ABSTRACT A collisionless plasma is modelled by the Vlasov-Poisson system in three space dimensions. A fixed background of positive charge—dependant upon only velocity—is assumed. The situation in which mobile negative ions balance the positive charge as | x | → ∞ is considered. Thus, the total positive charge and the total negative charge are both infinite. Smooth solutions with appropriate asymptotic behavior for large | x |, which were previously shown to exist locally in time, are continued globally. This is done by showing that the charge density decays at least as fast as | x |?6. This article also establishes decay estimates for the electrostatic field and its derivatives. 相似文献
Abstract A collisionless plasma is modeled by the Vlasov-Poisson system in three space dimensions. A fixed background of positive charge, which is independent of time and space, is assumed. The situation in which mobile negative ions balance the positive charge as |x|→∞ is considered. Hence the total positive charge and the total negative charge are infinite. Smooth solutions with appropriate asymptotic behavior are shown to exist locally in time. Conditions for continuation of these solutions are also established. 相似文献
In this note, we consider a finite set X and maps
W from the set $ \mathcal{S}_{2|2} (X) $ of all 2, 2-
splits of X into $ \mathbb{R}_{\geq 0} $. We show that such a map
W is induced, in a canonical way, by a binary
X-tree for which a positive length $ \mathcal{l} (e) $ is
associated to every inner edge e if and only if (i) exactly
two of the three numbers W(ab|cd),W(ac|bd), and
W(ad|cb) vanish, for any four distinct elements
a, b, c, d in X,
(ii) $ a \neq d \quad\mathrm{and}\quad W (ab|xc) + W(ax|cd) = W(ab|cd) $ holds for all
a, b, c, d, x
in X with
#{a, b, c, x} = #{b, c, d, x} = 4
and $ W(ab|cx),W(ax|cd) $ > 0, and (iii) $ W (ab|uv) \geq \quad \mathrm{min} (W(ab|uw), W(ab|vw)) $
holds for any five distinct elements a, b, u, v, w in
X. Possible generalizations
regarding arbitrary $ \mathbb{R} $-trees and applications regarding tree-reconstruction algorithms
are indicated.AMS Subject Classification: 05C05, 92D15, 92B05. 相似文献
We prove that for two elements x, y in a Hilbert C*-module V over a C*-algebra the C*-valued triangle equality |x + y| = |x| + |y| holds if and only if 〈x, y〉 = |x| |y|. In addition, if has a unit e, then for every x, y ∊ V and every ɛ > 0 there are contractions u, υ ∊ such that |x + y| ≦ u|x|u* + υ|y|υ* + ɛe.
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Samples of biological tissue are modelled as inhomogeneous fluids with density ?(X) and sound speed c(x) at point x. The samples are contained in the sphere |x| ? δ and it is assumed that ?(x) ? ?0 = 1 and c(x) ? c0 = 1 for |x| ? δ, and |γn(x)| ? 1 and |?γ?(x)| ? 1 where γ?(x) = ?(x) ? 1 and γn(x) = c?2(x) ? 1. The samples are insonified by plane pulses s(x · θ0 – t) where x = |θ0| = 1 and the scattered pulse is shown to have the form |x|?1es(|x| – t, θ, θ0) in the far field, where x = |x| θ. The response es(τ, θ, θ0) is measurable. The goal of the work is to construct the sample parameters γn and γ? from es(τ, θ, θ0) for suitable choiches of s, θ and θ0. In the limiting case of constant density: γ?(x)? 0 it is shown that Where δ represents the Dirac δ and S2 is the unit sphere |θ| = 1. Analogous formulas, based on two sets of measurements, are derived for the case of variable c(x) and ?(x). 相似文献
A detailed analysis is given to the solution of the cubic Schrödinger equation iqt + qxx + 2|q|2q = 0 under the boundary conditions as |x|→∞. The inverse-scattering technique is used, and the asymptotic state is a series of solitons. However, there is no soliton whose amplitude is stationary in time. Each soliton has a definite velocity and “pulsates” in time with a definite period. The interaction of two solitons is considered, and a possible extension to the perturbed periodic wave [q(x + T,t) = q(x,t) as |x|→∞] is discussed. 相似文献
It is shown that the Novikov-Veselov equation (an analogue of the KdV equation in dimension 2 + 1) at positive and negative energies does not have solitons with space localization stronger than O(|x|?3) as |x| →∞. 相似文献
In this paper, we consider the following fractional Schrödinger‐Poisson system where 0 < t ≤ α < 1, , and 4α+2t ≥3 and the functions V(x), K(x) and f(x) have finite limits as |x|→∞. By imposing some suitable conditions on the decay rate of the functions, we prove that the above system has two nontrivial solutions. One of them is positive and the other one is sign‐changing. Recent results from the literature are generally improved and extended. 相似文献
S.M. Lozinskii proved the exact convergence rate at the zero of Lagrange interpolation polynomials to |x| based on equidistant
nodes in [−1,1], In 2000, M. Rever generalized S.M. Lozinskii’s result to |x|α(0≤α≤1). In this paper we will present the exact rate of convergence at the point zero for the interpolants of |x|α(1<α<2). 相似文献
We prove the following statement, which is a quantitative form of the Luzin theorem on C-property: Let (X, d, μ) be a bounded metric space with metric d and regular Borel measure μ that are related to one another by the doubling condition. Then, for any function f measurable on X, there exist a positive increasing function η ∈ Ω (η(+0) = 0 and η(t)t−a decreases for a certain a > 0), a nonnegative function g measurable on X, and a set E ⊂ X, μE = 0 , for which
Let p be a prime, χ denote the Dirichlet character modulo p, f (x) = a0 + a1x + ... + akxk is a k-degree polynomial with integral coefficients such that (p, a0, a1, ..., ak) = 1, for any integer m, we study the asymptotic property of
The discrete dynamical system of absolute differences defined by the map Ψ(x1, x2, x3, x4) = (| x2 - x1 |, | x1 - x1|, |x1 - x1 |, |x1 - x4 |) has been studied by many authors and one of the interesting questions is how to locate quadruples which converge to the fixed point (0, 0, 0, 0) in large numbers of steps. An elementary method is offered for obtaining such quadruples. The method is also able to find quadruples that will not converge to (0, 0, 0, 0). 相似文献
We are dealing with the first vanishing time for solutions of the Cauchy–Neumann problem for the semilinear parabolic equation
∂tu − Δu + a(x)uq = 0, where
a(x) \geqslant d0exp( - \fracw( | x | )| x |2 ) a(x) \geqslant {d_0}\exp \left( { - \frac{{\omega \left( {\left| x \right|} \right)}}{{{{\left| x \right|}^2}}}} \right) , d0 > 0, 1 > q > 0, and ω is a positive continuous radial function. We give a Dini-like condition on the function ω which implies that any solution of the above equation vanishes in finite time. The proof is derived from semi-classical limits
of some Schr¨odinger operators. 相似文献