Irregular primes with respect to Genocchi numbers and Artin's primitive root conjecture

We introduce and study a variant of Kummer's notion of (ir)regularity of primes which we call G-irregularity and it is based on Genocchi numbers $G_n$, rather than Bernoulli number $B_n.$ We say that an odd prime $p$ is G-irregular if it divides at least one of the integers $G_2,G_4,\ldots, G_{p-3}$, and G-regular otherwise. We show that, as in Kummer's case, G-irregularity is related to the divisibility of some class number. Furthermore, we obtain some results on the distribution of G-irregular primes. In particular, we show that each primitive residue class contains infinitely many G-irregular primes and establish non-trivial lower bounds for their number up to a given bound $x$ as $x$ tends to infinity. As a by-product, we obtain some results on the distribution of primes in arithmetic progressions with a prescribed near-primitive root

Transmission, reflection and localization in a random medium with absorption or gain

We study reflection and transmission of waves in a random tight-binding system with absorption or gain for weak disorder, using a scattering matrix formalism. Our aim is to discuss analytically the effects of absorption or gain on the statistics of wave transport. Treating the effects of absorption or gain exactly in the limit of no disorder, allows us to identify short- and long lengths regimes relative to absorption- or gain lengths, where the effects of absorption/gain on statistical properties are essentially different. In the long-lengths regime we find that a weak absorption or a weak gain induce identical statistical corrections in the inverse localization length, but lead to different corrections in the mean reflection coefficient. In contrast, a strong absorption or a strong gain strongly suppress the effect of disorder in identical ways (to leading order), both in the localization length and in the mean reflection coefficient.Comment: Important revisions and expansion caused by a crucial property of $\hat Q

Allocative Efficiency of Resource use on Beekeeping in Chitwan District of Nepal

Agriculture is facing with increasing pollinators decline all over the world affecting the functioning of regulatory and production service of pollination in adverse manner. Study on ways to conserve pollinating agents like bee is crucial in modern intensive agriculture. In this context a study was conducted to estimate the productivity and resource use efficiency of bee keeping in Chitwan district of Nepal. The study used data collected from randomly selected 48 bee keepers using face to face interview technique in the year 2014. Descriptive statistics, gross margin analysis, benefit cost analysis and multiple regression analysis using Cob-Douglas form were employed to achieve study objectives. It was found that farmers were rearing honey bee on an average of about 34 hives per farm with annual productivity of bee products equivalent to 36 Kg honey per hive. Gross margin of beekeeping in the research area was found to be NRs. 3111.55 per hive with undiscounted benefit cost ratio of 1.71. Human labour use, expenditure on sugar, drugs and comb foundation and; migration cost were significantly contributing to the productivity of beekeeping and were required to increase their use by 39%, 34% and 74%, respectively to achieve optimum profit. It was suggested to increase the level of all variable inputs through loan, subsidy and insurance to promote beekeeping enterprise in the study area for ensuring optimum profit to farmers and conservation of the most important agent of pollination

Labour Market and Social Policy in Italy: Challenges and Changes. Bertelsmann Policy Brief #2016/02

vEight years after the outbreak of the financial crisis, Italy has still to cope with and overcome a plethora of economic and social challenges. On top of this, it faces an unfavourable demographic structure and severe disparities between its northern and southern regions. Some promising reforms have recently been enacted, specifically targeting poverty and social exclusion. However, much more remains to be done on the way towards greater economic stability and widely shared prosperity

