Some geometry and combinatorics for the S-invariant of ternary cubics

Given a real cubic form f(x,y,z), there is a pseudo-Riemannian metric given by its Hessian matrix, defined on the open subset of R^3 where the Hessian determinant h is non-zero. We determine the full curvature tensor of this metric in terms of h and the S-invariant of f, obtaining in the process various different characterizations of S. Motivated by the case of intersection forms associated with complete intersection threefolds in the product of three projective spaces, we then study ternary cubic forms which arise as follows: we choose positive integers d1, d2, d3, set r = d1 + d2 + d3 - 3, and consider the coefficient F(x,y,z) of H1^d1 H2^d2 H3^d3 in the product (x H1 + y H2 + z H3)^3 (a_1 H1 + b_1 H2 + c_1 H3) ... (a_r H1 + b_r H2 + c_r H3), the a_j, b_j and c_j denoting non-negative real numbers; we assume also that F is non-degenerate. Previous work of the author on sectional curvatures of Kahler moduli suggests a number of combinatorial conjectures concerning the invariants of F. It is proved here for instance that the Hessian determinant, considered as a polynomial in x,y,z and the a_j, b_j, c_j, has only positive coefficients. The same property is also conjectured to hold for the S-invariant; the evidence and background to this conjecture is explained in detail in the paper.Comment: 23 pages, plain Tex, updated and shortened, final versio

Novel superconductivity: from bulk to nano systems

We begin with an introduction of superconductivity by giving a brief history of the phenomenon. The phenomenological Ginzburg–Landau theory and the microscopic theory of Bardeen, Cooper and Schrieffer are outlined. In view of recently available multi-band superconductors, relevant theories of both types are discussed. Unlike the traditional GL theory an extended GL theory is developed relevant to temperatures below the critical temperature. Superconductivity in a nanosystem is the highlight of the remaining part of the paper. Theories and experiments are discussed to give an interested reader an updated account and overview of what is new in this active area of research

Operational alternatives for LANDSAT in California

Data integration is defined and examined as the means of promoting data sharing among the various governmental and private geobased information systems in California. Elements of vertical integration considered included technical factors (such as resolution and classification) and institutional factors (such as organizational control, and legal and political barriers). Attempts are made to fit the theoretical elements of vertical integration into a meaningful structure for looking at the problem from a statewide focus. Both manual (mapped) and machine readable data systems are included. Special attention is given to LANDSAT imagery because of its strong potential for integrated use and its primary in the California Integrated Remote Sensing System program

Fast readout of a single Cooper-pair box using its quantum capacitance

We have fabricated a single Cooper-pair box (SCB) together with an on-chip lumped element resonator. By utilizing the quantum capacitance of the SCB, its state can be read out by detecting the phase of a radio-frequency (rf) signal reflected off the resonator. The resonator was optimized for fast readout. By studying quasiparticle tunneling events in the SCB, we have characterized the performance of the readout and found that we can perform a single shot parity measurement in approximately 50 ns. This is an order of magnitude faster than previously reported measurements.Comment: 7 pages, 5 figure