Search results for " surface"

Die Relaxations-Korrektur in der Kapillar-Viskosimetrie

1952

Eine Kenngrose der Eigenschaft einer physikalischen Anordnung (eines Stoffes) kann nur aus dem Gesetz der Anordnung definiert werden. Eine Mesvorschrift kann nicht Grundlage einer Definition sein, sondern mus umgekehrt aus der Definition abgeleitet werden. Die Kapillar-Stromung Maxwellscher Flussigkeiten erster Art strebt demselben Poiseuilleschen Grenzzustand zu wie die Newtonscher Flussigkeiten. In der Energiebilanz tritt ein Einflus der Schubelastizitat auf, welcher als eine Relaxationskorrektur in Erscheinung tritt. Das bekannte Stromungsgesetz fur Newtonsche Flussigkeiten kann durch diese Relaxationskorrektur erweitert werden und umfast dann die Maxwellschen Flussigkeiten mit.

Molekulare Deutung der Umwandlungswärmen bei den Modifikationsübergängen des n-Tritriacontans

1978

Ausgehend von dem durch die Experimente nahegelegten Bild wurden Modellrechnungen angestellt, um die fur die drei Modifikationsumwandlungen desn-Tritriacontans gemessenen Umwandlungsenthalpien und -entropien molekular zu deuten.

Kommentar zu der Arbeit von Hans Craubner: „Lösefraktionierapparatur für makromolekulare Stoffe”

1976

Cyclopolymerisation bei zweifach-ungesättigten Monomeren

1967

Das Prinzip der Cyclopolymerisation wird erlautert; an Beispielen wird gezeigt, welche Verbindungen zu intra-intermolekularen Wachstumsschritten befahigt sind. Der Gehalt an cyclischen Grundbausteinen in den gebildeten Polymerisaten hangt auser von der Struktur der Monomeren auch von den Polymerisationsbedingungen ab. Es werden stereochemische Fragen behandelt, die im Zusammenhang mit Ringschlusreaktionen an 6- und hohergliedrigen Ringen auftreten. Chemische Umsetzungen an Cyclopolymeren konnen zu Copolymeren mit bestimmter Zusammensetzung und regelmasigem Aufbau fuhren.

Light Induced Excited Pair Spin State in an Iron(II) Binuclear Spin-Crossover Compound

1999

Light scattering - diagnostic methods for colloidal dispersions

1993

Abstract The increasing demand from the colloid research community for quick and noninvasive experimental techniques as well as the rapid progress of modern optics and electronics have led to a considerable expansion in the field of light scattering. This review introduces the basic concepts with some emphasis on novel approaches like the study of interacting particle systems, multiple scattering techniques, and non ergodic samples. Particular attention is then devoted to recent experimental progress towards more compact and rugged instruments.

Construction of 3D Triangles on Dupin Cyclides

2011

This paper considers the conversion of the parametric Bézier surfaces, classically used in CAD-CAM, into patched of a class of non-spherical degree 4 algebraic surfaces called Dupin cyclides, and the definition of 3D triangle with circular edges on Dupin cyclides. Dupin cyclides was discovered by the French mathematician Pierre-Charles Dupin at the beginning of the 19th century. A Dupin cyclide has one parametric equation, two implicit equations, and a set of circular lines of curvature. The authors use the properties of these surfaces to prove that three families of circles (meridian arcs, parallel arcs, and Villarceau circles) can be computed on every Dupin cyclide. A geometric algorithm …

Parabolic Equations Minimizing Linear Growth Functionals: L1-Theory

2004

Let Ω be a bounded set in ℝN with boundary of class C1. We are interested in the problem $$ \left\{ \begin{gathered} \frac{{\partial u}} {{\partial t}} = diva\left( {x,Du} \right)in Q = \left( {0,\infty } \right) \times \Omega , \hfill \\ u\left( {t,x} \right) = \phi \left( x \right)on S = \left( {0,\infty } \right) \times \partial \Omega , \hfill \\ u\left( {0,x} \right) = u_0 \left( x \right)in x \in \Omega \hfill \\ \end{gathered} \right. $$ (1) where ϕ ∈ L1(∂Ω), u0 ∈ L2(Ω) and a(x, ξ) = ∇ξ f(x, ξ, f being a function with linear growth in ‖ξ‖ as ‖ξ‖ → ∞. One of the classical examples is the nonparametric area integrand for which \( f(x,\xi ) = \sqrt {1 + \left\| \xi \right\|^2 } \). Prob…

Embeddings of Danielewski surfaces

2003

A Danielewski surface is defined by a polynomial of the form P=x nz −p(y). Define also the polynomial P ′ =x nz −r(x)p(y) where r(x) is a non-constant polynomial of degree ≤n−1 and r(0)=1. We show that, when n≥2 and deg p(y)≥2, the general fibers of P and P ′ are not isomorphic as algebraic surfaces, but that the zero fibers are isomorphic. Consequently, for every non-special Danielewski surface S, there exist non-equivalent algebraic embeddings of S in ℂ3. Using different methods, we also give non-equivalent embeddings of the surfaces xz=(y d n >−1) for an infinite sequence of integers d n . We then consider a certain algebraic action of the orthogonal group $\mathcal O(2)$ on ℂ4 which was…

On the signature of four-manifolds with universal covering spin

1993

In this note we study closed oriented 4-manifolds whose universal covering is spin and ask whether there are restrictions on the divisibility of the signature. Since any natural number appears as the signature of a connected sum of r 2,s, without the assumption on the universal covering there cannot exist any restrictions. Certainly, the most famous such restriction was proved by Rohlin in [10], where he showed that the signature a of a smooth 4-dimensional spin manifold is divisible by 16 (compare part (2) of our Main Theorem for a new proof). The Kummer surface K shows that this is the best possible general result. Dividing by a certain free holomorphic involution on K, one obtains the En…