Parameśvara's rule for the circumradius of a cyclic quadrilateral

The expression for the circumradius of a cyclic quadrilateral in terms of its sides, usually attributed to L'Huilier in 1782, was known in India to Parame?vara (circa 1430). The present paper contains the original Sanskrit text of the rule, its English translation, and a discussion of its derivation as given by Sankara Váriar in his Kriy$\text{a}$kramakar$\text{i}$ (16th Century) along with relevant historical remarks.     

On the preparation and the characterization of superconducting thin films of YBa2Cu3O7−x

The results of our initial efforts to deposit thin films of YBa₂Cu₃O_7−x system on sapphire substrate are described. The deposited films are shiny black in appearance and are of quite uniform chemical composition. The annealed films exhibit zero resistance superconducting transition temperatureT _c(R=0) ranging between 23 K and 30 K.     

Anomalous magnetic behavior of Ce1−xMxCo5(M=Zr,Hf) alloys

The compound CeCo₅ is ferromagnetically ordered with a Curie temperature (T_c) of 641 K and a moment (μ_Co) of 1.36μ_B per Co atom at 77 K. Replacement of Ce by Hf or Zr in CeCo₅ reduces the magnetic moment on cobalt but substantially increases the Curie temperature. For instance, in Ce_0.8Hf_0.2Co₅μ_Co=1.12μ_B at 77 K and T_c=846 K. These results indicate a much stronger d-d electron interaction in the ternary alloys than in CeCo₅. Ce in these systems behaves as if it is nearly quadrivalent.     

Managing a portfolio of long term service agreements

Long-term service agreements (LTSAs) for the maintenance of capital-intensive equipments such as gas turbines and aircraft engines are gaining wide acceptance. A typical LTSA contract spans over a period of around 10 years making a manufacturer fully responsible for maintaining the customer equipment. In this paper, we address the management of a portfolio of such contracts from the manufacturer’s perspective. The goal is to meet all the service requirements imposed by the contracts while minimizing total cost incurred. We develop a deterministic integer programming model to generate the optimal maintenance schedules that minimize the total portfolio cost. We then propose two heuristic algorithms for the problem.     

Syringic acid metabolism by some white-rot,soft-rot,and brown-rot fungi

Syringic acid metabolism by four white-rot, two soft-rot, and two brown-rot fungi has been studied. The pathways for syringic acid metabolism have been studied in detail for the white-rot fungus,Sporotrichum pulverulentum, and a reaction sequence proposed. According to identified metabolites, the following reactions occur: reduction of the carboxyl group, hydroxylation and simultaneous decarboxylation, demethylation, and methylation of thep-hydroxyl group. In the case of the two soft-rot fungi,Petriellidium boydii andPhialophora mutabilis, rapid metabolism of syringic acid was observed, and the medium was depleted of the acid within 12 h. The formation of trimethoxybenzoic acid indicates an ability within the soft-rot fungi also to methylate the p-hydroxylic group. The two brown-rot fungi,Daedalea quercina andFomes pinicola, were poor metabolizers of syringic acid. However, demethylation was observed withF. pinicola and an unidentified product appeared in the culture solution ofD. quercina.     

Eikonal model description of forward energy distribution in oxygen-induced reactions at 60 A GeV and 200 A GeV

The forward energy flow cross section is described in terms of the projectile-nucleon abrasion probability which is calculated in the impact parameter representation within the framework of the Glauber multiple scattering formalism. Realistic nuclear densities and the nucleon-nucleon inelastic cross section have been used in the calculation. The recent WA80 data are in reasonable agreement with the calculation. A simple relationship has been obtained between the abrased nucleons from the target and projectile and the zero degree energy.