Lelek?s problem is not a metric problem

We show that Lelek?s problem on the chainability of continua with span zero is not a metric problem: from a non-metric counterexample one can construct a metric one.     

Brouwer and cardinalities

This note is a somewhat personal account of a paper that L.E.J. Brouwer published in 1908 and that dealt with the possible cardinalities of subsets of the continuum. That paper is of interest because it represents the first time that Brouwer presented his ideas on foundations in an international forum.I found Brouwer’s notions and arguments at times hard to grasp if not occasionally perplexing. I hope that this note contributes to a further discussion of the definitions and reasonings as presented in Brouwer’s paper.     

Describing the soil physical characteristics of soil samples with cubical splines

The Mualem-Van Genuchten equations have become very popular in recent decades. Problems were encountered fitting the equations’ parameters through sets of data measured in the laboratory: parameters were found which yielded results that were not monotonic increasing or decreasing. Due to the interaction between the soil moisture retention and the hydraulic conductivity relationship, some data sets yield a fit that seems not to be optimal. So the search for alternatives started. We ended with the cubical spline approximation of the soil physical characteristics. Software was developed to fit the spline-based curves to sets of measured data. Five different objective functions are tested and their results are compared for four different data sets. It is shown that the well-known least-square approximation does not always perform best. The distance between the measured points and the fitted curve, as can be evaluated numerically in a simple way, appears to yield good fits when applied as a criterion in the optimization procedure. Despite an increase in computational effort, this method is recommended over the least square method.     

Ultrafast intramolecular charge transfer and internal conversion with tetrafluoro-aminobenzonitriles.

The five 2,3,5,6-tetrafluoro-4-aminobenzonitriles XABN4F with a dimethyl-amino (DMABN4F), diethyl-amino (DEABN4F), azetidinyl (AZABN4F), methyl-amino (MABN4F) or amino (ABN4F) group undergo ultrafast intramolecular charge transfer (ICT) at room temperature, in the polar solvent acetonitrile (MeCN) as well as in the nonpolar n-hexane. ICT also takes place with the corresponding non-fluorinated aminobenzonitriles DMABN, DEABN and AZABN in MeCN, whereas for these molecules in n-hexane only minor (DMABN, DEABN) or no (AZABN) ICT fluorescence is detected. For the secondary (MABN) and primary (ABN) amines, an ICT reaction does not occur, which makes ABN4F the first electron donor/acceptor molecule with an NH(2) group for which ICT is observed. The ICT state of the XABN4Fs has a dipole moment of around 14 D, clearly smaller than that of DMABN (17 D). This difference is attributed to the electron withdrawing from the CN group to the phenyl ring, exerted by the four F-substituents. The reaction from the initially prepared locally excited (LE) to the ICT state in n-hexane proceeds in the sub-picosecond time range: 0.35 ps (DMABN4F), 0.29 ps (DEABN4F) and 0.13 ps (AZABN4F), as determined from femtosecond transient absorption measurements. In the highly polar solvent MeCN, an ICT reaction time of around 90 fs is observed for all five XABN4Fs, irrespective of the nature of their amino group. This shows that with these molecules in MeCN the ICT reaction rate is limited by the solvent dielectric relaxation time of MeCN, for which a value of around 90 fs has been reported. It is therefore concluded that, during this ultrashort ICT reaction, a large-amplitude motion such as a full 90 degrees twist of the amino group is unlikely to occur in the XABN4Fs. The ICT state of the XABN4Fs is strongly quenched via internal conversion (IC), with a lifetime tau'(0) (ICT) down to 3 ps, possibly by a reaction passing through a conical intersection made accessible due to a deformation of the phenyl group by out-of-plane motions induced by vibronic coupling between low-lying pisigma* and pipi* states in the XABN4Fs.     

Structure-function relationships in the neurotoxin Vipoxin from the venom of Vipera ammodytes meridionalis

The neurotoxic complex Vipoxin is the lethal component of the venom of Vipera ammodytes meridionalis, the most toxic snake in Europe. It is a complex between a toxic phospholipase A2 (PLA2) and a non-toxic and catalytically inactive protein, stabilizing the enzyme and reducing the activity and toxicity. Structure-function relationships in this complex were studied by spectroscopic methods. A good correlation between the ionization behaviour and accessible surface area (ASA) of the tyrosyl residues was observed. In the toxic PLA2 subunit phenolic groups participate in H-bonding network that stabilizes the catalytically and pharmacologically active conformation. The tryptophan fluorescence decay of Vipoxin is well fitted by two exponentials with lifetimes of 0.1 (54%) and 2.5 (46%) ns. W20P, W31P and W31I are located in the interface between the two subunits and participate in hydrophobic interactions stabilizing the complex. Dissociation of the complex leads to a transition of the tryptophans from hydrophobic to hydrophilic environment, which influences mainly tau2. The longer lifetime is more sensitive to the polarity of the environment. Circular dichroism measurements demonstrate that the two components of the neurotoxin preserve their secondary structure after dissociation of the complex. The results of the spectroscopic studies are in accordance with a mechanism of blockade of transmission across the neuromuscular junctions of the breathing muscles by interaction of a dissociated toxic PLA2 with a membrane. The loss of toxicity is connected with slight changes in the secondary structure of PLA2. CD studies also show a substantial contribution of disulfide bonds to the stability of the neurotoxic complex and its components.     

