Ideals and solutions of nonlinear field equations

Families of horizontal ideals of contact manifolds of finite order are studied. Each horizontal ideal is shown to admit ann-dimensional module of Cauchy characteristic vectors that is also a module of annihilators (in the sense of Cartan) of the contact ideal. Since horizontal ideals are generated by 1-forms, any completely integrable horizontal ideal in the family leads to a foliation of the contact manifold by submanifolds of dimensionn on which the horizontal ideal vanishes. Explicit conditions are obtained under which an open subset of a leaf of this foliation is the graph of a solution map of the fundamental ideal that characterizes a given system of partial differential equations of finite order withn independent variables. The solution maps are obtained by sequential integration of systems of autonomous ordinary differential equations that are determined by the Cauchy characteristic vector fields for the problem. We show that every smooth solution map can be obtained in this manner. Let {_Vi¦1in} be a basis for the module of Cauchy characteristic vector fields that are in Jacobi normal form. If a subsidiary balance ideal admits each of then vector fieldsV _i as a smooth isovector field, then certain leaves of the foliation generated by the corresponding closed horizontal ideal are shown to be graphs of solution maps of the fundamental ideal. A subclass of these constructions agree with those of the Cartan-Kähler theorem. Conditions are also obtained under which every leaf of the foliation is the graph of a solution map. Solving a given system ofr partial differential equations withn independent variables on a first-order contact manifold is shown to be equivalent to the problem of constructing a complete system of independent first integrals. Properties of systems of first integrals are analyzed by studying the collection ISO[A _ij ] of all isovectors of the horizontal ideal. We show that ISO[A _ij ] admits the direct sum decomposition ^*[A _ij ]W[A _ij ] as a vector space, where ^*[A _ij ] is the module of Cauchy characteristics of the horizontal ideal. ISO[A _ij ] also forms a Lie algebra under the standard Lie product,^*[A _ij ] andW[A _ij ] are Lie subalgebras of ISO[A _ij ], and [A _ij ] is an ideal. A change of coordinates that resolves (straightens out) the canonical basis for ^*[A _ij ] is constructed. This change of coordinates is used to reduce the problem of solving the given system of PDE to the problem of root extraction of a system ofr functions ofn variables, and to establish the existence of solutions to a second-order system of overdetermined PDE that generate the subspaceW[A _ij ]. Similar results are obtained for second-order contact manifolds. Extended canonical transformations are studied. They are shown to provide algorithms for calculating large classes of closed horizontal ideals and a partial analog of classical Hamilton-Jacobi theory.     

Angular momentum decoupling approximations in the quantum dynamics of reactive systems

Two methods for implementing angular momentum decoupling approximations in quantum mechanical reactive scattering examined. Applications of both reactive and nonreactive H + H₂ collisions indicate that for the most intense individual reactive transitions and for all degeneracy-averaged ones, these decoupling methods (especially the “proper” decoupling method) yield results in good agreement with those of fully-coupled calculations. However, for the less intense reactive transitions and all individual nonreactive transitions, very large errors can result from use of these approximate methods.     

Intrazelluläre Lokalisierung und Funktion von NADPH-Cytochromc-Reduktase in Saccharomyces cerevisiae

Zusammenfassung Das Flavoprotein NADPH-Cytochromc-Reduktase aus Hefe ist im Gegensatz zu bisherigen Anschauungen kein Enzym der mitochondralen Atmungskette, sondern an bisher unbekannte subzelluläre Partikel gebunden, die nach Homogenisieren der Hefezellen von den Mitochondrien abgetrennt werden können. Die Beteiligung von Cytochromb ₂ oder einer Transhydrogenase-reaktion an der Elektronenübertragung von NADPH auf Cytochromc in einem Hefehomogenat konnte ausgeschlossen werden. Die Natur der neuen Hefepartikel sowie die physiologische Funktion des Enzyms NADPH-Cytochromc-Reduktase werden diskutiert.Abkürzungen NADPH reduziertes Nikotinamid-adenin-dinukleotidphosphat - NADH reduziertes Nikotinamid-adenin-dinukleotid - Tris Tris-(hydroxymethyl)aminomethan - BAL 1,2-Dimercapto-3-hydroxypropan - RNase Ribonuklease - ATPase Adenosintriphosphatase - EDTA Äthylendiamintetraessigsäure Mit 2 Abbildungen     

