Bifunctional Iminophosphorane-Catalyzed Enantioselective Nitroalkane Addition to Unactivated α,β-Unsaturated Esters**

Herein we describe the enantioselective intermolecular conjugate addition of nitroalkanes to unactivated α,β-unsaturated esters, catalyzed by a bifunctional iminophosphorane (BIMP) superbase. The transformation provides the most direct access to pharmaceutically relevant enantioenriched γ-nitroesters, utilizing feedstock chemicals, with unprecedented selectivity. The methodology exhibits a broad substrate scope, including β-(fluoro)alkyl, aryl and heteroaryl substituted electrophiles, and was successfully applied on a gram scale with reduced catalyst loading, and, additionally, catalyst recovery was carried out. The formal synthesis of a range of drug molecules, and an enantioselective synthesis of (S)-rolipram were achieved. Additionally, computational studies revealed key reaction intermediates and transition state structures, and provided rationale for high enantioselectivities, in good agreement with experimental results.     

Photophysics of diplatinum polyynediyl oligomers: chain length dependence of the triplet state in sp carbon chains

The series of polyynes with the structure trans, trans-[Ar-Pt(P 2)-(C[triple bond]C) n -Pt(P 2)-Ar], where P = tri( p-tolyl)phosphine, Ar = p-tolyl, and n = 3, 4, 5, 6 (6, 8, 10, 12 sp carbon atoms), has been subjected to a comprehensive photophysical investigation. At low temperature ( T < 140 K) in a 2-methyltetrahydrofuran (MTHF) glass, the complexes exhibit moderately efficient phosphorescence appearing as a series of narrow (fwhm < 200 cm (-1)) vibronic bands separated by ca. 2100 cm (-1). The emission is assigned to a (3)pi,pi* triplet state that is concentrated on the sp carbon chain, and the vibronic progression arises from coupling of the excitation to the -C[triple bond]C- stretch. The 0-0 energy of the phosphorescence decreases with increasing sp carbon chain length, spanning a range of over 6000 cm (-1) across the series. Transient absorption spectroscopy carried out at ambient temperature confirms that the (3)pi,pi* triplet is produced efficiently, and it displays a strongly allowed triplet-triplet absorption. In the MTHF solvent glass ( T < 140 K), the emission lifetimes increase with emission energy. Analysis of the triplet nonradiative decay rates reveals a quantitative energy gap law correlation. The nonradiative decay rates can be calculated by using parameters recovered from a single-mode Franck-Condon fit of the emission spectra.     

Mach stem hysteresis: Experiments addressing a novel explanation of clumpy astrophysical jet emission

Recent time-series observations of shock waves in stellar jets taken with the Hubble Space Telescope reveal localized bright knots that persist over nearly 15 years. While some of these features represent shock fronts caused by variable velocities in the flow, others appear at the intersection points between distinct bow shocks. Theoretically, when the angle between two intersecting shocks exceeds a certain critical value, a third shock (Mach stem) should form. Because Mach stems form perpendicular to the direction of flow, incoming particles encounter a normal shock instead of an oblique one, which results in brighter emission at this location. To study this phenomenon in a controlled laboratory setting, we have carried out experiments on the Omega laser aimed at understanding the formation, growth, and destruction of Mach stems in the warm dense plasma regime. Our experimental results indicate how the growth rate depends upon included angle, and numerical simulations indicate that it may be possible to stabilize an already-formed Mach stem below the critical angle when certain conditions are satisfied.     

Ultrasonic wave velocities and attenuation in IVb-Vb-VIb chalcogenide glasses: 2–300 K

The velocities and attenuation of longitudinal and shear ultrasonic (12 MHz) waves have been measured for several chalcogenide glasses (Ge₁₀Si₁₂As₃₀Te₄₈, Ge₂₀As₃₀Se₅₀, Si₂₀As₃₂Te₄₈, Ge₁₀Si₁₂As₂₉Te₄₉, Ge₁₂S₁₄As₃₅Te₄₉). The bulk, shear and Young's moduli and the Poisson ratio are found to be insensitive to the glass composition. The temperature dependences of the longitudinal and shear-wave velocities are negative at higher temperatures and approach 0 K with a zero slope. The ultrasonic attenuation does not exhibit either the broad loss peak or the smaller low-temperature peak found in many other glasses: the elastic and anelastic behaviour is quite different from that of oxide glasses — no evidence for the existence of two-level systems has been obtained from the ultrasonic measurements.     

Minimum Self-Repairing Graphs

A graph is self-repairing if it is 2-connected and such that the removal of any single vertex results in no increase in distance between any pair of remaining vertices of the graph. We completely characterize the class of minimum self-repairing graphs, which have the fewest edges for a given number of vertices.     

Coproducts of bounded distributive lattices: infinite distributivity

Summary It is shown that, if two bounded distributive lattices satisfy the join-infinite distributive law (JID), then their coproduct also satisfies this law. In 1986, Yaqub proved that generalized Post algebras with a finite lattice of constants satisfy JID, and stated that, in general, it is not known whether a generalized Post algebra satisfies JID when its lattice of constants satisfies JID. In this note, the statement is proved.     

Mathematical Programming Models for Cutting-Stock Problems in the Clothing Industry

The cutting-stock problem in the clothing industry does not conform to the classical representation of such problems. Waste minimization is only a subsidiary objective. The overall objective is to maximize long-run profitability, but operational planning requires limiting consideration to a series of problems covering short planning periods. This requires a more complex objective to incorporate interaction between periods. Production constraints with unique characteristics occur in the laying, cutting and sewing operations. The conventional pattern-design problem is dealt with by use of a commercial computer-aided graphical design system. The question addressed in this paper is how to combine such patterns so as to satisfy the various objectives and constraints. This leads to both integer and quadratic formulations of appropriate mathematical programming models.     

Priestley duality for order-preserving maps into distributive lattices

The category of bounded distributive lattices with order-preserving maps is shown to be dually equivalent to the category of Priestley spaces with Priestley multirelations. The Priestley dual space of the ideal lattice L of a bounded distributive lattice L is described in terms of the dual space of L. A variant of the Nachbin-Stone-ech compactification is developed for bitopological and ordered spaces. Let X be a poset and Y an ordered space; X ^Y denotes the poset of continuous order-preserving maps from Y to X with the discrete topology. The Priestley dual of L ^P is determined, where P is a poset and L a bounded distributive lattice.