Two 2,6‐Dioxabicyclo[3.3.1]nonan‐3‐ones from Phragmanthera capitata (Spreng.) Balle (Loranthaceae)

Phytochemical investigation of the leaves of Phragmanthera capitata collected on Cassia spectabilis tree led to the isolation of two natural lactones, rel‐(1R,5S,7S)‐7‐[2‐(4‐hydroxyphenyl)ethyl]‐2,6‐dioxabicyclo[3.3.1]nonan‐3‐one ( 1 ) and 4‐{2‐[rel‐(1R,3R,5S)‐7‐oxo‐2,6‐dioxabicyclo[3.3.1]non‐3‐yl]ethyl}phenyl 3,4,5‐trihydroxybenzoate ( 2 ) together with the known compounds betulinic acid ( 3 ), dodoneine ( 4 ), quercetin 3‐O‐α‐L ‐rhamnopyranoside ( 5 ), quercetin 3‐O‐α‐L ‐arabinofuranoside ( 6 ), quercetin ( 7 ), betulin ( 8 ), lupeol ( 9 ), and sitosterol ( 10 ). Their structures were established by means of modern spectroscopic techniques, and the relative configuration of compound 1 was confirmed by X‐ray analysis. Compounds 1 and 2 were tested in vitro for their antiplasmodial activity against the Plasmodium falciparum chloroquine sensitive‐strains NF54 and 3D7. Compound 2 exhibited good antiplasmodial activity against both strains with IC₅₀ of 2.4 and 4.9 μM , respectively, while compound 1 was inactive.     

Comparing Cyclophellitol N‐Alkyl and N‐Acyl Cyclophellitol Aziridines as Activity‐Based Glycosidase Probes

The synthesis and evaluation as activity‐based probes (ABPs) of three configurationally distinct, fluorescent N‐alkyl cyclophellitol aziridine isosteres for profiling GH1 β‐glucosidase (GBA), GH27 α‐galactosidase (GLA) and GH29 α‐fucosidase (FUCA) is described. In comparison with the corresponding acyl aziridine ABPs reported previously, the alkyl aziridine ABPs are synthesized easily and are more stable in mild acidic and basic media, and are thus easier to handle. The β‐glucose‐configured alkyl aziridine ABP proves equally effective in labeling GBA as its N‐acyl counterpart, whereas the N‐acyl aziridines targeting GLA and FUCA outperform their N‐alkyl counterparts. Alkyl aziridines can therefore be an attractive alternative in retaining glycosidase ABP design, but in targeting a new retaining glycosidase both N‐alkyl and N‐acyl aziridines are best considered at the onset of a new study.     

A Remarkably Simple Class of Imidazolium‐Based Lipids and Their Biological Properties

A series of imidazolium salts bearing two alkyl chains in the backbone of the imidazolium core were synthesized, resembling the structure of lipids. Their antibacterial activity and cytotoxicity were evaluated using Gram‐positive and Gram‐negative bacteria and eukaryotic cell lines including tumor cells. It is shown that the length of alkyl chains in the backbone is vital for the antibiofilm activities of these lipid‐mimicking components. In addition to their biological activity, their surface activity and their membrane interactions are shown by film balance and quartz crystal microbalance (QCM) measurements. The structure–activity relationship indicates that the distinctive chemical structure contributes considerably to the biological activities of this novel class of lipids.     

On the $${\mathcal {}}$$-free extension complexity of the TSP

It is known that the extension complexity of the TSP polytope for the complete graph \(K_n\) is exponential in n even if the subtour inequalities are excluded. In this article we study the polytopes formed by removing other subsets \({\mathcal {H}}\) of facet-defining inequalities of the TSP polytope. In particular, we consider the case when \({\mathcal {H}}\) is either the set of blossom inequalities or the simple comb inequalities. These inequalities are routinely used in cutting plane algorithms for the TSP. We show that the extension complexity remains exponential even if we exclude these inequalities. In addition we show that the extension complexity of polytope formed by all comb inequalities is exponential. For our proofs, we introduce a subclass of comb inequalities, called (h, t)-uniform inequalities, which may be of independent interest.     

Hochster’s small MCM conjecture for three-dimensional weakly F-split rings

We prove Hochster’s small maximal Cohen–Macaulay conjecture for three-dimensional complete F-pure rings. We deduce this from a more general criterion, and show that only a weakening of the notion of F-purity is needed, to wit, being weakly F-split. We conjecture that any complete ring is weakly F-split.     

The low Reynolds number turbulent flow and mixing in a confined impinging jet reactor

Turbulent mixing takes an important role in chemical engineering, especially when the chemical reaction is fast compared to the mixing time. In this context a detailed knowledge of the flow field, the distribution of turbulent kinetic energy (TKE) and its dissipation rate is important, as these quantities are used for many mixing models. For this reason we conduct a direct numerical simulation (DNS) of a confined impinging jet reactor (CIJR) at Re = 500 and Sc = 1. The data is compared with particle image velocimetry (PIV) measurements and the basic flow features match between simulation and experiment. The DNS data is analysed and it is shown that the flow is dominated by a stable vortex in the main mixing duct. High intensities of turbulent kinetic energy and dissipation are found in the impingement zone which decrease rapidly towards the exit of the CIJR. In the whole CIJR the turbulence is not in equilibrium. The strong mixing in the impingement zone leads to a rapid development of a monomodal PDF. Due to the special properties of the flow field, a bimodal PDF is generated in cross-sections downstream the impingement zone, that slowly relaxes under relaminarising conditions. The time required for meso-mixing is dominating the overall mixing performance.     

An Overview on Non-Ideal Vibrations

We analyze the dynamical coupling between energy sources and structural response that must not be ignored in real engineering problems, since real motors have limited output power.     

Stability of Relative Equilibria. Part I: Comparison of Four Methods

In this first part of the paper, we review methods for the investigation of stability of relative equilibria of symmetric Hamiltonian systems and explain them by means of the model problem of a rotating pendulum. For this example the modern approaches, known as energy momentum methods are compared with stability assessment by linearization and by the classical method of Routh.