Effects of a Trust Mechanism on Complex Adaptive Supply Networks: An Agent-Based Social Simulation Study

This paper models a supply network as a complex adaptive system (CAS), in which firms or agents interact with one another and adapt themselves. And it applies agent-based social simulation (ABSS), a research method of simulating social systems under the CAS paradigm, to observe emergent outcomes. The main purposes of this paper are to consider a social factor, trust, in modeling the agents\' behavioral decision-makings and, through the simulation studies, to examine the intermediate self-organizing processes and the resulting macro-level system behaviors. The simulations results reveal symmetrical trust levels between two trading agents, based on which the degree of trust relationship in each pair of trading agents as well as the resulting collaboration patterns in the entire supply network emerge. Also, it is shown that agents\' decision-making behavior based on the trust relationship can contribute to the reduction in the variability of inventory levels. This result can be explained by the fact that mutual trust relationship based on the past experiences of trading diminishes an agent\'s uncertainties about the trustworthiness of its trading partners and thereby tends to stabilize its inventory levels.Complex Adaptive System, Agent-Based Social Simulation, Supply Network, Trust

Uppers to zero and semistar operations in polynomial rings

Given a stable semistar operation of finite type $\star$ on an integral domain $D$, we show that it is possible to define in a canonical way a stable semistar operation of finite type $[\star]$ on the polynomial ring $D[X]$, such that $D$ is a $\star$-quasi-Pr\"ufer domain if and only if each upper to zero in $D[X]$ is a quasi-$[\star]$-maximal ideal. This result completes the investigation initiated by Houston-Malik-Mott \cite[Section 2]{hmm} in the star operation setting. Moreover, we show that $D$ is a Pr\"ufer $\star$-multiplication (resp., a $\star$-Noetherian; a $\star$-Dedekind) domain if and only if $D[X]$ is a Pr\"ufer $[\star]$-multiplication (resp., a $[\star]$-Noetherian; a $[\star]$-Dedekind) domain. As an application of the techniques introduced here, we obtain a new interpretation of the Gabriel-Popescu localizing systems of finite type on an integral domain $D$ (Problem 45 of \cite{cg}), in terms of multiplicatively closed sets of the polynomial ring $D[X]$

An overring-theoretic approach to polynomial extensions of star and semistar operations

Call a semistar operation $\ast$ on the polynomial domain $D[X]$ an extension (respectively, a strict extension) of a semistar operation $\star$ defined on an integral domain $D$, with quotient field $K$, if $E^\star = (E[X])^{\ast}\cap K$ (respectively, $E^\star [X]= (E[X])^{\ast}$) for all nonzero $D$-submodules $E$ of $K$. In this paper, we study the general properties of the above defined extensions and link our work with earlier efforts, centered on the stable semistar operation case, at defining semistar operations on $D[X]$ that are "canonical" extensions (or, "canonical" strict extensions) of semistar operations on $D$

The Sharp Log-Sobolev Inequality on a Compact Interval

We provide a proof of the sharp log-Sobolev inequality on a compact interval