Notes on equivalent stationary policies in Markov decision processes with total rewards

We construct examples of Markov Decision Processes for which, for a given initial state and for a given nonstationary transient policy, there is no equivalent (randomized) stationary policy, i.e. there is no stationary policy which occupation measure is equal to the occupation measure of a given policy. We also investigate the relation between the existence of equivalent stationary policies in special models and the existence of equivalent strategies in various classes of nonstationary policies in general models.     

Calculation of Kinetic Parameters for Crystallization Processes

In this work, kinetic data of crystallization processes have been determined by measurement of the intensities of reflection of X-ray diffraction spectra and modeled using the Avrami-Eroféev and Jander expressions. We have created a simple Microsoft Excel spreadsheet that allows students to calculate the kinetic data. Students will be able to calculate the kinetic parameters of any crystallization process, for example, hydrothermal crystallization of catalytic materials like zeolites. The possibility of using the spreadsheet with different models or expressions and discriminating among them is also validated by comparing the model results with experimental data (differential thermal analyses, DTA) from papers available in the recent literature.     

Synthesis, spectroscopic and electrochemical properties of manganese, nickel and iron octakis-(2-diethylaminoethanethiol)-phthalocyanine

The syntheses, spectroscopic and electrochemical properties of manganese (3), nickel (4) and iron (5) phthalocyanine complexes, octa-substituted at the peripheral positions with diethlyaminoethanethiol substituent, are reported. The electrochemistry of these complexes and the corresponding cobalt complex (6) are reported. Complex 3 showed two reversible reduction couples attributed to the Mn^IIIPc⁻²/Mn^IIPc⁻² (E_½ = −0.12 V versus Ag|AgCl) and Mn^IIPc⁻²/Mn^IIPc⁻³ (E_½ = −0.82 V versus Ag|AgCl) species. Two ring-based reduction couples were also observed for complex 4. Two reduction couples, assigned to the Fe^IIPc⁻²/Fe^IPc⁻² (E_½ = −0.35 V versus Ag|AgCl) and Fe^IPc⁻²/Fe^IPc⁻³ (E_½ = −0.96 V versus Ag|AgCl) species, and an oxidation couple, attributed to Fe^IIIPc⁻²/Fe^IIPc⁻² (E_½ = 0.26 V versus Ag|AgCl) species, were observed. For complex 6, two reductions and one oxidation were also observed with the potential range of 1.2 to −1.8 V versus Ag|AgCl Spectroelectrochemical studies were used to confirm some of the assigned processes.     

Analysis of the Solid-State Rearrangementof Hydrido-Alkynyl Ruthenium Complexesto their Vinylidene Tautomers

Summary.  The solid-state tautomerization of the hydrido-alkynyl derivatives [Cp ^*RuH(C&*CR)-(dippe)][BPh₄] (Cp^* = C₅Me₅; R = SiMe₃, Ph, H; dippe = 1,2-bis-(diisopropylphosphino)-ethane) to their vinylidene isomers [Cp ^*Ru*C*CHR(dippe)][BPh₄] was studied by IR spectroscopy. Characteristic isothermic αvs. t curves for each individual rearrangement process were recorded. Their shape, and hence the isomerization mechanism, depends strongly on the nature of the substituent R. The kinetic analysis of the above curves using the Avrami-Erofeev provided some mechanistic information about the isomerization process in the solid. Received July 7, 2000. Accepted August 29, 2000     

Unprecedented eta(1)-P(basal) coordination of P(4)X(3) molecules (X = S, Se). An experimental and theoretical study of the apical vs basal complexation dichotomy

Reaction of [(triphos)Re(CO)(2)(OTf)] (1) [triphos = MeC(CH(2)PPh(2))(3); OTf = OSO(2)CF(3)] with P(4)S(3) and P(4)Se(3) yields pairs of coordination isomers, namely, [(triphos)Re(CO)(2)[eta(1)-P(apical)-P(4)X(3)]](+) (X = S, 2; Se, 5) and [(triphos)Re(CO)(2)[eta(1)-P(basal)-P(4)X(3)]](+) (X = S, 3; Se, 6). The latter represent the first examples of the eta(1)-P(basal) coordination achieved by the P(4)X(3) molecular cage. Further reaction of 2/3 and 5/6 mixtures with 1 affords the dinuclear species [[(triphos)Re(CO)(2)](2)[mu,eta(1:1)-P(apical,)P(basal)-P(4)X(3)]](2+) (X = S, 4; Se, 7) in which the unprecedented M-eta(1)-P(basal)/eta(1)-P(apical)-M' bridging coordination of the P(4)X(3) molecule is accomplished. A theoretical analysis of the bonding properties of the two coordination isomers is also presented. The directionality of apical vs basal phosphorus lone pairs is also discussed in terms of MO arguments.     

Buffers for the Physiological pH Range: Studies of 4-(N-Morpholino)butanesulfonic Acid (MOBS) from 5 to 55 °C

In this study, we report the pH values of two buffer solutions without chloride ion and eight buffer solutions with NaCl with an ionic strength I=0.16 mol?kg^?1. Electromotive force (emf) techniques have been used to get the cell potentials at 12 temperatures from 5 to 55?°C, including 37?°C. An extended form of the Bates-Guggenheim convention is used in the entire ionic strength range, 0.04 to 0.16?mol?kg^?1. The residual liquid junction potentials (??E _j ) of the buffer solutions of MOBS have been estimated from previous measurements with a flowing junction cell. These values of ??E _j have been used for correction in order to ascertain the operational pH values of four buffer solutions of MOBS at 25 and 37?°C. These solutions are recommended as pH standards for physiological application in the pH range 7.4 to 7.7.