An approximate solution concerning strong evaporation into a half space

Evaporation of a liquid into a vacuum occupying a half space is investigated on the basis of the one-dimensional BGK model linearized about a drifting Maxwellian distribution. TheF _N method is used to deduce accurate numerical results for the perturbations in the density and temperature.

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Zusammenfassung Auf der Basis eines eindimensionalen BGK-Modells, das über eine driftende Maxwell-Verteilung linearisiert ist, wird die Verdampfung einer Flüssigkeit in ein einen Halbraum ausfüllendes Vakuum untersucht. DieF _N-Methode wird verwendet zur Ableitung von genauen numerischen Ergebnissen für die Störungen in Dichte und Temperatur.

     

A solution to the L space problem

In this paper I will construct a non-separable hereditarily Lindelöf space (L space) without any additional axiomatic assumptions. The constructed space is a subspace of where is the unit circle. It is shown to have a number of properties which may be of additional interest. For instance it is shown that the closure in of any uncountable subset of contains a canonical copy of .

I will also show that there is a function such that if are uncountable and , then there are in and respectively with . Previously it was unknown whether such a function existed even if was replaced by . Finally, I will prove that there is no basis for the uncountable regular Hausdorff spaces of cardinality .

The results all stem from the analysis of oscillations of coherent sequences of finite-to-one functions. I expect that the methods presented will have other applications as well.

     

State vector solutions for nonaxisymmetric problem of multilayered half space piezoelectric medium

A state space formulation is established for the nonaxisymmetric space problem of transversely isotropic piezoelectric media in a system of cylindrical coordinate by introducing the state vector. Using the Hankel transform and the Fourier series, the state vector equations are transformed into ordinary differential equations. By the use of the matrix methods, the analytical solutions of a single piezoelectric layer are presented in the form of the product of initial state variables and transfer matrix. The applications of state vector solutions are discussed. An analytical solution for a semiinfinite piezoelectric medium subjected to the vertical point forceP _z, horizontal point forceP _x along x-direction and point electric charge Q at the origin of the surface is presented. According to the continuity conditions at the interfaces, the general solution formulation forN-layered transversely isotropic piezoelectric media is given. Project supported by the National Natural Science Foundation of China (Grant No. 59648001).     

The third mixed problem for the Sonin equation in a half space

We consider follwing mixed boundary-value problem:

A solution of the finite-dimensional homogeneous Banach space problem

It is proved that if a finite-dimensional Banach space X has the property that all its αn-dimensional subspaces are K-isomorphic, for some 0 < α < 1 and K ≥ 1, then X is f(α, K)-isomorphic to a Hilbert space, where f(α, K) is cK^3/2, if 0 < α < 2/3 and cK², if 2/3 < α < 1, and where c = c(α) depends on α only. Part of the work on this paper was done while this author held a visiting position at Odense University sponsored by the Odense University and Danish Natural Sciences Council Grant No. 11-7639. Supported in part by National Sciences and Engineering Research Council Grant.     

EXPONENTIAL STABILIZATION OF THE SOLUTION FOR TIME DEPENDENT NEUTRON TRANSPORT EQUATION

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Measures on phase space as solutions of the one-dimensional neutron transport equation

Summary The linear integral transport operator for slab geometry is formulated and studied as a mapping on the set of measures on the phase space of the underlying system, with the expected number of neutrons emergent from a collision represented by a measure on the space of outgoing velocities. Under appropriate assumptions it is shown that, if c represents the maximum number of secondary particles per collision, then there exists c ₁ ≥1 such that the system is subcritical for c≤c ₁ . An example shows that c ₁ ≥1 is sharp in general, but further assumptions are given under which one can deduce c ₁ >1. The idealized laws of elastic and inelastic scattering are shown to satisfy our assumptions. Entrata in Redazione il 27 ottobre 1975.     

N-group neutron transport theory: A criticality problem in slab geometry

The steady-state equation for N-group neutron transport in slab geometry is written as an integral equation. A spectral analysis is made of the integral operator and related to the criticality problem. The method depends on a representation for the resolvent kernel for a subcritical slab and on analytic continuation in a complex parameter to characterize eigenvalues in terms of singularities of the resolvent. The analytic continuation is based on a bifurcation analysis of some nonlinear matrix integral equations whose solutions provide a matrix Wiener-Hopf factorization of the Fourier transform of the kernel of the transport operator.     

Generalized solution of non‐autonomous photon transport problem

The purpose of this paper is to show the existence of a generalized solution of a non‐autonomous transport problem. By means of the theory of equicontinuous evolution system on a sequentially complete locally convex topological vector space, we show that the perturbed abstract non‐autonomous Cauchy problem has a unique solution when the perturbation operator and forcing term function satisfy certain conditions. A consequence of the abstract result is that it can be directly applied to obtain a generalized solution of the non‐autonomous photon transport problem. Copyright © 2009 John Wiley & Sons, Ltd.     

半空间上Boussinesq方程组弱解的L2衰减估计

主要研究外力函数f 满足一定条件时,半空间上Boussinesq 方程组当n≥3时弱解的L2衰减。先假设解光滑,给出了光滑解的一致L2衰减估计,再通过构造逼近解,对逼近解序列作一致衰减估计,取极限得到弱解的一致L2衰减估计。     

Stokes’ first problem for a third grade fluid in a porous half space

In this study, we model the flow of a third grade fluid in a porous half space. Based on modified Darcy’s law, the flow over a suddenly moved flat plate is discussed numerically. The influence of various parameters of interest on the velocity profile is seen.     

Some properties of the solution space of the N-city traveling-salesman problem

For the matrix of variables in the N-city traveling-salesman problem, consider both the N row and the N column vectors. An orthogonality condition involving products of row and column vectors is shown to eliminate subtours. Also, a group representation of the problem is given to observe properties of the solution space. The matrix of variables is subsequently decomposed into a product of elementary transposition matrices. Numerous examples are provided to illustrate the properties of the problem.     

Analytical solution for the steady flow of the third grade fluid in a porous half space

In this study, we model the flow of a third grade fluid in a porous half space. Based on modified Darcy’s law, the flow over a suddenly moved flat plate is discussed analytically by using homotopy analysis method (HAM). The influence of various parameters of interest on the velocity profile is seen.     

On a parabolic problem with nonlinear term in a half space and global behavior of solutions

We take up the existence and global behavior of positive continuous solutions of the following nonlinear parabolic equation in (n?2) with boundary conditions u=0 on and u(x,0)=u₀(x). The nonlinear term is required to satisfy some conditions related to a functional class , which we introduce in this paper and will be called parabolic Kato class in the half space. Our approach is based on potential theory.     

Strong evaporation into a half space

Evaporation of a liquid into a vacuum occupying a half space is investigated on the basis of the one-dimensional BGK model linearized about a drifting Maxwellian distribution. A unique solution is shown to exist if the downstream speed remains subsonic. Exact analysis is used, and numerical results are given.

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Zusammenfassung Auf der Basis eines eindimensionalen BGK-Modells, das über eine driftende Maxwell-Verteilung linearisiert ist, wird die Verdampfung einer Flüssigkeit in ein einen Halbraum ausfüllendes Vakuum untersucht. Es wird gezeigt, daß nur eine einzige Lösung existiert, wenn die Geschwindigkeit im Unterschallbereich bleibt. Exakte Analysis wird verwendet und numerische Resultate angegeben.