We prove Szegö's strong limit theorem for Toeplitz determinants with a symbol having a nonstandard smoothness. We assume that the symbol belongs to the Wiener algebra and, moreover, the sequences of Fourier coefficients of the symbol with negative and nonnegative indices belong to weighted Orlicz classes generated by complementary \(N\)-functions both satisfying the \(\Delta_2^0\)-condition and by weight sequences satisfying some regularity, and compatibility conditions.

The technological evolution brought the society to a networked reality. New organizational forms are being created, towards a better response to market opportunities, both in terms of time-to-market and added-value creation. In this context the Collaborative Networked Organizations (CNO) paradigm appears as a good organizational form to attend market needs. To avoid the conventional barriers in the implementation of this new organizational form, education and training are very important activities, already building an international consensus. This paper surveys current work on teaching initiatives in the CNO area around the world.

In situ ATR-IR spectroscopy was used to simultaneously measure the sorption and swelling of carbon dioxide at high pressures in a biocompatible acrylate copolymer poly(methylmethacrylate-co-ethylhexylacrylate-co- ethyleneglycoldimethacrylate), P(MMA-EHA-EGDMA). The $ν$ 3 band of CO 2 dissolved in the polymer (at 2335 cm -1 ) was used to calculate the sorption data and the polymer swelling was determined by analyzing the changes in the absorbance of the $ν$(CO) band (at 1730 cm -1 ) of the polymer. Transmission spectroscopy in the near-IR region was also used to study the sorption of CO 2 in the polymer using combinational and overtone bands. The experiments were carried out in a pressure range of 2.0-12.0 MPa and in a temperature range of 27-40 °C. The data for CO 2 sorption in this polymer obtained by in situ spectroscopic methods have been compared to the data obtained by the gravimetric technique. © 2005 Elsevier B.V. All rights reserved.

We prove analogues of the Brown-Halmos and Nehari theorems on the norms of Toeplitz and Hankel operators, respectively, acting on subspaces of Hardy type of reflexive rearrangement-invariant spaces with nontrivial Boyd indices.

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We prove Fredholm criteria for singular integral operators of the form
\[
P_++M_bP_-+M_uUP_-,
\]
where \(P_\pm\) are the Riesz projections, \(U\) is the flip operator, and \(M_b,M_u\) are operators of multiplication by functions \(b,u\), respectively, on a reflexive rearrangement-invariant space with nontrivial Boyd indices over the unit circle. We assume a priori that \(M_b\) is bounded, but \(M_u\) may be unbounded. The function \(u\) belongs to a class of, in general, unbounded functions that relates to the Douglas algebra \(H^\infty+C\).

In this paper, the author proves that the set of all integrable functions whose sequences of negative (resp. nonnegative) Fourier coefficients belong to \(\ell^1\cap\ell^\Phi_{\varphi,w}\) (resp. to \(\ell^1\cap\ell^\Psi_{\psi,\varrho}\)), where \(\ell^\Phi_{\varphi,w}\) and \(\ell^\Psi_{\psi,\varrho}\) are two-weighted Orlicz sequence spaces, forms an algebra under pointwise multiplication whenever the weight sequences
\[
\varphi=\{\varphi_n\},\quad
\psi=\{\psi_n\},\quad
w=\{w_n\},\quad
\varrho=\{\varrho_n\}
\]
increase and satisfy the \(\Delta_2\)-condition.

According to the model proposed in previous papers [Pettigrew, G. W., Prazeres, S., Costa, C., Palma, N., Krippahl, L., and Moura, J. J. (1999) The structure of an electron-transfer complex containing a cytochrome c and a peroxidase, J. Biol. Chem. 274, 11383-11389; Pettigrew, G. W., Goodhew, C. F., Cooper, A., Nutley, M., Jumel, K., and Harding, S. E. (2003) Electron transfer complexes of cytochrome c peroxidase from Paracoccus denitrificans, Biochemistry 42, 2046-2055], cytochrome c peroxidase of Paracoccus denitrificans can accommodate horse cytochrome c and Paracoccus cytochrome c(550) at different sites on its molecular surface. Here we use H-1 NMR spectroscopy, analytical ultracentrifugation, molecular docking simulation, and microcalorimetry to investigate whether these small cytochromes can be accommodated simultaneously in the formation of a ternary complex. The pattern of perturbation of heme methyl and methionine methyl resonances in binary and ternary solutions shows that a ternary complex can be formed, and this is confirmed by the increase in the sedimentation coefficient upon addition of horse cytochrome c to a solution in which cytochrome c(550) fully occupies its binding site on cytochrome c peroxidase. Docking experiments in which favored binary solutions of cytochrome, c(550) bound to cytochrome c peroxidase act as targets for horse cytochrome c and the reciprocal experiments in which favored binary solutions of horse cytochrome c bound to cytochrome c peroxidase act as targets for cytochrome c(550) show that the enzyme can accommodate both cytochromes at the same time on adjacent sites. Microcalorimetric titrations are difficult to interpret but are consistent with a weakened binding of horse cytochrome c to a binary complex of cytochrome c peroxidase and cytochrome c(550) and binding of cytochrome c(550) to the cytochrome c peroxidase that is affected little by the presence of horse cytochrome c in the other site. The presence of a substantial capture surface for small cytochromes on the cytochrome c peroxidase has implications for rate enhancement mechanisms which ensure that the two electrons required for re-reduction of the enzyme after reaction with hydrogen peroxide are delivered efficiently.

The paper is devoted to the compactness of the commutators \(aS_\Gamma - S_\Gamma aI\) and \(W_\alpha S_\Gamma - S_\Gamma W_\alpha\), where \(S_\Gamma\) is the Cauchy singular integral operator, \(a\) is a bounded measurable function, \(W_\alpha\) is the shift operator given by \(W_\alpha f = f\circ\alpha\), and \(\alpha\) is a bi-Lipschitz homeomorphism (shift). The cases of the unit circle and the unit interval are considered. We prove that these commutators are compact on rearrangement-invariant spaces with nontrivial Boyd indices if and only if the function a or, respectively, the derivative of the shift a has vanishing mean oscillation.