Approximation of infinite delay and Volterra type equations

Summary We consider a class of infinite delay equations of neutral type which includes Volterrra type integral und integrodifferential equations. Using abstract approximation results (cf. Trotter-Kato-type) for strongly continuous semigroups we develop an approximation scheme which is based on approximation of the system state by Laguerre (and Legendre) polynomials. Numerical examples demonstrate the feasibility of the scheme and show infinite order convergence for smooth data.Supported in part by the Air Force Office of Scientific Research under Contracts AFORS-84-0398 and AFORS-85-0303 and the National Aeronautics and Space Administration under NASA Grant NAG-1-517 and by NSF under Grant UINT-8521208Supported in part by the Air Force Office of Scientific Research under Contract AFORS-84-0398 and in part by the Fonds zur Förderung der wissenschaftlichen Forschung, Austria, under project No. S3206     

Equivalence of functional-differential equations of neutral type and abstract Cauchy problems

Equivalence of functional-differential equations of neutral type to well-posed abstract Cauchy problems in the state spaces ⁿ }L ^p ,L ^p resp.C is investigated. The assumptions allow non-atomic difference operators.This work was supported by the Fonds zur Förderung der wissenschaftlichen Forschung (Austria) under Grant No. P4534.Work done by this author was done during a stay at the University of Graz from October 1981 till April 1984.     

A new inorganic-organic polymer for the passivation of thin film capacitors

Inorganic-organic polymers with barrier properties against water vapor, excellent electrical data (3, 2, R _D>10¹⁶ cm, E _D up to 400 V/µm) and good adhesion to various substrate materials have been developed. Tailored modifications of these materials provide an excellent protective coating for thin film capacitors. Several mm thick, expensive, encapsulations could be replaced by thin coatings (up to 10 µm). The polymer coating allows the use of thin film chip capacitors in surface-mount technology. As a measure for the efficiency of the coating, the capacitance decrease under controlled humidity has been used. The influence of the material composition, the type of catalyst during sol-gel processing and the curing conditions have been studied. Adhesion and water vapor permeation properties of the polymers and rheological properties of the coating solutions have been investigated. A protective coating is developed, which increases the withstandness of capacitors against humid conditions (90°C, 100% rel. humidity) by a factor of about 30 (compared to uncoated capacitors) and shows no crack formation during thermal cycling.     

Selective Uptake of Cylindrical Poly(2‐Oxazoline) Brush‐AntiDEC205 Antibody‐OVA Antigen Conjugates into DEC‐Positive Dendritic Cells and Subsequent T‐Cell Activation

To achieve specific cell targeting by various receptors for oligosaccharides or antibodies, a carrier must not be taken up by any of the very many different cells and needs functional groups prone to clean conjugation chemistry to derive well‐defined structures with a high biological specificity. A polymeric nanocarrier is presented that consists of a cylindrical brush polymer with poly‐2‐oxazoline side chains carrying an azide functional group on each of the many side chain ends. After click conjugation of dye and an anti‐DEC205 antibody to the periphery of the cylindrical brush polymer, antibody‐mediated specific binding and uptake into DEC205⁺‐positive mouse bone marrow‐derived dendritic cells (BMDC) was observed, whereas binding and uptake by DEC205^? negative BMDC and non‐DC was essentially absent. Additional conjugation of an antigen peptide yielded a multifunctional polymer structure with a much stronger antigen‐specific T‐cell stimulatory capacity of pretreated BMDC than application of antigen or polymer–antigen conjugate.     

Expressivism about Knowledge and the Value of Knowledge

The aim of the paper is to state a version of epistemic expressivism regarding knowledge, and to suggest how this expressivism about knowledge explains the value of knowledge. The paper considers how an account of the value of knowledge based on expressivism about knowledge responds to the Meno Problem, the Swamping Problem, and a variety of other questions that pertains to the value of knowledge, and the role of knowledge in our cognitive ecology.     

Degenerate difference-differential equations: Algebraic theory

In this paper we consider the algebraic aspects of the theory of degenerate difference-differential equations. It will be shown that the fundamental algebraic concepts to be used are module theoretic. We have to consider similarity of polynomial matrices in one or more indeterminates. In the case of systems with commensurable lags the underlying modules have a simple structure, because the corresponding ring of scalars is the principal ideal domain of polynomials in one indeterminate. This fact makes it possible to prove a structure theorem for degenerate difference-differential equations with commensurable lags. This theorem shows that degenerate systems of this type essentially are trivial in the sense of Henry [15], i.e., the characteristic quasipolynomial is a polynomial. Further it is shown that coordinate transforms with “time lag” play an essential role for the construction of degenerate equations. The power of the method is demonstrated by some examples, some of which are equations with incommensurable lags.     

Die Kinetik des thermischen Zerfalls von Kalziumkarbonat (Kinetik des Kalkbrennens)

Ohne Zusammenfassung Aktive Oxyde und Reaktionen fester Stoffe, 121. Mitt. Vgl. 119. Mitt.: G. F. Hüttig u. H. Kappel, Angew. Chem.53, 57 (1940).