Application of Homotopy Analysis Method for Solving various types of Problems of Ordinary Differential Equations

In this paper, various types of linear, non-linear, homogeneous, non homogeneous problems of ordinary differential equations discussed. Also shown that homotopy analysis method applied successfully for solving non homogeneous and non linear equations

Coexistence of superconductivity and ferromagnetism in Sr0.5Ce0.5FBiS2-xSex (x = 0.5 and 1.0), a non-U material with Tc < TFM

We have carried out detailed magnetic and transport studies of the new Sr0.5Ce0.5FBiS2-xSex (0.0 ≤ x ≤ 1.0) superconductors derived by doping Se in Sr0.5Ce0.5FBiS2. Se–doping produces several effects: it suppresses semiconducting–like behavior observed in the undoped Sr0.5Ce0.5FBiS2, the ferromagnetic ordering temperature, TFM, decreases considerably from 7.5 K (in Sr0.5Ce0.5FBiS2) to 3.5 K and the superconducting transition temperature, Tc, gets enhanced slightly to 2.9–3.3 K. Thus in these Se–doped materials, TFM is marginally higher than Tc. Magnetization studies provide evidence of bulk superconductivity in Sr0.5Ce0.5FBiS2-xSex at x ≥ 0.5 in contrast to the undoped Sr0.5Ce0.5FBiS2 (x = 0) where magnetization measurements indicate a small superconducting volume fraction. Quite remarkably, as compared with the effective paramagnetic Ce–moment (~2.2 μB), the ferromagnetically ordered Ce–moment in the superconducting state is rather small (~0.1 μB) suggesting itinerant ferromagnetism. To the best of our knowledge, Sr0.5Ce0.5FBiS2-x Sex (x = 0.5 and 1.0) are distinctive Ce–based bulk superconducting itinerant ferromagnetic materials with Tc < TFM. Furthermore, a novel feature of these materials is that they exhibit a dual and quite unusual hysteresis loop corresponding to both the ferromagnetism and the coexisting bulk superconductivity

Host transcriptome and microbiome interaction modulates physiology of full-sibs broilers with divergent feed conversion ratio

Efficient livestock production relies on effective conversion of feed into body weight gain (BWG). High levels of feed conversion are especially important in production of broiler chickens, birds reared for meat, where economic margins are tight. Traits associated with improved broiler growth and feed efficiency have been subjected to intense genetic selection, but measures such as feed conversion ratio (FCR) remain variable, even between full siblings (sibs). Non-genetic factors such as the composition and function of microbial populations within different enteric compartments have been recognized to influence FCR, although the extent of interplay between hosts and their microbiomes is unclear. To examine host–microbiome interactions we investigated variation in the composition and functions of host intestinal-hepatic transcriptomes and the intestinal microbiota of full-sib broilers with divergent FCR. Progeny from 300 broiler families were assessed for divergent FCR set against shared genetic backgrounds and exposure to the same environmental factors. The seven most divergent full-sib pairs were chosen for analysis, exhibiting marked variation in transcription of genes as well as gut microbial diversity. Examination of enteric microbiota in low FCR sibs revealed variation in microbial community structure and function with no difference in feed intake compared to high FCR sibs. Gene transcription in low and high FCR sibs was significantly associated with the abundance of specific microbial taxa. Highly intertwined interactions between host transcriptomes and enteric microbiota are likely to modulate complex traits like FCR and may be amenable to selective modification with relevance to improving intestinal homeostasis and health