Embedding surfaces into S3S^3 with maximum symmetry

We restrict our discussion to the orientable category. For $g > 1$, let $OE_g$ be the maximum order of a finite group $G$ acting on the closed surface $\Sigma_g$ of genus $g$ which extends over $(S^3, \Sigma_g)$, where the maximum is taken over all possible embeddings $\Sigma_g\hookrightarrow S^3$. We will determine $OE_g$ for each $g$, indeed the action realizing $OE_g$. In particular, with 23 exceptions, $OE_g$ is $4(g+1)$ if $g\ne k^2$ or $4(\sqrt{g}+1)^2$ if $g=k^2$, and moreover $OE_g$ can be realized by unknotted embeddings for all $g$ except for $g=21$ and $481$.Comment: 42 pages, 37 figures, 6 tables of figure

Graphs in the 3--sphere with maximum symmetry

We consider the orientation-preserving actions of finite groups $G$ on pairs $(S^3, \Gamma)$, where $\Gamma$ is a connected graph of genus $g>1$, embedded in $S^3$. For each $g$ we give the maximum order $m_g$ of such $G$ acting on $(S^3, \Gamma)$ for all such $\Gamma\subset S^3$. Indeed we will classify all graphs $\Gamma\subset S^3$ which realize these $m_g$ in different levels: as abstract graphs and as spatial graphs, as well as their group actions. Such maximum orders without the condition "orientation-preserving" are also addressed.Comment: 34 pages, to appear in Discrete Comput. Geo

Bordered surfaces in the 3-sphere with maximum symmetry

We consider finite group actions on the 3-sphere which leave invariant an embedded, compact, bounded surface of algebraic genus g > 1 (orientable or non-orientable), and determine for each g the maximum order of such an action. For example, the maximal possibility 12(g-1) is obtained for the finitely many values g = 2, 3, 4, 5, 9, 11, 25, 97, 121 and 241. For each g > 1, we classify the topological types of the surfaces and their embeddings into the 3-sphere

Techno‐Economic Assessment of a Microalgae Biorefinery

A preliminary techno-economic assessment of a microalgae biorefinery plant is reported, with pulsed electric field treatment (PEF) hydrothermal liquefaction as core technology. The results indicate that standalone production of microalgae biofuel would lead to an annual loss of 2.615 M€. PEF treatment could improve this scenario by bringing the microalgae biofuel to a competitive level (0.78 € kg$^{-1}$). Assuming that microalgae biofuel would be sold at the price of crude oil (0.44 € kg$^{-1}$), the minimum price of the amino-acid based product should be 7.56 € L$^{-1}$ for positive capital returns

Embedding compact surfaces into the 3-dimensional Euclidean space with maximum symmetry

We give the maximum orders of finite group actions on Euclidean 3-space which leave invariant an embedded compact bordered surface (orientable or non-orientable), in terms of the algebraic genus of the surface. We also identify the topological types of the bordered surfaces realizing the maximum order, and find simple representative embeddings for such surfaces