Mathematical simulation of the influence of surface roughness and mass loss on thermal protection

A mathematical model of the thermochemical destruction of carbon fiber-reinforced plastic in the presence of surface roughness and composite ablation is refined based on known theoretical results. It is shown that mass loss through rough surface ambiguously influences the intensity of heat exchange processes in thermal protective material. Results of numerical calculations are compared with known data

Poisson trace orders

The two main approaches to the study of irreducible representations of orders (via traces and Poisson orders) have so far been applied in a completely independent fashion. We define and study a natural compatibility relation between the two approaches leading to the notion of Poisson trace orders. It is proved that all regular and reduced traces are always compatible with any Poisson order structure. The modified discriminant ideals of all Poisson trace orders are proved to be Poisson ideals and the zero loci of discriminant ideals are shown to be unions of symplectic cores, under natural assumptions (maximal orders and Cayley--Hamilton algebras). A base change theorem for Poisson trace orders is proved. A broad range of Poisson trace orders are constructed based on the proved theorems: quantized universal enveloping algebras, quantum Schubert cell algebras and quantum function algebras at roots of unity, symplectic reflection algebras, 3 and 4-dimensional Sklyanin algebras, Drinfeld doubles of pre-Nichols algebras of diagonal type, and root of unity quantum cluster algebras.Comment: 24 page

Mathematical modeling of heat and mass transfer in a thermal protection coating with gas flow fluctuations

The thermochemical destruction of a carbon fiber-reinforced polymer when affected by a high enthalpy fluctuating gas flow is simulated numerically. The possibility of controlling the heat transfer process in the composite material is studied

Weak splittings of quotients of Drinfeld and Heisenberg doubles

We investigate the fine structure of the simplectic foliations of Poisson homogeneous spaces. Two general results are proved for weak splittings of surjective Poisson submersions from Heisenberg and Drinfeld doubles. The implications of these results are that the torus orbits of symplectic leaves of the quotients can be explicitly realized as Poisson-Dirac submanifolds of the torus orbits of the doubles. The results have a wide range of applications to many families of real and complex Poisson structures on flag varieties. Their torus orbits of leaves recover important families of varieties such as the open Richardson varieties.Comment: 20 pages, AMS Late

AC Conductance in Dense Array of the Ge0.7_{0.7}Si0.3_{0.3} Quantum Dots in Si

Complex AC-conductance, $\sigma^{AC}$, in the systems with dense Ge$_{0.7}$Si$_{0.3}$ quantum dot (QD) arrays in Si has been determined from simultaneous measurements of attenuation, $\Delta\Gamma=\Gamma(H)-\Gamma(0)$, and velocity, $\Delta V /V=(V(H)-V(0)) / V(0)$, of surface acoustic waves (SAW) with frequencies $f$ = 30-300 MHz as functions of transverse magnetic field $H \leq$ 18 T in the temperature range $T$ = 1-20 K. It has been shown that in the sample with dopant (B) concentration 8.2$\times 10^{11}$ cm$^{-2}$ at temperatures $T \leq$4 K the AC conductivity is dominated by hopping between states localized in different QDs. The observed power-law temperature dependence, $\sigma_1(H=0)\propto T^{2.4}$, and weak frequency dependence, $\sigma_1(H=0)\propto \omega^0$, of the AC conductivity are consistent with predictions of the two-site model for AC hopping conductivity for the case of $\omega \tau_0 \gg$1, where $\omega=2\pi f$ is the SAW angular frequency and $\tau_0$ is the typical population relaxation time. At $T >$ 7 K the AC conductivity is due to thermal activation of the carriers (holes) to the mobility edge. In intermediate temperature region 4$< T<$ 7 K, where AC conductivity is due to a combination of hops between QDs and diffusion on the mobility edge, one succeeded to separate both contributions. Temperature dependence of hopping contribution to the conductivity above $T^*\sim$ 4.5 K saturates, evidencing crossover to the regime where $\omega \tau_0 <$1. From crossover condition, $\omega \tau_0(T^*)$ = 1, the typical value, $\tau_0$, of the relaxation time has been determined.Comment: revtex, 3 pages, 6 figure

Agricultural technology of growing deciduous seedlings for reforestation purposes

A large variety of soil conditions in the forest fundof the Republic of Belarus requires reforestation by various tree species, of which a significant roleis played by deciduous species. Growing seedlings of deciduous species requires strict observance of all agricultural activities (preparation of soil, eradication of weeds, pests control, crown care, application of mineral and organic fertilizers, etc.). The paper dwells upon the study of technology and the growth of deciduous seedlings grown in close-planting forest nurseries of forest enterprises of the Republic of Belarus

Anatomical investigation of the papillary muscles of the septomarginal trabecula in fetal ontogenesis

The aim was to study papillary muscles of the right ventricular septomarginal trabecula. Materials and methods: 98 formalinfixed normal hearts from human fetuses aged 17 to 28 weeks were studied by means stereomicroscope. Results. Muscles in such position were found to be in 55.1%. The free-standing papillary muscles predominated over the muscles of fixe type. The muscles had monolithic base, one belly and mostly one apex. Tendinous chords of these muscles entered only the septal cusp of the right atrioventricular valve. A potential clinical importance of the papillary muscles was mentioned. Conclusion. The papillary muscles situated at the septomarginal trabecula are proposed to regard as particular subgroup of septal papillary muscles

The content of nutrients and the acidity of the substrate for growing containerized seedlings of pine and spruce

The results of studies of the content of mobile forms of phosphorus and potassium, ammonia nitro-gen, mobile iron compounds and the sum of exchangeable bases of calcium and magnesium in the sub-strate at the beginning and end of the growing season when seedlings of Scots pine and Norway spruce in containers. The content of nutrients in the substr ate to the end of the growing season has decreased significantly. The number of mobile forms of phosphorus has decreased in 2.3 times, potassium 2 times, ammonia nitrogen up to 19 times exchangeable bases of calcium and magnesium in 1.5 times. This is due to the consumption of the seedlings of nutrients, as well as their leaching from the substrate during irrigation. Therefore, to maintain the necessary balance of nutrients in the substrate during the vegetation period it is necessary to observe a scien tific system of fertilization.The acidity of the sub-strate also decreased from 5.2 to 6.3 pH. Water for irrigation has the acidity close to neutral (pH = 7.1). To maintain the optimum acidity of the substrate, the pH of irrigation water should be in the range of not higher than 5.5 to 6.0. Therefore, when using irrigation water with neutral acidity is necessary to carry out activities according to its acidification