Quasideterminant solutions of a non-Abelian Hirota-Miwa equation

A non-Abelian version of the Hirota-Miwa equation is considered. In an earlier paper [Nimmo (2006) J. Phys. A: Math. Gen. \textbf{39}, 5053-5065] it was shown how solutions expressed as quasideterminants could be constructed for this system by means of Darboux transformations. In this paper we discuss these solutions from a different perspective and show that the solutions are quasi-Pl\"{u}cker coordinates and that the non-Abelian Hirota-Miwa equation may be written as a quasi-Pl\"{u}cker relation. The special case of the matrix Hirota-Miwa equation is also considered using a more traditional, bilinear approach and the techniques are compared

Darboux dressing and undressing for the ultradiscrete KdV equation

We solve the direct scattering problem for the ultradiscrete Korteweg de Vries (udKdV) equation, over $\mathbb R$ for any potential with compact (finite) support, by explicitly constructing bound state and non-bound state eigenfunctions. We then show how to reconstruct the potential in the scattering problem at any time, using an ultradiscrete analogue of a Darboux transformation. This is achieved by obtaining data uniquely characterising the soliton content and the `background' from the initial potential by Darboux transformation.Comment: 41 pages, 5 figures // Full, unabridged version, including two appendice

Bäcklund transformations for noncommutative anti-self-dual Yang-Mills equations

We present Bäcklund transformations for the non-commutative anti-self-dual Yang–Mills equations where the gauge group is G = GL(2) and use it to generate a series of exact solutions from a simple seed solution. The solutions generated by this approach are represented in terms of quasi-determinants and belong to a non-commutative version of the Atiyah–Ward ansatz. In the commutative limit, our results coincide with those by Corrigan, Fairlie, Yates and Goddard

Matrix solutions of a noncommutative KP equation and a noncommutative mKP equation

Matrix solutions of a noncommutative KP and a noncommutative mKP equation which can be expressed as quasideterminants are discussed. In particular, we investigate interaction properties of two-soliton solutions.Comment: 2 figure

On a direct approach to quasideterminant solutions of a noncommutative KP equation

A noncommutative version of the KP equation and two families of its solutions expressed as quasideterminants are discussed. The origin of these solutions is explained by means of Darboux and binary Darboux transformations. Additionally, it is shown that these solutions may also be verified directly. This approach is reminiscent of the wronskian technique used for the Hirota bilinear form of the regular, commutative KP equation but, in the noncommutative case, no bilinearising transformation is available.Comment: 11 page

Optimum combinations of livestock enterprises and management practices on farms including supplementary dairy and poultry enterprises (An application of linear programming)

The object of this study is to determine (1) how scarce feed and other resources should be allocated between livestock enterprises and (2) which management practices or levels should be selected on farms producing a given feed supply. The situation selected for study is an average of 160-acre farms in northeast Iowa which have supplementary dairy and poultry enterprises (i.e., where these two enterprises are not on a large-scale or commercial basis). The cropping program on these farms results in production of 2,652 bushels of corn, 1,230 bushels of oats, 120 bushels of soybeans and 68 tons of forage from pasture and hay land. In addition, optimum programs have been worked out with only 48 tons of forage to determine the effects of restriction in this resource on enterprise combinations. Soybeans are considered to be sold for cash, while grain can be either fed to livestock or sold. Linear programming techniques are used in determining the most profitable management practices and resource allocations or enterprise combinations. In the major solutions, 43 activities or investment opportunities were included: dairy cows of above-average ability, average ability and below-average ability, each fed five different hay-grain combinations and using competitive labor; spring pigs of above-average, average and below-average efficiency; fall hogs with these same levels of efficiency; poultry with these three levels of efficiency, using competitive labor; beef cows; dairy cows as outlined above but using supplementary labor; and poultry as outlined above but using supplementary labor. Several different capital situations also were included in the optimum solutions

Building the field of health policy and systems research: framing the questions.

In the first of a series of articles addressing the current challenges and opportunities for the development of Health Policy & Systems Research (HPSR), Kabir Sheikh and colleagues lay out the main questions vexing the field

B\"acklund Transformations and the Atiyah-Ward ansatz for Noncommutative Anti-Self-Dual Yang-Mills Equations

We present Backlund transformations for the noncommutative anti-self-dual Yang-Mills equation where the gauge group is G=GL(2) and use it to generate a series of exact solutions from a simple seed solution. The solutions generated by this approach are represented in terms of quasideterminants. We also explain the origins of all of the ingredients of the Backlund transformations within the framework of noncommutative twistor theory. In particular we show that the generated solutions belong to a noncommutative version of the Atiyah-Ward ansatz.Comment: v2: 21 pages, published versio

Biologia reprodutiva da surucucu Lachesis muta (Serpentes: Viperidae) da Floresta Atlântica brasileira

The Neotropical genus Lachesis Daudin, 1803 includes snakes restricted to the humid forests of Central and South America. The species L. muta is the most widely dispersed, occurring throughout the Amazon rainforest, and with an isolated population in the Atlantic Forest, from the north of the state of Ceará to the south of the state of Rio de Janeiro, Brazil. We present information about the reproductive biology of L. muta from a large series of samples gathered in southern Bahia. Mature males L. muta are larger than females. Degree of sexual size dimorphism (SSD) is 0.16. Vitellogenic follicles and eggs are not distributed equally throughout the year. Clutch size was 3–14 oviductal eggs and was positively correlated with female SVL. Testes volume and ductus deferens diameter in mature individuals did not vary significantly throughout the year. The reproductive pattern of L. muta differs from that of the phylogenetically related genera because L. muta is oviparous, and has a discontinuous cycle and reproductive synchrony between the sexes.O gênero Neotropical Lachesis Daudin, 1803 inclui serpentes restritas às florestas úmidas da América do Sul e Central. A espécie Lachesis muta é mais amplamente distribuída, ocorrendo em toda a Floresta Amazônica e com uma população isolada na Mata Atlântica, desde o norte do estado do Ceará, ao sul do estado do Rio de Janeiro, Brasil. Apresentamos informações sobre a biologia reprodutiva de L. muta a partir da análise de uma grande série de amostras recolhidas no sul da Bahia. Os machos maduros de L. muta foram maiores que as fêmeas. O grau de dimorfismo sexual (SSD) foi 0,16. Folículos vitelogênicos e ovos não foram distribuídos homogeneamente ao longo do ano. O tamanho da ninhada foi 3–14 ovos e positivamente correlacionado com o CRC das fêmeas. O volume testicular e o diâmetro dos ductos deferentes nos indivíduos maduros não apresentaram variação significativa ao longo do ano. O padrão reprodutivo de L. muta difere daquele de gêneros filogeneticamente relacionados, pois essa espécie é ovípara, tem ciclo descontínuo e sincronia reprodutiva entre os sexos

Very Small Strangelets

We study the stability of small strangelets by employing a simple model of strange matter as a gas of non-interacting fermions confined in a bag. We solve the Dirac equation and populate the energy levels of the bag one quark at a time. Our results show that for system parameters such that strange matter is unbound in bulk, there may still exist strangelets with $A<100$ that are stable and/or metastable. The lifetime of these strangelets may be too small to detect in current accelerator experiments, however.Comment: 13 pages, MIT CTP#217