quantum numbers in the asymptotic rotor-model limit.Comment: no figure

The Gaussian formula and spherical aberration of the static and moving curved mirrors from Fermat's principle

The Gaussian formula and spherical aberrations of the static and relativistic curved mirrors are analyzed using the optical path length (OPL) and Fermat's principle. The geometrical figures generated by the rotation of conic sections about their symmetry axes are considered for the shapes of the mirrors. By comparing the results in static and relativistic cases, it is shown that the focal lengths and the spherical aberration relations of the relativistic mirrors obey the Lorentz contraction. Further analysis of the spherical aberrations for both static and relativistic cases have resulted in the information about the limits for the paraxial approximation, as well as for the minimum speed of the systems to reduce the spherical aberrations.Comment: 15 pages, 7 figures, uses iopart. Major revisions on the physical interpretations of the results. Accepted for publication in J. Op

Representation of the five‐dimensional harmonic oscillator with scalar‐valued U(5) ⊇ SO(5) ⊇ SO(3)–coupled VCS wave functions

Vector coherent state methods, which reduce the U(5) ⊇ SO(5) ⊇ SO(3) subgroup chain, are used to construct basis states for the five‐dimensional harmonic oscillator. Algorithms are given to calculate matrix elements in this basis. The essential step is the construction of SO(5) ⊇ SO(3) irreps of type [v,0]. The methodology is similar to that used in two recent papers except that one‐dimensional, as opposed to multidimensional, vector‐valued wave functions are used to give conceptually simpler results. Another significant advance is a canonical resolution of the SO(5) ⊇ SO(3) multiplicity problem. © 1995 American Institute of Physics.Peer Reviewedhttp://deepblue.lib.umich.edu/bitstream/2027.42/70418/2/JMAPAQ-36-9-4711-1.pd

Phenomenology of the Baryon Resonance 70-plet at Large N_c

We examine the multiplet structure and decay channels of baryon resonances in the large N_c QCD generalization of the N_c = 3 SU(6) spin-flavor 70. We show that this ``70'', while a construct of large N_c quark models, actually consists of five model-independent irreducible spin-flavor multiplets in the large N_c limit. The preferred decay modes for these resonances fundamentally depend upon which of the five multiplets to which the resonance belongs. For example, there exists an SU(3) ``8'' of resonances that is eta-philic and pi-phobic, and an ``8'' that is the reverse. Moreover, resonances with a strong SU(3) ``1'' component prefer to decay via a K-bar rather than via a pi. Remarkably, available data appears to bear out these conclusions.Comment: 26 pages, ReVTe

Vector coherent state theory of the generic representations of so(5) in an so(3) basis

For applications of group theory in quantum mechanics, one generally needs explicit matrix representations of the spectrum generating algebras that arise in bases that reduce the symmetry group of some Hamiltonian of interest. Here we use vector coherent state techniques to develop an algorithm for constructing the matrices for arbitrary finite-dimensional irreps of the SO(5) Lie algebra in an SO(3) basis. The SO(3) subgroup of SO(5) is defined by regarding SO(5) as linear transformations of the five-dimensional space of an SO(3) irrep of angular momentum two. A need for such irreps arises in the nuclear collective model of quadrupole vibrations and rotations. The algorithm has been implemented in MAPLE, and some tables of results are presented.Comment: 20 pages, uses multirow.sty, submitted to J. Math. Phy

Occupation probability of harmonic-oscillator quanta for microscopic cluster-model wave functions

We present a new and simple method of calculating the occupation probability of the number of total harmonic-oscillator quanta for a microscopic cluster-model wave function. Examples of applications are given to the recent calculations including $\alpha+n+n$-model for $^6$He, $\alpha+t+n+n$-model for $^9$Li, and $\alpha+\alpha+n$-model for $^9$Be as well as the classical calculations of $\alpha+p+n$-model for $^6$Li and $\alpha+\alpha+\alpha$-model for $^{12}$C. The analysis is found to be useful for quantifying the amount of excitations across the major shell as well as the degree of clustering. The origin of the antistretching effect is discussed.Comment: 9 page

Mass and Spin of Poincare Gauge Theory

We discuss two expressions for the conserved quantities (energy momentum and angular momentum) of the Poincar\'e Gauge Theory. We show, that the variations of the Hamiltonians, of which the expressions are the respective boundary terms, are well defined, if we choose an appropriate phase space for asymptotic flat gravitating systems. Furthermore, we compare the expressions with others, known from the literature.Comment: 16 pages, plain-tex; to be published in Gen. Rel. Gra