Integral-Type Darboux Transformations for the mKdV Hierarchy with Self-Consistent Sources

We present integral-type Darboux transformation for the mKdV hierarchy and for the mKdV hierarchy withself-consistent sources. In contrast with the normal Darboux transformation, the integral-type Darboux transformationscan offer non-auto-Backlund transformation between two (2n 1)-th mKdV equations with self-consistent sources withdifferent degrees. This kind of Darboux transformation enables us to construct the N-soliton solution for the mKdVhierarchy with self-consistent sources. We also propose the formulas for the m times repeated integral-type Darbouxtransformations for both mKdV hierarchy and mKdV hierarchy with self-consistent sources.     

推广的Kantorovich算子在Ba空间中的逼近

利用Ditzian-Totik光滑模,研究了推广的Kantorovich算子在Ba空间中的逼近,得到逼近的正定理与等价定理.所得结果改进、推广和统一了一些作者的结果.     

Counting unrooted maps on the plane

A planar map is a 2-cell embedding of a connected planar graph, loops and parallel edges allowed, on the sphere. A plane map is a planar map with a distinguished outside (“infinite”) face. An unrooted map is an equivalence class of maps under orientation-preserving homeomorphism, and a rooted map is a map with a distinguished oriented edge. Previously we obtained formulae for the number of unrooted planar n-edge maps of various classes, including all maps, non-separable maps, eulerian maps and loopless maps. In this article, using the same technique we obtain closed formulae for counting unrooted plane maps of all these classes and their duals. The corresponding formulae for rooted maps are known to be all sum-free; the formulae that we obtain for unrooted maps contain only a sum over the divisors of n. We count also unrooted two-vertex plane maps.     

Theoretical and numerical analysis on multispectral bioluminescence tomography

Recently, molecular imaging has been rapidly developed to studyphysiological and pathological processes in vivo at the cellularand molecular levels. Among molecular imaging modalities, opticalimaging has attracted a major attention for its unique advantages.In this paper, we establish a mathematical framework for multispectralbioluminescence tomography (BLT) that allows simultaneous studiesof multiple optical reporters. We show solution existence, uniquenessand continuous dependence on data as well as the limiting behaviourswhen the regularization parameter approaches zero or when thepenalty parameter approaches infinity. Then, we propose twonumerical schemes for multispectral BLT and derive error estimatesfor the corresponding solutions.     

多元线性回归法在互联网网间结算中的应用

本文建立一个理论模型研究互联网互联结算的问题。文章利用多元线性回归法对互联网骨干网运营商(IBPs:Internet Backbone Providers)的网络价值进行评估,利用IBPs各自的网络价值对其交换速率进行加权,从而得出网络价值加权速率,依据这个速率进行结算既可以反映了每个网络对互联的贡献程度,又反映了在互联中对网络资源的被占用程度。     

Optical Glucose Monitoring Based on Femtosecond Two-Color Pulse Interferometry

We demonstrate the potential of femtosecond two-color pulse interferometry for in vitro optical glucose monitoring, by dispersion of the group refractive index in a glucose solution sample with respect to a red-color light and a blue-color light. By comparison with femtosecond one-color pulse interferometry, the basic performance of the present system with regard to sensitivity, quantitativeness, and tolerance to surrounding disturbances, is evaluated. The resulting accuracy and precision of glucose determination are 77 and 118mg/dl for 10-mm-sample-thickness, respectively. This near-common-path configuration of the two-color pulse light provides good stability to fluctuations of sample temperature, which is important in clinical applications. Considering the performance of femtosecond two-color pulse interferometry as an optical glucose sensor, a suitable measurement site for in vivo optical glucose monitoring is discussed.     

Compact Dipole Antenna for Terrestrial Digital Multimedia Broadcasting Service

A compact dipole antenna for the terrestrial digital multimedia broadcasting (TDMB) application is presented. The length of the antenna is about 0.06λ at the TDMB resonance frequency of 190 MHz. Miniaturization of the antenna is achieved by using meander structures and lumped elements. The proposed antenna has two resonance frequencies and covers the TDMB band from 174 MHz to 216 MHz in Korea. The antenna has good impedance bandwidth and radiation characteristics for the TDMB. The experimental results of the designed dipole antenna are presented and analyzed.     

线性常微分方程的保线性变换及其应用

研究了线性常微分方程的保线性变换，得到任意两个二阶线性常微分方程等价的条件，并用于求解一类二阶线性变系数齐次常微分方程．对数学物理方法教学中怎样通过适当的变换把给定的二阶线性变系数齐次常微分方程化为可解的方程给出了合理解释。     

Sobolev-Type Classes of Functions with Values in a Metric Space. II

We prove equivalence of the definitions by the author and by Korevaar and Schoen of the Sobolev classes of mappings of a domain of an arithmetic n-dimensional space to a metric space.     

Eigenvalue and stability of singular differential delay systems

The eigenvalue and the stability of singular differential systems with delay are considered. Firstly we investigate some properties of the eigenvalue, then give the exact exponential estimation for the fundamental solution, and finally discuss the necessary and sufficient condition of uniform asymptotic stability.