On commutators of equivariant homeomorphisms

The long-standing problem of the perfectness of the compactly supported equivariant homeomorphism group on a G-manifold (with one orbit type) is solved in the affirmative. The proof is based on an argument different than that for the case of diffeomorphisms. The theorem is a starting point for computing H₁(HG(M)) for more complicated G-manifolds.     

The bicategories of corings

To a B-coring and a (B,A)-bimodule that is finitely generated and projective as a right A-module an A-coring is associated. This new coring is termed a base ring extension of a coring by a module. We study how the properties of a bimodule such as separability and the Frobenius properties are reflected in the induced base ring extension coring. Any bimodule that is finitely generated and projective on one side, together with a map of corings over the same base ring, lead to the notion of a module-morphism, which extends the notion of a morphism of corings (over different base rings). A module-morphism of corings induces functors between the categories of comodules. These functors are termed pull-back and push-out functors, respectively, and thus relate categories of comodules of different corings. We study when the pull-back functor is fully faithful and when it is an equivalence. A generalised descent associated to a morphism of corings is introduced. We define a category of module-morphisms, and show that push-out functors are naturally isomorphic to each other if and only if the corresponding module-morphisms are mutually isomorphic. All these topics are studied within a unifying language of bicategories and the extensive use is made of interpretation of corings as comonads in the bicategory Bim of bimodules and module-morphisms as 1-cells in the associated bicategories of comonads in Bim.     

Platonic Orthonormal Wavelets

We classify all orthonormal wavelets which occur in theL²space of the faces of a platonic solid.     

Stationarity of Lagrangian Velocity¶in Compressible Environments

We study the transport of a passive tracer particle by a random d-dimensional, Gaussian, compressible velocity field. It is well known, since the work of Lumley, see [13], and Port and Stone, see [20], that the observations of the velocity field from the moving particle, the so-called Lagrangian velocity process, are statistically stationary when the field itself is incompressible. In this paper we study the question of stationarity of Lagrangian observations in compressible environments. We show that, given sufficient temporal decorrelation of the velocity statistics, there exists a transformation of the original probability measure, under which the Lagrangian velocity process is time stationary. The transformed probability is equivalent to the original measure. As an application of this result we prove the law of large numbers for the particle trajectory. Received: 1 May 2001 / Accepted: 4 December 2001     

Component behavior near the critical point of the random graph process

We study the behavior of a random graph process (G(n, M))₀²ⁿ for M(n) = n/2 + s and ∣s∣³n^?;2 → ∞. Among others we find the number of components in G(n, M) and estimate the number of vertices and edges in the kth largest component of G(n, M), for any natural number k, Moreover, it is shown that, with probability 1 –o(1), when M(n) = n/2 + s, s³n^?2 →?∞, then during a random graph process in some step M¹ > M a “new” largest component will emerge, whereas when s³n^?2→∞, the largest component of G(n, M) remains largest until the very end of the process.     

Thermodynamic Characteristics of Phenacetin in Solid State and Saturated Solutions in Several Neat and Binary Solvents

The thermodynamic properties of phenacetin in solid state and in saturated conditions in neat and binary solvents were characterized based on differential scanning calorimetry and spectroscopic solubility measurements. The temperature-related heat capacity values measured for both the solid and melt states were provided and used for precise determination of the values for ideal solubility, fusion thermodynamic functions, and activity coefficients in the studied solutions. Factors affecting the accuracy of these values were discussed in terms of various models of specific heat capacity difference for phenacetin in crystal and super-cooled liquid states. It was concluded that different properties have varying sensitivity in relation to the accuracy of heat capacity values. The values of temperature-related excess solubility in aqueous binary mixtures were interpreted using the Jouyban–Acree solubility equation for aqueous binary mixtures of methanol, DMSO, DMF, 1,4-dioxane, and acetonitrile. All binary solvent systems studied exhibited strong positive non-ideal deviations from an algebraic rule of mixing. Additionally, an interesting co-solvency phenomenon was observed with phenacetin solubility in aqueous mixtures with acetonitrile or 1,4-dioxane. The remaining three solvents acted as strong co-solvents.     

A Bayesian Markov-Chain-Based Heteroscedastic Regression Model for the Analysis of <Superscript>18</Superscript>O-Labeled Mass Spectra

To reduce the influence of the between-spectra variability on the results of peptide quantification, one can consider the ¹⁸O-labeling approach. Ideally, with such labeling technique, a mass shift of 4 Da of the isotopic distributions of peptides from the labeled sample is induced, which allows one to distinguish the two samples and to quantify the relative abundance of the peptides. It is worth noting, however, that the presence of small quantities of ¹⁶O and ¹⁷O atoms during the labeling step can cause incomplete labeling. In practice, ignoring incomplete labeling may result in the biased estimation of the relative abundance of the peptide in the compared samples. A Markov model was developed to address this issue (Zhu, Valkenborg, Burzykowski. J. Proteome Res. 9, 2669–2677, 2010). The model assumed that the peak intensities were normally distributed with heteroscedasticity using a power-of-the-mean variance funtion. Such a dependence has been observed in practice. Alternatively, we formulate the model within the Bayesian framework. This opens the possibility to further extend the model by the inclusion of random effects that can be used to capture the biological/technical variability of the peptide abundance. The operational characteristics of the model were investigated by applications to real-life mass-spectrometry data sets and a simulation study.     