Solute clustering and precipitation in an Al–Cu–Mg–Ag–Si model alloy

Solute clustering and precipitation in an Al–Cu–Mg–Ag–Si model alloy has been investigated by atom probe tomography (APT) as well as high-angle annular dark-field (HAADF) imaging and electron energy loss spectroscopy (EELS) in the scanning transmission electron microscope (STEM). Nine types of solute clusters (Cu, Ag, Mg–Cu, Mg–Ag, Mg–Cu–Si, Mg–Ag–Si, Mg–Ag–Cu, Cu–Ag–Si and MgAgCuSi) were observed by APT in both the as-quenched alloy and after ageing the alloy at 180 °C for 1 h. Three types of precipitates (Ω (AlCuMgAg), θ (Al2Cu) and Mg2Si) were observed by APT and HAADF-STEM after further ageing at 180 °C for 24 h and 100 h. We propose that MgAgCu and MgAgCuSi clusters are likely to be responsible for the formation of the Ω (AlCuMgAg) phase. Furthermore, we also suggest that the θ (Al2Cu) phase forms from Cu clusters and the Mg2Si phase forms from the decomposition of MgAgSi and MgAgCuSi clusters by losing Ag to Ω phase growth. Many early binary clusters (Mg–Cu, Mg–Ag) do not seem to undergo a significant further growth during ageing; these are more likely to be transformed into complex ternary and quaternary clusters and be subsequently consumed during the growth of large clusters/precipitates. Furthermore, it is proposed that the plate-like Ω (AlCuMgAg) precipitates evolve continuously from the MgAgCu and MgAgCuSi clusters, rather than via heterogeneous nucleation on their precursors (i.e. MgAgCu and MgAgCuSi clusters). More interestingly, even after ageing at 180 °C for 100 h, the Ω (AlCuMgAg) precipitates remain coherent with the α-Al matrix, indicating that these precipitates have a high thermal stability. This can mainly be attributed to the presence of a single Mg–Ag-rich monolayer observed at the interface between the Ω precipitate and the α-Al matrix, significantly improving the coarsening resistance of the Ω (AlCuMgAg) precipitates. Our results thus reveal links between a variety of solute clusters and the different types of precipitates in the Al–Cu–Mg–Ag–Si model alloy. Such information can in the future be used to control the precipitation by tailoring solute clustering

The statistics of identifying differentially expressed genes in Expresso and TM4: a comparison

BACKGROUND: Analysis of DNA microarray data takes as input spot intensity measurements from scanner software and returns differential expression of genes between two conditions, together with a statistical significance assessment. This process typically consists of two steps: data normalization and identification of differentially expressed genes through statistical analysis. The Expresso microarray experiment management system implements these steps with a two-stage, log-linear ANOVA mixed model technique, tailored to individual experimental designs. The complement of tools in TM4, on the other hand, is based on a number of preset design choices that limit its flexibility. In the TM4 microarray analysis suite, normalization, filter, and analysis methods form an analysis pipeline. TM4 computes integrated intensity values (IIV) from the average intensities and spot pixel counts returned by the scanner software as input to its normalization steps. By contrast, Expresso can use either IIV data or median intensity values (MIV). Here, we compare Expresso and TM4 analysis of two experiments and assess the results against qRT-PCR data. RESULTS: The Expresso analysis using MIV data consistently identifies more genes as differentially expressed, when compared to Expresso analysis with IIV data. The typical TM4 normalization and filtering pipeline corrects systematic intensity-specific bias on a per microarray basis. Subsequent statistical analysis with Expresso or a TM4 t-test can effectively identify differentially expressed genes. The best agreement with qRT-PCR data is obtained through the use of Expresso analysis and MIV data. CONCLUSION: The results of this research are of practical value to biologists who analyze microarray data sets. The TM4 normalization and filtering pipeline corrects microarray-specific systematic bias and complements the normalization stage in Expresso analysis. The results of Expresso using MIV data have the best agreement with qRT-PCR results. In one experiment, MIV is a better choice than IIV as input to data normalization and statistical analysis methods, as it yields as greater number of statistically significant differentially expressed genes; TM4 does not support the choice of MIV input data. Overall, the more flexible and extensive statistical models of Expresso achieve more accurate analytical results, when judged by the yardstick of qRT-PCR data, in the context of an experimental design of modest complexity

Localization of Light: Dual Symmetry between Absorption and Amplification

We study the propagation of radiation through a disordered waveguide with a complex dielectric constant $\epsilon$, and show that dual systems, which differ only in the sign of the imaginary part of $\epsilon$, have the same localization length. Paradoxically, absorption and stimulated emission of radiation suppress the transmittance of the waveguide in the same way.Comment: Added a reference to the paper by Z.Q. Zhang, Phys.Rev.B. 52, 7960 (1995

Theory for the photon statistics of random lasers

A theory for the photon statistics of a random laser is presented. Noise is described by Langevin operators, where both fluctuations of the electromagnetic field and of the medium are included. The theory is valid for all lasers with small outcoupling when the laser cavity is large compared to the wavelength of the radiation. The theory is applied to a chaotic laser cavity with a small opening. It is known that a large number of modes can be above threshold simultaneously in such a cavity. It is shown the amount of fluctuations is increased compared to the Poissonian value by an amount that depends on that number