Note on hit-and-miss topologies

This is a continuation of [19]. We characterize first and second countability of the general hit-and-miss hyperspace topologyτ ₊ ^Δ for weakly-R ₀ base spaces. Further, metrizability ofτ ₊ ^Δ is characterized with no preliminary conditions on the base space and the generating family of closed sets and a new proof on uniformizability (i.e. complete regularity) ofτ ₊ ^Δ is given in this general setting, thus generalizing results of [3], [5] and [6].     

Torocyte shapes of red blood cell daughter vesicles

The shape of the newly described torocyte red blood cell endovesicles induced by octaethyleneglycol dodecylether (C12E8) is characterized. A possible explanation for the origin and stability of the observed torocyte endovesicles is suggested. Three partly complementary mechanisms are outlined, all originating from the interaction of C12E8 molecules with the membrane. The first is a preferential intercalation of the C12E8 molecule into the inner membrane layer, resulting in a membrane invagination which may finally close, forming an inside-out endovesicle. The second is a preference of the C12E8-induced membrane inclusions (clusters) for small local curvature which would favour torocyte endovesicle shape with large regions of small or even negative membrane mean curvatures, the C12E8 membrane inclusion being defined as a complex composed of the embedded C12E8 molecule and some adjacent phospholipid molecules which are significantly distorted due to the presence of the embedded C12E8 molecule. The preference of the C12E8 inclusions for zero or negative local curvature may also lead to the nonhomogeneous lateral distribution of the C12E8 inclusions resulting in their accumulation in the membrane of torocyte endovesicles. The third possible mechanism is orientational ordering of the C12E8-induced inclusions in the regions of torocyte endovesicles with high local membrane curvature deviator.     

Morse Theory and Evasiveness

M   is a non-contractible subcomplex of a simplex S then M is evasive. In this paper we make this result quantitative, and show that the more non-contractible M is, the more evasive M is. Recall that M is evasive if for every decision tree algorithm A there is a face of S that requires that one examines all vertices of S (in the order determined by A) before one is able to determine whether or not lies in M. We call such faces evaders of A. M is nonevasive if and only if there is a decision tree algorithm A with no evaders. A main result of this paper is that for any decision tree algorithm A, there is a CW complex M', homotopy equivalent to M, such that the number of cells in M' is precisely

Hyperinvariant subspaces ofC 0-operators over a multiply connected region

In this paper we find a relation between the lattice of hyperinvariant subspaces of an operatorT of classC ₀ over a multiply connected region and that of its Jordan modelT. It is shown that, generally, the lattice corresponding toT can be identified with a retract of that corresponding toT. Thus the Jordan model has the smallest lattice of hyperinvariant subspaces in a given quasisimilarity class.     

On the spectral properties of Witten-Laplacians, their range projections and Brascamp-Lieb's inequality

A study is made of a recent integral identity of B. Helffer and J. Sjöstrand, which for a not yet fully determined class of probability measures yields a formula for the covariance of two functions (of a stochastic variable); in comparison with the Brascamp-Lieb inequality, this formula is a more flexible and in some contexts stronger means for the analysis of correlation asymptotics in statistical mechanics. Using a fine version of the Closed Range Theorem, the identity's validity is shown to be equivalent to some explicitly given spectral properties of Witten-Laplacians on Euclidean space, and the formula is moreover deduced from the obtained abstract expression for the range projection. As a corollary, a generalised version of Brascamp-Lieb's inequality is obtained. For a certain class of measures occuring in statistical mechanics, explicit criteria for the Witten-Laplacians are found from the Persson-Agmon formula, from compactness of embeddings and from the Weyl calculus, which give results for closed range, strict positivity, essential self-adjointness and domain characterisations.Supported by TMR grant FMRX-CT960001 of the European Commision, PDE and QM at Université de Paris-Sud, France; partly by the Danish Natural Sciences Research Council, grant 9700987.     

Realizations for Schur upper triangular operators centered at an arbitrary point

Reproducing kernel spaces introduced by L. de Branges and J. Rovnyak provide isometric, coisometric and unitary realizations for Schur functions, i.e. for matrix-valued functions analytic and contractive in the open unit disk. In our previous paper [12] we showed that similar realizations exist in the nonstationary setting, i.e. when one considers upper triangular contractions (which appear in time-variant system theory as transfer functions of dissipative systems) rather than Schur functions and diagonal operators rather than complex numbers. We considered in [12] realizations centered at the origin. In the present paper we study realizations of a more general kind, centered at an arbitrary diagonal operator. Analogous realizations (centered at a point of the open unit disk) for Schur functions were introduced and studied in [3] and [4].     

A note on regularity for a class of quasilinear elliptic equations

The following regularity of weak solutions of a class of elliptic equations of the form are investigated.     

The Banach envelopes of Besov and Triebel-Lizorkin spaces and applications to partial differential equations

With “hat” denoting the Banach envelope (of a quasi-Banach space) we prove that if 0<p<1, 0<q<1, ℝ, while if 0<p<1, 1≤q<+∞, ∝, and if 1≤p<+∞, 0<q<1, ℝ. Applications to questions regarding the global interior regularity of solutions to Poisson type problems for the three-dimensional Lamé system in Lipschitz domains are presented.     

An end point estimate for maximal commutators

In this paper we prove that the maximal commutator of singular integral operator [b, T]^* satisfies the inequality: