Untersuchungen über die Adsorption von Gasgemischen

Zusammenfassung Es werden Mischadsorptionsmessungen am SystemAceton-Chloroform mit einem Dampfdrukminimum an homogenen Oberflächen an Mikroglaskügelchen (2 bis 12 ) in einem rel. Druckbereich zwischen 0,1 und 0,9 ausgeführt. Dabei ist der Sättigungsdruck jeweils der Dampfdruck der mit der Gasphase im Adsorptionsgleichgewicht korrespondierenden flüssigen Phase imp _o , -Diagramm. Zugleich wurde die Zusammensetzung der adsorbierten Mischphase bestimmt und daraus die partielle Adsorption der Komponenten als Funktion des rel. Druckes bei verschiedener Zusammensetzungen der Gasphase.Für partielle Adsorption wurde auf der Grundlage eines vonHill entwickelten Ansatzes in Verbindung mit einer Gl. vonTheimer eine Formel aufgestellt, die die experimentellen Ergebnisse gut wiedergibt.Es werden Adsorptionswärmen für die verschiedenen Belegungsdichten in Abhängigkeit von der Zusammensetzung der Gasphase bestimmt.Mit 18 AbbildungenHerrn Prof.L. Ebert zum 60. Geburtstag gewidmet.     

Positive dipole correlation at the I/B2 transition in the isotropic phase

The first evidence of a positive dipole correlation in the isotropic phase near to the I/B₂ transition is given.     

Mössbauer spectroscopic study of core and mantle of rattle stones

Mössbauer spectroscopy has been applied to two rattle stones found in the Netherlands, which have been formed under different pedoenvironment conditions in the past. Ultrafine particles of goethite are dominantly present in both core and mantle of these stones. The latter differs in both composition and mean particle size; this is related to the distinct manner of their formation.     

A note on adapting methods for continuous global optimization to the discrete case

In this note we show that various branch and bound methods for solving continuous global optimization problems can be readily adapted to the discrete case. As an illustration, we present an algorithm for minimizing a concave function over the integers contained in a compact polyhedron. Computational experience with this algorithm is reported.     

Malliavin calculus in abstract Wiener space using infinitesimals

Using infinitesimals, we develop Malliavin calculus on spaces which result from the classical Wiener space by replacing with any abstract Wiener space .We start from a Brownian motion b on a Loeb probability space Ω with values in the Banach space is the standard part of a ∗finite-dimensional Brownian motion B. Then we define iterated Itô integrals as standard parts of internal iterated Itô integrals. The integrator of the internal integrals is B and the values of the integrands are multilinear forms on , where is a ∗finite-dimensional linear space over between the Hilbert space and its ∗-extension .In the first part we prove a chaos decomposition theorem for L²-functionals on Ω that are measurable with respect to the σ-algebra generated by b. This result yields a chaos decomposition of L²-functionals with respect to the Wiener measure on the standard space of -valued continuous functions on [0,1]. In the second part we define the Malliavin derivative and the Skorohod integral as standard parts of internal operators defined on ∗finite-dimensional spaces. In an application we use the transformation rule for finite-dimensional Euclidean spaces to study time anticipating and non-anticipating shifts of Brownian motion by Bochner integrals (Girsanov transformations).     

A functional inequality for real-analytic functions

Summary Forf ( C ⁿ() and 0 t x letJ _n (f, t, x) = (–1)ⁿ f(–x)f ⁽ⁿ⁾(t) +f(x)f ⁽ⁿ⁾ (–t). We prove that the only real-analytic functions satisfyingJ _n (f, t, x) 0 for alln = 0, 1, 2, are the exponential functionsf(x) = c e ^x,c, . Further we present a nontrivial class of real-analytic functions satisfying the inequalitiesJ ₀ (f, x, x) 0 and ₀ ^x (x – t)^{n – 1}J_n(f, t, x)dt 0 (n 1).     

Global optimization of concave functions subject to quadratic constraints: An application in nonlinear bilevel programming

When the follower's optimality conditions are both necessary and sufficient, the nonlinear bilevel program can be solved as a global optimization problem. The complementary slackness condition is usually the complicating constraint in such problems. We show how this constraint can be replaced by an equivalent system of convex and separable quadratic constraints. In this paper, we propose different methods for finding the global minimum of a concave function subject to quadratic separable constraints. The first method is of the branch and bound type, and is based on rectangular partitions to obtain upper and lower bounds. Convergence of the proposed algorithm is also proved. For computational purposes, different procedures that accelerate the convergence of the proposed algorithm are analysed. The second method is based on piecewise linear approximations of the constraint functions. When the constraints are convex, the problem is reduced to global concave minimization subject to linear constraints. In the case of non-convex constraints, we use zero-one integer variables to linearize the constraints. The number of integer variables depends only on the concave parts of the constraint functions.Parts of the present paper were prepared while the second author was visiting Georgia Tech and the University of Florida.     

Infinitesimal obstructions to weakly mixing

Let ^t be the flow (parametrized with respect to arc length) of a smooth unit vector field v on a closed Riemannian manifold M ⁿ , whose orbits are geodesics. Then the (n-1)-plane field normal to v, v, is invariant under d ^t and, for each x M, we define a smooth real function _x (t) : (1 + _i (t)), where the _i(t) are the eigenvalues of AA ^T, A being the matrix (with respect to orthonormal bases) of the non-singular linear map d^2t , restricted to v at the point _x ^-t M ⁿ.Among other things, we prove the Theorem (Theorem II, below). Assume v is also volume preserving and that _x ^' (t) 0 for all x M and real t; then, if _x ^t : M M is weakly missng for some t, it is necessary that vx 0 at all x M.