ADB För Folkbokföring OCH Skatteuppbörd I Sverige

Summary A governmental Swedish committee has suggested conversion to ADP for the file maintenance involved in population registration, tax accounting etc. with a tape-oriented IBM 7070 and five IBM 1401 satellite computers. Investment in hardware, building etc. >6 M$; planning, programming, and file conversion 4 M$. Estimated annual savings, taking depreciation of initial costs into account: 2 M$/yr. Reduction of clerical force more than 1,000.     

Invariante Zwischenkörper endlicher Körpererweiterungen

Let KM be a finite field extension. An intermediate field L is called invariant if there is an affine algebraic K-group acting on M with L as its invariant field. The question, which intermediate fields are invariant, was studied by Bégueri [1] for purely inseparable extensions and by Sweedler [6] for arbitrary extensions, but only for a restricted class of groups. In this paper Bégueri's result is generalized to arbitrary field extensions. Additionally it is shown that one can check whether a given intermediate field is invariant or not by computing the rank of certain matrices. As an application we get a class of invariant intermediate fields.     

Zur Möbiusgeometrie über Alternativkörpern

Zusammenfassung Möbiusgeometrien (K, L) über nicht notwendig kommutativen KörpernKL – eine Definition dieser Geometrien findet man in [1] — sind Verallgemeinerungen der Geometrie der Kreise auf der Riemannschen Zahlenkugel (K=,L=). In der vorliegenden Note wollen wir, unter Verzicht auf die Assoziativität vonL, Möbiusgeometrien auch für den Fall betrachten, woK ein im Zentrum des AlternativkörpersL enthaltener Körper ist, und (in Abschnitt 2) die Gruppe der Kreisverwandtschaften von (K, L) angeben. Dabei benutzen wir, anders als in [1] und [5], nur den Doppelverhältniskalkül, den wir gleichwertig zu der von A. Schleiermacher in [6] vorgeschlagenen Verallgemeinerung für kollineare Punkte einer Moufarigebene definieren. Es ergibt sich damit ein neuer Beweis des Satzes über Kettenverwandtschaften von (K, L) auch im assoziativen Fall. Die Verwendung von Doppelverhältnissen beim Beweis — auch bei charL=2-wird insbesondere durch das in Abschnitt 2 bewiesene Lemma (2.4) (Verallgemeinerung des sog. von Staudtschen Theorems; vgl. [2], [3]) ermöglicht.     

Fixkörper vonp-Automorphismengruppen rein-transzendenter Körpererweiterungen vonp-Charakteristik

Ohne Zusammenfassung Karl Heinrich Weise zum 50. Geburtstag     

Zur Wellenausbreitung im heterogen-porösen Festkörper

Summary A method is developed which allows to describe analytically the two-dimensional elastic wave-field in porous media disturbed by heterogeneities. In the first place circular inclusions are regarded, later inclusions of arbitrary contour.     

Gitterpunktsanzahl und Parallelkörpervolumen von Eikörpern

LetΛ={x=(x ₁,...,x _d )|x _i ∈?} be a lattice in euclideand-spaceR ^d with respect to a rectangular coordinate system with unit vectors. Then for instance the following theorem holds: The number of lattice pointsG(K)=card (K∩Λ) of an arbitrary convex bodyK?R ^d is less or equal the volumeV(K _λd) of the outer parallel bodyK _λd ofK at a distance λ _d =ω _d ^-1/d (ω _d =Volume of thed-unitsphere, 2≤d≤5). The number λ is best possible.     

Zu den Lagrange'schen Lösungen des n-Körperproblems

Ohne Zusammenfassung     

On the freeness of Böröczky line arrangements

Periodica Mathematica Hungarica - In the present note, we focus on the freeness and some combinatorial properties of line arrangements in the projective plane having only double and triple points....     

Zu den Lagrange'schen Lösungen des n-Körperproblems II

Ohne Zusammenfassung     

Fastgeordnete Körper

Ohne Zusammenfassung     

Circular proofs for the Gödel-Löb provability logic

Sequent calculus for the provability logic GL is considered, in which provability is based on the notion of a circular proof. Unlike ordinary derivations, circular proofs are represented by graphs allowed to contain cycles, rather than by finite trees. Using this notion, we obtain a syntactic proof of the Lyndon interpolation property for GL.     

