Carboxyboronate: A Versatile C1 Building Block

The synthesis and applications of carboxy‐MIDA‐boronate, a novel C1 building block, are described. This molecule is accessible via a ruthenium tetraoxide‐mediated cleavage of commercially available ethynyl‐MIDA‐boronate. In the course of this study, carboxy‐MIDA‐boronate was found to possess ambident reactivity towards nucleophiles. Carboxylic acid derivatization produces a broad range of previously unknown carbamoyl‐, oxycarbo‐ and thiocarboboronates. Carboxy‐MIDA‐boronate and its derivatives undergo condensations to access borylated heterocycles with boron at positions that are difficult to access using alternate methods. The resulting heterocycles participate in the Suzuki–Miyaura cross‐coupling reaction, enabling entry into diverse bis(heteroaryl) motifs. The carbon monoxide‐releasing capacity of carboxy‐MIDA‐boronate was also examined and applied in palladium‐catalyzed carbonylation.     

The effect of two distinct fast time scales in the rotating,stratified Boussinesq equations: variations from quasi-geostrophy

Inspired by the use of fast singular limits in time-parallel numerical methods for a single fast frequency, we consider the limiting, nonlinear dynamics for a system of partial differential equations when two fast, distinct time scales are present. First-order slow equations are derived via the method of multiple time scales when the two small parameters are related by a rational power. We find that the resultant system depends only on the relationship of the two fast time scales, i.e. which fast time is fastest? Using the theory of cancellation of fast oscillations, we show that with the appropriate assumptions on the nonlinear operator of the full system, this reduced slow system is exactly that which the solution will converge to if each asymptotic limit is considered sequentially. The same result is also obtained via the method of renormalization. The specific example of the rotating, stratified Boussinesq equations is explored in detail, indicating that the most common distinguished limit of this system—quasi-geostrophy, is not the only limiting asymptotic system.     

A computational investigation of the finite-time blow-up of the 3D incompressible Euler equations based on the Voigt regularization

We report the results of a computational investigation of two blow-up criteria for the 3D incompressible Euler equations. One criterion was proven in a previous work, and a related criterion is proved here. These criteria are based on an inviscid regularization of the Euler equations known as the 3D Euler–Voigt equations, which are known to be globally well-posed. Moreover, simulations of the 3D Euler–Voigt equations also require less resolution than simulations of the 3D Euler equations for fixed values of the regularization parameter \(\alpha >0\). Therefore, the new blow-up criteria allow one to gain information about possible singularity formation in the 3D Euler equations indirectly, namely by simulating the better-behaved 3D Euler–Voigt equations. The new criteria are only known to be sufficient criterion for blow-up. Therefore, to test the robustness of the inviscid-regularization approach, we also investigate analogous criteria for blow-up of the 1D Burgers equation, where blow-up is well known to occur.     

Bismuth trichloride–mediated cleavage of phenolic methoxymethyl ethers

A simple and efficient method for removal of phenolic methoxymethyl ethers in the presence of 30 mol% of bismuth trichloride in acetonitrile/water is described. Notable features of the cleavage protocol entail use of an ecofriendly bismuth reagent, ease of handling, low cost, operational simplicity, and good functional group compatibility. A number of structurally varied phenolic methoxymethyl ethers were cleaved in good to excellent yields.     

Lowness for isomorphism,countable ideals,and computable traceability

We show that every countable ideal of degrees that are low for isomorphism is contained in a principal ideal of degrees that are low for isomorphism by adapting an exact pair construction. We further show that within the hyperimmune free degrees, lowness for isomorphism is entirely independent of computable traceability.     

Reactivity of Diarylnitrenium Ions

Hydride abstraction from diarylamines with the trityl ion is explored in an attempt to generate a stable diarylnitrenium ion, Ar₂N⁺. Sequential H-atom abstraction reactions ensue. The first H-atom abstraction leads to intensely colored aminium radical cations, Ar₂NH^.+, some of which are quite stable. However, most undergo a second H-atom abstraction leading to ammonium ions, Ar₂NH₂⁺. In the absence of a ready source of H-atoms, a unique self-abstraction reaction occurs when Ar=Me₅C₆, leading to a novel iminium radical cation, Ar=N^.+Ar, which decays via a second self H-atom abstraction reaction to give a stable iminium ion, Ar=N⁺HAr. These products differ substantially from those derived via photochemically produced diarylnitrenium ions.     

Reconfiguration graphs of shortest paths

For a graph $G$ and$a,b\in V\left(G\right)$, the shortest path reconfiguration graph of $G$ with respect to $a$ and$b$ is denoted by $S(G,a,b)$. The vertex set of $S(G,a,b)$ is the set of all shortest paths between $a$ and$b$ in $G$. Two vertices in $V\left(S(G,a,b)\right)$ are adjacent, if their corresponding paths in $G$ differ by exactly one vertex. This paper examines the properties of shortest path graphs. Results include establishing classes of graphs that appear as shortest path graphs, decompositions and sums involving shortest path graphs, and the complete classification of shortest path graphs with girth 5 or greater. We include an infinite family of well structured examples, showing that the shortest path graph of a grid graph is an induced subgraph of a lattice.     

The slow motion of two touching fluid spheres along their line of centers

The creeping motion along their line of centers of two fluid spheres in contact is analyzed. An exact solution is presented. Corrections to the Hadamard—Rybezynski equation are tabulated for various particle radii ratios and particle fluid to external fluid viscosity ratios. In the limit of infinite particle viscosity, these corrections are shown to agree with previous calculations for rigid spheres.     

The effect of hydrodynamic coupling on the thinning of a film between a drop and its homophase

The rate of thinning of a film trapped between a drop approaching its homophase according to a model incorporating hydrodynamic coupling is dramatically different from earlier, uncoupled models. Implications for film thinning of microflows analyzed in the preceding paper are here investigated using similar analytical methods to derive a nonautonomous, nonlinear evolution equation for the film thickness which has been solved numerically under a variety of conditions after asymptotic analytical behavior has been extracted. The applied force squeezing the film, together with the initial motion in the three phases, determines the rate of film thinning in a complicated manner through the coupling parameter R = (ρ_Aμ_A/ρ_Bμ_B)^{$\text{1}\text{2}$}. Experimental observations that normal drop circulation enhances thinning, whereas reversed drop circulation can cause thickening, are predicted theoretically for the first time. Films much more viscous than their surroundings are found to thin faster than the converse case, a conclusion at odds with offhand intuition but substantiated experimentally; both classes of systems behave differently, often qualitatively so, from predictions of hydrodynamically decoupled systems, and in particular film thinning rates are generally faster because of less resistance to drainage, although the limit of vanishing R does recover the special case of Reynolds' model. For short times, films are shown analytically to thin more rapidly if there is initially outward film motion and normal drop circulation, but with decreasing effectiveness as R increases, in contrast to the effect of R for intermediate and longer times; if there is initially inward film motion, thickening tendencies are enhanced by reverse drop circulation but with decreasing effectiveness as R increases. These and other detailed conclusions, most predicted theoretically for the first time, are not only in qualitative agreement with experimental observations, they are in quantitative agreement with available data.