Calculus of functors and model categories

The category of small covariant functors from simplicial sets to simplicial sets supports the projective model structure [B. Chorny, W.G. Dwyer, Homotopy theory of small diagrams over large categories, preprint, 2005]. In this paper we construct various localizations of the projective model structure and also give a variant for functors from simplicial sets to spectra. We apply these model categories in the study of calculus of functors, namely for a classification of polynomial and homogeneous functors. In the n-homogeneous model structure, the nth derivative is a Quillen functor to the category of spectra with Σn-action. After taking into account only finitary functors—which may be done in two different ways—the above Quillen map becomes a Quillen equivalence. This improves the classification of finitary homogeneous functors by T.G. Goodwillie [T.G. Goodwillie, Calculus. III. Taylor series, Geom. Topol. 7 (2003) 645-711 (electronic)].     

Optimal Investment Strategies for an Insurer with SAHARA Utility

In this paper, we consider the optimal investment strategy which maximizes the utility of the terminal wealth of an insurer with SAHARA utility functions. This class of utility functions has non-monotone absolute risk aversion, which is more flexible than the CARA and CRRA utility functions. In the case that the risk process is modeled as a Brownian motion and the stock process is modeled as a geometric Brownian motion, we get the closed-form solutions for our problem by the martingale method for both the constant threshold and when the threshold evolves dynamically according to a specific process. Finally, we show that the optimal strategy is state-dependent.     

ZnSe/SiO2复合薄膜光学常数与荧光光谱的研究

采用溶胶-凝胶工艺与原位生长技术，制备了ZnSe/SiO₂复合薄膜.X射线衍射分 析表明薄膜中ZnSe晶体呈立方闪锌矿结构.X射线荧光分析结果显示薄膜中Zn与Se摩尔比为1 ∶1.01—1∶1.19.利用场发射扫描电子显微镜观察了复合薄膜的表面形貌，结果表明复合薄 膜表面既存在尺寸约为400nm的ZnSe晶粒，也存在尺寸小于100nm的ZnSe晶粒.利用椭偏仪测 量了薄膜椭偏角Ψ，Δ与波长λ的关系，采用Maxwell-Garnett有效介质理论对薄膜的光学 常数、厚度、气孔率、ZnS 关键词： 2复合薄膜')" href="#">ZnSe/SiO₂复合薄膜 光学性质 椭偏光度法 荧光光谱     

Palladium catalyzed mild reduction of α,β-unsaturated compounds by triethylsilane

The palladium(II) chloride/triethylsilane system has been successfully applied for the selective hydrogenation of the carbon-carbon double bond of α,β-unsaturated ketones to yield the corresponding saturated carbonyl compounds. The reaction takes place under mild conditions and affords high yields.     

Regular variation of order 1 nonlinear AR-ARCH models

We prove both geometric ergodicity and regular variation of the stationary distribution for a class of nonlinear stochastic recursions that includes nonlinear AR-ARCH models of order 1. The Lyapounov exponent for the model, the index of regular variation and the spectral measure for the regular variation all are characterized by a simple two-state Markov chain.     

An Extension Landau-Lifshitz Model in Studying Soft Ferromagnetic Films

In this paper, we propose a model in studying soft ferromagnetic films, which is readily accessible experimentally. By using penalty approximation and compensated compactness, we prove that the dynamical equation in thin film has a local weak solution. Moreover, the corresponding linear equation is also dealt with in great detail.     

Bivariate Recursive Equations on Excess-of-loss Reinsurance

This paper investigates bivariate recursive equations on excess-of-loss reinsurance. For an insurance portfolio, under the assumptions that the individual claim severity distribution has bounded continuous density and the number of claims belongs to R1 （a, b） family, bivariate recursive equations for the joint distribution of the cedent＇s aggregate claims and the reinsurer＇s aggregate claims are obtained.     

Ultra <Emphasis Type="Italic">LI</Emphasis>-ideals in lattice implication algebras and <Emphasis Type="Italic">MTL</Emphasis>-algebras

A mistake concerning the ultra LI-ideal of a lattice implication algebra is pointed out, and some new sufficient and necessary conditions for an LI-ideal to be an ultra LI-ideal are given. Moreover, the notion of an LI-ideal is extended to MTL-algebras, the notions of a (prime, ultra, obstinate, Boolean) LI-ideal and an ILI-ideal of an MTL-algebra are introduced, some important examples are given, and the following notions are proved to be equivalent in MTL-algebra: (1) prime proper LI-ideal and Boolean LI-ideal, (2) prime proper LI-ideal and ILI-ideal, (3) proper obstinate LI-ideal, (4) ultra LI-ideal. This work was supported by the Zhejiang Provincial Natural Science Foundation of China (Grant No. Y605389) and K. C. Wong Magna Fund in Ningbo University.     

Confirmation of sable QTL that modifies the effects of the Ay allele on yellow coat color on mouse chromosome 1

F₁-A^y mice between RR (aabbCC) and C57BL/6J-A^y (A^yaBBCC) have a much darker yellow coat color than do C57BL/6J-A^y. Quantitative trait locus (QTL) analysis was carried out to identify genes responsible for the darker modification of the yellow coat color (this has been traditionally termed “sable”). A significant sable QTL was identified on chromosome 1 (Dmyaq4, LOD score 15.5 for lightness, and 13.4 for color difference), in a chromosomal position similar to that of Dmyaq2, a sable QTL previously identified in C3H/HeJ. Another significant sable QTL was identified on chromosome 4 (Dmyaq5, LOD score 5.6 for lightness, and 4.3 for color difference) near the tyrosinase-related protein 1 (Tyrp1) locus. The effect of Dmyaq5 was significant only in the presence of the RR allele at Dmyaq4, suggesting that the Dmyaq4 (as well as Dmyaq2) is a novel coat color gene that may act up-stream of Tyrp1 signaling to increase eumelanin production.