Numerical implementation of coherence for the example of the “Swiss Cross”

Summary We consider the two-dimensional Helmholtz equation u+u=0 inD with the boundary conditionsu=0 on D. D is the Swiss Cross — a region consisting of five unit squares. A method based on the concept of Coherence is utilized to determine an approximation for the first eigenvalue= ₁ more accurate than calculated by classical difference methods. The numerical result is used to illustrate isoperimetric upper and lower bounds for ₁, and to test some conjectures on its relations with torsional rigidity.Dedicated to the memory of Professor Lathar Collatz     

On error estimates of some higher order projection and penalty-projection methods for Navier-Stokes equations

Summary This paper is a continuation of our previous work [10] on projection methods. We study first existing higher order projection schemes in the semidiscretized form for the Navier-Stokes equations. One error analysis suggests that the precision of these schemes is most likely plagued by the inconsistent Neumann boundary condition satisfied by the pressure approximations. We then propose a penalty-projection scheme for which we obtain improved error estimates.This work is partially supported by NSF grant MS-8802596.     

Functional inequality characterizing nonnegative concave functions in (0, ∞) k

Summary In the present note we prove that every functionf: (0, ) [0, ) satisfying the inequalityaf(s) + bf(t) f(as + bt), s, t > 0, for somea andb such that 0 <a < 1 <a + b must be of the formf(t) = f(1)t, (t > 0). This improves our recent result in [2], where the inequality is assumed to hold for alls, t 0, and gives a positive answer to the question raised there.An analogue for functions of several real variables of the above result characterizes concave functions. Conjugate functions and some relations to Hölder's and Minkowski's inequalities are mentioned.     

Chern forms,chern numbers and curvature conditions on a Kähler-Einstein surface

In this paper we considered curvature conditions on a Kähler-Einstein surface of general type. In particular we showed that it has negative holomorphic sectional curvature if theL ²-norm of (3C ₂ ?C ₁ ² )/C ₁ ² is sufficiently small, whereC ₁ andC ₂ are the first and second Chern classes of the surfaces. This generalizes a result of Yau on the uniformization of Kähler-Einstein surfaces of general type and with 3C ₂ ?C ₁ ² = 0. Also in the process, we obtain a necessary condition in terms of an inequality between Chern numbers for a Kähler-Einstein metric to have negative holomorphic sectional curvature.     

Factorial regular representation of groups in complete graphs

A necessary and sufficient condition for the group of isomorphisms involved in a factorization of a complete graph into isomorphic factors is established.     

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.     

On bounds for the range of ordered variates II

Letx ₁, ,x _n be real numbers with ₁ ⁿ x _j =0, |x ₁ ||x ₂ ||x _n |, and ₁ ⁿ f(|x _i |)=A>0, wheref is a continuous, strictly increasing function on [0, ) withf(0)=0. Using a generalized Chebycheff inequality (or directly) it is easy to see that an upper bound for |x _m | isf ^–1 (A/(n–m+1)). If (n–m+1) is even, this bound is best possible, but not otherwise. Best upper bounds are obtained in case (n–m+1) is odd provided either (i)f is strictly convex on [0, ), or (ii)f is strictly concave on [0, ). Explicit best bounds are given as examples of (i) and (ii), namely the casesf(x)=x ^p forp>1 and 0<p<1 respectively.     

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.     

Obituary: Professor Dr.-Ing. Justus Mühlenpfordt

Abstract

The dose-dependent isotope fractionation during decarboxylation (¹³C/¹²C) amplifies the radiation effect in the relatively low dose range. The fractionation of the nitrogen isotopes during deamination (¹⁵N/¹⁴N) at the dose of 17 Gy was found to be smaller than that of decarboxylation.     

Füllstandsmessung mit Streustrahlungssonden

Es wird die Abhängigkeit der Impulsdichte vom Füllstand bei Meßanordnungen mit γ-Streustrahlungssonden verschiedener Länge untersucht. Verwendet werden die Nuklide ⁶⁰Co und ¹³⁷Cs. Ein nahezu linearer Anstieg der Impulsdichte mit dem Füllstand wird bei Füllgütern kleiner Ordnungszahl nur bei Sondenlängen L ≥ μ₀ ^?1.erzielt. Der Einfluß des Schüttwinkels und der Dichte des Füllgutes wird diskutiert.