The Exchange Value Embedded in a Transport System

This paper shows that a well designed transport system has an embedded exchange value by serving as a market for potential exchange between consumers. Under suitable conditions, one can improve the welfare of consumers in the system simply by allowing some exchange of goods between consumers during transportation without incurring additional transportation cost. We propose an explicit valuation formula to measure this exchange value for a given compatible transport system. This value is always nonnegative and bounded from above. Criteria based on transport structures, preferences and prices are provided to determine the existence of a positive exchange value. Finally, we study a new optimal transport problem with an objective taking into account of both transportation cost and exchange value.     

Mathematical aspects of ‘t Hooft’s eigenvalue problem in two-dimensional quantum chromodynamics

We consider the eigenvalue problem of t′ Hooft for the meson spectrum in 2-dimensional QCD. Various alternative formulations are discussed, and their equivalence is proved. Then, a variational characterization of the eigenfunctions and the eigenvalues is derived yielding that the spectrum is discrete and consists of denumerably many positive eigenvalues tending to infinity. The corresponding eigenfunctions are real analytic, and form a complete system in L₂ Finally, the number of nodes of each eigenfunctions is estimated.     

Numerical analysis of heat and moisture transport with a finite difference method

In this article, we study a system of nonlinear parabolic partial differential equations arising from the heat and moisture transport through textile materials with phase change. A splitting finite difference method with semi‐implicit Euler scheme in time direction is proposed for solving the system of equations. We prove the existence and uniqueness of a classical positive solution to the parabolic system as well as the existence and uniqueness of a positive solution to the splitting finite difference system. We provide optimal error estimates for the splitting finite difference system under the condition that the mesh size and time step size are smaller than a positive constant which solely depends upon the physical parameters involved. Numerical results are presented to confirm our theoretical analysis. © 2012 Wiley Periodicals, Inc. Numer Methods Partial Differential Eq 2013     

A characterization of some subsets of Schechter's essential spectrum and application to singular transport equation

The purpose of this paper is to provide a detailed treatment of some subsets of Schechter's essential spectrum of closed, densely defined linear operators subjected to additive perturbations. Our results are used to describe the essential approximate point spectrum and the essential defect spectrum of singular neutron transport operators in bounded geometries.     

一类抽象动力系统的C0群性质及其在迁移理论中的应用

本文研究一类抽象动力系统的性质.使用Hilbert空间的分解方法,获得了主算子的谱和相应的群的表示;使用有界线性算子的扰动理论,获得了抽象动力算子的谱分解.作为应用,研究了迁移理论中的一类积-微分方程.     

On convection in a fluid filling the cavity of a moving solid body

The problem of simultaneous motion about a fixed point O of a solid body and unevenly heated viscous incompressible fluid completely filling a finite cavity of the body is considered in linear formulation. The center of mass of the system body plus fluid in the state of mechanical equilibrium is assumed to coincide with point O. The theorem on solvability of the Cauchy problem for small unsteady equilibrium perturbations is proved, and normal perturbations and the spectrum of the problem arising in the analysis of such perturbations are investigated. It is shown that the whole spectrum consists of normal eigenvalues and lies in some half-band containing the real axis. It is shown that the respective system of root vectors is complete. Properties of the spectrum and the dependence on Rayleigh numbers are investigated. Rayleigh numbers for which the real parts of eigenvalues are positive,i.e. when the generated oscillating normal perturbations are damped in time, are evaluated in the case of the fluid being heated from below and above.     

On the peripheral spectrum of positive operators

This paper contributes to the analysis of the peripheral (point) spectrum of positive linear operators on Banach lattices. We show that, under appropriate growth and regularity conditions, the peripheral point spectrum of a positive operator is cyclic and that the corresponding eigenspaces fulfil a certain dimension estimate. A couple of examples demonstrates that some of our theorems are optimal. Our results on the peripheral point spectrum are then used to prove a sufficient condition for the peripheral spectrum of a positive operator to be cyclic; this generalizes theorems of Lotz and Scheffold.     

Hypocoercivity of the relativistic Boltzmann and Landau equations in the whole space

We study the hypocoercivity property for some kinetic equations in the whole space and obtain the optimal convergence rates of solutions to the equilibrium state in some function spaces. The analysis relies on the basic energy method and the compensating function introduced by Kawashima to the classical Boltzmann equation and developed by Glassey and Strauss in the relativistic setting. It is also motivated by the recent work (Duan et al., 2008 [8]) on the Boltzmann equation by combining the spectrum analysis and energy method. The advantage of the method introduced in this paper is that it can be applied to some complicated system whose detailed spectrum is not known. In fact, only some estimates through the Fourier transform on the conservative transport operator and the dissipation of the linearized operator on the subspace orthogonal to the collision invariants are needed.     

