Other Mathematics Commons^™

On The Nondegeneracy Of Constant Mean Curvature Surfaces, Nick Korevaar, Robert Kusner, Jesse Ratzkin

Robert Kusner

We prove that many complete, noncompact, constant mean curvature (CMC) surfaces $f:\Sigma \to \R^3$ are nondegenerate; that is, the Jacobi operator Δf+|Af|2 has no L2 kernel. In fact, if Σ has genus zero and f(Σ) is contained in a half-space, then we find an explicit upper bound for the dimension of the L2 kernel in terms of the number of non-cylindrical ends. Our main tool is a conjugation operation on Jacobi fields which linearizes the conjugate cousin construction. Consequences include partial regularity for CMC moduli space, a larger class of CMC surfaces to use in gluing constructions, and a surprising …

Place-Valued Logics Around Cybernetic Ontology, The Bcl And Afosr, Rudolf Kaehr

Rudolf Kaehr

No abstract provided.

From Ruby To Rudy, Rudolf Kaehr

Rudolf Kaehr

No abstract provided.

The Chinese Challenge. Hallucinations For Other Futures, Rudolf Kaehr

Rudolf Kaehr

The main question is: What can we learn from China that China is not teaching us? It is proposed that a study of polycontextural logic and morphogrammatics could be helpful to discover this new kind of rationality.

Fibonacci In Contextures, An Application, Rudolf Kaehr

Rudolf Kaehr

No abstract provided.

Contextures. Programming Dynamic Complexity, Rudolf Kaehr

Rudolf Kaehr

No abstract provided.

Gödel Games: "Cloning Gödel's Proofs", Rudolf Kaehr

Rudolf Kaehr

Gödel's Proofs in the context of beautifying (Hehner) and re-beautifying in polycontextural logic. Deconstruction of the relevance.

Lambda Calculi In Polycontextural Situations, Rudolf Kaehr

Rudolf Kaehr

No abstract provided.

Polylogics. Towards A Formalization Of Polycontextural Logics, Rudolf Kaehr

Rudolf Kaehr

No abstract provided.

Conformal Structures And Necksizes Of Embedded Constant Mean Curvature Surfaces, Robert Kusner

Robert Kusner

Let M = M_{g,k} denote the space of properly (Alexandrov) embedded constant mean curvature (CMC) surfaces of genus g with k (labeled) ends, modulo rigid motions, endowed with the real analytic structure described in [kmp]. Let P=Pg,k=rg,k×Rk+ be the space of parabolic structures over Riemann surfaces of genus g with k (marked) punctures, the real analytic structure coming from the 3g-3+k local complex analytic coordinates on the Riemann moduli space r_{g,k}. Then the parabolic classifying map, Phi: M --> P, which assigns to a CMC surface its induced conformal structure and asymptotic necksizes, is a proper, real analytic map. It …

The Topology, Geometry And Conformal Structure Of Properly Embedded Minimal Surfaces, Pascal Collin, Robert Kusner, William H. Meeks, Harold Rosenberg

Robert Kusner

This paper develops new tools for understanding surfaces with more than one end and infinite topology which are properly minimally embedded in Euclidean three-space. On such a surface, the set of ends forms a totally disconnected compact Hausdorff space, naturally ordered by the relative heights of the ends in space. One of our main results is that the middle ends of the surface have quadratic area growth, and are thus not limit ends. This implies that the surface can have at most two limit ends, which occur at the top and bottom of the ordering, and thus only a countable …

Miniaturen. Studien Zu Kalkül Und Kreativität 1998-2002, Rudolf Kaehr

Rudolf Kaehr

Informatik, künstlerische Praktik und Kunsttheorie der digitalen Bildtechnologien NULL&NICHTS; weder leer, noch nicht – oder Kraut und Rüben Gedanken zu einer autonomen Medienwissenschaft Das Menschenbild aus der Sicht einer polykontexturalen Systemtheorie Thesen zum trans-klassischen Menschenbild Gebaute Phantasien, unkontrollierbare Schwankungen Kreativität und Kalkül Ver_Endungen in/der Programmierbarkeit Diagrammatik: Denken a la Carte Zur Verstörung des (H)ortes der Zerstörung Zur Kenogrammatik der Medientheorie

Dynamic Semantic Web, Rudolf Kaehr

Rudolf Kaehr

Dynamic Semantic Web (DSW) is based at first on the techniques, methods and paradigms of the emerging Semantic Web movement and its applications. DSW is advancing one fundamental step further from a static to a dynamic concept of the Semantic Web with extended flexibility in the navigation between ontologies and more profound transparency of the informational system. Web Services are now redefinded by Semantic Web. To proof the advantages of DSW, it is the main aim of this project to develop the tools and methods necessary to develop a DSW based Web Service (DSW business application). The existing framework of …

The Second Hull Of A Knotted Curve, Jason Cantarella, Greg Kuperberg, Robert B. Kusner, John M. Sullivan

Robert Kusner

The convex hull of a set K in space consists of points which are, in a certain sense, "surrounded" by K. When K is a closed curve, we define its higher hulls, consisting of points which are "multiply surrounded" by the curve. Our main theorem shows that if a curve is knotted then it has a nonempty second hull. This provides a new proof of the Fary/Milnor theorem that every knotted curve has total curvature at least 4pi.

