Circulation hydrodynamics in the organs of the abdominal cavity in the presence of extracorporeal perfusion

The general hemodynamics and circulation in the organs of the abdominal cavity have been investigated in the presence of artificial circulation at a calculated rate of perfusion. The effect of vasoactive preparations (noradrenaline, Arfonad) on these characteristics is analyzed. The behavior of the microcirculation in the presence of artificial circulation created by an artificial circulation apparatus equipped with automatic control systems of original design has been studied. It has been found that disturbances of the microcirculation are responsible for the development of a state of hypoxia in organs and tissues in the presence of artificial circulation at a calculated rate of perfusion under conditions of controlled vasoconstriction or controlled hypotension. Stabilization of the arterial pressure and the functional state of the vascular bed in the presence of artificial circulation had a positive effect on the tissue blood flow and oxygen metabolism in the organs of the abdominal cavity.Paper presented at the First All-Union Conference on Engineering and Medical Biomechanics on the topic: Problems of Circulatory Hydrodynamics, Riga, October, 1975.D. I. Ulyanov Kuibyshev Medical Institute. Translated from Mekhanika Polimerov, No. 5, pp. 871–874, September–October, 1975.     

On the Gap in the Spectrum of the Translations

The spectrum of the translations in local quantum field theory will be analyzed in order to show that in a positive energy representation without vacuum vector and with lowest mass m₁ there is no gap in the spectrum which is larger than 2m₁. In particular in a zero mass representation there is no hole at all. These results are obtained with methods of analytic functions of several complex variables.     

Mathematics in the Memoirs of the Lisbon Academy of Sciences in the 19th century

From the end of the 18th century until the appearance of the first issue of the Jornal de Sciencias Mathematicas e Astronomicas in 1877, the Lisbon Royal Academy of Sciences, founded in 1779, was the main publisher in Portugal of periodicals that included mathematical papers. In this article I will give an overview of the mathematical papers which appeared in the Academy's Memoirs during the 19th century, in the context of the scientific output published in its pages. We will characterize the community of mathematicians around the Academy's journal and the changes in background and in themes researched throughout the century.     

Investment decisions in the rent-to-own industry in the absence of inventory

This study addresses the product investment decision faced by firms in the rent-to-own industry. In this setting, a customer arrives according to a random process and requests one unit of a product to rent (and eventually own should he/she choose to make all the required payments). At the time of request, if the product is available in inventory, the firm enters into a contractual agreement (by accepting the customer's offer) and rents the merchandise. More interesting and the case considered here, if the requested item is not in inventory, the firm must decide whether to purchase the item in order to rent it out or to simply reject the request. The customer's offer specifies the desired maximum contract length and the payment frequency—from which the firm determines the fixed periodic payment charged. The firm makes its investment decision based on the characteristics of the offer as well as those of the product (eg, initial and resale values, useful life and carrying costs) in essence performing a complicated cost benefit analysis. An extension is also considered whereby instead of simply rejecting the request the firm can adjust the required payment amount. Dynamic programming techniques are used to address the problem and to solve for the firm's optimal decision.     

Dynamic decision methods in the presence of uncertainty in the state and the dynamics

The article considers the problem of dynamic decision under uncertainty in the state and in its dynamics. Game models and identification and decision methods are developed that ensure consistency and asymptotic stationarity of dynamic equilibria.This study was partially financed by the Russian Foundation of Basic Research (95-01-01137).Translated from Nelineinye Dinamicheskie Sistemy: Kachestvennyi Analiz i Upravlenie — Sbornik Trudov. No. 3. pp. 10–22, 1993.     

Homogenization of boundary value problems in perforated domains with the third boundary condition and the resulting change in the character of the nonlinearity in the problem

We study the homogenization problem for the Poisson equation in a periodically perforated domain with a nonlinear boundary condition for the flux on the cavity boundaries. We show that, under certain relations on the problem scale, the homogenized equations may have different character of the nonlinearity. In each case considered, we obtain estimates for the convergence of solutions of the original problem to the solution of the homogenized problem in the corresponding Sobolev spaces.     

Gaps in the poset of projections in the Calkin algebra

We study the gap structure of the partial order of projections of the Calkin algebra of a complex, separable, infinite-dimensional Hilbert space. We prove the existence of an analytic Hausdorff gap in this partial order. As a consequence we obtain that under Todorcevic’s Axiom and MA the gap spectrum of P(C(H)) is strictly bigger than the gap spectrum of P(ω)/Fin.     

On choosing the location of the sources in the MFS

The satisfactory location for the sources outside the closure of the domain of the problem under consideration remains one of the major issues in the application of the method of fundamental solutions (MFS). In this work we investigate this issue by means of two algorithms, one based on the satisfaction of the boundary conditions and one based on the leave-one-out cross validation algorithm. By applying these algorithms to several numerical examples for the Laplace and biharmonic equations in a variety of geometries in two and three dimensions, we obtain locations of the sources which lead to highly accurate results, at a relatively low cost.     

On the continuity of the sharp constant in the Jackson-Stechkin inequality in the space L 2

This paper deals with the continuity of the sharp constant K(T,X) with respect to the set T in the Jackson-Stechkin inequality $E(f,L) \leqslant K(T,X)\omega (f,T,X),$ , where E(f,L) is the best approximation of the function f ∈ X by elements of the subspace L ? X, and ω is a modulus of continuity, in the case where the space L ²( $\mathbb{T}^d $ , ?) is taken for X and the subspace of functions g ∈ L ²( $\mathbb{T}^d $ , ?), for L. In particular, it is proved that the sharp constant in the Jackson-Stechkin inequality is continuous in the case where L is the space of trigonometric polynomials of nth order and the modulus of continuity ω is the classical modulus of continuity of rth order.     