Halbbeschränktheit gewöhnlicher Differentialoperatoren höherer Ordnung

Ohne ZusammenfassungAuf Grund des Nachlasses vonF. Rellich bearbeitet vonErhard Heinz in Stanford/California     

Hölder's inequality

In this paper, refinements of Holder's inequality are obtained and some concave functions are defined.     

Über höhere kritische Determinanten von Sternkörpern

Ohne ZusammenfassungDie vorliegende Arbeit verdankt ihre Entstehung und Förderung meinem verehrten Lehrer, Herrn Prof. Dr.E. Hlawka.     

On Möbius form and Möbius isoparametric hypersurfaces

An umbilic-free hypersurface in the unit sphere is called MSbius isoparametric if it satisfies two conditions, namely, it has vanishing MSbius form and has constant MSbius principal curvatures. In this paper, under the condition of having constant MSbius principal curvatures, we show that the hypersurface is of vanishing MSbius form if and only if its MSbius form is parallel with respect to the Levi-Civita connection of its MSbius metric. Moreover, typical examples are constructed to show that the condition of having constant MSbius principal curvatures and that of having vanishing MSbius form are independent of each other.     

Konkave Eikörperfunktionale und höhere Trägheitsmomente

Ohne Zusammenfassung     

Zur Definition der Nörlundschen Hauptlösung von Differenzengleichungen

φ: R→R. Nörlund [4] defined the principal solution f_N of the difference equation $$V (x, y) \varepsilon R \times R_ + : \frac{1}{y}\left[ {g(x + y, y) - g(x, y)} \right] = \phi (x)$$ by V (x, y) ? [b, ∞) ×R₊: $$f_N (x, y) : = \mathop {\lim }\limits_{s \to 0 + } ( \int\limits_a^\infty {\phi (t) e^{ - st} dt} - y \sum\limits_{\nu = 0}^\infty { \phi (x + \nu y) e^{ - s(x + \nu y )} } )$$ with suitable a,bεR and proved the existence of f_N under certain restrictions onφ. In this paper, another way of defining a principal solution of the difference equation above, which includes Nörlund's, is gone. As an application, we construct in an easy manner a class of limitation methods for getting a principal solution, generalizing results from Nörlund [5].¹)     

Hölder categories

Hölder categories are invented to provide an axiomatic foundation for the study of categories of archimedean lattice-ordered algebraic structures. The basis of such a study is Hölder’s Theorem (1908), stating that the archimedean totally ordered groups are precisely the subgroups of the additive real numbers ? with the usual addition and ordering, which remains the single most consequential result in the studies of lattice-ordered algebraic systems since Birkhoff and Fuchs to the present. This study originated with interest in W*, the category of all archimedean lattice-ordered groups with a designated strong order unit, and the ?-homomorphisms which preserve those units, and, more precisely, with interest in the epireflections on W*. In the course of this study, certain abstract notions jumped to the forefront. Two of these, in particular, seem to have been mostly overlooked; some notion of simplicity appears to be essential to any kind of categorical study of W*, as are the quasi-initial objects in a category. Once these two notions have been brought into the conversation, a Hölder category may then be defined as one which is complete, well powered, and in which (a) the initial object I is simple, and (b) there is a simple quasi-initial coseparator R. In this framework it is shown that the epireflective hull of R is the least monoreflective class. And, when I = R — that is, the initial element is simple and a coseparator — a theorem of Bezhanishvili, Morandi, and Olberding, for bounded archimedean f-algebras with identity, can be be generalized, as follows: for any Hölder category subject to the stipulation that the initial object is a simple coseparator, every uniformly nontrivial reflection — meaning that the reflection of each non-terminal object is non-terminal — is a monoreflection. Also shown here is the fact that the atoms in the class of epireflective classes are the epireflective hulls of the simple quasi-initial objects. From this observation one easily deduces a converse to the result of Bezhanishvili, Morandi, and Olberding: if in a Hölder category every epireflection is a monoreflection, then the initial object is a coseparator.