Isotopic Equivalence from Bezier Curve Subdivision

We prove that the control polygon of a Bezier curve B becomes homeomorphic and ambient isotopic to B via subdivision, and we provide closed-form formulas to compute the number of iterations to ensure these topological characteristics. We first show that the exterior angles of control polygons converge exponentially to zero under subdivision.Comment: arXiv admin note: substantial text overlap with arXiv:1211.035

Harper operators, Fermi curves, and Picard-Fuchs equations

This paper is a continuation of the work on the spectral problem of Harper operator using algebraic geometry. We continue to discuss the local monodromy of algebraic Fermi curves based on Picard-Lefschetz formula. The density of states over approximating components of Fermi curves satisfies a Picard-Fuchs equation. By the property of Landen transformation, the density of states has a Lambert series as the quarter period. A $q$-expansion of the energy level can be derived from a mirror map as in the B-model.Comment: v2, 13 pages, minor changes have been mad

What QCD sum rules tell about the rho meson

Using a simple parametrization of Breit-Wigner type for the hadronic side of the QCD sum rule for $\rho$ mesons in vacuum as well as in a nuclear medium we explore the range of values for the mass and the width of the $\rho$ meson which are compatible with the operator product expansion.Comment: 15 pages, Revtex, 2 figures include

The drivers of Chinese CO2 emissions from 1980 to 2030

China's energy consumption doubled within the first 25 years of economic reforms initiated at the end of the 1970s, and doubled again in the past 5 years. It has resulted of a threefold CO2 emissions increase since early of 1980s. China's heavy reliance on coal will make it the largest emitter of CO2 in the world. By combining structural decomposition and input–output analysis we seek to assess the driving forces of China's CO2 emissions from 1980 to 2030. In our reference scenario, production-related CO2 emissions will increase another three times by 2030. Household consumption, capital investment and growth in exports will largely drive the increase in CO2 emissions. Efficiency gains will be partially offset the projected increases in consumption, but our scenarios show that this will not be sufficient if China's consumption patterns converge to current US levels. Relying on efficiency improvements alone will not stabilize China's future emissions. Our scenarios show that even extremely optimistic assumptions of widespread installation of carbon dioxide capture and storage will only slow the increase in CO2 emissions

Analysis of Kaon Production at SIS Energies

We analyse the production and propagation of pions and kaons in heavy-ion reactions from 0.8 -- 1.8~A$\cdot$GeV within a coupled channel transport approach including the kaon production channels $BB \to K^+YN, \pi B\to K^+Y, BB \to NN K \bar{K}, \pi B\to N K\bar{K}, K^+B\to K^+B$ and $\pi \pi\to K \bar{K}$. Assuming the hyperon selfenergy to be 2/3 of the nucleon selfenergy we find that all inclusive experimental $K^+$ spectra at SIS energies can be reproduced reasonably well without any selfenergies for the kaons although a slightly repulsive kaon potential cannot be excluded by the present data on kaon spectra and flow.Comment: 19 pages, LaTeX, including 8 postscript figures, to appear in Nucl. Phys.