On the secondly quantized theory of many-electron atom

Traditional theory of many-electron atoms and ions is based on the coefficients of fractional parentage and matrix elements of tensorial operators, composed of unit tensors. Then the calculation of spin-angular coefficients of radial integrals appearing in the expressions of matrix elements of arbitrary physical operators of atomic quantities has two main disadvantages: (i) The numerical codes for the calculation of spin-angular coefficients are usually very time-consuming; (ii) f-shells are often omitted from programs for matrix element calculation since the tables for their coefficients of fractional parentage are very extensive. The authors suppose that a series of difficulties persisting in the traditional approach to the calculation of spin-angular parts of matrix elements could be avoided by using this secondly quantized methodology, based on angular momentum theory, on the concept of the irreducible tensorial sets, on a generalized graphical method, on quasispin and on the reduced coefficients of fractional parentage

Low-density genotype panel for both parentage verification and discovery in a multi-breed sheep population

peer-reviewedThe generally low usage of artificial insemination and single-sire mating in sheep, compounded by mob lambing (and lambing outdoors), implies that parentage assignment in sheep is challenging. The objective here was to develop a low-density panel of single nucleotide polymorphisms (SNPs) for accurate parentage verification and discovery in sheep. Of particular interest was where SNP selection was limited to only a subset of chromosomes, thereby eliminating the ability to accurately impute genome-wide denser marker panels. Data used consisted of 10,933 candidate SNPs on 9,390 purebred sheep. These data consisted of 1,876 validated genotyped sire–offspring pairs and 2,784 validated genotyped dam–offspring pairs. The SNP panels developed consisted of 87 SNPs to 500 SNPs. Parentage verification and discovery were undertaken using 1) exclusion, based on the sharing of at least one allele between candidate parent–offspring pairs, and 2) a likelihood-based approach. Based on exclusion, allowing for one discordant offspring–parent genotype, a minimum of 350 SNPs was required when the goal was to unambiguously identify the true sire or dam from all possible candidates. Results suggest that, if selecting SNPs across the entire genome, a minimum of 250 carefully selected SNPs are required to ensure that the most likely selected parent (based on the likelihood approach) was, in fact, the true parent. If restricting the SNPs to just a subset of chromosomes, the recommendation is to use at least a 300-SNP panel from at least six chromosomes, with approximately an equal number of SNPs per chromosome

Relations Between Coefficients of Fractional Parentage

For each of the (9/2), (11/2) and (13/2) single j shells we have only one state with J=j V=3 for a five particle system. For four identical particles there can be more than one state of seniority four. We note some ``ratio'' relations for the coefficients of fractional parentage for the four and five identical particle systems

A new intergeneric hybrid: x<i>Gastonialoe</i> 'Gordon Rowley'

A new intergeneric hybrid genus xGastonialoe is named for crosses with the parentage Gasteria x Gonialoe (Aloe). An attractive cultivar in this new nothogenus is named xGastonialoe 'Gordon Rowley', in honour of an ardent champion of such hybrids

Evaluating genetic traceability methods for captive bred marine fish and their applications in fisheries management and wildlife forensics

Growing demands for marine fish products is leading to increased pressure on already depleted wild populations and a rise in the aquaculture production. Consequently, more captive bred fish are released into the wild through accidental escape or deliberate restocking, stock enhancement and sea ranching programs. The increased mixing of captive bred fish with wild conspecifics may affect the ecological and/or genetic integrity of wild fish populations. From a fisheries management perspective unambiguous identification tools for captive bred fish will be highly valuable to manage risks. Additionally there is great potential to use these tools in wildlife forensics (i.e. tracing back escapees to their origin and determining mislabelling of seafood products). Using SNP data from captive bred and wild populations of Atlantic cod (Gadus morhua L.) and sole (Solea solea L.), we explored the efficiency of population and parentage assignment techniques for the identification and tracing of captive bred fish. Simulated and empirical data were used to correct for stochastic genetic effects. Overall, parentage assignment performed well when a large effective population size characterizes the broodstock and escapees originate from early generations of captive breeding. Consequently, parentage assignments are particularly useful from a fisheries management perspective to monitor the effects of deliberate releases of captive bred fish on wild populations. Population assignment proved to be more efficient after several generations of captive breeding, which makes it a useful method in forensic applications for well-established aquaculture species. We suggest the implementation of a case by case strategy when choosing the best method

Calculation of reduced coefficients and matrix elements in jj-coupling

A program RCFP will be presented for calculating standard quantities in the decomposition of many-electron matrix elements in atomic structure theory. The list of quantities wich are supported by the present program includes the coefficients of fractional parentage, the reduced coefficients of fractional parentage, the reduced matrix elements of the unit operator T^{(k)} as well as the completely reduced matrix elements of the operator W^{(k_jk_q)} in jj-coupling. These quantities are now available for all subshells (nj) with j \leq 9/2 including partially filled 9/2-shells. Our program is based on a recently developed new approach on the spin-angular integration which combines second quantization and quasispin methods with the theory of angular momentum in order to obtain a more efficient evaluation of many-electron matrix elements. An underlying Fortran 90/95 module can directly be used also in (other) atomic structure codes to accelerate the computation for open-shell atoms and ions

An Extension of the Fractional Parentage Expansion to Nonrelativistic and Relativistic SU(3)fSU(3)_{f} Dibaryon Calculations

The fractional parentage expansion method is extended from $SU(2)_{f}$ nonrelativistic to $SU(3)_{f}$ and relativistic dibaryon calculations. A transformation table between physical bases and symmetry bases for the $SU(3)_{f}$ dibaryon is provided. A program package has been written for dibaryon calculation based on the fractional parentage expansion method.Comment: 15 pages text plus 18 pages tables, latex, no figure