On weak convergence to Brownian motion

Summary We consider a minimal form of the usual conditions for the dependent central limit theorem and invariance principle for near martingales. We show that these conditions imply convergence to Brownian motion in a way that is slightly stronger than weak convergence in D[0,). On the other hand, if a sequence of processes with paths in D[0,) converges to Brownian motion in this way, then we can always find a sequence of partitions of the time axis that is such that these conditions hold for the corresponding array of increments.     

Absorptionsspektrographische Studien an l-Ascorbinsäure I

Ohne ZusammenfassungMit 9 Abbildungen.Vgl. hierzuE. Schauenstein, Chemie56, 156 (1943) bzw.R. Czmiel, W. Halden undE. Schauenstein, Naturwiss.30, 586 (1942). — Eine Zusammenfassung der vorliegenden Arbeit erschien bereits in dieser Zeitschrift [Mh. Chem.78, 415 (1948)] als vorläufige Mitteilung.     

A quartz crystal microbalance study of the adsorption of asphaltenes and resins onto a hydrophilic surface

The adsorption of extracted and purified samples of asphaltenes and resins onto gold surfaces has been studied as a function of bulk concentration using a quartz crystal microbalance with dissipation measurements (QCM-D). With this device, which works equally well in transparent, opaque, and nontransparent samples, the adsorbed amount is measured through a change in resonant frequency of the quartz oscillator. The measured change in dissipation reports on changes in layer viscoelasticity and slip of the solvent at the surface. The results show that the adsorbed amount for resins from heptane corresponds to a rigidly attached monolayer. The adsorbed amount decreases with increasing amount of toluene in the solvent and is virtually zero in pure toluene. Asphaltenes, on the other hand, adsorb in large quantities and the mass and dissipation data demonstrate the presence of aggregates on the surface. The aggregates are firmly attached and cannot be removed by addition of resins. On the other hand, resins and asphaltenes associate in bulk liquid and the adsorption from mixtures containing both resins and asphaltenes is markedly different from that obtained from the pure components. Hence, we conclude that preformed resin aggregates adsorb to the surface. These results are compared and discussed in relation to adsorption from crude oil diluted in heptane/toluene mixtures.     

Quantum Mechanics from Focusing and Symmetry

A foundation of quantum mechanics based on the concepts of focusing and symmetry is proposed. Focusing is connected to c-variables—inaccessible conceptually derived variables; several examples of such variables are given. The focus is then on a maximal accessible parameter, a function of the common c-variable. Symmetry is introduced via a group acting on the c-variable. From this, the Hilbert space is constructed and state vectors and operators are given a definite interpretation. The Born formula is proved from weak assumptions, and from this the usual rules of quantum mechanics are derived. Several paradoxes and other issues of quantum theory are discussed.