Extension of Isometries Between the Unit Spheres of Normed Space E and C（Ω）

In this paper, we study the extension of isometries between the unit spheres of normed space E and C（Ω）. We obtain that any surjective isometry between the unit spheres of normed space E and C（Ω） can be extended to be a linear isometry on the whole space E and give an affirmative answer to the corresponding Tingley＇s problem （where Ω be a compact metric space）.     

Journey Making group workshops as a research tool

Problem-structuring group workshops can be used in organizations as a consulting tool and as a research tool. One example of the latter is using a problem-structuring method (PSM) to help a group tackle an organizational issue; meanwhile, researchers collect the participants’ initial views, discussion of divergent views, the negotiated agreement, and the reasoning for outcomes emerging. Technology can help by supporting participants in freely sharing their opinions and by logging data for post-workshop analyses. For example, computers let participants share views anonymously and without being influenced by others (as well as logging those views), and video-cameras can record discussions and intra-group dynamics. This paper evaluates whether technology-supported Journey Making workshops can be effective research tools that can capture quality research data when compared against theoretical performance benchmarks and other qualitative research tools.     

Rheological properties of binary associating polymers

Dynamics of associating polymer solutions above the reversible gelation point are studied. Each macromolecule consists of a soluble backbone (B) and a small fraction of specific strongly interacting groups (A or C stickers) attached to B. A mixture of B–A and B–C associating polymers with 1:1 stoichiometric ratio is considered. As a result of AC association, the polymers reversibly gelate above the overlap concentration. It is shown that (1) the network strands are linear complexes (double chains) of B–A and B–C; (2) “diffusion” of the network junction points is characterized by an apparent activation energy, which can be significantly higher than the energy of one AC bond; (3) most importantly, the randomness of sticker distribution along the chain can significantly slow down the network relaxation leading to a markedly non-Maxwellian viscoelastic behavior. The theory elucidates the most essential features of rheological behavior of polysaccharide associating systems (with A = adamantyl moiety, C = β-cyclodextrin, B = either chitosan or hyaluronan) including similar behavior of G ^′ and G ^″ in a wide frequency range, strong temperature dependence of the characteristic frequency ω _x , and an extremely strong effect of added free stickers (fC) on the dynamics. This paper was presented at Annual European Rheology Conference (AERC) held in Hersonisos, Crete, Greece, April 27–29, 2006.     

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.     

Freedom and trying: Understanding agent-causal exertions

In this paper, I argue that trying is the locus of freedom and moral responsibility. Thus, any plausible view of free and responsible action must accommodate and account for free tryings. I then consider a version of agent causation whereby the agent directly causes her tryings. On this view, the agent is afforded direct control over her efforts and there is no need to posit—as other agent-causal theorists do—an uncaused event. I discuss the potential advantages of this sort of view, and its challenges.     

Another independent self-dual basis for the trivial variety

We give a new independent self-dual 3-basis for the trivial variety with two binary operations. Received October 24, 2006; accepted in final form January 25, 2007.     

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.     

Multisplitting Iteration Schemes for Solving a Class of Nonlinear Complementarity Problems

We consider several synchronous and asynchronous multisplitting iteration schemes for solving aclass of nonlinear complementarity problems with the system matrix being an H-matrix.We establish theconvergence theorems for the schemes.The numerical experiments show that the schemes are efficient forsolving the class of nonlinear complementarity problems.     

Time dependent analysis of finite buffer fluid flows and risk models with a dividend barrier

Based on the matrix-analytic approach to fluid flows initiated by Ramaswami, we develop an efficient time dependent analysis for a general Markov modulated fluid flow model with a finite buffer and an arbitrary initial fluid level at time 0. We also apply this to an insurance risk model with a dividend barrier and a general Markovian arrival process of claims with possible dependencies in successive inter-claim intervals and in claim sizes. We demonstrate the implementability and accuracy of our algorithms through a set of numerical examples that could also serve as test cases for comparing other solution approaches.