Entrywise perturbation theory and error analysis for Markov chains

Summary Grassmann, Taksar, and Heyman introduced a variant of Gaussian climination for computing the steady-state vector of a Markov chain. In this paper we prove that their algorithm is stable, and that the problem itself is well-conditioned, in the sense of entrywise relative error. Thus the algorithm computes each entry of the steady-state vector with low relative error. Even the small steady-state probabilities are computed accurately. The key to our analysis is to focus on entrywise relative error in both the data and the computed solution, rather than making the standard assessments of error based on norms. Our conclusions do not depend on any Condition numbers for the problem.This work was supported by NSF under grants DMS-9106207 and DDM-9203134     

Enthalpies of transfer of N-methylformamide,formamide, and N,N-dimethylformamide from methanol to methanol+dimethylsulfoxide mixtures

The enthalpies of transfer of formamide, N-methylformamide and N,N-dimethylformamide from methanol to methanol+dimethylsulfoxide solvent systems have been measured. These data are analysed in terms of a recently developed model of solvation in mixed solvents. The results of the data analyses indicate that preferential solvation of the different functional groups of the amides differs, the carbonyl oxygen being preferentially solvated by methanol and the nitrogen protons are by dimethylsulfoxide.     

Comparative Electrochemical Charge Storage Properties of Bulk and Nanoscale Vanadium Oxide Electrodes

Journal of Solid State Electrochemistry - Vanadium oxide nanostructures have been widely researched as a cathode material for Li-ion batteries due to their layered structure and shorter Li+...     

Physical Characterization and Reactivity of the Uranyl Peroxide [UO(2)(η(2)-O(2))(H(2)O)(2)]·2H(2)O: Implications for Storage of Spent Nuclear Fuels

The unusual uranyl peroxide studtite, [UO(2)(η(2)-O(2))(H(2)O)(2)]·2H(2)O, is a phase alteration product of spent nuclear fuel and has been characterized by solid-state cyclic voltammetry. The voltammogram exhibits two reduction waves that have been assigned to the U(VI/V) redox couple at -0.74 V and to the U(V/IV) redox couple at -1.10 V. This potential shows some dependence upon the identity of the cation of the supporting electrolyte, where cations with larger ionic radii exhibit more cathodic reduction potentials. Raman spectroelectrochemistry indicated that exhaustive reduction at either potential result in a product that does not contain peroxide linkers and is likely to be UO(2). On the basis of the reduction potentials, the unusual behavior of neptunium in the presence of studtite can be rationalized. Furthermore, the oxidation of other species relevant to the long-term storage of nuclear fuel, namely, iodine and iodide, has been explored. The phase altered product should therefore be considered as electrochemically noninnocent. Radiotracer studies with (241)Am show that it does not interact with studtite so mobility will not be retarded in repositories. Finally, a large difference in band gap energies between studtite and its dehydrated congener metastudtite has been determined from the electronic absorption spectra.     

Multiwavelength actively mode-locked fiber ring laser with a dispersion compensated cavity

A multiwavelength actively mode-locked fiber ring laser that utilises a single semiconductor optical amplifier as both a gain and mode-locking element is presented. It is verified experimentally that the number of mode-locked wavelengths may be maximised by compensating for the anomalous intra-cavity dispersion. This is achieved through the inclusion of an appropriate length of normal dispersion fiber in the laser cavity. Using this technique, the number of wavelengths simultaneously mode-locked at 10 GHz was increased from 2 to 5.     

Relative-error bounds for the LU decomposition via the GTH algorithm

Summary. Recently the author showed that the Grassmann-Taksar-Heyman (GTH) algorithm computes the steady-state distribution of a finite-state Markov chain with low relative error. Here it is shown that the LU decomposition computed in the course of the GTH algorithm also has low relative error. The proof requires a refinement of the methods used in the earlier paper. Received September 2, 1994 / Revised version received July 17, 1995     

Lipid bilayer assembly at a gold nanocavity array

The assembly of lipid bilayer membranes, using ultrasonic disruption of liposomes of L-α-Dimyristoyl phosphatidylcholine, across 820 nm diameter spherical cap gold cavity arrays is demonstrated.     

Coherent control of two nuclear spins using the anisotropic hyperfine interaction

We demonstrate coherent control of two nuclear spins mediated by the magnetic resonance of a hyperfine-coupled electron spin. This control is used to create a double-nuclear coherence in one of the two electron spin manifolds, starting from an initial thermal state, in direct analogy to the creation of an entangled (Bell) state from an initially pure unentangled state. We identify challenges and potential solutions to obtaining experimental gate fidelities useful for quantum information processing in this type of system.     

Diastereoselective sulfonate-directed carbonyl reduction of γ-keto-sulfonates

The diastereoselective reduction of γ-keto-sulfonates to afford α,γ-substituted γ-hydroxy sulfonates has been investigated. Herein we report the first example of a diastereoselective carbonyl reduction whereby hydride attack is directed via chelation of a neighbouring sulfonate group to a boron atom, thus affording prevalently trans γ-hydroxy sulfonates.     

Low temperature probe for dynamic nuclear polarization and multiple-pulse solid-state NMR

Here, we describe the design and performance characteristics of a low temperature probe for dynamic nuclear polarization (DNP) experiments, which is compatible with demanding multiple-pulse experiments. The competing goals of a high-Q microwave cavity to achieve large DNP enhancements and a high efficiency NMR circuit for multiple-pulse control lead to inevitable engineering tradeoffs. We have designed two probes-one with a single-resonance RF circuit and a horn-mirror cavity configuration for the microwaves and a second with a double-resonance RF circuit and a double-horn cavity configuration. The advantage of the design is that the sample is in vacuum, the RF circuits are locally tuned, and the microwave resonator has a large internal volume that is compatible with the use of RF and gradient coils.