Derived categories of Burniat surfaces and exceptional collections

We construct an exceptional collection $\Upsilon$ of maximal possible length 6 on any of the Burniat surfaces with $K_X^2=6$, a 4-dimensional family of surfaces of general type with $p_g=q=0$. We also calculate the DG algebra of endomorphisms of this collection and show that the subcategory generated by this collection is the same for all Burniat surfaces. The semiorthogonal complement $\mathcal A$ of $\Upsilon$ is an "almost phantom" category: it has trivial Hochschild homology, and K_0(\mathcal A)=\bZ_2^6.Comment: 15 pages, 1 figure; further remarks expande

Deformation theory of objects in homotopy and derived categories III: abelian categories

This is the third paper in a series. In part I we developed a deformation theory of objects in homotopy and derived categories of DG categories. Here we show how this theory can be used to study deformations of objects in homotopy and derived categories of abelian categories. Then we consider examples from (noncommutative) algebraic geometry. In particular, we study noncommutative Grassmanians that are true noncommutative moduli spaces of structure sheaves of projective subspaces in projective spaces.Comment: Alexander Efimov is a new co-author of this paper. Besides some minor changes, a new part (part 3) about noncommutative Grassmanians was adde

Deformation theory of objects in homotopy and derived categories II: pro-representability of the deformation functor

This is the second paper in a series. In part I we developed deformation theory of objects in homotopy and derived categories of DG categories. Here we extend these (derived) deformation functors to an appropriate bicategory of artinian DG algebras and prove that these extended functors are pro-representable in a strong sense.Comment: Alexander Efimov is a new co-author of this paper. New material was added: A_{\infty}-structures, Maurer-Cartan theory for A_{\infty}-algebras. This allows us to strengthen our main results on the pro-representability of pseudo-functors coDEF_{-} and DEF_{-}. We also obtain an equivalence between homotopy and derived deformation functors under weaker hypothese

Дослідження процесу біосорбції іонів важких металів осадами станцій біологічного знезалізнення

 The article considers the possibility of using the sediments from stations of biological iron removal for the biosorption of heavy metal ions (IHMs) from both natural groundwaters and washing waters of enterprises with galvanic cycles. The processes of extracting Zn2+ ions (up to 50 mg/dm3), Cu2+ (up to 16 mg/dm3), Ni2+ (up to 1.3 mg/dm3), Cr6+ (up to 2.0 mg/dm3) on the bacterial structures of iron bacteria consortia and the optimal parameters of passing this process are determined (for washing waters pH=8.5–9.0). The influence of constant magnetic field with intensity of 20–60 mT, as well as the influence of different kinds of sediments from stations of biological iron removal on the efficiency of the process of removing IHM have been investigated. A significant percentage of the removal of IHM using calcined precipitate (98 % for Cu2+, 97 % for Zn2+, 85 % for Ni2+) is due to the exoeffect that occurs at a wide temperature range of 200–400 ºС. In this case, there is a smooth decrease in the mass of the sediment, indicating the combustion of the organic component and the crystallization of the amorphous phase. As a result, goethite (a-FeOOH) and lepidocrocyte (g-FeOOH) are converted into hematite (a-Fe2O3) and magnetite (g-Fe2O3), which have magnetic properties. When using as a reagent a fresh sediment, active involvement in the process of adsorption of heavy metal ions is carried out by biominerals, cells and polymer matrices of iron bacteria that have a crystalline structure and a large specific surface. At the same time, the effectiveness of removing IHMs was, respectively: for Cu2+ 93 %; for Zn2+ 92 %; for Ni2+ 70 %.The efficiency of one-, two- and three-stage water purification schemes have been investigated. It was established that using the three-stage scheme with hydromechanical mixers and water alkalinization to pH 9.0, the efficiency of IHM removal was: for Cu2+ up to 96 %; For Zn2+ up to 99 %; for Ni2+ up to 85 %. The X-ray spectral microanalysis of the sediment of the surface of the Gallioella bacterium case revealed the accumulation of IHM in the structure. The process of adsorption of IHM on the bacterial structures of consortia of iron bacteria due to their electrostatic bonding with both anionic surface of cell wall and with organic polymers isolated by cells of iron bacteria is substantiated.Установлена возможность биосорбции ионов тяжелых металлов на бактериальных структурах консорциумов железобактерий. Исследован процесс очистки воды от ионов Cr6+ (до 2,0 мг/дм3), Zn2+ (до 50 мг/дм3), Cu2+ (до 16 мг/дм3), Ni2+(до1,3 мг/дм3) на различных видах осадков станции обезжелезивания. Определена эффективность их использования при извлечении ионов тяжелых металлов из природных подземных и промывных вод гальванического производстваВстановлено можливість біосорбції іонів важких металів на бактеріальних структурах консорціумів залізобактерій. Досліджено процес очищення води від іонів Cr6+ (до 2,0 мг/дм3), Zn2+ (до 50 мг/дм3), Cu2+ (до 16 мг/дм3), Ni2+ (до 1,3 мг/дм3)на різних видах осадів станції знезалізнення. Визначена ефективність їх застосування при вилученні іонів важких металів із природних підземних та промивних вод гальванічного виробництв

Deformation theory of objects in homotopy and derived categories I: general theory

This is the first paper in a series. We develop a general deformation theory of objects in homotopy and derived categories of DG categories. Namely, for a DG module $E$ over a DG category we define four deformation functors \Def ^{\h}(E), \coDef ^{\h}(E), \Def (E), \coDef (E). The first two functors describe the deformations (and co-deformations) of $E$ in the homotopy category, and the last two - in the derived category. We study their properties and relations. These functors are defined on the category of artinian (not necessarily commutative) DG algebras.Comment: Alexander Efimov is a new co-author of this paper. Besides some minor changes, Proposition 7.1 and Theorem 8.1 were correcte

