An Immobilized‐Dirhodium Hollow‐Fiber Flow Reactor for Scalable and Sustainable C−H Functionalization in Continuous Flow

A scalable flow reactor is demonstrated for enantioselective and regioselective rhodium carbene reactions (cyclopropanation and C?H functionalization) by developing cascade reaction methods employing a microfluidic flow reactor system containing immobilized dirhodium catalysts in conjunction with the flow synthesis of diazo compounds. This allows the utilization of the energetic diazo compounds in a safe manner and the recycling of the dirhodium catalysts multiple times. This approach is amenable to application in a bulk‐scale synthesis employing asymmetric C?H functionalization by stacking multiple fibers in one reactor module. The products from this sequential flow–flow reactor are compared with a conventional batch reactor or flow–batch reactor in terms of yield, regioselectivity, and enantioselectivity.     

A method for C2 acylation of 1,3-indandiones

The 1,3-indandione scaffold is an important structural motif used in the preparation of a large number of industrial chemical and pharmaceutical compounds. However, few approaches allow for the direct C2 acylation on these building blocks. A method was developed using DMAP and EDCI, which is mild in reactivity, covers a diverse range of carboxylic acid acylating agents, is compatible with electron releasing and withdrawing substituents on the 1,3-indandione partner, and performs well in a polar aprotic solvent (for solubility reasons) This method cleanly afforded twenty five different products in yields of 32–96%.     

Efficient CO2 Removal for Ultra‐Pure CO Production by Two Hybrid Ultramicroporous Materials

Removal of CO₂ from CO gas mixtures is a necessary but challenging step during production of ultra‐pure CO as processed from either steam reforming of hydrocarbons or CO₂ reduction. Herein, two hybrid ultramicroporous materials (HUMs), SIFSIX‐3‐Ni and TIFSIX‐2‐Cu‐i , which are known to exhibit strong affinity for CO₂, were examined with respect to their performance for this separation. The single‐gas CO sorption isotherms of these HUMs were measured for the first time and are indicative of weak affinity for CO and benchmark CO₂/CO selectivity (>4000 for SIFSIX‐3‐Ni ). This prompted us to conduct dynamic breakthrough experiments and compare performance with other porous materials. Ultra‐pure CO (99.99 %) was thereby obtained from CO gas mixtures containing both trace (1 %) and bulk (50 %) levels of CO₂ in a one‐step physisorption‐based separation process.     

Interfacial Nanoprecipitation toward Stable and Responsive Microbubbles and Their Use as a Resuscitative Fluid

A new approach has been developed to prepare stable microbubbles (MBs) by interfacial nanoprecipitation of bioabsorbable polymers at air/liquid interfaces. This facile method offers robust control over the morphology and chemophysical properties of MBs by simple chemical modifications. This approach is amenable to large‐scale manufacturing, and is useful to develop functional MBs for advanced biomedical applications. To demonstrate this, a MB‐based intravenous oxygen carrier was created that undergoes pH‐triggered self‐elimination. Intravenous injection of previous MBs increased the risk of pulmonary vascular obstruction. However, we show, for the first time, that our current design is superior, as they 1) yielded no evidence of acute risks in rodents, and 2) improved the survival in a disease model of asphyxial cardiac arrest (from 0 to 100 %), a condition that affects more than 100 000 in‐hospital patients, and carries a mortality of about 90 %.     

Generalizations of Non-Commutative Neutrix Convolution Products of Functions

The non-commutative neutrix convolution product of the functions x ^r cos_–(x) and x ^s cos₊(x) is evaluated. Further similar non-commutative neutrix convolution products are evaluated and deduced.     

Explicit Betti numbers for a family of nilpotent Lie algebras

Betti numbers for the Heisenberg Lie algebras were calculated by Santharoubane in his 1983 paper. However few other examples have appeared in the literature. In this note we give the Betti numbers for a family of -dimensional 2-step nilpotent extensions of by .

     

Weak amenability and the second dual of the Fourier algebra

Let be a locally compact group. We will consider amenability and weak amenability for Banach algebras which are quotients of the second dual of the Fourier algebra. In particular, we will show that if is weakly amenable, then has no infinite abelian subgroup.

     

Anticanonical Rational Surfaces

A determination of the fixed components, base points and irregularity is made for arbitrary numerically effective divisors on any smooth projective rational surface having an effective anticanonical divisor. All of the results are proven over an algebraically closed field of arbitrary characteristic. Applications, to be treated in separate papers, include questions involving: points in good position, birational models of rational surfaces in projective space, and resolutions for 0-dimensional subschemes of defined by complete ideals.

     

Molecular Structure of 1-Substituted Bicyclo[2.2.0]hexanes: A Combined X-Ray Structural and Ab Initio Study

The synthesis and X-ray crystal structure of the p-bromoanilide derivative of bicyclo[2.2.0]hexane-l-carboxylic acid (1), N-(4-bromophenyl)-bicyclo[2.2.0]hexane-l-carboxamide (2), is reported. N-(4-Bromophenyl)-bicyclo[2.2.0]hexane-l-carboxamide is synthesized in good yield via the DCC coupling of bicyclo[2.2.0]hexane-l-carboxylic acid (1) with p-bromoaniline. Low-temperature X-ray analysis of 2 reveals that the bonds of the bicyclo[2.2.0]hexane skeleton vicinal to the amide group show a slight lengthening due to conjugative interaction with the -accepting amide group. Ab initio calculations at the 6-31G* level of theory on bicyclo[2.2.0]hexane-l-carboxamide, a model for 2, and for other 1-substituted bicyclo[2.2.0]hexanes are also reported.     

Numerical Simulations of Random Walk in Random Environment

This paper is concerned with the numerical simulation of a random walk in a random environment in dimension d = 2. Consider a nearest neighbor random walk on the 2-dimensional integer lattice. The transition probabilities at each site are assumed to be themselves random variables, but fixed for all time. This is the random environment. Consider a parallel strip of radius R centered on an axis through the origin. Let X _R be the probability that the walk that started at the origin exits the strip through one of the boundary lines. Then X _R is a random variable, depending on the environment. In dimension d = 1, the variable X _R converges in distribution to the Bernoulli variable, X = 0, 1 with equal probability, as R . Here the 2-dimensional problem is studied using Gauss-Seidel and multigrid algorithms.