Fuzzy Markov Chains and Decision-Making

Decision-making in an environment of uncertainty and imprecision for real-world problems is a complex task. In this paper it is introduced general finite state fuzzy Markov chains that have a finite convergence to a stationary (may be periodic) solution. The Cesaro average and the -potential for fuzzy Markov chains are defined, then it is shown that the relationship between them corresponds to the Blackwell formula in the classical theory of Markov decision processes. Furthermore, it is pointed out that recurrency does not necessarily imply ergodicity. However, if a fuzzy Markov chain is ergodic, then the rows of its ergodic projection equal the greatest eigen fuzzy set of the transition matrix. Then, the fuzzy Markov chain is shown to be a robust system with respect to small perturbations of the transition matrix, which is not the case for the classical probabilistic Markov chains. Fuzzy Markov decision processes are finally introduced and discussed.     

The system Na2CO3–CaCO3–MgCO3 at 6 GPa and 900–1250°C and its relation to the partial melting of carbonated mantle

In order to constrain the Na₂CO₃–CaCO₃–MgCO₃ T–X diagram at 6?GPa in addition to the binary and pseudo-binary systems we conducted experiments along the Na₂CO₃–Ca_0.5Mg_0.5CO₃ join. At 900–1000°C, melting does not occur and isothermal sections are presented by one-, two- and three-phase regions containing Ca-bearing magnesite, aragonite, Na₂CO₃ (Na₂) and Na₂(Ca_1–0.9Mg_0-0.1)_3-4(CO₃)_4-5 (Na₂Ca_3-4), Na₄(Ca_1–0.6Mg_0–0.4)(CO₃)₃ (Na₄Ca), Na₂(Ca_0-0.08Mg_1–0.92)(CO₃)₂ (Na₂Mg) phases with intermediate compositions. The minimum melting point locates between 1000°C and 1100°C. This point would resemble that of three eutectics: Mgs–Na₂Ca₃–Na₂Mg, Na₂Mg–Na₂Ca₃–Na₄Ca or Na₂Mg–Na₄Ca–Na₂, in the compositional interval of [45Na₂CO₃·55(Ca_0.6Mg_0.4)CO₃]–[60Na₂CO₃·40Ca_0.6Mg_0.4CO₃]. The liquidus projection has seven primary solidification phase regions for Mgs, Dol, Arg, Na₂Ca₃, Na₄Ca, Na₂ and Na₂Mg. The results suggest that extraction of Na and Ca from silicate to carbonate components has to decrease minimum melting temperature of carbonated mantle rocks to 1000–1100°C at 6?GPa and yields Na-rich dolomitic melt with a Na# (Na₂O/(Na₂O?+?CaO?+?MgO))?≥?28?mol%.     

Hydrogen Production by Water Dissociation in Surface‐Modified BaCoxFeyZr1−x−yO3−δ Hollow‐Fiber Membrane Reactor with Improved Oxygen Permeation

A porous perovskite BaCo_xFe_yZr_0.9?x?yPd_0.1O_3?δ (BCFZ‐Pd) coating was deposited onto the outer surface of a BaCo_xFe_yZr_1?x?yO_3?δ (BCFZ) perovskite hollow‐fiber membrane. The surface morphology of the modified BCFZ fiber was characterized by scanning electron microscopy (SEM), indicating the formation of a BCFZ‐Pd porous layer on the outer surface of a dense BCFZ hollow‐fiber membrane. The oxygen permeation flux of the BCFZ membrane with a BCFZ‐Pd porous layer increased 3.5 times more than that of the blank BCFZ membrane when feeding reactive CH₄ onto the permeation side of the membrane. The blank BCFZ membrane and surface‐modified BCFZ membrane were used as reactors to shift the equilibrium of thermal water dissociation for hydrogen production because they allow the selective removal of the produced oxygen from the water dissociation system. It was found that the hydrogen production rate increased from 0.7 to 2.1 mL H₂ min^?1 cm^?2 at 950 °C after depositing a BCFZ‐Pd porous layer onto the BCFZ membrane.     

Photorearrangement of alpha-azoxy ketones and triplet sensitization of azoxy compounds

[reaction: see text] Although some aspects of azoxy group radical chemistry have been investigated, unhindered alpha-azoxy radicals remain poorly understood. Here we report the generation of alpha-azoxy radicals under mild conditions by irradiation of alpha-azoxy ketones 4a,b. These compounds undergo alpha-cleavage to yield radicals 5a,b, whose oxygen atom then recombines with benzoyl radicals to produce presumed intermediate 15. Formal Claisen rearrangement gives alpha-benzoyloxyazo compounds 8a,b, which are themselves photolabile, leading to both radical and ionic decomposition. The ESR spectrum of 5a was simulated to extract the isotropic hyperfine splitting constants, which showed its resonance stabilization energy to be exceptionally large. Azoxy compounds have been found for the first time to be good quenchers of triplet excited acetophenone, the main sensitized photoreaction of 7Z in benzene being deoxygenation. While this reaction has been reported previously, it was always in hydrogen atom donating solvents, where chemical sensitization occurred. The principal direct irradiation product of 4bZ and model azoxyalkane 7Z is the E isomer, whose thermal reversion to Z is much faster than that of previously studied analogues.     

H2O‐Catalyzed Route to Early Lanthanide Tribromide THF and DME Solvates from Oxides

A convenient one‐pot synthetic protocol towards THF and DME solvates of lanthanum and other early lanthanide tribromides was developed using the water‐catalyzed reaction of lanthanide(III) oxides with highly reactive Me₃SiBr in situ formed from commercially available disilane Si₂Me₆ and Br₂. This practical route allows to obtain the target lanthanum tribromide solvates [LaBr₃(thf)₄] ( 1a ) and [LaBr₃(dme)₂]₂ ( 1b ) as well as analogous early lanthanide molecular tribromide solvates [NdBr₃(thf)₄] ( 2a ), [NdBr₃(dme)₂] ( 2b ), [SmBr₃(thf)₂] ( 3a ), and [SmBr₃(dme)₂] ( 3b ) difficult to prepare by other solution‐based procedures. The molecular structure of 1b· 2CH₂Cl₂ was determined by an XRD study.     

Single wall carbon nanotubes density of states: comparison of experiment and theory

We study the electronic structure of a variety of single wall carbon nanotubes and report density of states obtained with the Perdew–Burke–Ernzerhof (PBE) generalized gradient approximation and hybrid PBE0 approximation of density functional theory using Gaussian orbitals and periodic boundary conditions. PBE gives very good results for metallic tubes but the addition of a portion of exact exchange in the hybrid PBE0 functional worsens the agreement between experiment and theory. On the other hand, the PBE0 hybrid significantly improves the theoretical predictions (compared to PBE) for semiconducting tubes.