Pd-catalyzed asymmetric allylic alkylation. A short route to the cyclopentyl core of viridenomycin

A palladium-catalyzed asymmetric allylic alkylation effects a dynamic kinetic asymmetric transformation of racemic isoprene monoepoxide and a surrogate for Nazarov's reagent in which a quaternary center is created with exellent ee. The resultant adduct allows easy access to a substrate for ring-closing metathesis to form a cyclopentenone and sets the stage for an 11-step synthesis of the cyclopentyl core of the antibiotic antitumor agent viridenomycin. [reaction: see text]     

Some jacobi matrices with decaying potential and dense point spectrum

We discuss doubly infinite matrices of the formM _ij= _i,j+1+ _i,j–1+V _{i ij} as operators on ². We present for each >0, examples of potentialsV _n with |V _n|=O(n ^–1/2+) and whereM has only point spectrum. Our discussion should be viewed as a remark on the recent work of Delyon, Kunz, and Souillard.Research partially supported by USNSF under grant MCS 81-20833     

Transference numbers for ultra concentrated solutions of aqueous hydrochloric acid at 25°C

Transference numbers of HCl(aq) solutions at 25°C, from 0.01 to 13.6 mol-kg^–1(m) have been obtained by measuring the emf of cells with transference using hydrogen gas/platinum electrodes. Good agreement is obtained at concentrations up to 1 m with all previous data, and our results strongly corroborate those of King and Spiro over the 2–8m concentration range. The transference numbers of the hydronium ion fit the empirical equation, _H ^HCl = 0.821 + 0.0457m ^1/2 – 2.476×10^–2m – 1.90×10^–4 m ² – 1.45×10^–5 m ³ the maximum deviation in T _H ^HCl being 0.003.     

Equality of the Spectral and Dynamical Definitions of Reflection

For full-line Jacobi matrices, Schrödinger operators, and CMV matrices, we show that being reflectionless, in the sense of the well-known property of m-functions, is equivalent to a lack of reflection in the dynamics in the sense that any state that goes entirely to x = ?∞ as t → ?∞ goes entirely to x = ∞ as t → ∞. This allows us to settle a conjecture of Deift and Simon from 1983 regarding ergodic Jacobi matrices.     

Low-temperature and ambient-pressure synthesis and shape evolution of nanocrystalline pure, La-doped and Gd-doped CeO2

Nanocrystalline cuboidal ceria has been synthesized by low-temperature hydrothermal reaction of cerium nitrate hexahydrate with hexamethylene tetramine. The particles have been doped with La and Gd by adding aqueous solution of the nitrate salts of the metals to the reaction mixture. The pure and doped particles are cubic in crystal structure and 10-25 nm in size. The pure and La-doped ceria are cuboidal in morphology, whereas the Gd-doped particles are irregular in shape. High-resolution TEM imaging and image simulation indicates that atomic level steps are present on the particle surfaces. The particles are faceted parallel to the {1 1 1} and {1 0 0} crystallographic planes and a continuous switching takes place between the two possible surface facets. It appears that the surface energies of the {1 1 1} and {1 0 0} facets are quite similar in magnitude and the interplay of surface energy determines the particle shape. Chemically sensitive imaging and spectroscopy shows that the dopants are homogeneously distributed within the particles and that the oxidation state of Ce is a mixture of +3 and +4. No preferential segregation either of the dopant or the oxidation state was observed. However, since the facet switching does depend on the chemistry of the dopant, there must be an affect on the atomic scale.     

Spectral-domain optical coherence phase microscopy for quantitative phase-contrast imaging

We describe a novel microscopy technique for quantitative phase-contrast imaging of a transparent specimen. The technique is based on depth-resolved phase information provided by common path spectral-domain optical coherence tomography and can measure minute phase variations caused by changes in refractive index and thickness inside the specimen. We demonstrate subnanometer level path-length sensitivity and present images obtained on reflection from a known phase object and human epithelial cheek cells.     

MR imaging findings in recurrent primary osseous Ewing sarcoma

The objective of this study was to determine the value of magnetic resonance (MR) imaging in diagnosing local recurrence of Ewing sarcoma. We retrospectively reviewed radiographs, Tc^99m-methylene diphosphonate (MDP) skeletal scintigraphy, computed tomography scans, and MR studies of 11 patients who had local recurrences of osseous Ewing sarcoma following initial responses to chemotherapy and local radiation. The MR images were compared to those of a control group of nine patients who had no evidence of relapse. T₁- and T₂-weighted MR images identified 9 of the 11 recurrences. Computed tomography was diagnostic in 4 of 6 cases evaluated, Tc^99m-MDP bone scintigraphy in 4 of 11 cases, and plain radiographs in 2 of 10. MR findings at relapse included changes in signal intensity, increased extent of abnormal marrow signal on T₁- and T₂-weighted images, and identification of a new soft tissue mass. These findings suggest that MR imaging is valuable in the routine follow-up of parimary osseous Ewing sarcoma.     

Efficient algorithm for optimizing adaptive quantum metrology processes

Quantum-enhanced metrology infers an unknown quantity with accuracy beyond the standard quantum limit (SQL). Feedback-based metrological techniques are promising for beating the SQL but devising the feedback procedures is difficult and inefficient. Here we introduce an efficient self-learning swarm-intelligence algorithm for devising feedback-based quantum metrological procedures. Our algorithm can be trained with simulated or real-world trials and accommodates experimental imperfections, losses, and decoherence.     

Inconsistency in the application of the adiabatic theorem

The adiabatic theorem states that an initial eigenstate of a slowly varying Hamiltonian remains close to an instantaneous eigenstate of the Hamiltonian at a later time. We show that a perfunctory application of this statement is problematic if the change in eigenstate is significant, regardless of how closely the evolution satisfies the requirements of the adiabatic theorem. We also introduce an example of a two-level system with an exactly solvable evolution to demonstrate the inapplicability of the adiabatic approximation for a particular slowly varying Hamiltonian.