On self-majorizing elements in Archimedean vector lattices

A finite element in an Archimedean vector lattice is called self-majorizing if its modulus is a majorant. Such elements exist in many vector lattices and naturally occur in different contexts. They are also known as semi-order units as the modulus of a self-majorizing element is an order unit in the band generated by the element. In this paper the properties of self-majorizing elements are studied systematically, and the relations between the sets of finite, totally finite and self-majorizing elements of a vector lattice are provided. In a Banach lattice an element \(\varphi \) is self-majorizing , if and only if the ideal and the band both generated by \(\varphi \) coincide.     

Characterization and functionalization of cellulose microbeads for extracorporeal blood purification

In the frame of this work, cellulose microbeads with an average particle size of 2.3 μm were characterized with respect to porosity using a batch solute exclusion method and two groups of model substances, namely proteins and polystyrene sulfonates. The pores of the microbeads were almost completely accessible to proteins with Stokes radii below 2.5 nm. More than 60% of the pores were accessible to albumin, which is relevant for the application in blood purification, since many target substances are albumin bound. Activation of the microbeads with increasing amounts of sodium metaperiodate yielded matrices with dialdehyde contents between 100 and 1,000 μmol/g. The activated beads were well suited for the covalent attachment of functional ligands, such as antibodies. Immobilization of antibodies against the pro-inflammatory cytokine TNF-α resulted in efficient TNF-α adsorbents which possess application potential in extracorporeal blood purification, e.g. for the modulation of cytokine levels as supportive therapy for sepsis and other inflammatory disorders.     

A chart preserving the normal vector and extensions of normal derivatives in weighted function spaces

Given a domain Ω of class C ^k,1, k ∈ ℕ, we construct a chart that maps normals to the boundary of the half space to normals to the boundary of in the sense that (∂/∂x _n )α(x′, 0) = − N(x′) and that still is of class C ^k,1. As an application we prove the existence of a continuous extension operator for all normal derivatives of order 0 to k on domains of class C ^k,1. The construction of this operator is performed in weighted function spaces where the weight function is taken from the class of Muckenhoupt weights.