Nonseparable closed vector subspaces of separable topological vector spaces

In 1983 P. Domański investigated the question: For which separable topological vector spaces E, does the separable space Open image in new window have a nonseparable closed vector subspace, where \(\hbox {c}\) is the cardinality of the continuum? He provided a partial answer, proving that every separable topological vector space whose completion is not q-minimal (in particular, every separable infinite-dimensional Banach space) E has this property. Using a result of S.A. Saxon, we show that for a separable locally convex space (lcs) E, the product space Open image in new window has a nonseparable closed vector subspace if and only if E does not have the weak topology. On the other hand, we prove that every metrizable vector subspace of the product of any number of separable Hausdorff lcs is separable. We show however that for the classical Michael line \(\mathbb M\) the space of all continuous real-valued functions on \(\mathbb M\) endowed with the pointwise convergence topology, \(C_p(\mathbb M)\) contains a nonseparable closed vector subspace while \(C_p(\mathbb M)\) is separable.     

Experimental observation of different-order components of a vibrational wave packet in a bulk dielectric using high-order Raman scattering

We use high-order Raman scattering in a bulk dielectric to characterize coherent dynamics with precision typical for gas phase experiments. The experimental pump-probe approach allows for the simultaneous observation and separation in space and time of the individual contributions of different-order Raman processes to a coherent wave packet without relying on phase-matching conditions and within the same experimental geometry. We propose a novel technique to discriminate between stimulated excitation of vibronic levels in the impulsive and intermediate excitation regimes, futhermore allowing us to distinguish between different pathways contributing to the same fifth-order Raman processes.     

Synchronization,zero-resistance states and rotating Wigner crystal

We show, in a framework of a classical nonequilibrium model, that rotational angles of electrons moving in two dimensions (2D) in a perpendicular magnetic field can be synchronized by an external microwave field whose frequency is close to the Larmor frequency. The synchronization eliminates collisions between electrons and thus creates a regime with zero diffusion corresponding to the zero-resistance states observed in experiments with high mobility 2D electron gas (2DEG). For long range Coulomb interactions electrons form a rotating hexagonal Wigner crystal. Possible relevance of this effect of synchronization-induced self-assembly for planetary rings is discussed.     

From complete to modulated synchrony in networks of identical Hindmarsh-Rose neurons

In most cases tendency to synchrony in networks of oscillatory units increases with the coupling strength. Using the popular Hindmarsh-Rose neuronal model, we demonstrate that even for identical neurons and simple coupling the dynamics can be more complicated. Our numerical analysis for globally coupled systems and oscillator lattices reveals a new scenario of synchrony breaking with the increase of coupling, resulting in a quasiperiodic, modulated synchronous state.     

Interaction of 1,3,2,4-benzodithiadiazines and their 1-Se congeners with Ph3P and some properties of the iminophosphorane products

Interaction between Ph(3)P and 1,3,2,4-benzodithiadiazine (1); its 6,7-difluoro (2), 5,6,8-trifluoro (3) and 5,6,7,8-tetrafluoro (4) derivatives; and 5,6,8-trifluoro-3,1,2,4-benzothiaselenadiazine (5) proceeded via a 1:1 condensation to give Ph(3)P═N-R iminophosphoranes (1a-5a, R = corresponding 1,2,3-benzodichalcogenazol-2-yls), which are inaccessible by general approaches based on the Staudinger and Kirsanov reactions. In contrast, neither Ph(3)As nor Ph(3)Sb reacted with 1 and 4. Molecular structures of 1a-5a and 5 were confirmed by X-ray diffraction (XRD). The crystals formed by chiral molecules of 2a-5a were racemic, whereas the crystal of 1a was formed by a single enantiomer. In all of the Ph(3)P═N-R derivatives, one of the Ph rings is oriented face-to-face to the hetero ring, R. Upon heating to ～120 °C in squalane (1a, 3a, 4a) or dissolving in chloroform at ambient temperatures (1a, 2a, 4a), the Ph(3)P═N-R derivatives generated the 1,2,3-benzodithiazolyls (1b-4b, respectively) whose identity was confirmed by electron paramagnetic resonance (EPR). 2,1,3-Benzothiaselenazolyls 5b and 6b were detected by EPR as the main paramagnetic products of solution thermolysis of 5 and its 5,6,7,8-tetrafluoro congener (6), respectively. Passing a chloroform solution of 4a through silica column unexpectedly gave 5-6-6-6 tetracyclic (9) and 6-10-6 tricyclic (10) sulfur-nitrogen compounds, which were characterized by XRD.     

TPGS-750-M: a second-generation amphiphile for metal-catalyzed cross-couplings in water at room temperature

An environmentally benign surfactant (TPGS-750-M), a diester composed of racemic α-tocopherol, MPEG-750, and succinic acid, has been designed and readily prepared as an effective nanomicelle-forming species for general use in metal-catalyzed cross-coupling reactions in water. Several "name" reactions, including Heck, Suzuki-Miyaura, Sonogashira, and Negishi-like couplings, have been studied using this technology, as have aminations, C-H activations, and olefin metathesis reactions. Physical data in the form of DLS and cryo-TEM measurements suggest that particle size and shape are key elements in achieving high levels of conversion and, hence, good isolated yields of products. This new amphiphile will soon be commercially available.     

Cross-couplings of alkyl halides with heteroaromatic halides, in water at room temperature

Zn-mediated, Pd-catalyzed cross-coupling reactions between heteroaromatic and alkyl halides can be done at room temperature in pure water using a commercially available Pd catalyst and PTS, a nanomicelle-forming amphiphile. Notably, zinc metal inserts selectively into a carbon sp³-halide bond, while palladium adds oxidatively to a carbon sp²-bond.     

Employing modular polyketide synthase ketoreductases as biocatalysts in the preparative chemoenzymatic syntheses of diketide chiral building blocks

Chiral building blocks are valuable intermediates in the syntheses of natural products and pharmaceuticals. A scalable chemoenzymatic route to chiral diketides has been developed that includes the general synthesis of α-substituted, β-ketoacyl N-acetylcysteamine thioesters followed by a biocatalytic cycle in which a glucose-fueled NADPH-regeneration system drives reductions catalyzed by isolated modular polyketide synthase (PKS) ketoreductases (KRs). To identify KRs that operate as active, stereospecific biocatalysts, 11 isolated KRs were incubated with 5 diketides and their products were analyzed by chiral chromatography. KRs that naturally reduce small polyketide intermediates were the most active and stereospecific toward the panel of diketides. Several biocatalytic reactions were scaled up to yield more than 100?mg of product. These syntheses demonstrate the ability of PKS enzymes to economically and greenly generate diverse chiral building blocks on a preparative scale.