In the present paper, an elliptic equation with singular cylindrical growth is considered. By using the Nehari manifold and mountain pass theorem, the existence of at least four distinct solutions is obtained. The result depends crucially on the parameters k, λ,g and µ.

The structural, magnetic and magnetocaloric properties of Ni0.6Cu0.4Fe1.5Cr0.5O4 sample have been investigated. The sample was synthesized by sol-gel method. The X-ray diffraction result indicates that the ferrite sample has a cubic spinel type structure (Fd3̅m space group). Magnetization versus temperature showed that sample exhibits a second-order paramagnetic (PM) -ferromagnetic (FM) phase transitions with Curie temperature TC equal to 660 K. Magnetocaloric properties were obtained by measuring a family of M(H, T) curves near TC and calculating both magnetic entropy change (ΔSM) and relative cooling power (RCP). The magnetic entropy change reaches a maximum value |∆SM max| of about 1.39 J.K-1 .kg -1 for μ0H= 5 T corresponding to relative cooling power (RCP) of 142 J.kg-1 . These values are comparable to that of some other ferrite materials considered as possible candidates for magnetic refrigeration.  

Using the concept of w -distance, a result on the existence of fixed points for multivalued maps is proved. Consequently, provide the previous works done by others and then compare them with the presented one explicitly, of a new condition that is deduced from the properties of w -distance.

Density functional methods have been used to study the crystal, electronic and magnetic structures of new ordered double perovskites A2NRuO6 (A2 = Ba2, Bala; N = V, Cr, Fe). In the doped compounds, A-site was replaced by 1:1 of Ba2+ and La3+ cations, BaLaNRuO6. All compounds of A2NRuO6 crystallize in cubic symmetry with (space group Fm-3m and tilt system a0a0a0). The electronic and magnetic calculations were performed by the full-potential linear muffin-tin orbital (PF-LMTO) method using both the generalized gradient approximation (GGA) and GGA plus on-site electron correlation effect (GGA+U). In GGA method, Ba2NRuO6 shows half-metallic (HM), semiconducting and metallic behavior for N = V, Cr, Fe, respectively, completely change to HM when A2 = BaLa. While, GGA+U method yields clearly HM state in all compounds, except for Ba2FeRuO6, which shows an insulating behavior. Also, the results of magnetic structures calculations reveal that the A2NRuO6 compounds show a ferrimagnetic (FI) nature if N = V and Cr, switch to ferromagnetic (FM) nature when N = Fe. The V3+, Cr3+, Fe3+, and Ru5+ ions are in high spin magnetic moments states due to the antiferromagnetic coupling N (3d)–O (2p)–Ru (4d).

Infants' milk powder can be used in many countries because it contains vitamins, proteins and minerals, which are essential to grow infants. Therefore, the main objectives of this study were to measure the natural radionuclides concentrations (226Ra, 232Th, and 40K). Gamma ray Spectroscopy, NaI(Tl) detector was used for measuring the radionuclides concentrations of 15 brands for new born till six months. The average radionuclides concentrations were 2.1±0.04 BqKg-1, 1.6±0.03 BqKg-1 and 111.1±0.5 BqKg-1 for 226Ra, 232Th and 40K respectively. The average and range of the effective dose due to annual intake from infants' milk powder were estimated to be 75.1(19.8-109.5) μSvy-1, 27.5(1.9-40.3) μSvy-1 and 177.4(57.8-247.2) μSvy-1 for 226Ra, 232Th and 40K respectively. These values were lower than the recommended limit determined by ICRP-60, IAEA-152 and UNSCEAR. The comparison was obtained between our results and other published papers in different countries. The resulting data may serve as base-line levels of activity concentration in powdered milk in the area of study.