Zero-sum stochastic games with unbounded costs: Discounted and average cost cases

Zero-sum stochastic games with countable state space and with finitely many moves available to each player in a given state are treated. As a function of the current state and the moves chosen, player I incurs a nonnegative cost and player II receives this as a reward. For both the discounted and average cost cases, assumptions are given for the game to have a finite value and for the existence of an optimal randomized stationary strategy pair. In the average cost case, the assumptions generalize those given in Sennott (1993) for the case of a Markov decision chain. Theorems of Hoffman and Karp (1966) and Nowak (1992) are obtained as corollaries. Sufficient conditions are given for the assumptions to hold. A flow control example illustrates the results.     

Variable temperature and EPR frequency study of two aqueous Gd(III) complexes with unprecedented sharp lines

We present an EPR study of two Gd(III) complexes in aqueous solution at multiple temperatures and EPR frequencies. These two complexes, [Gd(TPATCN)] and [Gd(DOTAM)(H(2)O)](3+), display remarkably sharp lines (i.e. slow transverse electron spin relaxation) in comparison with all complexes studied in the past, especially at X-band ( approximately 9.08 GHz). These unprecedented spectra even show, for the first time in solution, a distinct influence of hyperfine coupling to two magnetically active Gd isotopes ((155)Gd 14.8%, I = 3/2, gamma = -0.8273 x 10(7) s(-1) T(-1) and (157)Gd, 15.65%, I = 3/2, -1.0792 x 10(7) s(-1) T(-1)). The hyperfine coupling splitting in [Gd(TPATCN)] was determined accurately for a (157)Gd-enriched complex, and the value A((157)Gd)/gmu(B) = 5.67 G seems to be a good estimation for most chelates of interest. Consequently, we can safely assert that neglecting the Gd isotopes in line shape studies is not a significant source of error as long as the apparent peak-to-peak width is greater than 10-20 G. This is generally the case, except at very high EPR frequencies (>150 GHz). Analyzing the spectra within the physical model of Rast et al. we find that the slow electron spin relaxation is due to a nearly zero static ZFS. We discuss some structural features that might explain this interesting electron structure.     

On the structure and conformation of polymer chains in latex particles. I. Small-angle neutron scattering characterization of polystyrene latexes of small diameter

Polystyrene latexes with 40-60 nm diameter and molecular weights ranging from 6 × 10⁴ to 6 × 10⁶ g/mol were synthesized by a two-step equilibrium swelling method, with deuterated polymer forming either the first or second step. Below about 1 × 10⁶ g/mol, small-angle neutron scattering gave zero-angle scattering intensities much higher than expected on the basis of gel permeation chromatography molecular weights. Several models were examined, the leading model based on a core-shell latex structure. The development of such structure was found to depend on the ratio of the radius of gyration of the polymer chain to that of the diameter of the latex particle, reaching a maximum in the range where the polymer chain dimensions are about half that of the latex particle. For the highest molecular weights, normal scattering intensities were found. These results lead to the finding that the polymer chains were compressed in the latex particles with constraining in the range of one to four, for this molecular weight range.     

Expanded Analogs of Three-Dimensional Lead-Halide Hybrid Perovskites

Replacing the Pb−X octahedral building unit of A^IPbX₃ perovskites (X=halide) with a pair of edge-sharing Pb−X octahedra affords the expanded perovskite analogs: A^IIPb₂X₆. We report seven members of this new family of materials. In 3D hybrid perovskites, orbitals from the organic molecules do not participate in the band edges. In contrast, the more spacious inorganic sublattice of the expanded analogs accommodates larger pyrazinium-based cations with low-lying π* orbitals that form the conduction band, substantially decreasing the band gap of the expanded lattice. The molecular nature of the conduction band allows us to electronically dope the materials by reducing the organic molecules. By synthesizing derivatives with A^II=pyridinium and ammonium, we can isolate the contributions of the pyrazinium-based orbitals in the band gap transition of A^IIPb₂X₆. The organic-molecule-based conduction band and the inorganic-ion-based valence band provide an unusual electronic platform with localized states for electrons and more disperse bands for holes upon optical or thermal excitation.     

Evolved Gas Analysis‐Mass Spectrometry to Identify the Earliest Organic Binder in Aegean Style Wall Paintings

An organic binder was identified in the painted fragments from the Canaanite palace of Tel Kabri, Israel. Recently dated to the late 18th century B.C.E. by ¹⁴C, Tel Kabri is the most ancient of the Eastern Mediterranean sites in which Aegean style paintings have been found. The application of pigments was suspected to be using an organic binding medium, particularly for the Egyptian Blue pigment. Samples of blue paint were examined using evolved gas analysis‐mass spectrometry (EGA‐MS) in order to overcome the analytical challenges imposed by highly degraded aged proteinaceous materials. Egg was identified as the binder based on the presence of hexadecanonitrile and octadecanonitrile, confirming the use of a secco painting technique. Lysozyme C from Gallus gallus was detected by proteomics analysis, confirming the presence of egg. To our knowledge, this is the earliest use of egg as a binder in Aegean style wall paintings.     

