On some combinatorial properties of algebraic matroids

It was proved implicitly by Ingleton and Main and explicitly by Lindström that if three lines in the algebraic matroid consisting of all elements of an algebraically closed field are not coplanar, but any two of them are, then they pass through one point. This theorem is extended to a more general result about the intersection of subspaces in full algebraic matroids. This result is used to show that the minimax theorem for matroid matching, proved for linear matroids by Lovász, remains valid for algebraic matroids.     

CARS measurements of temperature and species concentrations in an IC engine

Temperature measurements alone, and also simultaneous CO₂ concentration and temperature measurements, have been performed inside a fired IC engine. To tackle the two main problems encounted when making measurements in an engine (i.e., cycle-to-cycle variations and beam steering by density gradients), the shot-by-shot referencing technique and the in situ referencing technique using N₂ to determine [CO₂] were used. The temperature is deduced from the broadband N₂ CARS signal and narrow band detection is used for CO₂. A representative example of temperature measurements is given which shows a correlation between temperature and knocking intensity in the burnt gas of a knocking engine. The first simultaneous determinations of temperature and [CO₂] are also reported; so far these are reliable only during the compression stoke.     

Partial differential equations with differential constraints

A geometric setting for constrained exterior differential systems on fibered manifolds with n-dimensional bases is proposed. Constraints given as submanifolds of jet bundles (locally defined by systems of first-order partial differential equations) are shown to carry a natural geometric structure, called the canonical distribution. Systems of second-order partial differential equations subjected to differential constraints are modeled as exterior differential systems defined on constraint submanifolds. As an important particular case, Lagrangian systems subjected to first-order differential constraints are considered. Different kinds of constraints are introduced and investigated (Lagrangian constraints, constraints adapted to the fibered structure, constraints arising from a (co)distribution, semi-holonomic constraints, holonomic constraints).     

ChemInform Abstract: A New n = 4 Layered Ruddlesden—Popper Phase K2.5Bi2.5Ti4O13 Showing Stoichiometric Hydration.

Polycrystalline K_2.5Bi_2.5Ti₄O₁₃ (I) is prepared by solid state reaction of KNO₃, Bi₂O₃, and TiO₂ (Al₂O₃ crucible, 750 °C, 16 h).     

Biomimetic total synthesis and structure confirmation of myrtucommulone K

A confirmed structure of meroterpenoid myrtucommulone K, which is vastly different from the originally reported one, is conducted. The first biomimetic total synthesis towards the assignment of its absolute configuration has been efficiently accessed in 5 steps, and key to the success was a heteroatom Diels-Alder cycloaddition. The structure of myrtucommulone K was re-elucidated and confirmed by extensive spectroscopic interpretation of 1D and 2D NMR.     

Enantioselective Synthesis of (+)-Mitomycin K by a Palladium-Catalyzed Oxidative Tandem Cyclization

The mitomycins, a family of bioactive natural products, feature a compact 6/5/5-fused polycyclic ring structure densely decorated with highly reactive and/or fragile quinone, amino ketal, and aziridine as well as carbamate moieties. It is this striking feature that has defeated numerous synthetic attempts towards these apparently small molecules, rendering them one of the most formidable targets for total synthesis. We herein report the first enantioselective synthesis of (+)-mitomycin K, a representative of G series mitomycins. The key step of this synthesis is an enantioselective oxidative cyclization catalyzed by a palladium/(+)-sparteine system that had previously been developed by our group. The robustness of this method bodes well for further applications in the asymmetric total synthesis of natural products, particularly those with characteristic 6/5/5-fused pyrroloindole skeletons.     

Anti-inflammatory chromone alkaloids and glycoside from Dysoxylum binectariferum

Herein we report isolation of a new chromone alkaloid chrotacumine K (12) from fruits and a chromone glycoside schumaniofioside A (13) from leaves of Dysoxylum binectariferum Hook f. Schumaniofioside A is reported for the first time from Meliaceae family. Other known alkaloids isolated include rohitukine (1) and chrotacumine E (6). The structure of new alkaloid 12 was elucidated on the basis of extensive 1D and 2D NMR analysis, synthesis and chemical hydrolysis. Chemically, chrotacumine K (12) is a 3′-O-acetyl rohitukine which on chemical or enzymatic hydrolysis produces rohitukine. The new alkaloid 12 is also present in seeds and stem-barks of this plant. The glycoside schumaniofioside A (13) is present only in leaves, and in abundance (～1% w/w of dried leaves). The isolated compounds and extracts were evaluated for in vitro effect on the proinflammatory cytokines (TNF-α and IL-6) in human monocytic THP-1 cells. The alkaloid 12 displayed potent inhibition (57%) of TNF-α at 0.3 µM, and was non-toxic to THP-1 cells up to 40 µM, indicating its excellent therapeutic window. Furthermore, a nitrobenzoyl ester analog 15e showed better inhibition of IL-6 than parent natural product chrotacumine K.     

On a Serrin-Type Regularity Criterion for the Navier–Stokes Equations in Terms of the Pressure

We prove a Serrin-type regularity result for Leray–Hopf solutions to the Navier–Stokes equations, extending a recent result of Zhou [28].     

Spectral Element Discretization of the Circular Driven Cavity. Part IV: The Navier-Stokes Equations

This paper deals with the spectral element discretization of the Navier-Stokes equations in a disk with discontinuous boundary data, which is known as the driven cavity problem. The numerical treatment does not involve any regularization of these data. Relying on a variational formulation in the primitive variables of velocity and pressure, we describe a discretization of these equations and derive error estimates in appropriate weighted Sobolev spaces. We propose an algorithm to solve the nonlinear discrete system and present numerical experiments to verify its efficiency.