Probing Lewis acidity of Y(BH4)3 via its reactions with MBH4 (M = Li, Na, K, NMe4)

High-energy milling of Y(BH(4))(3) (containing LiCl as a by-product, which has not been removed) with MBH(4) (M = Li, Na, K, (CH(3))(4)N) leads to the first two examples of quasi-ternary yttrium borohydrides: KY(BH(4))(4) and (CH(3))(4)NY(BH(4))(4), while no chemical reaction is observed for LiBH(4) and NaBH(4). KY(BH(4))(4) is isostructural to NaSc(BH(4))(4) (Cmcm, a = 8.5157(4) ?, b = 12.4979(6) ?, c = 9.6368(5) ?, V = 1025.62(9) ?(3), Z = 4), while (CH(3))(4)NY(BH(4))(4) crystallises in primitive orthorhombic cell, similarly to KSc(BH(4))(4) (Pnma, a = 15.0290(10) ?, b = 8.5164(6) ?, c = 12.0811(7) ?, V = 1546.29(17) ?(3), Z = 4). The thermal decomposition of hydrogen-rich KY(BH(4))(4) (8.6 wt.% H) involves the formation of an unidentified intermediate at 200 °C and recovery of KBH(4) at higher temperatures; at 410 °C, KCl and YH(2) are observed. The thermal decomposition of (CH(3))(4)NY(BH(4))(4) occurs via two partly overlapping endothermic steps with concomitant emission of H(2) and organic compounds. Heating of a NaBH(4)/Y(BH(4))(3) mixture above 165 °C results in a mixed-cation mixed-anion borohydride, NaY(BH(4))(2)Cl(2), but not NaY(BH(4))(4). The reduced reactivity of Y(BH(4))(3) towards borohydride Lewis bases when compared to hypothetical scandium borohydride can be explained by the lower Lewis acidity of Y(BH(4))(3) than Sc(BH(4))(3).     

Heterogeneous binding of dioxygen: EPR and DFT evidence for side-on nickel(II)-superoxo adduct with unprecedented magnetic structure hosted in MFI zeolite

This article reports on the activation of dioxygen on nickel(I) dispersed inside the nanopores of the ZSM-5 zeolite, which can be regarded as a heterogeneous mimetic system (zeozyme) for Ni-bearing enzymes. The side-on η(2)-coordination of the resulting nickel-bound superoxo adduct was ascertained by detailed analysis of the EPR spectra of both (16)O(2) and (17)O(2) species supported by computer simulations of the spectra and relativistic DFT calculations of the EPR signatures. Molecular analysis of the g and A((17)O) tensors (g(xx) = 2.0635, g(yy) = 2.0884, g(zz) = 2.1675; |A(xx)| ≈ 1.0 mT, |A(yy)| = 5.67 mT, |A(zz)| ≈ 1.3 mT) and quantum chemical modeling revealed an unusual electronic and magnetic structure of the observed adduct (with g(zz)(g(max)) > g(yy)(g(mid)) > g(xx)(g(min)) and the largest O-17 hyperfine splitting along the g(mid) direction) in comparison to the known homogeneous and enzymatic nickel-superoxo systems. It is best described as a mixed metalloradical with two supporting oxygen donor ligands and even triangular spin-density redistribution within the η(2)-{NiO(2)}(11) magnetophore. The semioccupied molecular orbital (SOMO) is constituted by highly covalent δ overlap between the out-of-plane 2p(π(g)*) MO of dioxygen and the 3d(x(2)(-y(2))) MO of nickel. By means of the extended transition state-natural orbitals for the chemical valence approach (ETS-NOCV), three distinct orbital channels (associated with σ, π, and δ overlap) of congruent and incongruent charge and spin density flows within the η(2)-{NiO(2)}(11) unit, contributing jointly to activation of the attached dioxygen, were identified. Their individual energetic relevance was quantified, which allowed for explaining the oxygen binding mechanism with unprecedented accuracy. The nature and structure sensitivity of the g tensor was rationalized in terms of the contributions due to the magnetic field-induced couplings of the relevant molecular orbitals that control the g-tensor anisotropy. The calculated O-17 hyperfine coupling constants correspond well with the experimental parameters, supporting assignment of the adduct. To the best of our knowledge, the η(2)-{NiO(2)}(11) superoxo adducts have not been observed yet for digonal mononuclear nickel(I) centers supported by oxygen donor ligands.     

Robust control of microdomain orientation in thin films of block copolymers by zone casting

Block copolymers with chemically immiscible segments exhibit a variety of microphase-separated nanostructures on the scale of 10-100 nm. Controlling the orientation of these microphase separated nanostructures is vital in many applications such as lithography, membranes, data storage, and so forth. Typical strategies involve the use of external fields or patterned substrates. Here, we report a robust zone casting technique to achieve highly ordered thin films of block copolymers on centimeter-scale substrates. The robustness of this technique is its powerful control on diverse morphologies and exceptional tolerance on versatility of block copolymer chemistry as well as allowance of a wide spectrum of substrates. We demonstrate that perpendicular orientations with respect to the surface are achieved for block copolymers with both lamellar and cylindrical morphologies by controlling solution casting rate, temperatures, and block copolymer chemical structures. Thin films of both noncrystalline and crystalline block copolymers exhibit excellent orientational order and lateral order. However, the lateral order in the thin films of crystalline block copolymers shows dependence on casting temperature and melting temperature of the crystalline segment. Remarkably, all the ordering is independent of the substrates on which the block copolymer films are cast.