Motion of a symmetric rigid body under the action of a body-fixed force

Approximative method for predicting motion of symmetric rigid body subjected to body-fixed forc

Differential Entropy on Statistical Spaces

We show that the previously introduced concept of distance on statistical spaces leads to a straightforward definition of differential entropy on these statistical spaces. These spaces are characterized by the fact that their points can only be localized within a certain volume and exhibit thus a feature of fuzziness. This implies that Riemann integrability of relevant integrals is no longer secured. Some discussion on the specialization of this formalism to quantum states concludes the paper.Comment: 4 pages, to appear in the proceedings of the joint meeting of the 2nd International Conference on Cybernetics and Information Technologies, Systems and Applications (CITSA 2005) and the 11th International Conference on Information Systems Analysis and Synthesis (ISAS 2005), to be held in Orlando, USA, on July 14-17, 200

Monitoring Costs and the Mode of International Investment

contract, vertical integration, opportunism, international investment, China

Effect of unitary impurities in non-STM-types of tunneling in high-T_c superconductors

Based on an extended Hubbard model, we present calculations of both the local (i.e., single-site) and spatially-averaged differential tunneling conductance in d-wave superconductors containing nonmagnetic impurities in the unitary limit. Our results show that a random distribution of unitary impurities of any concentration can at most give rise to a finite zero-bias conductance (with no peak there) in spatially-averaged non-STM type of tunneling, in spite of the fact that local tunneling in the immediate vicinity of an isolated impurity does show a conductance peak at zero bias, whereas to give rise to even a small zero-bias conductance peak in the former type of tunneling the impurities must form dimers, trimers, etc. along the [110] directions. In addition, we find that the most-recently-observed novel pattern of the tunneling conductance around a single impurity by Pan et al. [Nature (London) 403,746 (2000)] can be explained in terms of a realistic model of the tunneling configuration which gives rise to the experimental results reported there. The key feature in this model is the blocking effect of the BiO and SrO layers which exist between the tunneling tip and the CuO_2 layer being probed.Comment: 9 pages, 7 ps-figures, to appear in Phys. Rev. B (Sep. 1, 2000); typos corrected, references added, figure 6 changed to expand the explanation on recent experimental measurements by S.H. Pan et al. [Nature (London) 403, 746 (2000)

Monitoring Costs and the Mode of International Investment

Our central proposition is that monitoring costs increase with physical distance, and hence, direct investments located further from the foreign investor’s home base should be more likely formed as joint ventures. Tests on a data set of Taiwanese direct investments in Mainland China provide robust support to the hypothesis. A project that was located 1000 kilometers further away was 13-17% more likely to be formed as a joint venture.contract, vertical integration, opportunism, international investment, China

Thermal and nonthermal dust sputtering in hydrodynamical simulations of the multiphase interstellar medium

We study the destruction of interstellar dust via sputtering in supernova (SN) shocks using three-dimensional hydrodynamical simulations. With a novel numerical framework, we follow both sputtering and dust dynamics governed by direct collisions, plasma drag and betatron acceleration. Grain-grain collisions are not included and the grain-size distribution is assumed to be fixed. The amount of dust destroyed per SN is quantified for a broad range of ambient densities and fitting formulae are provided. Integrated over the grain-size distribution, nonthermal (inertial) sputtering dominates over thermal sputtering for typical ambient densities. We present the first simulations that explicitly follow dust sputtering within a turbulent multiphase interstellar medium. We find that the dust destruction timescales $\tau$ are 0.35 Gyr for silicate dust and 0.44 Gyr for carbon dust in solar neighborhood conditions. The SN environment has an important impact on $\tau$. SNe that occur in preexisting bubbles destroy less dust as the destruction is limited by the amount of dust in the shocked gas. This makes $\tau$ about 2.5 times longer than the estimate based on results from a single SN explosion. We investigate the evolution of the dust-to-gas mass ratio (DGR), and find that a spatial inhomogeneity of $\sim$ 14\% develops for scales below 10 pc. It locally correlates positively with gas density but negatively with gas temperature even in the exterior of the bubbles due to incomplete gas mixing. This leads to a $\sim$ 30\% lower DGR in the volume filling warm gas compared to that in the dense clouds.Comment: 20 pages, 16 figures, accepted versio

Quantum annealing for systems of polynomial equations

Numerous scientific and engineering applications require numerically solving systems of equations. Classically solving a general set of polynomial equations requires iterative solvers, while linear equations may be solved either by direct matrix inversion or iteratively with judicious preconditioning. However, the convergence of iterative algorithms is highly variable and depends, in part, on the condition number. We present a direct method for solving general systems of polynomial equations based on quantum annealing, and we validate this method using a system of second-order polynomial equations solved on a commercially available quantum annealer. We then demonstrate applications for linear regression, and discuss in more detail the scaling behavior for general systems of linear equations with respect to problem size, condition number, and search precision. Finally, we define an iterative annealing process and demonstrate its efficacy in solving a linear system to a tolerance of $10^{-8}$.Comment: 11 pages, 4 figures. Added example for a system of quadratic equations. Supporting code is available at https://github.com/cchang5/quantum_poly_solver . This is a post-peer-review, pre-copyedit version of an article published in Scientific Reports. The final authenticated version is available online at: https://www.nature.com/articles/s41598-019-46729-