An efficient method for oxygen diffusion in a spherical cell with nonlinear oxygen uptake kinetics

In this paper, a novel numerical technique, the first-order Smooth Composite Chebyshev Finite Difference method, is presented. Imposing a first-order smoothness of the approximation polynomial at the ends of each subinterval is originality of the method. Both round-off and truncation error analyses of the method are performed beside the convergence analysis. Diffusion of oxygen in a spherical cell including nonlinear uptake kinetics is solved by using the method. The obtained results are compared with the existing methods in the literature and it is observed that the proposed method gives more reliable results.

Method of Constructing an Asymmetric Human Bronchial Tree in Normal and Pathological Cases

The goal of the study is the analytical design of the full asymmetric human bronchial tree (irregular dichotomy) for healthy patients and patients with obstructive pulmonary diseases. For this purpose, the author has derived the special analytical formulas. All surfaces of the bronchial tree are matched with the second-order smoothness (there are no acute angles or ribs). The geometric characteristics of the human bronchial tree in the pathological case are modeled by a “starry” shape of the inner structure of the bronchus; a level of the pathology is defined by two parameters: bronchus constriction level and level of distortion of the cylindrical shape of the bronchus. Closed analytical formulas allow a researcher to construct the human bronchial tree of an arbitrary complexity (up to alveoli); moreover, the parametric dependences make it possible to specify any desirable level of airway obstruction.

Matching conditions for values of characteristic oblique derivative at the end of a string, initial data and right-hand side of the wave equation

Sufficient matching conditions the time-dependent characteristic first derivatives in the boundary mode with the initial conditions and the more general vibration equation of a semi-bounded string are derived in the sets of solutions of all higher order smoothness orders. They generalize the previously found sufficient matching conditions in the case of a similar mixed problem for the simplest string vibration equation. The characteristic of non-stationary first oblique derivatives in the boundary mode means that at each moment of time they are directed along the critical characteristic.

Analytical Design of the Human Bronchial Tree for Healthy Patients and Patients with Obstructive Pulmonary Diseases

The study is aimed at the analytical design of the full human bronchial tree for healthy patients and patients with obstructive pulmonary diseases. Analytical formulas for design of the full bronchial tree are derived. All surfaces of the bronchial tree are matched with the second-order smoothness (there are no acute angles or ribs). The geometric characteristics of the human bronchial tree in the pathological case are modeled by a “starry” shape of the inner structure of the bronchus; the pathology degree is defined by two parameters: bronchus constriction level and degree of distortion of the cylindrical shape of the bronchus. Closed analytical formulas allow the human bronchial tree of an arbitrary complexity (up to alveoli) to be designed; moreover, the parametric dependences make it possible to specify any desirable degree of airway obstruction.

Computational Algorithms For Modeling of One-Dimensional Contours Through k In Advance Given Points

In this paper have been proposed theoretical bases for formation one-dimensional contours of the first order smoothness, passing through k in advance given points, including requirements to the contour in general, and the contour’s arcs in particular, as well as representations for tangents in extreme and intermediate contour sections, which determine the contour arc shape. Based on this theoretical material have been developed computational algorithms for simulation of closed (A5, A6) and open (A1-A4) contours according to postulated conditions, which allow form irregular composite curves and surfaces with different degree of complexity, docked together on the first order smoothness. The proposed computational algorithms can also be used to construct contours of higher orders smoothness using arcs of the same ratio curves. For analytical description of computational algorithms for one-dimensional contours simulation is used the mathematical apparatus of BN-calculation (Balyuba – Naidysh point calculation). The obtained algorithms have been presented in a point form, which is a symbolic form. For transition from point equations to a system of parametric equations, it is necessary to perform a coordinate-by-coordinate calculation, which can be presented geometrically as population of projections on the global coordinate system’s axes. As an example has been presented a computational algorithm that provides the use a system of parametric equations instead of symbolic point recording. The proposed algorithms have been successfully used for computer modeling and prediction for the impact of geometric shape imperfections on the strength and stability of engineering structures’ thin-walled shells. In particular, a numerical study method for a stress-strain state of steel vertical cylindrical reservoirs with regard to imperfections of theirs geometric shapes has been proposed.

Smoothness of refinable function vectors on ℝn

Let [Formula: see text] be a dilation matrix, an [Formula: see text] expansive matrix that maps [Formula: see text] into itself. Let [Formula: see text] be a finite subset of [Formula: see text] and for [Formula: see text] let [Formula: see text] be [Formula: see text] complex matrices. The refinement equation corresponding to [Formula: see text] and [Formula: see text] is [Formula: see text] A solution [Formula: see text] if one exists, is called a refinable vector function or a vector scaling function of multiplicity [Formula: see text] This paper characterizes the higher-order smoothness of compactly supported solutions of the refinement equation, in terms of the [Formula: see text]-norm joint spectral radius of a finite set of finite matrices determined by the coefficients [Formula: see text]