Starting from Lagrange interpolation of the exponential function ${\rm e}^z$ in the complex plane, and using an integral representation formula for holomorphic functions on Banach spaces, we obtain Lagrange interpolating polynomials for representable functions defined on a Banach space $E$. Given such a representable entire funtion $f\colon E \to \mathbb C$, in order to study the approximation problem and the uniform convergence of these polynomials to $f$ on bounded sets of $E$, we present a sufficient growth condition on the interpolating sequence.
This study addresses a particular phenomenon in open channel flows for which the basic assumption of hydrostatic pressure distribution is essentially invalid, and expands previous suggestions to flows where streamline curvature is significant. The proposed model incorporates the effects of the vertical curvature of the streamline and steep slope, in making the pressure distribution non-hydrostatic, and overcomes the accuracy problem of the Saint-Venant equations when simulating curvilinear free surface flow problems. Furthermore, the model is demonstrated to be a higher-order one-dimensional model that includes terms accounting for wave-like variations of the free surface on a constant slope channel. Test results of predicted flow surface and pressure profiles for flow in a channel transition from mild to steep slopes, transcritical flow over a short-crested weir and flow with dual free surfaces are compared with experimental data and previous numerical results. A good agreement is attained between the experimental and computed results. The overall simulation results reveal the satisfactory performance of the proposed model in simulating rapidly varied gravity-driven flows with predominant non-hydrostatic pressure distribution effects. This study suggests that a higher-order pressure equation should be used for modelling the pressure distribution of a curvilinear flow in a steeply sloping channel.
The preparation of Dl/D2/cytochrome 6559 complex isolated from pea (Pisum sativum h.) was photoinactivated by "white light" (140 W m‘2) at 20 and 4 "C in both the presence and absence of oxygen. The inactivation was followed by measuring the decline of the photoinduced absorbance change A/4683 (the photoaccumulation of reduced pheophytin), by measuring absorption spectra and fluorescence emission, and by polypeptide analysis. In the presence of oxygen, the ability of the DUDUcyi 6559 complex to acciunulate reduced pheophytin was lost with the halftime im of about 3 min and fluorescence quantum yield declined with ti/2 of about 30 min at both 20 and 4 ^C. The D\ and Dl polypeptides were rapidly modified at 20 °C as reflected by the presence of their large aggregates at the start of the electrophoretic gel and by a decrease of the mobility of remaining Dl and Dl monomers. This modification was substantially limited at 4 “C. Subímits of cytochrome 6559 were not modified at any temperature. When oxygen was removed, the halftime of the A/1683 decline increased by about one order of magnitude, fluorescence emission did not decline, but slightly increased, and the polypeptide pattem was only slightly affected during irradiation.
The aim of this paper is to show the complex thermal analyses used to design of aircraft electronic control unit. Control Power Supply for Jet (CPSJ). The goal is to examine thermal conditions of power and control electronics components. With respect to aircraft application a computational fluid dynamics (CFD) method is used for heat transfer coefficient determination. This method is compared to analytic solution based on Petuchov equation of Nusselt number. The temperature conditions inside the CPSI unit are presented as results. and Obsahuje seznam literatury
Let $q$ be a positive integer, $\chi $ denote any Dirichlet character $\mod q$. For any integer $m$ with $(m, q)=1$, we define a sum $C(\chi, k, m; q)$ analogous to high-dimensional Kloosterman sums as follows: $$ C(\chi, k, m; q)=\sum _{a_1=1}^{q}{}' \sum _{a_2=1}^{q}{}' \cdots \sum _{a_k=1}^{q}{}' \chi (a_1+a_2+\cdots +a_k+m\overline {a_1a_2\cdots a_k}), $$ where $a\cdot \overline {a}\equiv 1\bmod q$. The main purpose of this paper is to use elementary methods and properties of Gauss sums to study the computational problem of the absolute value $|C(\chi, k, m; q)|$, and give two interesting identities for it.