A Central Limit Theorem for intransitive dice

Intransive dice $D^{(1)}, \ldots, D^{(\ell)}$ are dice such that $D^{(1)}$ has advantage with respect to $D^{(2)}$, dice $D^{(2)}$ has advantage with respect to $D^{(3)}$ and so on, up to $D^{(\ell)}$, which has advantage over $D^{(1)}$. In this twofold work, we present: first, (deterministic) results on existence of general intransitive dice. Second and mainly, a central limit theorem for the vector of normalized victories of a die against the next one in the list when the faces of a die are i.i.d.\ random variables and all dice are independent, but different dice may have distinct distributions associated to, as well as they may have distinct number of faces. From this central limit theorem we derive a criteria to assure that the asymptotic probability of observing intransitive dice is null, which applies for many cases, including all continuous distributions and many discrete ones.Comment: 37 pages, 3 figure

A comparison of production control systems in a flexible flow shop

Production control in make-to-order must address the companies’ need for short delivery times and on-time deliveries. Several production control systems may be used to meet these needs. This paper presents a simulation study to evaluate the delivery performance of the TKS, GKS and POLCA production co ntrol systems, in the context of a make-to-order flexible flow shop. Since TKS is used for make-to-stock manufacturing, an adaptation of it is made to use in make-to-order. Results of a simulation study show that the adapted TKS outperforms POLCA, but performs worse than GKS. The study is a contribution for the alignment of production control theory to the industrial practice.This work had the financial support of FCT- Fundacao para a Ciencia e Tecnologia of Portugal under the project PEst2015-2020: UID/CEC/00319/2013.info:eu-repo/semantics/publishedVersio

Adsorptive potential of Zn–Al and Mg–Fe layered double hydroxides for the removal of 2–nitrophenol from aqueous solutions

Two layered double hydroxides (LDH) of the type Zn–Al and Mg–Fe were synthesized, characterized and used as adsorbents to uptake 2–nitrophenol (2–NP) from aqueous solutions. XRD, FTIR, SEM, EDS, AFM and N2 adsorption/desorption curves were used to characterize the Zn–Al–LDH and Mg–Fe–LDH. The potential of both layered double hydroxides to adsorb 2–NP was investigated by adsorption kinetics, equilibrium, thermodynamics and consecutive adsorption/desorption cycles. The characterization indicated a high crystallinity degree and a well–organized and lamellar structure, confirming the efficiency of the synthesis. Elovich was the better kinetic model to describe the 2–NP adsorption onto Zn–Al–LDH, while Pseudo–second order was the best for Mg–Fe–LDH. For both LDHs, the adsorption equilibrium followed the Freundlich model. The process was endothermic, being the maximum adsorption capacities of 290 and 165 mg g–1 for Zn–Al–LDH and Mg–Fe–LDH, respectively. LDHs can be applied for five adsorption/desorption cycles with excellent adsorption capacities. It can be concluded that Zn–Al–LDH and Mg–Fe–LDH are promising materials to treat waters and wastewaters containing 2–nitropheno

The Chemodynamical Nature of the Triangulum-Andromeda Overdensity

We present a chemodynamical study of the Triangulum-Andromeda overdensity (TriAnd) employing a sample of 31 candidate stars observed with the GRACES high-resolution ($R$=40,000) spectrograph at the Gemini North (8.1 m) telescope. TriAnd is a stellar substructure found toward the outer disk of the Milky Way, located at $R_{\rm GC}\sim 18$ kpc from the Sun, toward Galactic latitude $b \sim 25${\deg}. Most stars in our sample have dynamical properties compatible with a disk stellar population. In addition, by applying an eccentricity cut, we are able to detect a stellar contamination that seems to be consistent with an accreted population. In chemical abundance space, the majority of our TriAnd candidates are similar to the outer thin-disk population, suggesting that the overdensity has an \textit{in situ} origin. Finally, the found accreted halo interlopers spatially overlapping with TriAnd should explain the historical discussion of the overdensity's nature due to its complex chemical patterns.Comment: Published in The Astrophysical Journal (ApJ