Approximation of conformal mappings using conformally equivalent triangular lattices

Consider discrete conformal maps defined on the basis of two conformally equivalent triangle meshes, that is edge lengths are related by scale factors associated to the vertices. Given a smooth conformal map $f$, we show that it can be approximated by such discrete conformal maps $f^\epsilon$. In particular, let $T$ be an infinite regular triangulation of the plane with congruent triangles and only acute angles (i.e.\ $<\pi/2$). We scale this tiling by $\epsilon>0$ and approximate a compact subset of the domain of $f$ with a portion of it. For $\epsilon$ small enough we prove that there exists a conformally equivalent triangle mesh whose scale factors are given by $\log|f'|$ on the boundary. Furthermore we show that the corresponding discrete conformal maps $f^\epsilon$ converge to $f$ uniformly in $C^1$ with error of order $\epsilon$.Comment: 14 pages, 3 figures; v2 typos corrected, revised introduction, some proofs extende

Constructing solutions to the Bj\"orling problem for isothermic surfaces by structure preserving discretization

In this article, we study an analog of the Bj\"orling problem for isothermic surfaces (that are more general than minimal surfaces): given a real analytic curve $\gamma$ in ${\mathbb R}^3$, and two analytic non-vanishing orthogonal vector fields $v$ and $w$ along $\gamma$, find an isothermic surface that is tangent to $\gamma$ and that has $v$ and $w$ as principal directions of curvature. We prove that solutions to that problem can be obtained by constructing a family of discrete isothermic surfaces (in the sense of Bobenko and Pinkall) from data that is sampled along $\gamma$, and passing to the limit of vanishing mesh size. The proof relies on a rephrasing of the Gauss-Codazzi-system as analytic Cauchy problem and an in-depth-analysis of its discretization which is induced from the geometry of discrete isothermic surfaces. The discrete-to-continuous limit is carried out for the Christoffel and the Darboux transformations as well.Comment: 29 pages, some figure

Carbon stock in topsoil, standing floor litter and above ground biomass in Tectona grandis plantation 10-years after establishment in Ile-Ife, Southwestern Nigeria

This paper provides information on carbon stock at the habitat level in the above ground biomass (ABG), standing floor litter and soils in a 10 year-old Tectona grandis plantation following restoration of a degraded secondary forest at Obafemi Awolowo University, Ile-Ife Nigeria. Four sample plots 25 m x 25 m, two in Tectona grandis plantation and two in a nearby degraded secondary forest were studied. Soil samples were randomly collected at 0-20 cm and bulk density determined. Standing floor litter was randomly collected at five points every three months for one year, sorted into different litter components. Soil and standing floor litters carbon concentration and C stock were determined. Above ground biomass (ABG) and carbon stock were significantly (p=0.003 and p=0.0001) higher in the plantation, the order is ABG &gt; soil &gt; standing floor leaf litter &gt; standing floor wood litter. Soil C stock varies from 10.47 t ha-1 in the plantation to 10.58 t ha-1 C in the forest. Above ground biomass, standing leaf and wood litter were estimated as 18.26-5.81, 0.49-0.36, 0.06-0.08 t ha-1 C, respectively (plantation to secondary forest). Reforestation after 10 years has increased C stocks by 45% in ABG in the plantations.Keywords: Carbon stock, degraded forest, plantation, reforestation, standing litter

Efficiency optimization in a correlation ratchet with asymmetric unbiased fluctuations

The efficiency of a Brownian particle moving in periodic potential in the presence of asymmetric unbiased fluctuations is investigated. We found that there is a regime where the efficiency can be a peaked function of temperature, which proves that thermal fluctuations facilitate the efficiency of energy transformation, contradicting the earlier findings (H. kamegawa et al. Phys. Rev. Lett. 80 (1998) 5251). It is also found that the mutual interplay between asymmetry of fluctuation and asymmetry of the potential may induce optimized efficiency at finite temperature. The ratchet is not most efficiency when it gives maximum current.Comment: 10 pages, 7 figure

Minsky machines and algorithmic problems

This is a survey of using Minsky machines to study algorithmic problems in semigroups, groups and other algebraic systems.Comment: 19 page

Quantum anti-Zeno effect without rotating wave approximation

In this paper, we systematically study the spontaneous decay phenomenon of a two-level system under the influences of both its environment and continuous measurements. In order to clarify some well-established conclusions about the quantum Zeno effect (QZE) and the quantum anti-Zeno effect (QAZE), we do not use the rotating wave approximation (RWA) in obtaining an effective Hamiltonian. We examine various spectral distributions by making use of our present approach in comparison with other approaches. It is found that with respect to a bare excited state even without the RWA, the QAZE can still happen for some cases, e.g., the interacting spectra of hydrogen. But for a physical excited state, which is a renormalized dressed state of the atomic state, the QAZE disappears and only the QZE remains. These discoveries inevitably show a transition from the QZE to the QAZE as the measurement interval changes.Comment: 14 pages, 8 figure

Congenital ranula

The authors describe a case of congenital ranula diagnosed by a routine prenatal ultrasonography at 21 weeks of gestation. The fetal kariotype was normal. Follow-up ultrasound scans revealed no changes in the size or the position of the cyst. Fetal growth was normal as was the amniotic fluid volume. Surgical treatment was performed 3 days after a normal vaginal delivery, with excellent results