Coexistence of Intermetallic Complexions and Bulk Particles in Grain Boundaries in the ZEK100 Alloy

Magnesium-based alloys are highly sought after in the industry due to their lightweight and reliable strength. However, the hexagonal crystal structure of magnesium results in the mechanical properties’ anisotropy. This anisotropy is effectively addressed by alloying magnesium with elements like zirconium, zinc, and rare earth metals (REM). The addition of these elements promotes rapid seed formation, yielding small grains with a uniform orientation distribution, thereby reducing anisotropy. Despite these benefits, the formation of intermetallic phases (IP) containing Zn, Zr, and REM within the microstructure can be a concern. Some of these IP phases can be exceedingly hard and brittle, thus weakening the material by providing easy pathways for crack propagation along grain boundaries (GBs). This issue becomes particularly significant if intermetallic phases form continuous layers along the entire GB between two neighboring GB triple junctions, a phenomenon known as complete GB wetting. To mitigate the risks associated with complete GB wetting and prevent the weakening of the alloy’s structure, understanding the potential occurrence of a GB wetting phase transition and how to control continuous GB layers of IP phases becomes crucial. In the investigation of a commercial magnesium alloy, ZEK100, the GB wetting phase transition (i.e., between complete and partial GB wetting) was successfully studied and confirmed. Notably, complete GB wetting was observed at temperatures near the liquidus point of the alloy. However, at lower temperatures, a coexistence of a nano-scaled precipitate film and bulk particles with nonzero contact angles within the same GB was observed. This insight into the wetting transition characteristics holds potential to expand the range of applications for the present alloy in the industry. By understanding and controlling GB wetting phenomena, the alloy’s mechanical properties and structural integrity can be enhanced, paving the way for its wider utilization in various industrial applications

The influence of the shape and size of dust fractions on their distribution and accumulation in mine workings when changing the structure of air flow

The results of the analysis of statistical data on accidents at Russian mines caused by explosions in the workings space have shown that explosions of methane-dust-air mixtures at underground coal mines are the most severe accidents in terms of consequences. A detailed analysis of literature sources showed that in the total number of explosions prevails total share of hybrid mixtures, i.e. with the simultaneous participation of gas (methane) and coal dust, as well as explosions with the possible or partial involvement of coal dust. The main causes contributing to the occurrence and development of dust-air mixture explosions, including irregular monitoring of by mine engineers and technicians of the schedule of dust explosion protective measures; unreliable assessment of the dust situation, etc., are given.  The main problem in this case was the difficulty of determining the location and volume of dust deposition zones in not extinguished and difficult to access for instrumental control workings. Determination of the class-shape of coal dust particles is a necessary condition for constructing a model of the dust situation reflecting the aerosol distribution in the workings space. The morphological composition of coal mine dust fractions with dispersion less than 0.1 has been studied. Particle studies conducted using an LEICA DM 4000 optical microscope and IMAGE SCOPE M software made it possible to establish the different class-shapes of dust particles found in operating mines. It was found that the coal dust particles presented in the samples correspond to the parallelepiped shape to the greatest extent. The mathematical model based on the specialized ANSYS FLUENT complex, in which this class-form is incorporated, is used for predicting the distribution of explosive and combustible coal dust in the workings space. The use of the obtained model in production conditions will allow to determine the possible places of dust deposition and to develop measures to prevent the transition of coal dust from the aerogel state to the aerosol state and thereby prevent the formation of an explosive dust-air mixture

Overview: Recent advances in the understanding of the northern Eurasian environments and of the urban air quality in China – a Pan-Eurasian Experiment (PEEX) programme perspective

The Pan-Eurasian Experiment (PEEX) Science Plan, released in 2015, addressed a need for a holistic system understanding and outlined the most urgent research needs for the rapidly changing Arctic-boreal region. Air quality in China, together with the long-range transport of atmospheric pollutants, was also indicated as one of the most crucial topics of the research agenda. These two geographical regions, the northern Eurasian Arctic-boreal region and China, especially the megacities in China, were identified as a "PEEX region". It is also important to recognize that the PEEX geographical region is an area where science-based policy actions would have significant impacts on the global climate. This paper summarizes results obtained during the last 5 years in the northern Eurasian region, together with recent observations of the air quality in the urban environments in China, in the context of the PEEX programme. The main regions of interest are the Russian Arctic, northern Eurasian boreal forests (Siberia) and peatlands, and the megacities in China. We frame our analysis against research themes introduced in the PEEX Science Plan in 2015. We summarize recent progress towards an enhanced holistic understanding of the land-atmosphere-ocean systems feedbacks. We conclude that although the scientific knowledge in these regions has increased, the new results are in many cases insufficient, and there are still gaps in our understanding of large-scale climate-Earth surface interactions and feedbacks. This arises from limitations in research infrastructures, especially the lack of coordinated, continuous and comprehensive in situ observations of the study region as well as integrative data analyses, hindering a comprehensive system analysis. The fast-changing environment and ecosystem changes driven by climate change, socio-economic activities like the China Silk Road Initiative, and the global trends like urbanization further complicate such analyses. We recognize new topics with an increasing importance in the near future, especially "the enhancing biological sequestration capacity of greenhouse gases into forests and soils to mitigate climate change" and the "socio-economic development to tackle air quality issues".Peer reviewe