Sets of constant distance from a Jordan curve

We study the $\epsilon$-level sets of the signed distance function to a planar Jordan curve $\Gamma$, and ask what properties of $\Gamma$ ensure that the $\epsilon$-level sets are Jordan curves, or uniform quasicircles, or uniform chord-arc curves for all sufficiently small $\epsilon$. Sufficient conditions are given in term of a scaled invariant parameter for measuring the local deviation of subarcs from their chords. The chordal conditions given are sharp

Doubling measures, monotonicity, and quasiconformality

We construct quasiconformal mappings in Euclidean spaces by integration of a discontinuous kernel against doubling measures with suitable decay. The differentials of mappings that arise in this way satisfy an isotropic form of the doubling condition. We prove that this isotropic doubling condition is satisfied by the distance functions of certain fractal sets. Finally, we construct an isotropic doubling measure that is not absolutely continuous with respect to the Lebesgue measure.Comment: 20 pages. Revised to address referee's comment

Non-removability of Sierpinski spaces

We prove that all Sierpi\'nski spaces in ${\mathbb{S}}^n$, $n\geq 2$, are non-removable for (quasi)conformal maps, generalizing the result of the first named author arXiv:1809.05605. More precisely, we show that for any Sierpi\'nski space $X\subset \mathbb{S}^n$ there exists a homeomorphism $f\colon \mathbb{S}^n\to \mathbb{S}^n$, conformal in $\mathbb{S}^n\setminus X$, that maps $X$ to a set of positive measure and is not globally (quasi)conformal. This is the first class of examples of non-removable sets in higher dimensions.Comment: 10 page

Production of Silicon Carbide Liquid Fertilizer by Hydrothermal Carbonization Processes from Silicon Containing Agricultural Waste Biomass

Wastes from agriculture or sewage systems have several properties, such as huge volume, high humidity, and high organic composition. According to past studies, sugarcane extract, peanut shells and rice husks have high silicon content. Chemical conversion of biomass feedstock will enhance usage and provide value to agricultural waste. In this research, we applied hydrothermal carbonization to convert silicon-rich waste biomass to produce silicon-doped liquid fertilizer. The experimental trial comprised five different treatments: the application of rice husks, peanut shells and sugarcane extract, silicon carbide fertilizer, water and soil without any additives. Concentrations used were 6% rice husk, peanut shells and sugarcane extract carbide liquid fertilizer, 30% water and 50% dried soil. The concentration effect of synthesized liquid on plant growth was compared. The statistical comparison showed that peanut shell application had a significant effect on cabbage seed germination and improved the plant's growth rate when silicon carbide content was increased. When the content of silicon carbide in the liquid fertilizer was higher than 12%, crop growth was inhibited