Structural phase transitions in yttrium under ultrahigh pressures

X-ray diffraction studies were carried out on the rare earth metal yttrium up to 177?GPa in a diamond anvil cell at room temperature. Yttrium was compressed to 37% of its initial volume at the highest pressure. The rare earth crystal structure sequence hcp?→?Sm?type?→?dhcp?→?mixed(dhcp?+?fcc)?→?distorted fcc (dfcc) is observed in yttrium below 50?GPa. The dfcc (hR24) phase has been observed to persist in the pressure range of 50-95?GPa. A structural transition from dfcc to a low symmetry phase has been observed in yttrium at 99?±?4?GPa with a volume change of -?2.6%. This low symmetry phase has been identified as a monoclinic C2/m phase, which has also been observed in other rare earth elements under high pressures. The appearance of this low symmetry monoclinic phase in yttrium shows that its electronic structure under extreme conditions resembles that of heavy rare earth metals, with a significant increase in d-band character of the valence electrons and possibly some f-electron states near the Fermi level.     

Absolute bounds on optimal cost for a class of set covering problems

We study the class of (m constraint,n variable) set covering problems which have no more thank variables represented in each constraint. Letd denote the maximum column sum in the constraint matrix, letr=[m/d]?1, and letZ _g denote the cost of a greedy heuristic solution. Then we prove $$\begin{gathered} Zg \leqslant 1 + r + m - d - \left[ {mk \cdot MAX\left\{ {\frac{{2r}}{{2n - r - 1}},\ln \frac{n}{{n - r}}} \right\}} \right. \hfill \\ \left. { - kd \cdot MIN\left\{ {\frac{{r(r + 1)}}{{2(n - r)}},n \cdot \ln \frac{{n - 1}}{{n - r - 1}} - 1} \right\}} \right]. \hfill \\ \end{gathered} $$ This provides the firsta priori nontrivial upper bound discovered on heuristic solution cost (and thus on optimal solution cost) for the set covering problem. An example demonstrates that this bound is attainable, both for a greedy heuristic solution and for the optimal solution. Numerical examples show that this bound is substantially better than existing bounds for many problem instances. An important subclass of these problems occurs when the constraint matrix is a circulant, in which casem=n andk=d=[αη] for some 0<α<1. For this subclass we prove $$\mathop {\lim }\limits_{n \to \infty } Zg/n \leqslant \frac{{\alpha ^2 }}{2}[1/\alpha ][1/\alpha ].$$      

Studies on the geochemical behaviour of uranium isotopes in Tuwa springs and Khari river sediments

High activities of radium were observed in the spring waters of Tuwa in Panchamahal district of Gujarat state. These determinations have led to further studies on geochemical behaviour of uranium in the surface sediments of this region. Labile uranium from the surface of the sediment particles is leached with saturated solution of ammonium carbonate. Uranium is chemically separated from the leachates by cellulose column chromatography. Unusually high activity ratios of²³⁴U/²³⁸U in the range of 2.3 to 2.77 were observed on the surface of the particles. The core of the particles exhibited a ratio of 1.00 indicating soluble²³⁴U fraction has migrated.     

Pareto optimality and a class of set covering heuristics

The set covering problem has many diverse applications to problems arising in crew scheduling, facility location and other business areas. Since the problem is known to be hard to solve optimally, a number of approximate (heuristic) approaches have been designed for it. These approaches (with one exception) divide into two main groups, greedy heuristics and dual saturation heuristics. We use the concept of a Pareto optimal dual solution to show that an arbitrary dual saturation heuristic has the same worst-case performance guarantee as the two best known heuristics of that type. Moreover, this poor performance level is always attainable by those two heuristics.     

Novel gamma-phase of titanium metal at megabar pressures

Group IV transition metals titanium, zirconium, and hafnium are expected to transform from an ambient hexagonal close packed (hcp, alpha-phase) to a body centered cubic (bcc, beta-phase) at high pressures. This transition path is usually facilitated by the occurrence of an intermediate hexagonal phase (distorted bcc, omega-phase). The existence of a bcc phase in zirconium and hafnium at high pressures has been known for the past ten years; however, its occurrence in titanium has been theoretically predicted but never observed. We report a novel unexpected transformation in titanium metal from an omega phase to an orthorhombic phase (distorted hcp, gamma-phase) at a pressure of 116+/-4 GPa.