Asymptotic centers and best compact approximation of operators intoC(K)

The existence of best compact approximations for all bounded linear operators fromX intoC(K) is related to the behavior of asymptotic centers inX ^*. IfK is just one convergent sequence, the condition is that everyω ^*-convergent sequence inX ^* will have an asymptotic center. We first study this property, solving some open problems in the theory of asymptotic centers. IfK is more “complex,” the asymptotic centers should behave “continuously.” We use this observation to construct operators fromC[0,1] intoC(ω ²) and from ?₁ intoL ₁ without best compact approximation. We also construct spacesX ₁,X ₂, isomorphic to a Hilbert space, and operatorsT ₁,∶X ₁→C(ω ²),T ₂∶?₁→X ₂ without best compact approximations.     

Automated antenna positioning algorithms for wireless fixed-access networks

This article addresses a real-life problem - obtaining communication links between multiple base station sites, by positioning a minimal set of fixed-access relay antenna sites on a given terrain. Reducing the number of relay antenna sites is considered critical due to substantial installation and maintenance costs. Despite the significant cost saved by eliminating even a single antenna site, an inefficient manual approach is employed due to the computational complexity of the problem. From the theoretical point of view we show that this problem is not only NP hard, but also does not have a constant approximation. In this paper we suggest several alternative automated heuristics, relying on terrain preprocessing to find educated potential points for positioning relay stations. A large-scale computer-based experiment consisting of approximately 7,000 different scenarios was conducted. The quality of alternative solutions was compared by isolating and displaying factors that were found to affect the standard deviation of the solutions supplied by the tested heuristics. The results of the simulation based experiments show that the saving potential increases when more base stations are needed to be interconnected. The designs of a human expert were compared to the automatically generated solutions for a small subset of the experiment scenarios. Our studies indicate that for small networks (e.g., connecting up to ten base stations), the results obtained by human experts are adequate although they rarely exceed the quality of automated alternatives. However, the process of obtaining these results in comparison to automated heuristics is longer. In addition, when more base station sites need to be interconnected, the human approach is easily outperformed by our heuristics, both in terms of better results (fewer antennas) and in significant shorter calculation times.     

Single-scan NMR spectroscopy at arbitrary dimensions

Multidimensional nuclear magnetic resonance (NMR) provides one of the foremost analytical tools available to elucidate the structure and dynamics of complex molecules in their native states. Executing this kind of experiment generally requires collecting an n-dimensional time-domain signal S, from which the spectrum arises via an appropriate Fourier analysis of its various time variables. This time-domain signal is actually measured directly only along one of the time axes, while the effects introduced by the remaining time variables are monitored via a parametric incrementation of their values throughout independent experiments. Two-dimensional (2D) NMR experiments thus usually require longer acquisition times than unidimensional experiments, 3D NMR is orders-of-magnitude more time consuming than 2D spectroscopy, etc. Very recently, we proposed and demonstrated an approach whereby data acquisition in 2D NMR can be parallelized, enabling the collection of complete 2D spectral sets within a single transient. The present paper discusses the extension of this 2D NMR methodology to an arbitrary number of dimensions. The principles of the ensuing ultrafast n-dimensional NMR approach are described, and a variety of homo- and heteronuclear 3D and 4D NMR spectra collected within a fraction of a second are presented.     

Enol-enamine tautomerism in crystals of 1,3-bis(pyridin-2-yl) propan-2-one: a combined crystallographic and quantum-chemical investigation of the effect of packing on tautomerization processes

The enolpyridine, OH-ketoenamime, NH equilibrium in crystals of 1,3-bis(pyridin-2-yl)propan-2-one was studied using temperature-dependent single-crystal X-ray diffraction. The relative population of the different tautomers was found to be sensitive to the temperature in the range of 100-300 K, illustrating the small thermodynamic difference between these two tautomers. This energy resemblance is partially attributed to the molecular packing in the crystal, where the molecules are arranged in the form of dimers. Ab initio electronic energy calculations (HF/6-31G** and MP2/6-31G**) reveal the effect of dimerization in the crystal on the electronic energy levels. Several tautomeric states were identified in the dimer of 1,3-bis(pyridin-2-yl)propan-2-one. A model is proposed in which four of these dimer states are populated in the crystal at ambient temperatures. The crystallographic data were treated according to this four-state dimer model, suggesting that the free energy of the OH-NH dimers is higher than that of the OH-OH dimers by 120 +/- 10 cal mol(-1) and that the NH-NH dimers are yet higher in free energy by 50 +/- 10 cal mol(-1).     

Apartments and the cayley-algebra module for G2(k)

The 7-dimensional Cayley-algebra module for the group G₂(k) over a field k has a presentation by 1-subspaces corresponding to the points of the associated hexagon, subject to relations determined by the lines, and one further relation on the neighbors of a point.The proof is geometric, based on spanning by apartments of the building.     

Amine-tetrachloromethane charge transfer complexes: a structural and computational study

Abstract

Amine-tetrachloromethane charge-transfer complexes have recently been shown to be useful intermediates in transition-metal free solar light-assisted organic synthetic chemistry. Of particular promise is the complex of 1,4-diazabicyclo[2.2.2]octane (DABCO) which may serve as a starting point for several potential reactions involving oxidation of organic compounds. Here we disclose the crystal structure of the [DABCO???CCl₄] complex, and computational studies of two possible complex structures in their ground state, as well as in their first singlet and first triplet excited states.     

High-definition,single-scan 2D MRI in inhomogeneous fields using spatial encoding methods

An approach has been recently introduced for acquiring two-dimensional (2D) nuclear magnetic resonance images in a single scan, based on the spatial encoding of the spin interactions. This article explores the potential of integrating this spatial encoding together with conventional temporal encoding principles, to produce 2D single-shot images with moderate field of views. The resulting “hybrid” imaging scheme is shown to be superior to traditional schemes in non-homogeneous magnetic field environments. An enhancement of previously discussed pulse sequences is also proposed, whereby distortions affecting the image along the spatially encoded axis are eliminated. This new variant is also characterized by a refocusing of T₂^* effects, leading to a restoration of high-definition images for regions which would otherwise be highly dephased and thus not visible. These single-scan 2D images are characterized by improved signal-to-noise ratios and a genuine T₂ contrast, albeit not free from inhomogeneity distortions. Simple postprocessing algorithms relying on inhomogeneity phase maps of the imaged object can successfully remove most of these residual distortions. Initial results suggest that this acquisition scheme has the potential to overcome strong field inhomogeneities acting over extended acquisition durations, exceeding 100 ms for a single-shot image.     

Sensitive and selective photoinduced-electron-transfer-based sensing of alkylating agents

Photoinduced-electron-transfer (PET)-based chemosensing is a very elegant way of reporting the presence of a guest species in solution. This method was successfully applied for the detection of different ionic species, such as cations, anions, and protons. Herein, we report on the application of the PET chemosensing concept for the efficient and selective detection of different alkylating agents. 2-(2-Dimethylaminoethyl)benzo[de]isoquinoline-1,3-dione (1) was found to be a highly selective and effective PET chemosensor that turns luminescent upon reacting with different alkylating agents. This PET-based system detected even rather weak alkylating agents, such as dichloromethane. A PET-based sensor that consists of 1 as the active component could detect rather low concentrations of alkylating agents in solution and in the gas phase.