Counting Non-Convex 5-Holes in a Planar Point Set

Let S be a set of n points in the general position, that is, no three points in S are collinear. A simple k-gon with all corners in S such that its interior avoids any point of S is called a k-hole. In this paper, we present the first algorithm that counts the number of non-convex 5-holes in S. To our best knowledge, prior to this work there was no known algorithm in the literature except a trivial brute force algorithm. Our algorithm runs in time O(T+Q), where T denotes the number of 3-holes, or empty triangles, in S and Q that denotes the number of non-convex 4-holes in S. Note that T+Q ranges from Ω(n2) to O(n3), while its expected number is Θ(n2logn) when the points in S are chosen uniformly and independently at random from a convex and bounded body in the plane.

Energy metabolism of cells in the macula flava of the newborn vocal fold from the aspect of mitochondrial microstructure

Objective Cells in the vocal fold of maculae flavae are likely to be tissue stem cells. Energy metabolism of the cells in newborn maculae flavae was investigated from the aspect of mitochondrial microstructure. Method Five normal newborn vocal folds were investigated under transmission electron microscopy. Results Mitochondria consisted of a double membrane bounded body containing matrices and a system of cristae. However, these membranes were ambiguous. In each mitochondrion, the lamellar cristae were sparse. Intercristal space was occupied by a mitochondrial matrix. Some mitochondria had fused to lipid droplets and rough endoplasmic reticulum, and both the mitochondrial outer and inner membranes had incarcerated and disappeared. Conclusion The features of the mitochondria of the cells in the newborn maculae flavae showed that their metabolic activity and oxidative phosphorylation were low. The metabolism of the cells in the newborn maculae flavae seems to be favourable to maintain the stemness and undifferentiation of the cells.

Determination of thermal diffusivity of the material by numerical-analytical model of a semi-bounded body

A mathematical description of the material thermal diffusivity aт in a semi-bounded body is proposed with a relatively simple algorithm for its numerical and analytical by solving the inverse problem of thermal conductivity. To solve the problem, it is necessary to obtain the temperature values of the unbounded plate as a result of a thermophysical experiment. A plate can be conditionally considered as a semi-bounded body as long as the Fourier number Fo ≤ Foк (Foк ≈ 0.04–0.06). It is assumed that the temperature distribution over cross-section of the heated layer of the plate R is sufficiently described by a power function whose exponent depends linearly on the Fourier number. A simple algebraic expression is obtained for calculating aт in the time interval ∆τ from the dynamics of temperature change T(Rп , τ) of a plate surface with thickness Rп heated under boundary conditions of the second kind. Temperature of the second surface of the plate T(0, τ) is used only to determine the time of the end of experiment τк. The moment of time τк, in which the temperature perturbation reaches the adiabatic surface x = 0, can be set by the condition T(Rп , τк) – T(0, τ = 0) = 0,1 K. The method of approximate calculation of dynamics of changes in depth of the heated layer R by the values of Rп , τк , and τ is proposed. Calculation of a т for the time interval ∆τ is reduced to an iterative solution of a system of three algebraic equations by matching the Fourier number, for example, using a standard Microsoft Excel procedure. Estimation of the accuracy of a т calculation was made by the test (initial) temperature field of the refractory plate with the thickness Rп = 0.05 m, calculated by the finite difference method under the initial condition T(x, τ = 0) = 300 (0 ≤ x ≤ Rп) at radiation-convective heating. The heating time was 260 s. Calculation of aт, i was performed for 10 time moments τi + 1 = τi + Δτ, τ = 26 s. Average mass temperature of the heated layer for the whole time was T = 302 K. The arithmetic-mean absolute deviation of aт(T = 302 K) from the initial value at the same temperature was 2.8 %. Application of the method will simplify the conduct and processing of experiments to determine the thermal diffusivity of materials.

“Not Our Own”

Chapter 3 begins an inquiry into the constitutive role of antiblackness for the logics of scientific taxonomical species hierarchies. The chapter identifies the agentic capaciousness of embodied somatic processes and investigates how matter’s efficacies register social inscription. The chapter also provides a reading of risk, sex, and embodiment in Octavia Butler’s “Bloodchild,” a text that affirms the continued importance of risk for establishing new modes of life and worlding, despite historical violence and embodied vulnerability. “Bloodchild” is instructive for situating the racial, gendered-sexual politics of the idea of evolutionary association, or symbiogenesis, in the historical discourses of evolutionary and cell biology as well as deposing a cross-racially hegemonic conception of the autonomous, bounded body that underwrites phantasies of possessive individualism, self-ownership, and self-determination.

ORIGINATION AND PROPAGATION OF TEMPERATURE SOLITONS WITH WAVE HEAT TRANSFER IN THE BOUNDED AREA DURING ADDITIVE TECHNOLOGICAL PROCESSES

Within this work, based on analyses of problems on wave heat transfer in bounded bodies, the theory of thermally isolated waves (solitons) is developed to investigate the heat transfer processes in the initial time vicinity and in the vicinity of the bounded body, that is the time scales are commensurate with the relaxation time (nanoseconds), and the scales of the spatial variable are measured in nanometers. A new analytical solution of the wave heat transfer based on the heat conduction equation of hyperbolic type under the action of a series of solitons was received, based on which the interaction of individual solitons with each other, absorption and reflection of the solitons from the body boundaries was analyzed. Analysis of a large number of results made clear that thermal solitons reflect not as mechanical ones, since first there is absorption of the soliton thermal energy by the heat-insulated boundary on the heat-insulated walls, and then the energy is rejected by the thermal conductivity in the opposite direction. It was found that the temperature gradient inside the soliton is negative in the forward direction and positive in the reflected direction. The results of the paper can be used in thermal interaction of high-power radiation with solid surfaces, as well as in the problems of quantum mechanics.