卷 11, 编号 3 (2017)

We introduce a model of volumetric growth of biological materials which is based on the theory of finite elastic deformations. Surface effects at the boundary of the growing material are taken into account. Some newmathematical results for the model are obtained, and most significant among them is the existence of a global solution. The proof of this is presented in complete form. These results can be useful in further scientific developments at the confluence of biology and mechanics.

We deduce the law of nonstationary recursion which makes it possible, for given a primitive set A = {a₁,...,a_k}, k > 2, to construct an algorithm for finding the set of the numbers outside the additive semigroup generated by A. In particular, we obtain a new algorithm for determining the Frobenius numbers g(a₁,...,a_k). The computational complexity of these algorithms is estimated in terms of bit operations. We propose a two-stage reduction of the original primitive set to an equivalent primitive set that enables us to improve complexity estimates in the cases when the two-stage reduction leads to a substantial reduction of the order of the initial set.

We consider the m-Peripatetic Salesman Problem (m-PSP) on random inputs with discrete distribution function. In this paper we present a polynomial approximation algorithm which, under certain conditions, with high probability (w.h.p.) gives optimal solution for both the m-PSP on random inputs with identical weight functions and the m-PSP with different weight functions.

Complete description is given of the linear pointwise degenerate fourth-order delay-differential systems (with constant coefficients) whose active matrix is semisimple and the passive matrix is nonnilpotent. These systems are described with the help of the language of geometrical invariants of certain elements of the semigroup generated by the matrices of the system.

Under study is the one-dimensional stationary regime of gas motion through porous objects with periodically distributed intensity of energyrelease and some given pressure difference on the open boundaries of the object, i.e. under a kind of self-regulation of the gas flow rate through the object. The obtained numerical-analytical solution of the problem is analyzed in a wide range of key parameters, and the basic regularities of the process under study are revealed. It is shown that, under a periodical distribution of the energyrelease sources, the dependence of the phase temperatures, filtration rate, and gas density on the height of the object is also oscillatory; however, pressure changes monotonically.We show that the local maxima of the solidmedium temperature and energy release do not coincide, whereas their local minima can coincide only at those points where the heat release is absent. We show that, under a periodical distribution of the energyrelease sources, the maximum heating and other parameters can differ substantially from those for the uniform energyrelease with the same total heat release.We demonstrate that, as the frequency of oscillations increases of the heat-release intensity, the values of all defined parameters converge to those under the uniform energyrelease with the same total heat release as in the case of all frequencies that are even integer.

The nonstationary process of filmwise condensation of vapor on curvilinear fins with condensate suction from interfin grooves is numerically simulated with account taken of surface tension and gravity. The problem is reduced to solving a nonlinear evolution equation for the thickness of the condensate film. We performed calculations of the ethanol vapor condensation at atmospheric pressure on the fins of constant curvature for various temperature differences between the fin surface and the vapor saturation and for various values of the rate of condensate suction from the interfin space. Numerical calculations show that the condensation process is stable in the device (i.e., in the condenser) with condensate suction. Filling the interfin space leads to diminishing the zone of intense condensation and reducing the condensate inflow; therefore, this yields stable equilibrium between the condensation and condensate suction. The changes of the condenser temperature at a constant condensate suction entail variation of the filling level of the interfin groove and establishment of a stationary process, provided that the fin temperature becomes constant.

Under consideration is the problem of synthesis of irredundant logic circuits in the basis {&, ∨, ¬} which implement Boolean functions of n variables and allow some short single diagnostic tests regarding uniform constant faults at outputs of gates. For each Boolean function permitting implementation by an irredundant circuit, the minimal possible length value of such a test is found. In particular, we prove that this value is at most 2.

The existence of a generalized weak solution is proved for the nonstationary problem of motion of a rigid body in the flow of a viscous incompressible fluid filling a cylindrical pipe of arbitrary cross-section. The fluid flow conforms to the Navier–Stokes equations and tends to the Poiseuille flow at infinity. The body moves in accordance with the laws of classical mechanics under the influence of the surrounding fluid and the gravity force directed along the cylinder. Collisions of the body with the boundary of the flow domain are not admitted and, by this reason, the problem is considered until the body approaches the boundary.