Latin cubes of order ⩽5

If c_n represents the number of reduced Latin cubes of order n then c₁ = c₂ = c₃ = 1, c₄ = 64 and c₅ = 40246. Moreover ifλ_n and λ′_n denote the number of disjoint isomorphism and isotopy classes of reduced Latin cubes of order n respectively, then λ_n = λ′_n = 1 for n ? 3 while λ₄ = 19, λ′₄ = 12, and λ₅ = 1860.     

Proton-detected solid-state NMR spectroscopy of fully protonated proteins at 40 kHz magic-angle spinning

Remarkable progress in solid-state NMR has enabled complete structure determination of uniformly labeled proteins in the size range of 5-10 kDa. Expanding these applications to larger or mass-limited systems requires further improvements in spectral sensitivity, for which inverse detection of 13C and 15N signals with 1H is one promising approach. Proton detection has previously been demonstrated to offer sensitivity benefits in the limit of sparse protonation or with approximately 30 kHz magic-angle spinning (MAS). Here we focus on experimental schemes for proteins with approximately 100% protonation. Full protonation simplifies sample preparation and permits more complete chemical shift information to be obtained from a single sample. We demonstrate experimental schemes using the fully protonated, uniformly 13C,15N-labeled protein GB1 at 40 kHz MAS rate with 1.6-mm rotors. At 500 MHz proton frequency, 1-ppm proton line widths were observed (500 +/- 150 Hz), and the sensitivity was enhanced by 3 and 4 times, respectively, versus direct 13C and 15N detection. The enhanced sensitivity enabled a family of 3D experiments for spectral assignment to be performed in a time-efficient manner with less than a micromole of protein. CANH, CONH, and NCAH 3D spectra provided sufficient resolution and sensitivity to make full backbone and partial side-chain proton assignments. At 750 MHz proton frequency and 40 kHz MAS rate, proton line widths improve further in an absolute sense (360 +/- 115 Hz). Sensitivity and resolution increase in a better than linear manner with increasing magnetic field, resulting in 14 times greater sensitivity for 1H detection relative to that of 15N detection.     

Dynamic axial ligand-site exchange in facially discriminated ruthenium(II) carbonyl and rhodium(III) halide metalloporphyrins

For a series of six-coordinate RuII(CO)L or RhIII(X-)L porphyrins, which are facially differentiated by having a naphthoquinol- or hydroquinol-containing strap across one face, we show that ligand migration from one face to the other can occur under mild conditions and that ligand-site preference is dependent on the nature of L and X-. For bulky nitrogen-based ligands, the strap can be displaced sideways to accommodate the ligand on the same side as the strap. For the ligand pyrazine, we show 1H NMR evidence for monodentate and bridging binding modes on both faces, dependent on ligand concentration and metalloporphyrin structure, and that interfacial migration is rapid under normal conditions. For monodentate substituted pyridine ligands, there is a site-dependence on structure, and we show clear evidence of dynamic ligand migration through a series of ligand-exchange reactions.     

The Cascade Reactions of Indigo with Propargyl Substrates for Heterocyclic and Photophysical Diversity

The synthesis of structurally diverse heterocycles for chemical space exploration was achieved via the cascade reactions of indigo with propargylic electrophiles. New pyrazinodiindolodione, naphthyridinedione, azepinodiindolone, oxazinoindolone and pyrrolodione products were prepared in one pot reactions by varying the leaving group (-Cl, -Br, -OMs, -OTs) or propargyl terminal functionality (-H, -Me, -Ph, -Ar). Mechanistic and density functional theory studies revealed that the unsaturated propargyl moiety can behave as an electrophile when aromatic terminal substitutions are made, and therefore competes with leaving group substitution for new outcomes. Selected products from the cascade reactions were investigated for their absorption and fluorescence properties, including transient absorption spectroscopy. This revealed polarity dependent excited state relaxation pathways, fluorescence, and triplet formation, thus highlighting these reactions as a means to access diverse functional materials rapidly.     

Diastereoselective 1,3-dipolar cycloaddition of pyrylium ylides with chiral enamides

Chiral enamides 5f-i were found to react with pyrylium ylides to give cycloadducts 6d-i in good yields with an excellent level of stereoselectivity. The chiral auxiliary was successfully removed on hydrogenolysis of compound 6f in continuous flow (H-Cube) resulting in the first asymmetric synthesis of complex amine 8.     

Morphology of U<Subscript>3</Subscript>O<Subscript>8</Subscript> materials following storage under controlled conditions of temperature and relative humidity

Changes in the visual characteristics of uranium oxide surfaces and morphology following storage under different conditions of temperature and relative humidity may provide insight into the history of an unknown sample. Sub-samples of three α-U₃O₈ materials—one that was phase-pure and two that were phase-impure—were stored under controlled conditions for two years. Scanning electron microscopy was used to image the oxides before and after storage, and a morphology lexicon was used to characterize the images. Temporal changes in morphology were observed in some sub-samples, and changes were greatest following exposure to high relative humidity.     

Sudoku-like arrays,codes and orthogonality

This paper is concerned with constructions and orthogonality of generalized Sudoku arrays of various forms. We characterize these arrays based on their constraints; for example Sudoku squares are characterized by having strip and sub-square constraints. First, we generalize Sudoku squares to be multi-dimensional arrays with strip and sub-cube constraints and construct mutually orthogonal sets of these arrays using linear polynomials. We add additional constraints motivated by elementary intervals for low discrepancy sequences and again give a construction of these arrays using linear polynomials in detail for 3 dimensional and a general construction method for arbitrary dimension. Then we give a different construction of these hypercubes due to MDS codes. We also analyze the orthogonality of all of the Sudoku-like hypercubes we consider in this paper.