A simple multi-scroll hyperchaotic system

We propose a simple autonomous hyperchaotic system that can generate multi-scroll attractors. The proposed system has a canonical structure, one control parameter, and a switching-type nonlinearity. If multiple breakpoints are added to the system nonlinearity, multi-scroll behavior can be obtained. We numerically demonstrate hyperchaotic behavior of the proposed system, under different nonlinearities, as its control parameter is changed. Furthermore, we study hyperchaos in the proposed system when it assumes a fractional order, and demonstrate that hyperchaotic behavior can be obtained in systems less than fourth order. Throughout the study, hyperchaos is verified by examining the Lyapunov spectrum, where the presence of multiple positive Lyapunov exponents in the spectrum is indicative of hyperchaos.     

Some useful properties of Legendre polynomials and its applications to neutron transport equation in slab geometry

In this paper, we describe a new scattering kernel and general theoretical scheme for the evolution of the discrete and continuum eigenvalue spectrum in one-dimensional slab geometry neutron transport equation. Firstly, some useful properties of the Legendre polynomials which revealed during the definition of the new scattering kernel are discussed. By using the scattering kernel in one-dimensional neutron transport equation we obtained an integral equation for angular part of the angular flux. For the solution of this integral equation and eigenvalue equations, some comments are given.     

Critical Spectrum and Spectral Mapping Theorems in Transport Theory

We give spectral mapping theorems for general neutron transport semigroups on unbounded convex domains. The mathematical analysis relies on the critical spectrum, some related stability results and Fourier analysis of transport equations.     

Spectra of positive and negative energies in the linearized NLS problem

We study the spectrum of the linearized NLS equation in three dimensions in association with the energy spectrum. We prove that unstable eigenvalues of the linearized NLS problem are related to negative eigenvalues of the energy spectrum, while neutrally stable eigenvalues may have both positive and negative energies. The nonsingular part of the neutrally stable essential spectrum is always related to the positive energy spectrum. We derive bounds on the number of unstable eigenvalues of the linearized NLS problem and study bifurcations of embedded eigenvalues of positive and negative energies. We develop the L²‐scattering theory for the linearized NLS operators and recover results of Grillakis [5] with a Fermi golden rule. © 2004 Wiley Periodicals, Inc.     

Spectral analysis of a two body problem with zero-range perturbation

We consider a class of singular, zero-range perturbations of the Hamiltonian of a quantum system composed by a test particle and a harmonic oscillator in dimension one, two and three and we study its spectrum. In fact we give a detailed characterization of point spectrum and its asymptotic behavior with respect to the parameters entering the Hamiltonian. We also partially describe the positive spectrum and scattering properties of the Hamiltonian.     

Boundary conditions of Sturm-Liouville operators with mixed spectra

We study bounds on averages of spectral functions corresponding to Sturm-Liouville operators on the half line for different boundary conditions. As a consequence constraints are obtained which imply existence of singular spectrum embedded in a.c. spectrum for sets of boundary conditions with positive measure and potentials vanishing in an interval [0,N]. These constraints are related to estimates on the measure of sets where the spectral density is positive.     

Properties of the Schrödinger Operator Spectrum in a Magnetic Field

The properties of the spectrum of the Schrödinger operator with magnetic and electric potentials are investigated. We prove that the operator has no positive eigenvalues and its spectrum is absolutely continuous on the positive semiaxis.     

On the numerical solution of ill‐conditioned linear systems by regularization and iteration

We propose to reduce the (spectral) condition number of a given linear system by adding a suitable diagonal matrix to the system matrix, in particular by shifting its spectrum. Iterative procedures are then adopted to recover the solution of the original system. The case of real symmetric positive definite matrices is considered in particular, and several numerical examples are given. This approach has some close relations with Riley's method and with Tikhonov regularization. Moreover, we identify approximately the aforementioned procedure with a true action of preconditioning.     

板模型迁移算子的渐近点谱及其聚点(英文)

In this paper we investigate the asymptotic spectrum and accumulation of a transport operator A in slab geometry with continuous energy, anisotropic scattering and inhomogeneous medium. In L^p （1 ≤ p 〈 ＋∞） space we show a series of new results for the asymptotic point spectrum and accumulation of A.     

正压缩算子Jordan积的最大最小谱点

主要讨论了正压缩算子Jordan积的谱,刻画了正压缩算子Jordan积的最大最小谱点以及正交投影Jordan积的谱.     

迁移算子离散本征值及其聚点的分布

讨论了各向异性、能量相关、非均匀有界凸体介质中迁移算子的谱,在省略某些不符合实际的 特殊条件的情况下,对这类算子离散本征值及其聚点的位置分布,同样获得了一个类似的结果.     

种群细胞增生中一类Rotenberg模型研究

本文在Lp（1（≤）p＜＋∞）空间上,研究了种群细胞增生中一类具非光滑边界条件的Rotenberg模型,讨论了这类模型相应的迁移算子的谱分析,证明了该迁移算子的本征值的存在性,得到了该迁移算子的谱在某半平面上仅由有限个具有限代数重数的离散本征值组成等结果.