Subweakly Biased Pairs and Jungck Contractions with Applications

The existence of common fixed point results for a weakly biased pair under Jungck contraction is established. We define a new class of subweakly biased pair which properly contains the classes of C _q -commuting, pointwise R-subweakly commuting and R-subweakly commuting maps and establish common fixed point results for this class of maps. As applications several invariant best approximation results are proved which unify, extend, and complement the well-known results.     

The Limits of Common Cause Approach to EPR Correlation

It is often argued that no local common cause models of EPR correlation exist. However, Szabó and Rédei pointed out that such arguments have the tacit assumption that plural correlations have the same common causes. Furthermore, Szabó showed that for EPR correlation a local common cause model in his sense exists. One of his requirements is that common cause events are statistically independent of apparatus settings on each side. However, as Szabó knows, to meet this requirement does not entail that different combinations of common cause events (e.g. meet and join in lattice-theoretic terminology) are statistically independent of measurement settings. This further condition is formulated in two ways. First, the apparatus settings are completely independent of such combinations. Second, the apparatus settings on each side are independent of such combinations. Does a common cause model which meets the former and the latter respectively exist? This problem is considered. In particular, the latter version is Szabó’s and Rédei’s open problem. Negative answers are given to both versions.     

Electrospinnability study of pea (Pisum sativum) and common bean (Phaseolus vulgaris L.) using the conformational and rheological behavior of their protein isolates

Pea protein isolate (PPI) and bean protein concentrate (BPC) were evaluated as fiber-forming vegetal source materials through electrospinning using various solvents. The effects of hexafluoroisopropanol (HFIP), trifluoroethanol (TFE), trifluoroacetic acid (TFA), formic acid (FA) and water on rheological and conformational properties of the protein solutions were determined. The morphology and molecular organization of the electrospun structures were studied. All PPI and BPC solutions displayed pseudoplastic behavior. Circular dichroism spectroscopy revealed that β-type turns and β-sheets were the dominant protein conformations in water, HFIP, and TFE. After electrospinning, most of the solutions afforded beads. Fiber-like morphologies were only obtained when BPC was dissolved in HFIP. BPC demonstrated better performance in the electrospinning process than PPI. Denaturation of the protein isolates was not sufficient to form fibers, the viscosity of the solution as well as the vapor pressure of the solvents played an important role in defining the morphology.     

A new method for assigning common spot boundaries for multiple gels in two-dimensional gel electrophoresis

The benefits of defining common spot boundaries when several gels from 2-DE are compared and analyzed have lately been stressed by both commercial software producers and users of this software. Though the importance of common spot boundaries is clearly stated, few reports exist that target this issue explicitly. In this study a method for defining common spots boundaries is developed, called the spot density method. The method consists of the following steps: segmentation and spot identification on each individual gel, transferring the spot-center coordinates for all gels onto a single new gel, collecting spot centers clustered together in the new gel and finally assigning pixels and new spot boundaries based on the spots in each cluster. The method is compared to a synthetic gel approach, and validated by visual inspection of three representative areas in the gels. The gel images need to be aligned prior to segmentation and spot identification, but the method can be used regardless of the choice of segmentation procedure. This makes the method an easy extension to existing methods for spot identification and matching. Conclusions based on the visual inspection are that the spot density method identifies partly overlapping spots and low-intensity spots better than the synthetic gel approach.     

特征值反问题的唯一性

证明了由特征值及特征向量反求矩阵时,特征值在对角矩阵中的排序可以是任意的,只须将对应特征向量作相应排序,所得矩阵唯一。对于重特征值的线性无关的特征向量可任意选取,所得矩阵唯一。     

满足AB=αBA的方阵A,B和AB的特征值的性质及其联系

设m阶方阵A,B满足AB=αBA,其中α=e~(2kπi/n),k,n为互素整数且n≥2.证明了σ(AB)■{α~(j-((n-1)/2))λ_AλB|λA∈σ(A),λB∈σ(B),j=0,1,…,n-1}及其它相关的结果,其中σ(A)表示方阵A的所有特征值的集合.     

A New Hybrid Iteration Method for I-Asymptotically Nonexpansive Mappings

In this article, convergence theorems are established for a new hybrid iteration for a finite family of I-asymptotically nonexpansive mappings. Our results extend, generalize, and unify various known results in the existing literature.     

Convergence Theorems for Pointwise Asymptotically Strict Pseudo-Contractions in Hilbert Spaces

A new class of contractive mappings called pointwise asymptotically ?-strict pseudo-contractions in Hilbert spaces is introduced and weak convergence of the sequence generated by Mann's iterative scheme to a fixed point of a uniformly Lipschitzian and pointwise asymptotically ?-strict pseudo-contractive mapping T in a Hilbert space is established. Also, a new kind of monotone hybrid method which is a modification of Mann's iterative scheme for finding a common fixed point of an infinitely countable family of uniformly Lipschitzian and pointwise asymptotically ?-strict pseudo-contractive mappings is proposed. Strong convergence of the sequence generated by the proposedmonotone hybrid method for an infinitely countable family of uniformly Lipschitzian and pointwise asymptotically ?-strict pseudo-contractive mappings in a Hilbert space is also shown. The results presented in this article extend and improve some known results in the literature.     

Optimal mean–variance investment and reinsurance problems for the risk model with common shock dependence

In this paper, we study the optimal investment–reinsurance problems in a risk model with two dependent classes of insurance business, where the two claim number processes are correlated through a common shock component. Under the criterion of mean–variance, two cases are considered: One is the optimal mean–variance problem with bankruptcy prohibition, i.e., the wealth process of the insurer is not allowed to be below zero at any time, which is solved by standard martingale approach, and the closed form solutions are derived; The other is the optimal mean–variance problem without bankruptcy prohibition, which is discussed by a very different method—stochastic linear–quadratic control theory, and the explicit expressions of the optimal results are obtained either. In the end, a numerical example is given to illustrate the results and compare the values in the two cases.