Efficient synthesis of (3R,3aS,6aR)- hexahydrofuro[2,3-b]furan-3-ol from glycolaldehyde

A one-step diastereoselective (up to 98:2) synthesis of the bis-furan alcohol of Darunavir and other HIV drug candidates has been achieved utilizing the novel cyclization of glycolaldehyde and 2,3-dihydrofuran. The cycloaddition was catalyzed by a variety of catalysts including those formed from tin(II) triflate and common chiral ligands such as BINAP and Evans's box ligands. An efficient and unique enzymatic process enhanced the enantiomeric purity to provide the target in optically pure form.     

Explicit Density Approximations for Local Volatility Models Using Heat Kernel Expansions

Heat kernel perturbation theory is a tool for constructing explicit approximation formulas for the solutions of linear parabolic equations. We review the crux of this perturbative formalism and then apply it to differential equations which govern the transition densities of several local volatility processes. In particular, we compute all the heat kernel coefficients for the CEV and quadratic local volatility models; in the later case, we are able to use these to construct an exact explicit formula for the processes’ transition density. We then derive low order approximation formulas for the cubic local volatility model, an affine-affine short rate model, and a generalized mean reverting CEV model. We finally demonstrate that the approximation formulas are accurate in certain model parameter regimes via comparison to Monte Carlo simulations.     

The random <Emphasis Type="Italic">k</Emphasis> cycle walk on the symmetric group

We study the random walk on the symmetric group \(S_n\) generated by the conjugacy class of cycles of length k. We show that the convergence to uniform measure of this walk has a cut-off in total variation distance after \(\frac{n}{k}\log n\) steps, uniformly in \(k = o(n)\) as \(n \rightarrow \infty \). The analysis follows from a new asymptotic estimation of the characters of the symmetric group evaluated at cycles.     

Student Perceptions of a Summer Ventures in Science and Mathematics Camp Experience

“As the world becomes increasingly technological, the value of (the ideas and skills of its population) will be determined in no small measure by the effectiveness of science, technology, engineering, and mathematics (STEM) education in the United States” and “STEM education will determine whether the United States will remain a leader among nations and whether we will be able to solve immense challenges in such areas as energy, health, environmental protection, and national security” (President's Council of Advisors on Science and Technology, 2010, p. vii). Research on the effectiveness of STEM‐focused school and other learning experiences (e.g., short‐term camps) on student attitudes and performance outcomes is sparse. In this study, we documented the influence of an intensive STEM summer program on high school students’ attitudes toward STEM concepts and interests in STEM careers. Attending the summer program was associated with gains on students’ attitudes toward some aspects of STEM as well as specific career interests. Notably, students reported statistically significant views of important aspects of STEM and their attitudes toward science and mathematics were more positive than their attitudes about engineering and technology.     

ROC-curve approach for determining the detection limit of a field chemical sensor

The detection limit of a field chemical sensor under realistic operating conditions is determined by receiver operator characteristic (ROC) curves. The chemical sensor is an ion mobility spectrometry (IMS) device used to detect a chemical marker in diesel fuel. The detection limit is the lowest concentration of the marker in diesel fuel that obtains the desired true-positive probability (TPP) and false-positive probability (FPP). A TPP of 0.90 and a FPP of 0.10 were selected as acceptable levels for the field sensor in this study. The detection limit under realistic operating conditions is found to be between 2 to 4 ppm (w/w). The upper value is the detection limit under challenging conditions. The ROC-based detection limit is very reliable because it is determined from multiple and repetitive sensor analyses under realistic circumstances. ROC curves also clearly illustrate and gauge the effects data preprocessing and sampling environments have on the sensor's detection limit.     

Hearing loss from interrupted, intermittent, and time varying Gaussian noise exposures: the applicability of the equal energy hypothesis

Eight groups of chinchillas (N=74) were exposed to various equivalent energy [100 or 106 dB(A) sound pressure level (SPL)] noise exposure paradigms. Six groups received an interrupted, intermittent, time varying (IITV) Gaussian noise exposure that lasted 8 h/d, 5 d/week for 3 weeks. The exposures modeled an idealized workweek. At each level, three different temporal patterns of Gaussian IITV noise were used. The 100 dB(A) IITV exposure had a dB range of 90-108 dB SPL while the range of the 106 dB(A) IITV exposure was 80-115 dB SPL. Two reference groups were exposed to a uniform 100 or 106 dB(A) SPL noise, 24 h/d for 5 days. Each reference group and the three corresponding IITV groups comprised a set of equivalent energy exposures. Evoked potentials were used to estimate hearing thresholds and surface preparation histology quantified sensory cell populations. All six groups exposed to the IITV noise showed threshold toughening effects of up to 40 dB. All IITV exposures produced hearing and sensory cell loss that was similar to their respective equivalent energy reference group. These results indicate that for Gaussian noise the equal energy hypothesis for noise-induced hearing loss is an acceptable unifying principle.     

Hydrothermal Synthesis and Crystal Structure of a New Manganese（Ⅱ） Complex with 2,4-Pyridine-dicarboxylic Acid and 2,2′-Bipyridine Ligands

A new metal-organic complex [Mn2（PDC）2（bipy）2（H2O）2] （H2PDC = 2,4-pyridine-dicarboxylic acid, bipy = 2,2′-bipyridine） 1 has been hydrothermally synthesized and structurally characterized by elemental analysis, IR spectrum, TG and single-crystal X-ray diffraction. The compound crystallizes in triclinic, space group P ^-1 with a = 7.376（3）, b = 9.990（4）, c = 11.950（5） A^°, α= 75.217（5）, β = 78.052（5）, γ = 70.655（5）°, V = 796.0（5）A^°3, C34HE6Mn2N6O10, Mr = 788.49, De = 1.645 g/cm^3,μ（MoKa） = 0.866 mm^-1, F（000） = 235, Z = 1, the final R = 0.0425 and wR = 0.0700 for 1971 observed reflections （I 〉 2σ（I））. In the crystal structure, the manganese atom is six-coordinated by two carboxylate oxygen atoms from two different PDC ligands, one aqua ligand, and three nitrogen atoms from 2,2′-bipy and PDC ligands, giving a distorted octahedral geometry. It exhibits a three-dimensional supramolecular network defined by O-H…O hydrogen-bonding interactions.     

Fast liquid chromatography separation and multiple‐reaction monitoring mass spectrometric detection of neurotransmitters

We describe here the fast LC‐MS/MS separation of a mixture of neurotransmitters consisting of dopamine, epinephrine, norepinephrine, 3,4‐dihydroxybenzylamine (DHBA), salsolinol, serotonin, and γ‐aminobutyric acid (GABA). The new UltiMate® 3000 Rapid Separation system (RSLC) was successfully coupled to the 4000 QTRAP mass spectrometer operating in multiple‐reaction monitoring (MRM) mode. The separation was attained using a 100 mm length, 2.2 μm particle size Acclaim column at a flow rate of 0.5 mL/min. The column back pressure was 350 bar, while the total run time including column re‐equilibration was 5.2 min. The peak resolution was minimally affected by the fast separation. The RSLC‐MRM separation was found to have a precision range based on peak area for 50 replicate runs of 2–5% CV for all analytes, and the reproducibility of the retention time for all analytes was found to range from 0–2% CV. The described method represents an almost seven times shorter analysis time of neurotransmitters using LC/MRM which is very useful in screening large quantities of biological samples for various neurotransmitters.