Enantiopure 1,5-diols from dynamic kinetic asymmetric transformation. Useful synthetic intermediates for the preparation of chiral heterocycles

Dynamic kinetic asymmetric transformation (DYKAT) of a series of 1,5-diols has been performed in the presence of Candida antarctica lipase B (CALB), Pseudomonas cepacia lipase II (PS-C II), and ruthenium catalyst 4. The resulting optically pure 1,5-diacetates are useful synthetic intermediates, which was demonstrated by the syntheses of both an enantiopure 2,6-disubstituted piperidine and an enantiopure 3,5-disubstituted morpholine.     

Stochastic Liouville equation treatment of the electron paramagnetic resonance line shape of an S-state ion in solution

The current approaches used for the analysis of electron paramagnetic resonance spectra of Gd3+ complexes suffer from a number of drawbacks. Even the elaborate model of [Rast et al., J. Chem. Phys. 113, 8724 (2000)] where the electron spin relaxation is explained by the modulation of the zero-field splitting (ZFS), by molecular tumbling (the so called static contribution), and deformations (transient contribution), is only readily applicable within the validity range of the Redfield theory [Advances in Magnetic Resonance, edited by J.-S. Waugh (Academic, New York, 1965), Vol. 1, p. 1], that is, when the ZFS is small compared to the Zeeman energy and the rotational and vibrational modulations are fast compared to the relaxation time. Spin labels (nitroxides and transition metal complexes) have been studied for years in systems that violate these conditions. The theoretical framework commonly used in such studies is the stochastic Liouville equation (SLE). The authors shall show how the physical model of Rast et al. can be cast into the SLE formalism, paying special attention to the specific problems introduced by the [Uhlenbeck and Ornstein, Phys. Rev. 36, 823 (1930)] process used to model the transient ZFS. The resulting equations are very general and valid for arbitrary correlation times, magnetic field strength, electron spin S, or symmetry. The authors demonstrate the equivalence of the SLE approach with the Redfield approximation for two well-known Gd3+ complexes.     

Effective Rheology of Two-Phase Flow in Three-Dimensional Porous Media: Experiment and Simulation

We present an experimental and numerical study of immiscible two-phase flow of Newtonian fluids in three-dimensional (3D) porous media to find the relationship between the volumetric flow rate (Q) and the total pressure difference (\(\Delta P\)) in the steady state. We show that in the regime where capillary forces compete with the viscous forces, the distribution of capillary barriers at the interfaces effectively creates a yield threshold (\(P_t\)), making the fluids reminiscent of a Bingham viscoplastic fluid in the porous medium. In this regime, Q depends quadratically on an excess pressure drop (\(\Delta P-P_t\)). While increasing the flow rate, there is a transition, beyond which the overall flow is Newtonian and the relationship is linear. In our experiments, we build a model porous medium using a column of glass beads transporting two fluids, deionized water and air. For the numerical study, reconstructed 3D pore networks from real core samples are considered and the transport of wetting and non-wetting fluids through the network is modeled by tracking the fluid interfaces with time. We find agreement between our numerical and experimental results. Our results match with the mean-field results reported earlier.     

Exploring Effects of Protease Choice and Protease Combinations in Enzymatic Protein Hydrolysis of Poultry By-Products

A study of the effects of single and combined protease hydrolysis on myofibrillar versus collagenous proteins of poultry by-products has been conducted. The aim was to contribute with knowledge for increased value creation of all constituents of these complex by-products. A rational approach was implemented for selecting proteases exhibiting the most different activity towards the major protein-rich constituents of mechanically deboned chicken residue (MDCR). An initial activity screening of 18 proteases on chicken meat, turkey tendons and MDCR was conducted. Based on weight yield, size exclusion chromatography (SEC) and SDS-PAGE, stem Bromelain and Endocut-02 were selected. Studies on hydrolysis of four different poultry by-products at 40 °C, evaluated by protein yield, SEC, and SDS-PAGE, indicate that the proteases’ selectivity difference can be utilized in tailor-making hydrolysates, enriched in either meat- and collagen-derived peptides or gelatin. Three modes of stem Bromelain and Endocut-02 combinations during hydrolysis of MDCR were performed and compared with single protease hydrolysis. All modes of the protease combinations resulted in a similar approximately 15% increase in product yield, with products exhibiting similar SEC and SDS-PAGE profiles. This shows that irrespective of the modes of combination, the use of more than one enzyme in hydrolysis of collagen-rich material can provide means to increase the total protein yield and ultimately contribute to increased value creation of poultry by-products.