Codimension-one minimal projections onto Haar subspaces

Let H_n be an n-dimensional Haar subspace of and let H_n−1 be a Haar subspace of H_n of dimension n−1. In this note we show (Theorem 6) that if the norm of a minimal projection from H_n onto H_n−1 is greater than 1, then this projection is an interpolating projection. This is a surprising result in comparison with Cheney and Morris (J. Reine Angew. Math. 270 (1974) 61 (see also (Lecture Notes in Mathematics, Vol. 1449, Springer, Berlin, Heilderberg, New York, 1990, Corollary III.2.12, p. 104) which shows that there is no interpolating minimal projection from C[a,b] onto the space of polynomials of degree n, (n2). Moreover, this minimal projection is unique (Theorem 9). In particular, Theorem 6 holds for polynomial spaces, generalizing a result of Prophet [(J. Approx. Theory 85 (1996) 27), Theorem 2.1].     

Bernstein's “lethargy” theorem in metrizable topological linear spaces

A version of Bernstein's lethargy theorem is given in a class of vector spaces includingF-spaces and Orlicz-Musielak spaces with condition ₂. This extends results obtained in [9] and [11].     

Advances in Modeling Sorption and Diffusion of Moisture in Porous Reactive Materials

Water‐vapor‐uptake experiments were performed on a silica‐filled poly(dimethylsiloxane) (PDMS) network and modeled by using two different approaches. The data was modeled by using established methods and the model parameters were used to predict moisture uptake in a sample. The predictions are reasonably good, but not outstanding; many of the shortcomings of the modeling are discussed. A high‐fidelity modeling approach is derived and used to improve the modeling of moisture uptake and diffusion. Our modeling approach captures the physics and kinetics of diffusion and adsorption/desorption, simultaneously. It predicts uptake better than the established method; more importantly, it is also able to predict outgassing. The material used for these studies is a filled‐PDMS network; physical interpretations concerning the sorption and diffusion of moisture in this network are discussed.     

Minimal Extensions in Tensor Product Spaces

LetX,Ybe two separable Banach spaces and letVXandWYbe finite dimensional subspaces. Suppose thatVSX,WZYand letM (S, V),N (Z, W). We will prove that ifαis a reasonable, uniform crossnorm onXYthenλ_MN(V_αW,X_αY)=λ_M(V, X) λ_N(W, Y).Here for any Banach spaceX,VSXandM (S, V)

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Also some applications of the above mentioned result will be presented.     

Hydrogen control of ferromagnetism in a dilute magnetic semiconductor

We show that upon exposure to a remote dc hydrogen plasma, the magnetic and electronic properties of the dilute magnetic semiconductor Ga1-xMnxAs change qualitatively. While the as-grown Ga1-xMnxAs thin films are ferromagnetic at temperatures T less, similar 70 K, the samples are found to be paramagnetic after the hydrogenation, with a Brillouin-type magnetization curve even at T=2 K. Comparing magnetization and electronic transport measurements, we conclude that the density of free holes p is significantly reduced by the plasma process, while the density of Mn magnetic moments does not change.     

Barbilian’s metrization procedure in the plane yields either Riemannian or Lagrange generalized metrics

In the present paper we answer two questions raised by Barbilian in 1960. First, we study how far can the hypothesis of Barbilian’s metrization procedure can be relaxed. Then, we prove that Barbilian’s metrization procedure in the plane generates either Riemannian metrics or Lagrance generalized metrics not reducible to Finslerian or Langrangian metrics.     

Notiz zur qualitativen Analyse der schwefelsauren, schwefligsauren und thioschwefelsauren Salze

Ohne Zusammenfassung     

Optimal and one-complemented subspaces

Let X be a real Banach space and let V ⊂ X be a closed linear subspace. In [4, Prop. 5] it has been proven that if X is strictly convex, reflexive and smooth and V is an optimal subset of X then V is one-complemented in X. In this note we would like to extend this result to non-smooth Banach spaces. In particular, we show that any existence subspace of c,c _o and l ₁ is one-complemented. Also some results concerning non-smooth Musielak-Orlicz sequence spaces equipped with the Luxemburg norm will be presented. The first author was supported by Polish State Committee for Scientific Research Grant KBN 1 PO3A O10 26. Authors’ addresses: Grzegorz Lewicki, Department of Mathematics, Jagiellonian University, 30-059 Kraków, Reymonta 4, Poland; Giulio Trombetta, Department of Mathematics, University of Calabria, 87036 Arcavacata di Rende, Cosenza, Italy     

Molecular origin of model membrane bending rigidity

The behavior of the bending modulus kappa of bilayers in lamellar phases was studied by Small Angle X-ray Scattering technique for various nonionic C(i)E(j) surfactants. The bilayers are either unswollen and dispersed in water or swollen by water and dispersed in dodecane. For unswollen bilayers, the values of kappa decrease with both an increase in the area per surfactant molecule and in the polar head length. They increase when the aliphatic chain length increases at constant area per surfactant molecule. Whereas for water-swollen membranes, the values of kappa decrease as the content of water increases converging to the value of the single monolayer bending modulus. Such a behavior results from the decoupling of the fluctuations of the two surfactant membrane monolayers. Our results emphasize the determinant contribution of the surfactant conformation to kappa.