A method for rapidly evaluating the linearity of calibration data

Simple technique determines whether or not a set of five data points lies within a specified close tolerance of a linear fit

The State of Pakistan’s Dairy Sector : An Assessment

While there is a plethora of research documenting a multitude of dimensions of the crop sector of Pakistan, there is virtual absence of meaningful economic analysis of the dairy economy that is surprising. No serious attempt has been made in the past to clarify the micro-level potential of this sector in creating an impact on rural economy. This paper is a pioneering attempt to provide an objective assessment of the state of Pakistans dairy and to point out areas of further research. The paper analyzes some core issues and highlights the potentials, and recommends measures that could be adopted.dairy, rural economy, research areas

The State of Pakistan’s Dairy Sector: An Assessment

While there is a plethora of research documenting a multitude of dimensions of the crop sector of Pakistan, the virtual absence of meaningful economic analysis of the dairy economy is surprising. No serious attempt has been made in the past to clarify the microlevel potential of this sector to impact rural economy. This paper is a pioneering attempt to provide an objective assessment of the state of Pakistan’s dairy and to point out areas of further research. The paper analyses some core issues, highlights the potential of this sector, and recommends the measures to be adopted towards such a goal.Dairy Industry, Pakistan

Leptogenesis with heavy neutrino flavours: from density matrix to Boltzmann equations

Leptogenesis with heavy neutrino flavours is discussed within a density matrix formalism. We write the density matrix equation, describing the generation of the matter-antimatter asymmetry, for an arbitrary choice of the right-handed (RH) neutrino masses. For hierarchical RH neutrino masses lying in the fully flavoured regimes, this reduces to multiple-stage Boltzmann equations. In this case we recover and extend results previously derived within a quantum state collapse description. We confirm the generic existence of phantom terms. However, taking into account the effect of gauge interactions, we show that they are washed out at the production with a wash-out rate that is halved compared to that one acting on the total asymmetry. In the N_1-dominated scenario they cancel without contributing to the final baryon asymmetry. In other scenarios they do not in general and they have to be taken into account. We also confirm that there is a (orthogonal) component in the asymmetry produced by the heavier RH neutrinos which completely escapes the washout from the lighter RH neutrinos and show that phantom terms additionally contribute to it. The other (parallel) component is washed out with the usual exponential factor, even for weak washout. Finally, as an illustration, we study the two RH neutrino model in the light of the above findings, showing that phantom terms can contribute to the final asymmetry also in this case.Comment: 39 pages, 5 figures; v2: added Appendix and discussion in 2.2 on lepton-antilepton flavour compositions difference (eq. (28) is a new result); footnotes 4 and 5; new effect of gauge interactions in inducing wash-out of phantom terms but with halved wash-out rate compared to the total asymmetry wash-out rate; matches JCAP versio

Leptogenesis in the two right-handed neutrino model revisited

We revisit leptogenesis in the minimal non-supersymmetric type I see-saw mechanism with two right-handed (RH) neutrinos, including flavour effects and allowing both RH neutrinos N_1 and N_2 to contribute, rather than just the lightest RH neutrino N_1 that has hitherto been considered. By performing scans over parameter space in terms of the single complex angle z of the orthogonal matrix R, for a range of PMNS parameters, we find that in regions around z \sim \pm \pi/2, for the case of a normal mass hierarchy, the N_2 contribution can dominate the contribution to leptogenesis, allowing the lightest RH neutrino mass to be decreased by about an order of magnitude in these regions, down to M_1 \sim 1.3*10^11 GeV for vanishing initial N_2-abundance, with the numerical results supported by analytic estimates. We show that the regions around z \sim \pm \pi /2 correspond to light sequential dominance, so the new results in this paper may be relevant to unified model building.Comment: 41 pages, 10 figures; v2 matches published version in PR