On application of asymptotic generalized discrepancy principle to the analysis of epidemiology models

Various implementations of the discrepancy principle (DP) for linear ill-posed problems are given in a large number of papers. In all of these papers, the DP has been justified for special types of regularization strategies. In our paper, a unified approach to the construction of the DP is presented that does not require any special structure of the regularizing operator. In that respect, the new method generalizes all prior results on the DP principle for linear irregular operator equations with noisy data. The efficiency of the proposed scheme is demonstrated for a parameter identification problem in avian influenza. In solving this particular inverse problem, it turned out to be beneficial to use some regularization strategies, for which the earlier (structure-based) discrepancy principles were not applicable. This motivated the development of a novel DP put forth in the current paper.     

Solving nonlinear inverse problems by evolution equations based on Gauss–Newton methods

In this article, we solve nonlinear inverse problems by an evolution equation method which can be viewed as the continuous analogue of the Gauss–Newton method. Under certain conditions we prove the convergence and derive the rate of convergence when the discrepancy principle is coupled.     

On v-Domains and Star Operations

Let * be a star operation on an integral domain D. Let f (D) be the set of all nonzero finitely generated fractional ideals of D. Call D a *-Prüfer (respectively, (*, v)-Prüfer) domain if (FF ^?1)* = D (respectively, (F ^v F ^?1)* = D) for all F ∈  f (D). We establish that *-Prüfer domains (and (*, v)-Prüfer domains) for various star operations * span a major portion of the known generalizations of Prüfer domains inside the class of v-domains. We also use Theorem 6.6 of the Larsen and McCarthy book [30 Larsen , M. D. , McCarthy , P. J. ( 1971 ). Multiplicative Theory of Ideals . New York : Academic Press . [Google Scholar]], which gives several equivalent conditions for an integral domain to be a Prüfer domain, as a model, and we show which statements of that theorem on Prüfer domains can be generalized in a natural way and proved for *-Prüfer domains, and which cannot be. We also show that in a *-Prüfer domain, each pair of *-invertible *-ideals admits a GCD in the set of *-invertible *-ideals, obtaining a remarkable generalization of a property holding for the “classical” class of Prüfer v-multiplication domains. We also link D being *-Prüfer (or (*, v)-Prüfer) with the group Inv*(D) of *-invertible *-ideals (under *-multiplication) being lattice-ordered.     

Stability and Clifford Regularity with Respect to Star Operations

In the last few years, the concepts of stability and Clifford regularity have been fruitfully extended by using star operations. In this article we deepen the study of star stable and star regular domains and relate these two classes of domains to each other.     

A superconvergent universality induced by non-associativity

The star products in symbolic dynamics, as effective algebraic operations for describing self-similar bifurcation structure in classical dynamical systems, are found to have either associativity or non-associativity. In this Letter, non-associative star products in trimodal iterative dynamical systems are considered. As the left and right operations have different effects, right-associative star products break the conventional Feigenbaum's metric universality. Through high precision parallel computation, it is found that period-p-tupling bifurcation processes described by right-associative star products exhibit a superconvergent universality of double exponential form.     

Core-shell type multiarm star poly(ε-caprolactone) with high molecular weight hyperbranched polyethylenimine as core: Synthesis, characterization and encapsulation properties

Core-shell type multiarm star copolymers with poly(ε-caprolactone) (PCL) as shells and hyperbranched polyethylenimine (PEI) as core have been successfully prepared by the Sn(Oct)₂ catalyzed ring-opening polymerization of ε-caprolactone (CL) using high molecular weigh PEIs directly as macroinitiators. The initiation efficiency is in the range of 91-95% for PEI with M_n = 10⁴ (PEI10K) and only around 60% for PEI with M_n = 2.5 × 10⁴ (PEI25K), leading to star polymers with an average arm number in the range of 155-276. The thermal property of the obtained multiarm star polymers were also investigated by DSC. The melting and crystallization temperatures of the star polymers increase as the PCL arm length increases when the PEI core is fixed. The fusion enthalpy, crystalline enthalpy and degree of crystallinity values of the star polymers with PEI10K core are less than those with PEI1.8K core. Due to the polarity difference between PCL arm and PEI core, the resulting multiarm star polymers can act as inverted micellar nanocapsules capable of extracting and encapsulating water soluble guests. Increasing the size and polarity of the hydrophilic PEI core of the star nanocapsules are two effective ways to enhance their hydrophilic guest encapsulation capacity. Increasing the hydrophobic PCL arm length can increase the molar ratio, whereas reduce the weight ratio of the encapsulated hydrophilic guests to the star nanocapsules. Unexpectedly, the obtained nanocapsules can entrap the bigger size hydrophilic congo red guests more than the smaller size methyl orange.     

星模拟器星点能量中心修正方法的研究

对星模光学系统中各种像差对几何中心位置的影响及像差对显示星点能量中心位置造成的偏差进行了分析与综合评估.分析结果表明,视场位置越大的星点产生的像点能量越不均匀,重心偏移越明显,系统中慧差和畸变对于星点能量中心影响较大.根据球面镜组成的共轴光学系统性质可知,能量中心的偏移发生在星点所在极半径方向上,因此提出了一种基于极坐标的星点位置修正方法,只需在星点所在方向对极半径进行修正.该方法简化了基于二维坐标轴分区修正的过程,减少了数据计算量.利用极坐标修正方法对星模拟器修正前后的单星位置误差进行了测试,实验结果表明极坐标修正过程较以往修正方法简单快捷,且修正结果更加准确.     

n-Star modules over ring extensions

We give conditions under which an n-star module extends to an n-star module, or an n-tilting module, over a ring extension R of A. In case that R is a split extension of A by Q, we obtain that is a 1-tilting module (respectively, a 1-star module) if and only if is a 1-tilting module (respectively, a 1-star module) and generates both and (respectively, generates ), where is an injective cogenerator in the category of all left A-modules. These extend results in [I. Assem, N. Marmaridis, Tilting modules over split-by-nilpotent extensions, Comm. Algebra 26 (1998) 1547–1555; K.R. Fuller, *-Modules over ring extensions, Comm. Algebra 25 (1997) 2839–2860] by removing the restrictions on R and Q.     

Cross -sections of star bodies and dual mixed volumes

In this paper, we establish an extension of Funk's section theorem. Our result has the following corollary: If is a star body in whose central -slices have the same volume (with appropriate dimension) as the central -slices of a centered body , then the dual quermassintegrals satisfy , for any , with equality if and only if . The case that is a centered body implies Funk's section theorem.