Finite strains at the tip of a crack in a sheet of hyperelastic material: I. Homogeneous case

This paper describes an asymptotic analysis of the strain and stress fields at the tip of a crack in a sheet of incompressible hyperelastic material. The investigations are carried out within the framework of finite elastostatics and for the class of Generalized Neo-Hookean materials. Both the symmetric (mode I) and non-symmetric (mixed-mode) cases are considered. It is shown that the latter situation corresponds locally to a rigid body rotation of the symmetric fields. The effect of the hardening parameter on crack tip blunting is investigated analytically and numerically.     

Quantitative determination of chloride by means of flow injection analysis with spectrophotometric detection in the UV/VIS range

Chloride is determined indirectly by Spectrophotometric flow injection analysis. Two systems are compared, both based on the principle of ion exchange of easily detectable anions versus chloride from suitable mercury salts. The first method is based on the exchange of chloride with chloranilate which is detected at 332 nm or at 306 nm in neutral or in acidic medium respectively. In the second case, chloride reacts with Hg(SCN)₂. The liberated thiocyanate forms a strongly coloured complex with Fe(III) in acidic solution with an absorption maximum at 460 nm. Both methods have a detection limit of about 5 mol Cl^–/l (175 ng/ml). In the case of the thiocyanate method, the relative standard deviation is about 2% (7 measurements) in the range of 5 to 150 mol/l and decreases significantly to a value of approximately 0.2% at higher concentrations; for the chloranilate method it is 10% for lower and about 1% for higher concentrations respectively.     

The drift of a one-dimensional self-repellent random walk with bounded increments

Summary Consider a one-dimensional walk (S _k ) _k having steps of bounded size, and weight the probability of the path with some factor 1–(0,1) for every single self-intersection up to timen. We prove thatS _n /S S converges towards some deterministic number called the effective drift of the self-repellent walk. Furthermore, this drift is shown to tend to the basic drift as tends to 0 and, as tends to 1, to the self-avoiding walk's drift which is introduced in [10]. The main tool of the present paper is a representation of the sequence of the local times as a functional of a certain Markov process.Partially supported by Swiss National Sciences Foundation Grant 20-36305.92     

Time-resolved vibrational spectroscopy

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Time-resolved vibrational spectroscopy     

A characterization of subgroups of the orthogonal group

LetG be a subgroup of the general linear group GL_n(K), where charK 2. Put Kⁿ =V. AssumeG is generated by the setS of all elements inG for which dimV( – 1) = 1, and suppose ²=1_V for each inS. If {V(–1)¦S} contains a simplex, if – 1_V G, and if inG is a product of dim v(–1) elements inS wheneverV(–1) is not contained in the kernel of–1, thenG is a subgroup of an orthogonal group.This research was supported in part by NSERC Canada grant A7251.To Helmut Mäurer on his 60th birthday     

Inhomogeneous quantum groups and their quantized universal enveloping algebras

The quantum group IGL _q (N), the inhomogenization of GL _q (N), is formulated with -matrices. Theq-deformed universal enveloping algebra is constructed as the algebra of regular functionals in this formulation and contains the partial derivatives of the covariant differential calculus on the quantum space.     

Northcott's theorem on heights I. A general estimate

Given a pointP=(a _o:...:a _n) of projective space ⁿ = ⁿ (A) whereA is the field of algebraic numbers, letd(P) be its degree andH(P) its absolute multiplicative height. Northcott's Theorem says that givend, n andX, there are only finitely many pointsP ⁿ withd(P)d andH(P)X. We will show that there are at mostc(d, n)X ^d(d+n) such points.Supported in part by NSF grant DMS-9108581.     

A Nonlinear Dirichlet Problem on the Unit Ball

In the present paper, we consider the nonlinear Dirichlet problem - Δu(x) u^β(x) = 0 is the unit ball and q is a continuous radially symmetric function on B which may be singular on ?B. We state some mild conditions for the function q so that the Dirichlet problem has a positive classical solution.     

Der “thermo-stat” — eine ergänzung der verfahren zur bestimmung katalytisch wirksamer substanzen

The “Thermo-Stat” — a new device for the determination of catalyticaily active substancesA device for the determination of catalytically active substances, called a “ThermoStat”, is described. An additional heater is used to keep constant an arbitrarily preset temperature gradient between the reaction mixture and a cooling coil. Any heat produced by the catalysed reaction induces a deviation from the preset parameter and thus cuts out the additional heater. These breaks are plotted versus time by an integrating recorder. The slope of the reaction curve obtained is a measure of the concentration of the catalyst. As examples, determinations of copper in the range 0.1–2.0μg and molybdenum in the range 5–50 μg are discussed.