The Parity of the Number of Irreducible Factors for Some Pentanomials

It is well known that Stickelberger-Swan theorem is very important for determining reducibility of polynomials over a binary field. Using this theorem it was determined the parity of the number of irreducible factors for some kinds of polynomials over a binary field, for instance, trinomials, tetranomials, self-reciprocal polynomials and so on. We discuss this problem for type II pentanomials namely x^m +x^{n+2} +x^{n+1} +x^n +1 \in\ IF_2 [x]. Such pentanomials can be used for efficient implementing multiplication in finite fields of characteristic two. Based on the computation of discriminant of these pentanomials with integer coefficients, it will be characterized the parity of the number of irreducible factors over IF_2 and be established the necessary conditions for the existence of this kind of irreducible pentanomials.

Parity of the Number of Irreducible Factors for Composite Polynomials

Various results on parity of the number of irreducible factors of given polynomials over finite fields have been obtained in the recent literature. Those are mainly based on Swan’s theorem in which discriminants of polynomials over a finite field or the integral ring Z play an important role. In this paper we consider discriminants of the composition of some polynomials over finite fields. The relation between the discriminants of composed polynomial and the original ones will be established. We apply this to obtain some results concerning the parity of the number of irreducible factors for several special polynomials over finite fields.

Influence of occupation number of single particle levels on K - K charge transfer in collisions of 90 keV - Ne{^9+} on Ne

The influence of the occupation of the single particle levels on the impact parameter dependent K - K charge transfer occuring in collisions of 90 keV Ne{^9+} on Ne was studied using coupled channel calculations. The energy eigenvalues and matrixelements for the single particle levels were taken from ab initio self consistent MO-LCAO-DIRAC-FOCK-SLATER calculations with occupation numbers corresponding to the single particle amplitudes given by the coupled channel calculations.

Agri-environmental evaluation of traditional and alternative corn production systems in Chiapas, Mexico

This study evaluates the effects of environmental variables on traditional and alternative agroecosystems in three Ejidos (communal lands) in the Chiapas rainforest in Mexico. The tests occurred within two seasonal agricultural cycles. In spring-summer, experiments were performed with the traditional slash, fell and burn (S-F-B) system, no-burn systems and rotating systems with Mucuna deeringiana Bort., and in the autumn-winter agricultural cycle, three no-burn systems were compared to evaluate the effect of alternative sowing with corn (no-burn and topological modification of sowing). The results show a high floristic diversity in the study area (S_S = 4 - 23%), with no significant differences among the systems evaluated. In the first cycle, the analysis of the agronomical variables of the corn indicated better properties in the fallowing systems, with an average yield of 1950 kg ha^‑1, but there was variation related to the number of years left fallow. In the second cycle, the yields were positive for the alternative technology (average yield 3100 kg ha^‑1). The traditional S-F-B systems had reduced pests and increased organic matter and soil phosphorous content. These results are the consequence of fallow periods and adaptation to the environment; thus, this practice in the Chiapas rainforest constitutes an ethnocultural reality, which is unlikely to change in the near future if the agrosystems are managed based on historical principles.

Suppression of root-knot nematode through innovative mustard biofumigation

The nematicidal activity of mustard plant against hatching, migration and mortality of the root-knot nematode Meloidogyne javanica was investigated. In vitro test confirmed that mixing the sandy clay soil mixture with mustard as 4% as a biofumigant significantly reduce the percentage of egg hatching at all different incubation periods 24, 48, 72, 96 and 168 h, compared to control treatment (un-amended mixture soil and eggs in free water). Results indicate that the percentage of egg hatching reduction was 88.5, 90, 81.4, 74 and 69.4%, respectively. Mustard mixed with soil as a biofumigant led to high percentage of larval mortality at the different intervals periods in vitro. The percentage of larval mortality was 94, 100, 90.5, 90.5, and 79.4%, respectively compared to control. Laboratory results confirmed that the highest reduction in egg hatching and larval mortality was obtained after incubation period for 48 h. In vivo experiment reveals that the incorporation of the soil pots with mustard at all different doses used 3, 5% (48 h before nematode inoculation, or soil infestation with nematode), and 5% (one week before nematode inoculation or 7% of soil weight) significantly reduces all the nematode parameters compared to plant treated nematode alone. All nematode parameters i.e. the number of galls per root system, gall index, number of egg masses per root system, as well as number of juveniles per 250g soil showed high reduction with mixing the soil pots with mustard at 5% (one week before nematode inoculation), followed by the same treatment for 48h before nematode inoculation. Mustard application, one week before nematode inoculation, reduced the nematode parameters by 97, 64, 97, and 93%, respectively, compared to control. The percent of chemical components i.e. total sugars, total amino acids and total phenols were markedly enhanced compared to positive and negative control. The highest percentage was obtained with mustard at 5% one week before nematode inoculation by 68.7, 57.3 and 45%, respectively. Finally, we have to conclude that this modified technology is an innovative and can be used efficiently to control Root-knot nematode under organic agriculture and Global GAP agricultural systems instead of these carcinogenic nematicides.