Well-fuctioning home composters

In recent years, the Work Efficiency Institute (TTS) has compared thermal composters, regulating materials and compost accelerators and studied user's experiences on home composting by a questionnaire. The aim has been to produce information on composting, so that home composting can be made as easy as possible

Unipotent elements forcing irreducibility in linear algebraic groups

Let $G$ be a simple algebraic group over an algebraically closed field $K$ of characteristic $p > 0$. We consider connected reductive subgroups $X$ of $G$ that contain a given distinguished unipotent element $u$ of $G$. A result of Testerman and Zalesski (Proc. Amer. Math. Soc., 2013) shows that if $u$ is a regular unipotent element, then $X$ cannot be contained in a proper parabolic subgroup of $G$. We generalize their result and show that if $u$ has order $p$, then except for two known examples which occur in the case $(G, p) = (C_2, 2)$, the subgroup $X$ cannot be contained in a proper parabolic subgroup of $G$. In the case where $u$ has order $> p$, we also present further examples arising from indecomposable tilting modules with quasi-minuscule highest weight.Comment: 33 page

Magnetic fields of cool giant and supergiant stars: models versus observations

The recent years have brought great advances in our knowledge of magnetic fields in cool giant and supergiant stars. For example, starspots have been directly imaged on the surface of an active giant star using optical interferometry, and magnetic fields have been detected in numerous slowly rotating giants and even on supergiants. Here, I review what is currently known of the magnetism in cool giant and supergiant stars, and discuss the origin of these fields and what is theoretically known about them.Comment: 7 pages, 2 figures, invited review in the conference "Stars with a stable magnetic field: from pre-main sequence to compact remnants", to be published in Contributions of the Astronomical Observatory Skalnate Ples

Invariant forms on irreducible modules of simple algebraic groups

Let $G$ be a simple linear algebraic group over an algebraically closed field $K$ of characteristic $p \geq 0$ and let $V$ be an irreducible rational $G$-module with highest weight $\lambda$. When $V$ is self-dual, a basic question to ask is whether $V$ has a non-degenerate $G$-invariant alternating bilinear form or a non-degenerate $G$-invariant quadratic form. If $p \neq 2$, the answer is well known and easily described in terms of $\lambda$. In the case where $p = 2$, we know that if $V$ is self-dual, it always has a non-degenerate $G$-invariant alternating bilinear form. However, determining when $V$ has a non-degenerate $G$-invariant quadratic form is a classical problem that still remains open. We solve the problem in the case where $G$ is of classical type and $\lambda$ is a fundamental highest weight $\omega_i$, and in the case where $G$ is of type $A_l$ and $\lambda = \omega_r + \omega_s$ for $1 \leq r < s \leq l$. We also give a solution in some specific cases when $G$ is of exceptional type. As an application of our results, we refine Seitz's $1987$ description of maximal subgroups of simple algebraic groups of classical type. One consequence of this is the following result. If $X < Y < \operatorname{SL}(V)$ are simple algebraic groups and $V \downarrow X$ is irreducible, then one of the following holds: (1) $V \downarrow Y$ is not self-dual; (2) both or neither of the modules $V \downarrow Y$ and $V \downarrow X$ have a non-degenerate invariant quadratic form; (3) $p = 2$, $X = \operatorname{SO}(V)$, and $Y = \operatorname{Sp}(V)$.Comment: 46 pages; to appear in J. Algebr

The first close-up of the "flip-flop" phenomenon in a single star

We present temperature maps of the active late-type giant FK Com which exhibit the first imagining record of the ``flip-flop'' phenomenon in a single star. The phenomenon, in which the main part of the spot activity shifts 180 degrees in longitude, discovered a decade ago in FK Com, was reported later also in a number of RS CVn binaries and a single young dwarf. With the surface images obtained right before and after the ``flip-flop'', we clearly show that the ``flip-flop'' phenomenon in FK Com is caused by changing the relative strengths of the spot groups at the two active longitudes, with no actual spot movements across the stellar surface, i.e. exactly as it happens in other active stars.Comment: 4 pages, accepted by A&A Letter