This paper is concerned with the spectral analysis of transport operator with general boundary conditions in L1-setting. This problem will be investigated under results from the theory of positive linear operators, irreducibility and regularity of the collision operator. The basic problems treated here are notions of essential spectra, spectral bound and leading eigenvalues. 相似文献
The paper studies the existence of fixed points for some nonlinear (ws)-compact, weakly condensing and strictly quasibounded operators defined on an unbounded closed convex subset of a Banach space. Applications of the newly developed fixed point theorems are also discussed for proving the existence of positive eigenvalues and surjectivity of quasibounded operators in similar situations. The main condition in our results is formulated in terms of axiomatic measures of weak noncompactness. 相似文献
In this paper, we essentially compute the set of x,y>0 such that the mapping \(z\longmapsto(1-r+re^{z})^{x}(\frac{\lambda}{\lambda-z})^{y}\) is a Laplace transform. If X and Y are two independent random variables which have respectively Bernoulli and Gamma distributions, we denote by μ the distribution of X+Y. The above problem is equivalent to finding the set of x>0 such that μ*x exists. 相似文献
Motivated by a mathematical model of an age structured proliferating cell population, we state some new variants of Leray-Schauder
type fixed point theorems for (ws)-compact operators. Further, we apply our results to establish some new existence and locality principles for nonlinear boundary
value problem arising in the theory of growing cell population in L1-setting. Besides, a topological structure of the set of solutions is provided. 相似文献
The main purpose of this paper is to prove a collection of new fixed point theorems and existence theorems for the nonlinear
operator equation F(x) =αx (α ≥ 1) for so-called 1-set weakly contractive operators on unbounded domains in Banach spaces. We also introduce the concept
of weakly semi-closed operator at the origin and obtain a series of new fixed point theorems and the existence theorems for
the nonlinear operator equation F(x) = αx (α ≥ 1) for such class of operators. As consequences, the main results generalize and improve the relevant results, which are
obtained by O’Regan and A. Ben Amar and M. Mnif in 1998 and 2009 respectively. In addition, we get the famous fixed point
theorems of Leray-Schauder, Altman, Petryshyn and Rothe type in the case of weakly sequentially continuous, 1-set weakly contractive
(μ-nonexpansive) and weakly semi-closed operators at the origin and their generalizations. The main condition in our results
is formulated in terms of axiomatic measures of weak compactness. 相似文献
In this work we investigate an unusual transport phenomenon observed in two-dimensional electron gas under integer quantum Hall effect conditions. Our calculations are based on the screening theory, using a semi-analytical model. The transport anomalies are dip and overshoot effects, where the Hall resistance decreases (or increases) unexpectedly at the quantized resistance plateaus intervals. We report on our numerical findings of the dip effect in the Hall resistance, considering GaAs/AlGaAs heterostructures in which we investigated the effect under different experimental conditions. We show that, similar to overshoot, the amplitude of the dip effect is strongly influenced by the edge reconstruction due to electrostatics. It is observed that the steep potential variation close to the physical boundaries of the sample results in narrower incompressible strips, hence, the experimental observation of the dip effect is limited by the properties of these current carrying strips. By performing standard Hall resistance measurements on gate defined narrow samples, we demonstrate that the predictions of the screening theory is in well agreement with our experimental findings. 相似文献
Forced convection hybrid nanofluid flow over a backward-facing step under a non-uniform magnetic field is numerically studied using a finite volume method. The external magnetic source is placed in the step edge. The study is performed for a range of nanoparticles volume fraction, φ, from 0 to 2%, Hartmann number, Ha, from 0 to 50, and Reynolds number, Re, from 100 to 300. Results show that the reattachment length reduces by increasing volume fraction of nanoparticles and by decreasing Reynolds number. The recirculation bubble weakens and the conductive heat transfer mode growth by increasing Hartmann number at weak magnetic field intensity. It totally disappears at high Hartmann number when the convective mode dominates. The average Nusselt number increases by increasing volume fraction of nanoparticles and varies with the Hartmann number. The effects of Lorentz force and hybrid nanoparticles on the heat transfer enhancement rates are strongly linked with volume fraction of nanoparticles and Hartmann and Reynolds numbers.