Heuristics for class numbers and lambda invariants

Let be an imaginary quadratic field and let be the associated real quadratic field. Starting from the Cohen-Lenstra heuristics and Scholz's theorem, we make predictions for the behaviors of the 3-parts of the class groups of these two fields as varies. We deduce heuristic predictions for the behavior of the Iwasawa -invariant for the cyclotomic -extension of and test them computationally.

     

Exact boundary controllability of a hybrid system of elasticity

A hybrid control system is presented: an elastic beam, governed by a partial differential equation, linked to a rigid body which is governed by an ordinary differential equation and to which control forces and torques are applied. The entire system, elastic beam plus rigid body, is proved to be exactly controllable by smooth open-loop controllers applied to the rigid body only, and in arbitrarily short durations. This system is modeled as a two-dimensional space-structure.This research was partially supported by NSF grant DMS 84-13129, and Markus also received support from SERC.     

Total Synthesis of Ramonanins A–D

The first total synthesis of the ramonanin family of lignan natural products is described. The short synthesis involves a 2,5‐diaryl‐3,4‐dimethylene tetrahydrofuran intermediate, which participates in an unexpectedly facile Diels–Alder dimerization, generating all four natural products. Insights into the reactivity and stereoselectivity of the key dimerization are provided through computational studies employing B3LYP/6‐31G(d) and M06‐2X/6‐31G(d) model chemistries.     

Metal‐Mediated Production of Isocyanates,R3ENCO from Dinitrogen,Carbon Dioxide,and R3ECl

A highly efficient and versatile chemical cycle has been developed for the production of isocyanates through the molecular fixation of N₂, CO₂ and R₃ECl (E=C, Si, and Ge). Key steps include a ‘one‐pot’ photolytic N? N bond cleavage of a Group 6 dinuclear dinitrogen complex with in situ trapping by R₃ECl to provide a metal terminal imido complex that can engage in simultaneous nitrene‐group transfer and oxygen‐atom transfer to generate an intermediate metal terminal oxo complex with release of the isocyanate product. Reaction of the oxo complex with additional equivalents of R₃ECl regenerates a metal dichloride that is the precursor for dinuclear dinitrogen starting material.     

Irradiance,Photofrin® Dose and Initial Tumor Volume are Key Predictors of Response to Interstitial Photodynamic Therapy of Locally Advanced Cancers in Translational Models

The objective of the present study was to develop a predictive model for Photofrin^®-mediated interstitial photodynamic therapy (I-PDT) of locally advanced tumors. Our finite element method was used to simulate 630-nm intratumoral irradiance and fluence for C3H mice and New Zealand White rabbits bearing large squamous cell carcinomas. Animals were treated with light only or I-PDT using the same light settings. I-PDT was administered with Photofrin^® at 5.0 or 6.6 mg kg⁻¹, 24 h drug-light interval. The simulated threshold fluence was fixed at 45 J cm⁻² while the simulated threshold irradiance varied, intratumorally. No cures were obtained in the mice treated with a threshold irradiance of 5.4 mW cm⁻². However, 20–90% of the mice were cured when the threshold irradiances were ≥8.6 mW cm⁻². In the rabbits treated with I-PDT, 13 of the 14 VX2 tumors showed either local control or were cured when threshold irradiances were ≥15.3 mW cm⁻² and fluence was 45 J cm⁻². No tumor growth delay was observed in VX2 treated with light only (n = 3). In the mouse studies, there was a high probability (92.7%) of predicting cure when the initial tumor volume was below the median (493.9 mm³) and I-PDT was administered with a threshold intratumoral irradiance ≥8.6 mW cm⁻².     

Optimal Prefix-Free Codes for Unequal Letter Costs: Dynamic Programming with the Monge Property

In this paper we discuss the problem of finding optimal prefix-free codes for unequal letter costs, a variation of the classical Huffman coding problem. Our problem consists of finding a minimal cost prefix-free code in which the encoding alphabet consists of unequal cost (length) letters, with lengths α and β. The most efficient algorithm known previously requires O(n^{2 + max(α, β)}) time to construct such a minimal-cost set of n codewords, provided α and β are integers. In this paper we provide an O(n^max(α, β)) time algorithm. Our improvement comes from the use of a more sophisticated modeling of the problem, combined with the observation that the problem possesses a “Monge property” and that the SMAWK algorithm on monotone matrices can therefore be applied.     

Lasing in thulium-doped polarizing photonic crystal fiber

We describe lasing of a thulium-doped polarizing photonic crystal fiber. A 4 m long fiber with 50 μm diameter core, 250 μm diameter cladding, and d/Λ ratio of 0.18 was pumped with a 793 nm diode and produced a polarized output with a polarization extinction ratio (PER) of 15 dB and an M(2) of <1.15. An intracavity polarizer and half-wave plate minimally increased the PER to 16 dB. The output power had 35% slope efficiency relative to the absorbed pump power. The maximum cw output power was limited to 4 W due to the quantum defect heating of the fiber.     

A quantitative explanation for the apparent anomalous temperature dependence of OH + HO2 = H2O + O2 through multi-scale modeling

Kinetic models for complex chemical mechanisms are comprised of tens to thousands of reactions with rate constants informed by data from a wide variety of sources – rate constant measurements, global combustion experiments, and theoretical kinetics calculations. In order to integrate information from distinct data types in a self-consistent manner, a framework for combustion model development is presented that encapsulates behavior across a wide range of chemically relevant scales from fundamental molecular interactions to global combustion phenomena. The resulting kinetic model consists of a set of theoretical kinetics parameters (with constrained uncertainties), which are related through kinetics calculations to temperature/pressure/bath-gas-dependent rate constants (with propagated uncertainties), which in turn are related through physical models to combustion behavior (with propagated uncertainties). Direct incorporation of theory in combustion model development is expected to yield more reliable extrapolation of limited data to conditions outside the validation set, which is particularly useful for extrapolating to engine-relevant conditions where relatively limited data are available. Several key features of the approach are demonstrated for the H₂O₂ decomposition mechanism, where a number of its constituent reactions continue to have large uncertainties in their temperature and pressure dependence despite their relevance to high-pressure, low-temperature combustion of a variety of fuels. Here, we use the approach to provide a quantitative explanation for the apparent anomalous temperature dependence of OH + HO₂ = H₂O + O₂ – in a manner consistent with experimental data from the entire temperature range and ab initio transition-state theory within their associated uncertainties. Interestingly, we do find a rate minimum near 1200 K, although the temperature dependence is substantially less pronounced than previously suggested.     

Comparison of water isotope-ratio determinations using two cavity ring-down instruments and classical mass spectrometry in continuous ice-core analysis

We present a detailed comparison between subsequent versions of commercially available wavelength-scanned cavity ring-down water isotope analysers (L2120-i and L2130-i, Picarro Inc.). The analysers are used in parallel in a continuous mode by adaption of a low-volume flash evaporation module. Application of the analysers to ice-core analysis is assessed by comparison between continuous water isotope measurements of a glacial ice-core from Severnaya Zemlya with discrete isotope-ratio mass spectrometry measurements performed on parallel samples from the same ice-core. The great advances between instrument versions, particularly in the measurement of δ²H, allow the continuous technique to achieve the same high level of accuracy and precision obtained using traditional isotope spectrometry techniques in a fraction of the experiment time. However, when applied to continuous ice-core measurements, increased integration times result in a compromise of the achievable depth resolution of the ice-core records.