Isoperimetric Constants of Infinite Plane Graphs

   Abstract. Let G be an infinite locally finite plane graph with one end and let H be a finite plane subgraph of G . Denote by a(H) the number of finite faces of H and by l(H) the number of the edges of H that are on the boundary of the infinite face or a finite face not in H . Define the isoperimetric constant h (G) to be inf _H l(H) / a(H) and define the isoperimetric constant h (δ) to be inf _G h (G) where the infimum is taken over all infinite locally finite plane graphs G having minimum degree δ and exactly one end. We establish the following bounds on h (δ) for δ ≥ 7 :

Symmetry Reductions of the Combined KdV—mKdV Equation

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Linear low-rank approximation and nonlinear dimensionality reduction

We present our recent work on both linear and nonlinear data reduction methods and algorithms: for the linear case we discuss results on structure analysis of SVD of column-partitioned matrices and sparse low-rank approximation; for the nonlinear case we investigate methods for nonlinear dimensionality reduction and manifold learning. The problems we address have attracted great deal of interest in data mining and machine learning.     

三维介观超导环涡旋态的研究

通过数值求解非线性金兹堡-朗道(G-L)方程组,研究了三维介观超导环中的涡旋态。发现了在细环中只能存在巨涡旋态,以及存在顺磁、抗磁迈斯纳效应和间隙性超导现象。在粗环中,发现了多涡旋态和巨涡旋态共存的混合态。相应讨论有助于理解介观超导环中涡旋态相变。     

Electron correlation forms in the LiH molecule—fermi correlation

Correlation forms for electrons of the same spin small molecules are analyzed by taking the LiH molecule as an example. The analyses are carried out on the basis of the reduced density matrix theory and for both the ground state and the first excited state. It turns out that although there is a certain similarity, the correlated motions of parallel-spin electrons in this four-electron molecule are more complicated than those found for the two-electron molecule. The correlation forms are not always constant. They vary essentially from one state to another, but are insensitive to fairly large changes of the internuclear distance for a given state.     

A novel route to prepare pH- and temperature-sensitive nanogels via a semibatch process

A novel method via a semibatch process in the absence of surfactant has been adopted to prepare pH- and temperature-sensitive nanogels. The shape, charge distribution, temperature, and pH-induced volume phase transition behavior of the latexes were investigated by scanning electronic microscopy, zeta potentials, dynamic laser light scattering, and UV/vis spectroscopy. It was found that, in the absence of surfactant, with increasing the amount of AAc from 5 to 20 mol% of N-isopropylacrylamide (NIPAM), the hydrodynamic diameters (D_H) decrease from 230 to 60 nm. With increasing pH value from 3 to 11, the D_H values increase slightly, which is different than the dramatic increase seen when using a conventional batch method with a range from 680 to 1700 nm. However, at pH 3, the turbidity curves of these kinds of particles increase dramatically at temperatures between 33 and 37 °C, while remaining constant at first and then increasing directly at pH 11. Furthermore, the distribution of carboxylic groups located not only on the interior but also on the exterior of colloidal particles as a result of adoption of the semibatch method, other than simple surface distribution of poly(NIPAM-co-AAc) latexes via the batch method.     

An optimal insurance strategy for an individual under an intertemporal equilibrium

In this paper, we discuss how a risk-averse individual under an intertemporal equilibrium chooses his/her optimal insurance strategy to maximize his/her expected utility of terminal wealth. It is shown that the individual’s optimal insurance strategy actually is equivalent to buying a put option, which is written on his/her holding asset with a proper strike price. Since the cost of avoiding risk can be seen as a risk measure, the put option premium can be considered as a reasonable risk measure. Jarrow [Jarrow, R., 2002. Put option premiums and coherent risk measures. Math. Finance 12, 135-142] drew this conclusion with an axiomatic approach, and we verify it by solving the individual’s optimal insurance problem.