Partition identities and quiver representations

We present a particular connection between classical partition combinatorics and the theory of quiver representations. Specifically, we give a bijective proof of an analogue of A. L. Cauchy’s Durfee square identity to multipartitions. We then use this result to give a new proof of M. Reineke’s identity in the case of quivers \({\mathcal {Q}}\) of Dynkin type A. Our identity is stated in terms of the lacing diagrams of S. Abeasis–A. Del Fra, which parameterize orbits of the representation space of \({\mathcal {Q}}\) for a fixed dimension vector.     

Continuous-wave far-infrared ESR spectrometer for high-pressure measurements

We present a newly-developed microwave probe for performing sensitive high-field/multi-frequency electron spin resonance (ESR) measurements under high hydrostatic pressures. The system consists of a BeCu-made pressure-resistant vessel, which accommodates the investigated sample and a diamond microwave coupling window. The probe’s interior is completely filled with a pressure-transmitting fluid. The setup operates in reflection mode and can easily be assembled with a standard oversized microwave circuitry. The probe-head withstands hydrostatic pressures up to 1.6 GPa and interfaces with our home-built quasi-optical high-field ESR facility, operating in a millimeter/submillimeter frequency range of 105–420 GHz and in magnetic fields up to 16 T. The overall performance of the probe was tested, while studying the pressure-induced changes in the spin-relaxation mechanisms of a quasi-1D conducting polymer, KC₆₀. The preliminary measurements revealed that the probe yields similar signal-to-noise ratio to that of commercially available low-frequency ESR spectrometers. Moreover, by observing the conduction electron spin resonance (CESR) linewidth broadening for KC₆₀ in an unprecedented microwave frequency range of 210–420 GHz and in the pressure range of up to 1.6 GPa, we demonstrate that a combination of high-pressure ESR probe and high-field/multi-frequency spectrometer allows us to measure the spin relaxation rates in conducting spin systems, like the quasi-1D conductor, KC₆₀.     

In-situ fabrication of three-dimensionally confined GaAs and InAs volumes via growth on non-planar patterned GaAs(001) substrates

Three-dimensionally confined GaAs/AlGaAs and InAs/GaAs structures on 100 oriented square mesas patterned onto GaAs(001) substrates are realized, in-situ, via size-reducing molecular beam epitaxy. Two stages of mesa top pinch-off involving {103} and subsequently {101} side facets are revealed. GaAs and InAs quantum boxes with lateral linear dimensions down to 40 nm and confined by AlGaAs and GaAs, respectively, are reported. For InAs, the strain relief in mesas is found to enhance the well known 2 ML thickness for three-dimensional island formation on unpatterned substrates to, remarkably, >5 ML for mesa size 75 nm. Cathodoluminescence emission from the InAs on the mesa top attests to its good optical quality.     

Enantioselective Synthesis of (−)‐Halenaquinone

The efficient, 12–14 step (LLS) total synthesis of (?)‐halenaquinone has been achieved. Key steps in the synthetic sequence include: (a) proline sulfonamide‐catalyzed, Yamada–Otani reaction to establish the C6 all‐carbon quaternary stereocenter, (b) multiple, novel palladium‐mediated oxidative cyclizations to introduce the furan moiety, and (c) oxidative Bergman cyclization to form the final quinone ring.     

Total synthesis of cytotoxic macrolide amphidinolide B1 and the proposed structure of amphidinolide B2

The first enantioselective total syntheses of cytotoxic macrolide amphidinolide B1 and the proposed structure for amphidinolide B2 have been accomplished. Key features of the syntheses include a diastereoselective aldol condensation, a spontaneous Wadsworth-Emmons macrocyclization and a directed epoxidation/elimination sequence.     

Synthesis of tetra-ortho-substituted, phosphorus-containing and carbonyl-containing biaryls utilizing a Diels-Alder approach

The application of the Diels-Alder approach to biaryls (DAB) is described for the synthesis of tetra-ortho-substituted biaryl compounds containing orthogonally functionalized substituents. The syntheses of phosphorus-containing, disubstituted alkynes and carbonyl-containing, disubstituted alkynes were accomplished in two to three steps from commercially available reagents. Subsequent Diels-Alder cycloadditions with a range of oxygenated dienes yielded the target biaryls. Further functionalization through palladium-couplings is demonstrated on the phosphorus-containing biaryls. In addition, selective manipulation of each of the remaining ortho substituents on the phosphorus-containing biaryls is demonstrated. One of these phosphorus-containing derivatives is utilized as a highly active catalyst for Suzuki coupling. For the carbonyl-containing series, a wide range of dienophile substituents were screened including esters, ketones, and amides. The key Diels-Alder cycloadditions proceeded smoothly with the commercially available 1-methoxy-1,3-cyclohexadiene to yield the resultant tetra-ortho-substituted biaryls with excellent regioselectivity. The scope of the cycloaddition process was also explored on the carbonyl-containing dienophiles with a series of cyclic dienes. Acyclic dienes were also screened; however, they did not prove effective in the Diels-Alder process with the carbonyl-containing acetylenes. The ability to isolate enantiomerically pure biaryl atropisomers using a benzyl oxazolidinone is disclosed. Finally, the subsequent conversion to an axially chiral anilino alcohol is also reported.     

Stereoselective synthesis of a MCHr1 antagonist

Melanin-concentrating hormone (MCH) is implicated in the feeding behavior in mammals affording a potential target to control overeating in people. Compound 1 (AMG 076) has been identified as a potent MCHr1 antagonist for the treatment of obesity. A synthesis suitable for the large-scale preparation of this lead candidate was developed to support preclinical studies. A Robinson annulation of benzylpiperidone and resolution of the desired enone from a mixture of the diastereomers afforded key intermediate 6 after a stereoselective hydrogenation. Subsequent Fischer indole synthesis with hydrazine 5 then provided the advanced intermediate, indole 2. Two complementary reductive amination strategies employing either aldehyde 3 or lactol 4 led to the synthesis of title compound 1.     

Increasing the pump-up rate to polarize He gas using spin-exchange optical pumping method

In recent years, polarized ³He gas has increasingly been used as neutron polarizers and polarization analyzers. Two of the leading methods to polarize the ³He gas are the spin-exchange optical pumping (SEOP) method and the meta-stable exchange optical pumping (MEOP) method. At present, the SEOP setup is comparatively compact due to the fact that it does not require the sophisticated compressor system used in the MEOP method. The temperature and the laser power available determine the speed, at which the SEOP method polarizes the ³He gas. For the quantity of gas typically used in neutron scattering work, this speed is independent of the quantity of the gas required, whereas the polarizing time using the MEOP method is proportional to the quantity of gas required. Currently, using the SEOP method to polarize several bar-liters of ³He to 70% polarization would require 20−40 h. This is an order of magnitude longer than the MEOP method for the same quantity of gas and polarization. It would therefore be advantageous to speed up the SEOP process. In this article, we analyze the requirements for temperature, laser power, and the type of alkali used in order to shorten the time required to polarize ³He gas using the SEOP method.