Development of a beam of very slow polarized muons

During the last few decades, a variety of methods has been developed which makes use of polarized positive muons as a microscopic probe of the magnetic properties of condensed matter (muon spin rotation, relaxation, resonance,SR). Until now, available beams for SR studies have delivered 100% polarized muons with energies in the MeV range, resulting in a deep penetration of the muons into the sample material under investigation. This presently limits the applications of theSR technique to the study of the bulk characteristics of matter. To be able to control the implantation depth, a very low energy beam of polarized muons is being developed at the Paul Scherrer Institute. Very slow polarized muons (kinetic energy 10 eV, polarization 90%) are obtained from the moderation of a high energy muon beam in a thin film of an appropriate condensed gas. These muons can be used as a source for a beam of tunable energy between a few tens of eV and some tens of keV. Implantation depths in the range of few to a few hundreds of nanometers can thus be achieved by varying the energy.     

Generalized logic and the representation of rings

Following the progression towards weaker logics, a number of authors have considered the notion of a sheaf over a quantale or, equivalently, a quantale valued set. In this paper, we use ideas from enriched category theory to motivate the definition of a quantic sheaf. Given a localic subquantale of Q, a quantic sheaf over Q gives a sheaf in the usual sense. As an application, we derive a series of sheaf representations for commutative rings including the familiar Pierce representation.     

Non-reactive metal/semiconductor interfaces: a combined AES,AFM andPAC study

Thin In films on Ge(100), Si(100) andSi(111) are investigated using Auger-electron spectroscopy (AES), atomic force microscopy (AFM) andperturbed -angular correlation (PAC) spectroscopy, respectively. The growth mode of the metal films is characterized by in situ AES measurements, indicating distinct differences between the different substrate surfaces. Additional AFM investigations are used to monitor the film topography at higher metal coverage. Finally, the local crystalline structure of the films is studied by the PAC technique.     

Über die Reaktion von Δ9,12-Linolsäureester in Wasser, 5. Mitt.: Mechanismus der Glykolysehemmung bei Tumorzellen durch wasserlösliche Fettsäureester-Hydroperoxyde

Zusammenfassung In vorangegangenen Arbeiten dieser Mitteilungsreihe konnte die Hemmwirkung der wasserlöslichen Lipid-hydroperoxyde auf Atmung und Glykolyse vonEhrlich-Ascites-Tumorzellen festgestellt werden.Ferner wurde gefunden, daß die Lipid-hydroperoxyde (LHPO) nicht über eine Schädigung des intrazellulären DPN-Systems wirksam sind und ihrer Hemmwirkung wahrscheinlich eine oxydative Inaktivierung der SH-Enzyme der Glykolysekette zugrunde liegt. Zur experimentellen Prüfung dieser Annahme werden daher zunächst die isolierten Glykolyseenzyme Hexokinase, Glucose-6-phosphat-Dehydrogenase, Aldolase, Glycerinaldehydphosphat-Dehydrogenase (GAPDH) und Lactat-Dehydrogenase (LDH) nach Einwirkung von Präparat LHPO getestet. Die Messungen ergeben, daß nur die GAPDH und die LDH durch Präparat LHPO inaktiviert werden. Bestimmt man nun die Aktivität dieser beiden Enzyme in einem Extrakt, der aus den intakten und mit LHPO inkubierten Tumorzellen gewonnen wurde, so findet man hier eine vollständige Inaktivierung (halbmaximale Dosis 7,1·10^–5m Lipid-hydroperoxyd/l). Damit scheint der Wirkungsmechanismus von Präparat LHPO hinsichtlich der Glykolysehemmung klargestellt.Mit 1 AbbildungHerrn Prof. Dr.A. Zinke anläßlich seines 70. Geburtstages mit den besten Wünschen überreicht.