On Representations of Markov Chains by Random Smooth Maps

In this paper, we consider the problem of representing a Markovchain on a smooth manifold by a measurable collection of smoothmaps, and establish sufficient conditions for such a representationto exist.     

Rigidity of Continuous Coboundaries

We consider the functional equation F_oT–F=f, where T isa measure-preserving transformation and f is a continuous function.We show that if there is an L function F which satisfies thisequation, then F is constrained to satisfy a number of regularityconditions, and, in particular, if T is a one-sided Bernoullishift, then we show that there is a continuous function F satisfyingthis equation. We show that this is not the case for the two-sidedshift. 1991 Mathematics Subject Classification 28D05, 58F11.     

Criteria for -continuity

Bernoullicity is the strongest mixing property that a measure-theoretic dynamical system can have. This is known to be intimately connected to the so-called metric on processes, introduced by Ornstein. In this paper, we consider families of measures arising in a number of contexts and give conditions under which the measures depend -continuously on the parameters. At points where there is -continuity, it is often straightforward to establish that the measures have the Bernoulli property.

     

1-Ethoxycarbonyl-3-ferrocenyl-propan-1,3-dion und Ferrocen-1,1'bis(2,4-dioxobutansäureethylester) als Liganden für Übergangsmetallionen. Kristallstruktur von Bis(1-ethoxycarbonyl-3-ferrocenyl-propan-1,3dionato)kupfer(II)

1-Ethoxycarbonyl-3-ferrocenyl-propane-1,3-dion and Ferrocene-1,1′bis(2,4-dioxobutanoic acid ethylester) as Ligands for Transition Metal Ions. Crystal Structure of Bis(1-ethoxycarbonyl-3-ferrocenyl-propane-1,3dionato)copper(II) The ligands 1-ethoxycarbonyl-3-ferrocenyl-propane-1,3-dion and ferrocene-1,1′-bis(2,4-dioxo-butanoic acid ethylester) have been prepared by reaction of acetylferrocene or 1,1′-diacetylferrocene and diethyl oxalate. They yield neutral chelates with Cu^II, Ni^II, Zn^II, Co^II, and Mn^II. The acid dissociation constants of the ligands and the stability constants of their metal complexes including Fe^II complexes are reported. The structure of bis(1-ethoxycarbonyl-3-ferrocenyl-propane-1,3-dionato)copper(II) was determined by X-ray structure analysis. A cis arrangement with a nearly square planar coordination sphere at the Cu atom is found.     

Stochastic Stability of Lyapunov Exponents and Oseledets Splittings for Semi‐invertible Matrix Cocycles

We establish (i) stability of Lyapunov exponents and (ii) convergence in probability of Oseledets spaces for semi‐invertible matrix cocycles subjected to small random perturbations. The first part extends results of Ledrappier and Young to the semi‐invertible setting. The second part relies on the study of evolution of subspaces in the Grassmannian; the analysis developed here is based on higher‐dimensional Möbius transformations and is likely to be of wider interest. © 2015 Wiley Periodicals, Inc.     

A Generic C1 Expanding Map¶has a Singular S–R–B Measure

We show that for a generic C¹ expanding map T of the unit circle, there is a unique equilibrium state for − log T′ that is an S–R–B measure for T, and whose statistical basin of attraction has Lebesgue measure 1. We also present some results related to the question of whether a generic C¹ expanding map preserves a σ-finite measure, absolutely continuous with respect to Lebesgue measure. Received: 8 December 2000 / Accepted: 27 March 2001     

Tris{2‐[N‐(diethylaminothiocarbonyl)benz(‐amidino;‐imidoxy;‐imidothio)‐N′‐yl]ethyl}amine – neue tripodale Liganden. Darstellung,Komplexstabilität und Extraktionsverhalten ihrer Silber(I)‐Komplexe

Tris{2‐[ N ‐(diethylaminothiocarbonyl)benz(‐amidino; imidoxy; ‐imidothio)‐ N ′‐yl]ethyl}amines – New Tripodal Ligands. Synthesis, Complex Stability, and Extraction Behaviour of their Silver(I) Complexes N‐(Thiocarbamoyl)‐benzimidoylchlorides react with trivalent nucleophiles to give four novel tripodal ligands. Two of them have been characterized by X‐ray methods. The ligands form with silver(I) cationic mononuclear complexes in which the three arms of the ligand are coordinated monodentately via sulfur. The results of FAB and ESI mass spectrometry as well as ESCA and NMR investigations verify this binding mode. The protonation constants of the ligands and the stability constants of silver(I) complexes have been determined potentiometrically. The novel tripodal compounds behave as powerful extractands for silver(I).     

Percolation in Voronoi tilings

We consider a percolation process on a random tiling of ℝ^d into Voronoi cells based on points of a realization of a Poisson process. We prove the existence of a phase transition as the proportion p of open cells is varied and provide estimates for the critical probability p_c. Specifically, we prove that for large d, 2^−d(9d log d)⁻¹ ≤ p_c(d) ≤ C2^−d log d. © 2004 Wiley Periodicals, Inc. Random Struct. Alg., 2005     

Ergodic averaging sequences

We consider generalizations of the pointwise and mean ergodic theorems to ergodic theorems averaging along different subsequences of the integers or real numbers. The Birkhoff and Von Neumann ergodic theorems give conclusions about convergence of average measurements of systems when the measurements are made at integer times. We consider the case when the measurements are made at timesa(n) or ([a(n)]) where the functiona(x) is taken from a class of functions called a Hardy field, and we also assume that |a(x)| goes to infinity more slowly than some positive power ofx. A special, well-known Hardy field is Hardy’s class of logarithmico-exponential functions. The main theme of the paper is to point out that for a functiona(x) as described above, a complete characterization of the ergodic averaging behavior of the sequence ([a(n)]) is possible in terms of the distance ofa(x) from (certain) polynomials. This research was supported by grants from the NSF.     

Flüssig–Flüssig‐Extraktion von Silber(I) mit Aroylthiocarbamidsäure‐O‐estern – Einfluss von Solvens und Struktur der Extragentien

Liquid–Liquid Extraction of Silver(I) with Aroylthiocarbamic‐ O ‐esters Influence of the Solvents and of the Structure of Extractants Five bisbidentate (H₂L) and two bidentate (HL) aroylthiocarbamic‐O‐esters were synthesized and used for the liquid–liquid extraction of silver(I). A silver(I) complex was characterized in solid state. The distribution ratio D_Ag and the compositions of the extracted complexes were obtained for the silver extraction from nitric acid solutions depending on the pH value and the organic solvent. D_Ag values are decreasing in the sequence of the solvents decane, decane/toluene, toluene, chloroform. The bisbidentate extractants are more effective than the bidentate ones. Hetero atoms in the bridging molecule group of the bisbidentate compounds increase the D_Ag values. The extraction behavior is discussed with regard to the calculated protonation constants and stability constants.