A new application of (polyfluoroorgano)trifluoroborate salts: the palladium-catalysed cross-coupling reaction with substituted benzenediazonium tetrafluoroborates

For the first time (polyfluoroorgano)trifluoroborate salts, namely K[C₆F₅BF₃], K[C₆HF₄BF₃] (all three isomers), K[3,4,5-C₆H₂F₃BF₃], and K[CF₂CFBF₃] were principally applied as reagents to Pd-catalysed cross-coupling reactions. A series of polyfluorinated biphenyls C₆H_5−nF_n-C₆H₄X-4′ were obtained from K[C₆H_5−nF_nBF₃] and the substrates [4-XC₆H₄N₂][BF₄] in the presence of Pd catalysts. The influence of the number and the position of the fluorine atoms in the (polyfluorophenyl)trifluoroborate salts on the reactivity in the coupling reaction was elucidated. In addition to (polyfluorophenyl)trifluoroborate salts, the cross-coupling was expanded to a first example of a perfluoroalkenyl reagent. K[CF₂CFBF₃] reacted with [4-FC₆H₄N₂][BF₄] and formed CF₂CF-C₆H₄F-4.     

Oxidative addition reactions of dicyclopentadienyltin(II) and of tin(II) bis(acetylacetonate) with organic halides. The preparation of compounds of the type RSn(acac)2X

Oxidative addition reactions of tin(II) bis(acetylacetonate) with organic halides provide a route to new monoorganotin(IV) bis(acetylacetonate) halides. Dicyclopentadienyltin(II) undergoes oxidative addition with methyl iodide, diiodomethane and ethyl bromoacetate, but with allyl bromide, benzyl bromide and triphenylmethyl bromide carbon—carbon coupling reactions and the formation of the corresponding cyclopentadienyltin(II) halide take place. Some of the reactions are accelerated by light. NMR spectroscopic data show that the RSn(acac)₂X compounds have a cis-configuration. The compounds YCH₂Sn(acac)₂X (e.g. Y = I, CHCH₂, COOEt) provide the first examples of diastereo-topic non-equivalence of methylene protons in organotin compounds containing a hexacoordinate chiral tin centre.     

Polyfluoroorganoboron‐Oxygen Compounds. 5 Feasible Routes to Perfluoroalkyltrimethoxyborates M[CnF2n+1B(OMe)3] (n ≥ 3)

A well applicable preparative method for lithium perfluoroalkyltrimethoxyborates, Li[C_nF_2n+1B(OMe)₃] (n = 3, 4, 6), was elaborated which is based on the reaction of B(OMe)₃ with C_nF_2n+1Li generated from C_nF_2n+1H and t‐BuLi. Alternative perfluoroalkylation reactions of B(OMe)₃ with perfluoropropyllithium generated from C₃F₇I and RLi, perfluoropropylmagnesium bromide, or perfluoropropyltrimethylsilane and potassium fluoride gave less satisfactory results for M[C₃F₇B(OMe)₃]. The conversion of M[C_nF_2n+1B(OMe)₃] salts (M = Li, BrMg) into K[C_nF_2n+1B(OMe)₃] salts and basic properties of the new salts are reported.     

Spectroscopic observation of the resonance-stabilized 1-phenylpropargyl radical

The gas-phase laser-induced fluorescence (LIF) spectrum of a 1-phenylpropargyl radical has been identified in the region 20,800-22,000 cm(-1) in a free jet. The radical was produced from discharges of hydrocarbons including benzene. Disregarding C2, C3, and CH, this radical appears as the most strongly fluorescing product in a visible wavelength two-dimensional fluorescence excitation-emission spectrum of a jet-cooled benzene discharge. The structure of the carrier was elucidated by measurement of a matching resonant two-color two-photon ionization spectrum at m/z = 115 and density functional theory. The assignment was proven conclusively by observation of the same excitation spectrum from a low-current discharge of 3-phenyl-1-propyne. The apparent great abundance of the 1-phenylpropargyl radical in discharges of benzene and, more importantly, 1-hexyne may further underpin the proposed importance of the propargyl radical in the formation of complex hydrocarbons in combustion and circumstellar environments.