Quadratically constrained least squares and quadratic problems

Summary We consider the following problem: Compute a vectorx such that Ax–b₂=min, subject to the constraint x₂=. A new approach to this problem based on Gauss quadrature is given. The method is especially well suited when the dimensions ofA are large and the matrix is sparse.It is also possible to extend this technique to a constrained quadratic form: For a symmetric matrixA we consider the minimization ofx ^T A x–2b ^T x subject to the constraint x₂=.Some numerical examples are given.This work was in part supported by the National Science Foundation under Grant DCR-8412314 and by the National Institute of Standards and Technology under Grant 60NANB9D0908.     

On the topology of compact smooth three-dimensional Levi-flat hypersurfaces

We study topological conditions that must be satisfied by a compactC ^∞ Levi-flat hypersurface in a two-dimensional complex manifold, as well as related questions about the holonomy of Levi-flat hypersurfaces. As a consequence of our work, we show that no two-dimensional complex manifold admits a subdomain Ω with compact nonemptyC ^∞ boundary such that Ω ? ?².     

Conditional solubility versus pO2− of cerium(III) oxide in molten equimolar NaCl+KCl at 727°C

Reactions between cerium trichloride and oxide ions were studied in NaCl+KCl (1/1) at 1000°K, by potentiometry with a calcia-stabilized zirconia membrane electrode. Titration curves clearly demonstrated the existence of soluble cerium oxychloride (CeO⁺) and precipitated cerium oxide (Ce₂O₃), with respective dissociation constants 10^?11 and 10^?30 (molality scale). The corresponding conditional solubility diagram {log S (Ce^III)=f(pO^2?)} is presented and discussed.     

Foaming and Structural Studies on the Acidic Subunit of Amaranth 11S Globulin Modified with Antihypertensive Peptides as a Function of pH and Ionic Strength

Some studies aimed at revealing the relationship between protein structure and their functional properties. However, the majority of these reports have been carried out using protein isolates. There are limited reports on the possible relationship between the functional properties and the structure of a purified protein. In this work the amaranth 11S globulin acidic subunit (AAC) and five mutations of the same protein that were modified in their variable regions with antihypertensive peptides (VYVYVYVY and RIPP), were analyzed at two ionic strength (2.9 and 17.6 g/L NaCl) and pH (3.0–7.0). Results revealed better solubility for the proteins mutated at the terminal ends (AACM.1 and AACM.4) and lower solubility for the protein inserted with RIPP peptide. Spectroscopy studies revealed an increase of β-sheet structure at high salt concentration for all proteins. It was also observed that salt concentration acted as a modulator, which allowed a better foam features for all modified proteins limiting movement of side chains and reducing red-shifted displacement of λmax. All proteins showed foam capacity ranging from 76 to 93% although foam stability was twofold better for modified proteins than for AAC at high salt concentration. This study allowed better understanding about the structural changes that influence the foaming properties of engineered proteins.     

Zur Anreicherung der stabilen Isotope des Schwefels durch Fest-Flüissig-Austausch unter Verwendung von Ionenaustauschern

An verschiedenen Systemen chemischer Verbindungen wurden Versuche zur Anreicherung des stabilen Isotopes ³⁴S unter Verwendung der Ionenaustauscher Wofatit L 150, SBW und SBK nach den Methoden der Frontalchromatographie und der Bandenverdrāngungschromatographie ausgeführt. Beim Isotopenaustauschsystem Hydrogensulfit (am Ionenaustauscher)/Schwefeldioxid (in wäβriger Lösung) wurden Verfahrensweise und Betriebsparameter hinsichtlich des Anreicherungsgrades optimiert. Mit Hilfe einer einfachen Methode gelang es, aus den Versuchsergebnissen Werle für den elementaren Trennfaktor und die Trennstufenhöhe zu berechnen.     

TrigonometricR matrices related to ‘dilute’ Birman-Wenzl-Murakami algebra

Explicit expressions for three series ofR matrices which are related to a dilute generalisation of the Birman-Wenzl-Murakami algebra are presented. Of those, one series is equivalent to the quantumR matrices of theD _n+1 ⁽²⁾ generalised Toda systems, whereas the remaining two series appear to be new.     

Bianchi transformation between the real hyperbolic Monge-Ampère equation and the Born-Infeld equation

By casting the Born-Infeld equation and the real hyperbolic Monge-Ampère equation into the form of equations of hydrodynamic type, we find that there exists an explicit transformation between them. This is Bianchi transformation.     

Hubbard-type solution in the planar approximation

The Hubbard solution to the Hubbard model showed a non-trivial metal-insulator transition. The value of the one-particle density of states at the Fermi energy in that solution decreased continuously with increasing value of the Hubbard interaction and vanished at a critical value of the interaction. Such a solution is derived from a planar model, as an approximation to the exact construction of the model's one-particle Green function.     

Extended non-abelian gauge symmetries in the classical WZNW model

Higher spin extensions of the non-Abelian gauge symmetries for the classical WZNW model are considered. Both linear and nonlinear realizations of the extended affine Kac-Moody algebra are obtained. It is a characteristic property of the WZNW model that it admits a higher spin linear realization of the extended affine Kac-Moody algebra which is equivalent to the corresponding higher spin nonlinear realization of the same algebra. However, in both cases, the higher spin Noether currents do not span an invariant space with respect to their generating transformations. Here, the current space is extended to an invariant space which allows us to gauge the symmetry.Supported by Bulgarian Foundation on Fundamental Research under contract Ph-318/93-95.     

A sublogarithmic convex hull algorithm

We present a parallel algorithm for finding the convex hull of a sorted set of points in the plane. Our algorithm runs inO(logn/log logn) time usingO(n log logn/logn) processors in theCommon crcw pram computational model, which is shown to be time and cost optimal. The algorithm is based onn ^1/3 divide-and-conquer and uses a simple pointer-based data structure.Part of this work was done when the last three authors were at the Department of Computer and Information Science, Linköping University. The research of the second author was supported by the Academy of Finland.