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Hyperdoping with gallium (Ga) has been established as a route to observe superconductivity in silicon (Si). The relatively large critical temperatures (T$_{\rm c}$) and magnetic fields (B$_{\rm c}$) make this phase attractive for cryogenic circuit applications, particularly for scalable hybrid superconductor--semiconductor platforms. However, the robustness of Si:Ga superconductivity at millikelvin temperatures is yet to be evaluated. Here, we report the presence of a reentrant resistive transition below T$_{\rm c}$ for Si:Ga whose strength strongly depends on the distribution of the Ga clusters that precipitate in the implanted Si after annealing. By monitoring the reentrant resistance over a wide parameter space of implantation energies and fluences, we determine conditions that significantly improve the coherent coupling of Ga clusters, therefore, eliminating the reentrant transition even at temperatures as low as 20~mK.

This is a translation. I have added translations for (possibly) outdated definitions in an appendix at the end. In this paper, we define distributive groups and show some properties of them. We then concern ourselves with the homogeinity of distributive groups, before showing how they can be generated from both associative and distributive groups. After that, we look at subgroups and define an index theorem for distributive groups before describing the structure of distributive groups. Finally, we present two addenda with several theorems that we proved while trying to prove that $\left|(A.p).(A.q)\right|=\left|A\right|$., Comment: 24 pages

Goal:i) Characterization of the role of the main immune reactive cell types contributing to the cellular immune response in the in-vitro DTH and ii) Validation of the in-vitro DTH under different clinical and field conditions. Methods:As positive control whole blood was incubated in the in-vitro DTH, supernatants were gathered after 12, 24 and 48h. Readout parameters of this test are cytokines in the assay's supernatant. To determine the role of T-cells, monocytes and natural killer (NK), these cell populations were depleted using magnetic beads prior to in-vitro-DTH incubation. Validation of the test has occurred under clinical (HIV-patients, ICU) and field-conditions (parabolic/space-flights, confinement). Results:T-cell depletion abandoned almost any IL-2 production and reduced IFN-gamma production irrespective of the type of antigen, whereas CD56 depleted cultures tended to lower IL-2 secretion and IFN-gamma and to parallel a IL-10-increase after viral challenge. This IL-10-increase was seen also in CD14-depleted setups. DTH read-out was significantly different under acute stress (parabolic flight) or chronic stress (ISS), respectively. Preliminary data of HIV infected patients demonstrate that this test can display the contemporary immune status during an antiviral therapy. Conclusion:The in-vitro DTH mirrors adaptive and innate immune activation and may serve as tool also for longitudinal follow up of Th1/Th2 weighed immune response under adverse life conditions on earth and in space. It is planned to implement the assay in the on the ISS (MoCISS).