Stability of the bicarbonate system in the blood

In this paper, we describe a mathematical model about the reaction-diffusion kinetics of bicarbonate system, which it plays a key role in regulating blood pH. It is very important to know the determinants of blood pH in both experimental and theoretical studies, in order to help to investigate the hidden mechanism of acid-base disorders in the clinical setting. We explore the dynamics of the bicarbonate system under the closed condition. This condition yields that the total amount of carbon dioxide is conserved and the difference in concentrations between anions and cations is conserved. For the stability of the model, we hypothesize that the amount of initial concentrations perturbed around an equilibrium point is less than a certain constant depending on a rate constant. With an application of Liapunov's method, we prove that the model in the form of reaction-diffusion system is globally stable under the hypothesis. We also provide the blood pH profile, which is computed in our model with the experimentally observed rate constants.     

Satellites in the gravitational field of the moon

Expressions are derived correct to the first order in the ellipticities of the Moon for the radial shift and the rotation of the unperturbed orbit of a close satellite in the plane of its instantaneous motion. Criteria for the rotation to be a libration lead to the existence of a critical range of values of orbital inclination as against a single value cos^?1 (·2)^1/2=63·4° quoted for the Earth satellites. It appears that mean radial shift and the perturbation in the period of the satellite, also possess similar ranges. The perturbation in the velocity vector is then analysed and it is shown that the angle between the unperturbed and real trajectories vanishes only at points where the radial distance of the satellite from the selenocentre attains extreme values. The interesting case of nearly circular trajectories is considered next in some detail. It is deduced that the critical inclination for the orbital libration is given byα=60° for an Earth satellite in this case. The paper concludes with numerical results based on Jeffreys’ estimates.     

旋风分离器内流动的三维分析

本文详细阐述了旋风分离器内流动在球坐标系中的数学表述和结果,应用质量守恒定律和定常流动的运动定律,在轴对称的考虑下,用流函数方法详尽推导了流动的三个速度分量.此讨论是从三维的整体观点来全面分析流动状况的.此外,对文[1]中的一些结果作了必要的修正.     

Hydroelastic phenomena in the neighborhood of the bifurcation of the aorta

The mechanical behavior of the vessels and the blood near a bifurcation is analyzed. A single-layer homogeneous shell is taken as a model of the aorta on the assumption that the intima is much less stiff than the other layers. In analyzing the blood flow in large vessels, the blood is treated as a viscous Newtonian liquid, whose motion is described by the Navier-Stokes equations and the continuity equation.Zhukovskii Air Force Engineering Academy, Moscow; Institute of Polymer Mechanics, Academy of Sciences of the Latvian SSR, Riga. Translated from Mekhanika Polimerov, No. 1, pp. 164–166, January–February, 1971.     

Existence and regularity in the small in the calculus of variations

A local existence theorem is proved for the basic problem in the calculus of variations, that of minimizing ∝L(t, x, /.x) dt over a class of functions x assuming given boundary conditions. The Lagrangian L is only assumed to be locally Lipschitz and strictly convex in its /.x variable.     

Acceleration of the convergence of the Laguerre series in the problem of inverting the Laplace transform

When the Laplace transform is inverted numerically, the original function is sought in the form of a series in the Laguerre polynomials. To accelerate the convergence of this series, the Euler-Knopp method is used. The techniques for selecting the optimal value of the parameter of the transform on the real axis and in the complex plane are proposed.     

Weak asymptotic solution of the phase-field system in the case of fusion of free boundaries in the Stefan-Gibbs-Thomson problem

The process of fusion of free boundaries in binary media in the Stefan-Gibbs-Thomson problem is analyzed. By using the weak asymptotics method, the formula for the weak asymptotic solution of the phase-field system global in time is constructed in the case considered. __________ Translated from Fundamentalnaya i Prikladnaya Matematika, Vol. 12, No. 6, pp. 49–66, 2006.     

On the determination of the coefficients in the viscoelasticity equations

For the integrodifferential viscoelasticity equations, we study the problem of determining the coefficients of the equations and the kernels occurring in the integral terms of the system of equations. The density of the medium is assumed to be given. We suppose that the inhomogeneity support of the sought functions is included in some compact domain B ₀. We consider a series of inverse problems in which an impulse source is concentrated at the points y of the boundary of B ₀. The point y is the parameter of the problem. The given information about the solution is the trace of the solution to the Cauchy problem with zero initial data. This trace is given on the boundary of B ₀ for all y ∈ ?B ₀ and for a finite time interval. The main result of the article consists in obtaining uniqueness theorems for a solution to the initial inverse problem.     

Precise rates in the law of the logarithm in the Hilbert space

Let be a sequence of i.i.d. random variables taking values in a real separable Hilbert space (H,‖⋅‖) with covariance operator Σ, and set Sn=X₁+?+Xn, n?1. Let . We prove that, for any 1<r<3/2 and a>−d/2,

     

份额——偏离分析法在河北省工业产业定位分析中的应用

对河北省工业产业进行定位分析,首先对份额——偏离分析法及区位商分析法做了简单的介绍;然后利用S-S分析法和区位商分析法对河北省工业产业的相对优势进行了分析,同时分析了河北省工业在区域内的绝对优势;最后结合以上两方面分析结论对河北省工业产业进行了定位分析.