Strukturationen Der Interaktivität, Rudolf Kaehr

Rudolf Kaehr

No abstract provided.

Joachim Castella: Studien Zur Thematik "Kalkül Und Kreativität", Rudolf Kaehr

Rudolf Kaehr

Utopie der Zeichen – Zeichen der Utopie Vilém Flusser und Gotthard Günther als Komplement einer neuen Medienphilosophie Medientheorie als Theoriemedium Prolegomena einer allgemeinenMedientheorie Philosophie des LMR Joachim Castella 2000/2001

Grundlagenreflexionen Zur Thematik Anthropomorpher Schnittstellen, Rudolf Kaehr

Rudolf Kaehr

Report for the EMBASSI Project

Mass Transfer With Chemical Reaction In The Process Of Ammonia Desorption From Aqueous Solutions Containing Carbon Dioxide, Wojciech M. Budzianowski

Wojciech Budzianowski

No abstract provided.

The Moduli Space Of Complete Embedded Constant Mean Curvature Surfaces, Robert Kusner, Rafe Mazzeo, Daniel Pollack

Robert Kusner

We examine the space of surfaces in $\RR^{3}$ which are complete, properly embedded and have nonzero constant mean curvature. These surfaces are noncompact provided we exclude the case of the round sphere. We prove that the space $\Mk$ of all such surfaces with k ends (where surfaces are identified if they differ by an isometry of $\RR^{3}$) is locally a real analytic variety. When the linearization of the quasilinear elliptic equation specifying mean curvature equal to one has no L2−nullspace we prove that $\Mk$ is locally the quotient of a real analytic manifold of dimension 3k−6 by a finite group …

Disseminatorik. Zur Dekonstruktion Der Techno-Logik, Rudolf Kaehr

Rudolf Kaehr

POLYKONTEXTURALE LOGIK. Zur Konzeption, Formalisierung und Validierung. PROÖMIK UND DISSEMINATORIK Abbreviaturen transklassischen Denkens. DISKONTEXTURALITATEN: WOZU NEUE FORMEN DES DENKENS? Zur Kritik der logischen Voraussetzungen der Second Order Cybernetics und der Systemtheorie DISSEMINATORIK: ZUR LOGIK DER 'SECOND ORDER CYBERNETICS' Von den 'Laws of Form' zur Logik der Reflexionsform VOM 'SELBST' IN DER SELBSTORGANISATION Reflexionen zu den Problemen der Konzeptionalisierung und Formalisierung selbstbezüglicher Strukturbildungen SUFI´S DRAI: WOZU DISKONTEXTURALITATEN IN DER AI ? KALKÜLE FÜR SELBSTREFERENTIALITAT ODER SELBSTREFERENTIELLE KALKÜLE? SKIZZE EINER GRAPHEMATISCHEN SYSTEMTHEORIE Zur Problematik der Heterarchie verteilter Systeme im Kontext der New „second-order“ Cybernetics EINÜBUNG IN EINE ANDERE LEKTÜRE. Diagramm einer Rekonstruktion …

Encryption/Decryption Dickwads Of Cipherspace, Raleigh Muns

Raleigh Muns

Band Matrices With Toeplitz Inverses, William F. Trench, T N. E. Greville

William F. Trench

No abstract provided.

Paul Feyerabend, Against Method (Typoscript 1969), Rudolf Kaehr

Rudolf Kaehr

Facsimile of Paul Feyerabend's AGAINST METHOD Original typoscript of Against Methods from 1968 with handwritten corrections. Last sentence, p. 116: "We must take care that it does not lose its ability to make such a choice."

Paul Feyerabend's Telegram, Rudolf Kaehr

Rudolf Kaehr

6-page telegram from Paul Feyerabend (London) to Rolf Kaehr (Westberlin) Telegram 1 I am ill. Please let the seminar continue in my absence. Inform Prof Landmann and Prof Huebner, cancel the hotel reservation and read the following final message to my class on tuesday 1pm: I am sorry that I cannot give what Telegram 2 would have been my last lecture to you. In this lecture I would have elaborated on Verons argument and would have tried to show that it also excludes consience, self expression, identification. Turning back to the empiricist methodology and demand for theoretical unification I would …