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We determine the complete degeneration picture inside the variety of nilpotent associative algebras of dimension 3 over an algebraically closed field of characteristic not equal to 2. Comparing with the discussion in [Ivanova N.M. and Pallikaros C.A., Degenerations of complex associative algebras of dimension three via Lie and Jordan algebras, {\it Advances in Group Theory and Applications}, 18 (2024), 41-79], for some of the arguments in the present article we needed to develop alternative techniques which are now valid over an arbitrary algebraically closed field. There is a dichotomy of cases concerning the results obtained, corresponding to whether the characteristic of the field is 2 or not., Comment: In this new version the case where the field has characteristic equal to two is also discussed

Let $\boldsymbol\Lambda_3(\mathbb C)\,(=\mathbb C^{27})$ be the space of structure vectors of $3$-dimensional algebras over $\mathbb C$ considered as a $G$-module via the action of $G={\rm GL}(3,\mathbb C)$ on $\boldsymbol\Lambda_3(\mathbb C)$ `by change of basis'. We determine the complete degeneration picture inside the algebraic subset $\mathcal A^s_3$ of $\boldsymbol\Lambda_3(\mathbb C)$ consisting of associative algebra structures via the corresponding information on the algebraic subsets $\mathcal L_3$ and $\mathcal J_3$ of $\boldsymbol\Lambda_3(\mathbb C)$ of Lie and Jordan algebra structures respectively. This is achieved with the help of certain $G$-module endomorphisms $\phi_1$, $\phi_2$ of $\boldsymbol\Lambda_3(\mathbb C)$ which map $\mathcal A^s_3$ onto algebraic subsets of $\mathcal L_3$ and $\mathcal J_3$ respectively.

This work is devoted to a method to generate particle cluster assemblies, and connected to evaporative lithography. Experiments are carried out using nonuniform evaporation of an isopropanol film containing polystyrene microspheres in a cylindrical cell. The local inhomogeneity of the vapor flux density is achieved by exploiting the temperature gradient. A copper rod is mounted in the central part of the bottom of the cell for further heating. The thermocapillary flow resulting from the surface tension gradient, due in turn to the temperature drop, transfers the particles that were originally at rest at the bottom of the cell. The effect of the initial thickness of the liquid layer on the height and base area of the cluster formed in the central region of the cell is studied. The velocity is measured using particle image velocimetry. A model describing the initial stage of the process is developed. The equations of heat transfer and thermal conductivity are used to define the temperature distribution in the liquid and in the cell. The fluid flow is simulated using the lubrication approximation. The particle distribution is modeled using the convection-diffusion equation. The evaporation flux density is calculated using the Hertz-Knudsen equation. The dependence of the liquid viscosity on the particle concentration is described by Mooney's formula. Numerical results show that the liquid film gradually becomes thinner in the central region, as the surface tension decreases with the increasing temperature. The liquid flow is directed to the heater near the substrate, and it transfers the particles to the center of the cell. The volume fraction of the particles increases over time in this region. The heat flow from the heater affects the geometry of the cluster for two reasons: first, the Marangoni flow velocity depends on the temperature gradient, and second, the decrease ...

The dynamical production of low-mass X-ray binaries and brighter cataclysmic variables (CVs) in dense globular clusters is well-established. We investigate how the X-ray emissivity of fainter X-ray binaries (principally CVs and coronally active binaries) varies between different environments. We compile calculations (largely from the literature) of the X-ray emissivity of old stellar populations, including open and globular clusters and several galaxies. We investigate three literature claims of unusual X-ray sources in low-density stellar populations. We show that a suggested quiescent neutron star in the open cluster NGC 6819 is a foreground M dwarf. We show that the suggested diffuse X-ray emission from an old nova shell in the globular cluster NGC 6366 is actually a background galaxy cluster. And we show that a suggested population of quiescent X-ray binaries in the Sculptor Dwarf Galaxy is mostly (perhaps entirely) background galaxies. We find that above densities of $10^4$ M$_{\odot}$/pc$^3$, the X-ray emissivity of globular clusters increases, due to dynamical production of X-ray emitting systems. Below this density, globular clusters have lower X-ray emissivity than the other populations, and we do not see a strong dependence of X-ray emissivity due to density effects. We find significant correlations between X-ray emissivity and binary fraction, metallicity, and density. Sampling these fits via bootstrap techniques gives less significant correlations, but confirms the effect of metallicity on low-density populations, and that of density on the full globular cluster sample., Comment: 28 pages, 23 figures. MNRAS, in press

The formation of low-mass X-ray binaries (LMXBs) is an ongoing challenge in stellar evolution. The important subset of LMXBs are the binary systems with a neutron star (NS) accretor. In NS LMXBs with non-degenerate donors, the mass transfer is mainly driven by magnetic braking. The discrepancies between the observed mass transfer (MT) rates and the theoretical models were known for a while. Theory predictions of the MT rates are too weak and differ by an order of magnitude or more. Recently, we showed that with the standard magnetic braking, it is not possible to find progenitor binary systems such that they could reproduce -- at any time of their evolution -- most of the observed persistent NS LMXBs. In this ${\it Letter}$ we present a modified magnetic braking prescription, CARB (Convection And Rotation Boosted). CARB magnetic braking combines two recent improvements in understanding stellar magnetic fields and magnetized winds -- the dependence of the magnetic field strength on the outer convective zone and the dependence of the Alfv\`en radius on the donor's rotation. Using this new magnetic braking prescription, we can reproduce the observed mass transfer rates at the detected mass ratio and orbital period for all well-observed to-the-date Galactic persistent NS LMXBs. For the systems where the effective temperature of the donor stars is known, theory agrees with observations as well., Comment: 7 pages, 3 figures, 1 table. Published in Astrophysical Journal Letters, Volume 886, Issue 2, article id. L31, 5 pp. (2019). The typo in the equation 5 is fixed in this version. No results presented here are affected. All follow-up papers used the correct version of the equation (without the typo)