The indefinite metric of R. Mrugala and the geometry of the thermodynamical phase space

We study the indefinite metric $G$ in the contact phase space $(P,\theta)$ of a homogeneous thermodynamical system introduced by R. Mrugala. We calculate the curvature tensor, Killing vector fields, second fundamental form of Legendre submanifolds of $P$ - constitutive surfaces of different homogeneous thermodynamical systems. We established an isomorphism of the space $(P,\theta ,G)$ with the Heisenberg Lie group $H_{n}$ endowed with the right invariant contact structure and the right invariant indefinite metric. The lift \tG of the metric $G$ to the symplectization \tP of contact space $(P,\theta)$, its curvature properties, and its Killing vector fields are studied. Finally we introduce the "hyperbolic projectivization" of the space (\tP,{\tilde \theta}, \tG) that can be considered as the natural {\bf compactification} of the thermodynamical phase space $(P,\theta, G).

Wire winding increases lifetime of oxide coated cathodes

Refractory-metal heater base wound with a thin refractory metal wire increases the longevity of oxide-coated cathodes. The wire-wound unit is impregnated with the required thickness of metal oxide. This cathode is useful in magnetohydrodynamic systems and in electron tubes

Operation of a forced circulation, croloy 9 m, mercury loop to study corrosion product separation techniques

Forced circulation, Croloy 9M mercury loop designed to investigate corrosion product separation technique

Ophthalmic method and apparatus

A method and apparatus for removing material and components such as the lens from an eye is described. High speed rotary cutting members at one end of a rod macerate the lens while an annular tubing disposed around the cutting members vibrates ultrasonically to coact with the cutting members in macerating the lens. At the same time, a liquid is supplied to the chamber behind the cornea of the eye. Spiral grooves extending along the rotating rod from the cutting members evacuate the liquid and the macerated material from the eye. An alternate embodiment of the apparatus includes a tube through which liquid is supplied to the operative site of the ultrasonically vibrating tube and the cutting members in the area of the lens

Approximation of real error channels by Clifford channels and Pauli measurements

The Gottesman-Knill theorem allows for the efficient simulation of stabilizer-based quantum error-correction circuits. Errors in these circuits are commonly modeled as depolarizing channels by using Monte Carlo methods to insert Pauli gates randomly throughout the circuit. Although convenient, these channels are poor approximations of common, realistic channels like amplitude damping. Here we analyze a larger set of efficiently simulable error channels by allowing the random insertion of any one-qubit gate or measurement that can be efficiently simulated within the stabilizer formalism. Our new error channels are shown to be a viable method for accurately approximating real error channels.Comment: 6 pages, 4 figure