Magnetostriction of TbxHo0.75−xPr0.25(Fe0.9B0.1)2 (x=0–0.3) compounds

The Tb_xHo_0.75−xPr_0.25(Fe_0.9B_0.1)₂ (x=0, 0.1, 0.15, 0.2, 0.25, and 0.3) compounds are found to stabilize in a cubic Laves phase structure. The lattice parameter, magnetostriction (at 10 kOe), and Curie temperature are found to increase with increasing Tb content. The compound with x=0.15 exhibits a possible anisotropy compensation between the Tb and (Ho/Pr) sublattices. The easy magnetization direction rotates towards the 〈1 1 1〉 from the 〈1 0 0〉 direction, with increasing Tb content. The splitting of the (4 4 0) peak accompanied by the spontaneous magnetostriction-induced rhombohedral distortion is observed for compounds with x?0.15 and the spontaneous magnetostriction (λ_1 1 1) is found to increase with Tb content.     

External bremsstrahlung spectral shape dependence on target thickness

Spectral shapes of bremsstrahlung were measured when³²P and⁴⁵Ca beta rays were absorbed in several elements Al, Cu, Sn and Pb of different thicknesses. While in aluminium, the experimental values and Bethe-Heitler theory agree for all thicknesses, in the case of the other elements an increase in the experimental value is observed which increases with Z of the target material and thickness of the target.     

On a class of restricted phase problems in the plane

Certain geometrical necessary and sufficient conditions are developed for the optimal control of a class of second order systems with restrictions on the phase coordinates. The phase constraint set in the plane is assumed to be convex, and under additional hypotheses, it is shown that an optimal trajectory is the one that encloses the least possible area with the optimal trajectory in the unrestricted case.     

On the convergence of iterates

THIS PAPER points out that some of Thron's [5] results on the convergence of iterates of a real valued function of a real variable can be extended to general situations afforded, for instance, by metric and gauge spaces. A few examples are given at the end to illustrate the existence of the special type of operators dealt with in this paper.     

Lattice theory for certain classes of rings

Conclusion We observe that every Boolean ring is aP ₁-ring, where each element is its own minimal idempotent duplicator; a Boolean ring with unity is also aP ₂-ring, where each element is the maximal idempotent annihilator of its complement; and thus,P ₁-rings andP ₂-rings are generalisations of a Boolean ring in terms of its lattice structure. Then, it is only natural that these two classes of rings have such close affiliations with the lattice structure of a Boolean ring.