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Vol 41, No 3 (2017)
- Year: 2017
- Articles: 7
- URL: https://journals.rcsi.science/0278-6419/issue/view/10803
Article
Properties of grid boundary value problems for functions defined on grid cells and faces
Abstract
Properties of a version of MFD method are studied for a grid problem on a polyhedral grid in which the grid scalars are defined on grid cells and the grid flows are specified by their local normal coordinates on the plane faces of cells. In a domain with curvilinear boundary, a grid inhomogeneous boundary value problem for stationary diffusion-type equations is considered. An operator statement of the grid problem is given, and a local approximation of the equations and boundary conditions is studied.
105-112
The Cauchy problem for singularly perturbed weakly nonlinear second-order differential equations: An iterative method
Abstract
For a singularly perturbed weakly nonlinear second-order differential equation, we construct a sequence converging to the Cauchy problem solution. This is an asymptotical sequence because the deviation (in the sense of the norm of the space of continuous functions) of its nth element from the solution to the problem is proportional to the (n + 1)th power of the perturbation parameter. Such a sequence can be used to justify the asymptotics obtained by using boundary functions.
113-121
Nontrivial stationary points of two-species self-structured communities
Abstract
The two-species model of self-structured stationary biological communities proposed by U. Dieckmann and R. Law is considered. A way of investigating the system of integro-differential equations describing the model equilibrium is developed, nontrivial stationary points are found, and constraints on the model parameter space resulting in similar stationary points are studied. The results are applied to a number of widely known biological scenarios.
122-129
130-133
The asymptotically best method for synthesizing limited-depth Boolean recursive schemes
Abstract
A model of limited-depth recursive schemes for the functions of Boolean algebra (Boolean functions), constructed from multi-output functional elements, is considered. A lower estimate of the Shannon function for the complexity of schemes of this class is derived. Upper estimates for the complexity of some specific functions and systems of functions in this class of schemes are obtained. A method is proposed for synthesizing schemes of this class for arbitrary functions that allow us (using the derived lower estimate) to determine the asymptotics of the Shannon function for their complexity.
134-141
Universal functions for classes of Boolean polynomials
Abstract
The following problem is considered: Find Boolean function f of n variables with the property that, given any polynomial p of degree at most s, there exists a set of n-tuples such that p is the only polynomial of degree at most s taking the same values as f at these n-tuples. It is shown that for any fixed s and sufficiently large n, such a function exists and can be chosen from among those with domains of cardinality that grow as O(ns).
142-144
Computation scheduling in multiprocessor systems with several types of additional resources and arbitrary processors
Abstract
The problem of feasible preemptive scheduling in a multiprocessor system is considered for when scheduled intervals are assigned, processor performance can be arbitrary, there are several types of additional resources, and the time for executing tasks depends linearly on the amount of additional resources allocated to them. Polynomial algorithms based on reducing the original problem to a flow problem and a linear programming problem are developed.
145-151