We study model theory of actions of finite groups on substructures of a stable structure. We give an abstract description of existentially closed actions as above in terms of invariants and PAC structures. We show that if the corresponding PAC property is first order, then the theory of such actions has a model companion. Then, we analyze some particular theories of interest (mostly various theories of fields of positive characteristic) and show that in all the cases considered the PAC property is first order.

We show that the theory of Galois actions of a torsion Abelian group A is companionable if and only if, for each prime p, the p-primary part of A is either finite or it coincides with the Prüfer p-group. We also provide a model-theoretic description of the model companions we obtain.

We study model theory of fields with actions of a fixed finite group scheme. We prove the existence and simplicity of a model companion of the theory of such actions, which generalizes our previous results about truncated iterative Hasse–Schmidt derivations [13] and about Galois actions [14]. As an application of our methods, we obtain a new model complete theory of actions of a finite group on fields of finite imperfection degree.

Computational modeling is an important aspect of the research on nuclear waste materials. In particular, atomistic simulations, when used complementary to experimental efforts, contribute to the scientific basis of safety case for nuclear waste repositories. Here we discuss the state-of-the-art and perspectives of atomistic modeling for nuclear waste management on a few cases of successful synergy of atomistic simulations and experiments. In particular, we discuss here: (1) the potential of atomistic simulations to investigate the uranium oxidation state in mixed-valence uranium oxides and (2) the ability of cementitious barrier materials to retain radionuclides such as 226Ra and 90Sr, and of studtite/metastudtite secondary peroxide phases to incorporate actinides such as Np and Am. The new contribution we make here is the computation of the incorporation of Sr by C-S-H (calcium silicate hydrate) phases.

This research paper addresses the hypothesis that calcium salts combined with whole linseed and heat-treated rapeseed cake in one feed additive may efficiently stimulate the productivity of dairy cows and have a positive effect on the functional (health-promoting) properties of milk fat. The article proposes the composition of such an additive (EFA) and evaluates its nutritional effect in the diet of mid-lactation dairy cows. Forty multiparous Polish Holstein-Friesian (PHF) dairy cows were allocated to one of four treatments (10 cows/treatment) and fed a TMR diet without EFA or with EFA in the amount of 1, 2 or 3 kg/d per head for a 63-d-period. Individual intake of dry matter (DMI) and nutrients was determined, as was milk yield and composition, including fatty acid profile, fat soluble vitamins, cholesterol and phospholipids (PLs). Irrespective of the treatment group, cows fed diets with EFA had higher (P < 0.05) DMI, milk yield and milk vitamin D3 and K2 concentration but lower (P < 0.01) milk protein, fat and cholesterol contents. The additive did not affect the milk concentrations of β-carotene or vitamin A or E. The PLs content was correlated with fat concentration in the milk and decreased as the level of EFA in the diet increased. An increase in phosphatidylcholine in total PLs was accompanied by a reduction in the proportion of sphingomyelin (P < 0.05). The use of EFA increased the proportion of polyunsaturated fatty acids (PUFA) in the total fatty acids in the milk. The addition of EFA in the amount of 3 kg increased the proportion of PUFA by 77% (P < 0.05). In conclusion, the use of an energy-protein feed additive (EFA) increases feed intake and milk yield in cows and alters milk fat composition, improving its functional properties. Higher milk production compensates for the decrease in solids concentration in the milk, which has no effect on their daily yield.

We prove a positive characteristic version of Ax’s theorem on the intersection of an algebraic subvariety and an analytic subgroup of an algebraic group [Ax, Some topics in differential algebraic geometry. I. Analytic subgroups of algebraic groups, Amer. J. Math.94 (1972), 1195–1204]. Our result is stated in a more general context of a formal map between an algebraic variety and an algebraic group. We derive transcendence results of Ax–Schanuel type.

Because of steady increase in the availability of computing power, ab initio methods of computational materials science become everyday investigation tools in various research fields. This popularity of the first-principle-based atomistic modeling is in large part due to the performance of density functional theory (DFT), which could be used for simulations of chemically and structurally complex materials, including minerals, fluids and melts. However, because of intrinsic approximations, DFT is not always able to deliver reliable predictions. This is especially pronounced for f-elements bearing materials such as nuclear materials considered in nuclear waste management. Properties such as reaction enthalpies or electronic state are often badly predicted. In this contribution we discuss our experience with different computational methods, including the parameter free DFT+U method, in which the Hubbard U parameter is derived ab initio, for prediction of various properties of f electrons bearing materials. We show significant improvement obtained for structural and thermochemical parameters of various lanthanide-bearing ceramic materials and actinide-bearing molecular and solid compounds when the f electrons correlations are explicitly accounted for. Last, but not least, we demonstrate that complementary experimental and atomistic modeling studies result in superior and more complete characterization of challenging materials considered in nuclear waste management.

We prove that if a strongly minimal nonlocally modular reduct of an algebraically closed valued field of characteristic 0 contains +, then this reduct is bi-interpretable with the underlying field.

There are several ways planets can survive the giant phase of the host star, hence one can consider the case of Earth-like planets orbiting white dwarfs. As a white dwarf cools from 6000 K to 4000 K, a planet orbiting at 0.01 AU from the star would remain in the continuous habitable zone (CHZ) for about 8 Gyr. Polarisation due to a terrestrial planet in the CHZ of a cool white dwarf (CWD) is 102 (104) times larger than it would be in the habitable zone of a typical M-dwarf (Sun-like star). Polarimetry is thus a powerful tool to detect close-in planets around white dwarfs. Multi-band polarimetry would also allow one to reveal the presence of a planet atmosphere, even providing a first characterisation. With current facilities a super-Earth-sized atmosphereless planet is detectable with polarimetry around the brightest known CWD. Planned future facilities render smaller planets detectable, in particular by increasing the instrumental sensitivity in the blue. Preliminary habitability study show also that photosynthetic processes can be sustained on Earth-like planets orbiting CWDs and that the DNA-weighted UV radiation dose for an Earth-like planet in the CHZ is less than the maxima encountered on Earth, hence white dwarfs are compatible with the persistence of complex life from the perspective of UV irradiation.

We discuss main degradation mechanisms present in nitride based laser diodes operating in 400-440 nm spectral range. We can clearly divide the aging processes into these occurring on the exposed facets of the device and into the bulk phenomena. Surface processes are predominantly connected with photochemical reactions on the laser mirrors and manifest by the formation of the carbon deposits. The nature of these photochemical reactions resembles very closely the mechanism known as Package Induced Failure observed previously in case of 980 nm laser diodes. Degradation involving bulk like effects is much less understood. The experimental results by other group are not sufficient for proposing an unambiguous model of the physical effects involved. In particular, it consists in observation related to dopants diffusion and recombination mechanisms. Magnesium diffusion from the p-type layers into the active layer was proposed as a possible degradation path. However, our study of SIMS profiles in the device subjected to over 8 000 h of electrical stress reveals no visible modification in the Mg profile. The same holds for the hydrogen spatial distribution thus substantially limiting candidates for the diffusion processes. Nevertheless, it seems that the diffusion mechanism is involved in bulk degradation. The claim is supported by two facts: well confirmed stability of the extended defects network in nitride emitters and characteristic square-root time-dependence of the degradation rate.

We prove that the theory of fields with a derivation of Frobenius has the model companion which is stable and admits elimination of quantifiers up to the level of the λ-functions. Along the way, we give new geometric axioms of DCFp.

A certain property of some type-definable subgroups of superstable groups with finite U-rank is closely related to the Mordell–Lang conjecture. This property is discussed in the context of algebraic groups.