Modules-at-infinity for quantum vertex algebras

This is a sequel to \cite{li-qva1} and \cite{li-qva2} in a series to study vertex algebra-like structures arising from various algebras such as quantum affine algebras and Yangians. In this paper, we study two versions of the double Yangian $DY_{\hbar}(sl_{2})$, denoted by $DY_{q}(sl_{2})$ and $DY_{q}^{\infty}(sl_{2})$ with $q$ a nonzero complex number. For each nonzero complex number $q$, we construct a quantum vertex algebra $V_{q}$ and prove that every $DY_{q}(sl_{2})$-module is naturally a $V_{q}$-module. We also show that $DY_{q}^{\infty}(sl_{2})$-modules are what we call $V_{q}$-modules-at-infinity. To achieve this goal, we study what we call $\S$-local subsets and quasi-local subsets of \Hom (W,W((x^{-1}))) for any vector space $W$, and we prove that any $\S$-local subset generates a (weak) quantum vertex algebra and that any quasi-local subset generates a vertex algebra with $W$ as a (left) quasi module-at-infinity. Using this result we associate the Lie algebra of pseudo-differential operators on the circle with vertex algebras in terms of quasi modules-at-infinity.Comment: Latex, 48 page

Entropy analysis on convective film flow of power-law fluid with nanoparticles along an inclined plate

Entropy generation in a two-dimensional steady laminar thin film convection flow of a non-Newtonian nanofluid (Ostwald-de-Waele-type power-law fluid with embedded nanoparticles) along an inclined plate is examined theoretically. A revised Buongiorno model is adopted for nanoscale effects, which includes the effects of the Brownian motion and thermophoresis. The nanofluid particle fraction on the boundary is passively rather than actively controlled. A convective boundary condition is employed. The local nonsimilarity method is used to solve the dimensionless nonlinear system of governing equations. Validation with earlier published results is included. A decrease in entropy generation is induced due to fluid friction associated with an increasing value of the rheological power-law index. The Brownian motion of nanoparticles enhances thermal convection via the enhanced transport of heat in microconvection surrounding individual nanoparticles. A higher convective parameter implies more intense convective heating of the plate, which increases the temperature gradient. An increase in the thermophoresis parameter decreases the nanoparticle volume fraction near the wall and increases it further from the wall. Entropy generation is also reduced with enhancement of the thermophoresis effect throughout the boundary layer

Single or dual sourcing: decision-making in the presence of supply chain disruption risks

The focus of this paper is placed on evaluating the impacts of supply disruption risks on the choice between the famous single and dual sourcing methods in a two-stage supply chain with a non-stationary and price-sensitive demand. The expected profit functions of the two sourcing modes in the presence of supply chain disruption risks are first obtained, and then compared so that the critical values of the key factors affecting the final choice are identified. Finally, the sensitivity of the buyer's expected profit to various input factors is examined through numerical examples, which provide guidelines for how to use each sourcing method.Supply chain disruption Sourcing Supply management Risk management Sensitivity analysis Decision-making/process