Cyclodehydration of diphenyl-trifluoromethyl-carbinols

The halochromic product from di-(p-fluorophenyl) -trifluoromethylcarbinol and sulphuric acid gives with ethyl mercaptan 3-ethylthio-6 fluoro-9-trifluoromethylfluorene. Analogous reactions have been observed with (p-chlorophenyl)-(p-fluorophenyl)-, with (p-fluorophenyl)-phenyl-. and with diphenyl-trifluoromethyl-carbinol.

The infra-red spectra of the fluorene derivatives formed are discussed.     

Adsorption of charged macromolecules at a gold electrode

Using an optical reflectometer with impinging-jet system, the adsorption from aqueous solution onto gold of three charged macromolecules has been studied: the strong linear-chain polyelectrolyte polyvinyl pyridine (PVP(+)), the fifth-generation poly(propylene imine) dendrimer DAB-64, which has a pH-dependent charge and a relatively fixed shape, and the protein lysozyme, of which both the charge and the structure-stability are dependent on solution composition. Experimental conditions that have been varied include the adsorbate concentration, electrolyte concentration, pH, and externally applied potential across the gold/solution interface. Making use of the earlier established dependency of the double layer potential of the gold substrate on solution conditions and externally applied potential, the results of measurements as a function of pH and as a function of external potential control are compared. The total set of results enables us to draw conclusions with respect to the relative importance of electrostatic interactions for the adsorption process. PVP(+) adsorption follows the electric potential of the gold/solution interface and is further determined by a rather strong nonelectrostatic affinity between segments and surface. The adsorption behavior of DAB-64 is not quite understood, but electrostatic interactions with the gold surface seem to play a minor role. For lysozyme, surface-induced conformational changes dominate the adsorption process. The extent of spreading of the molecules decreases with increasing polarity of the surface, resulting in a minimum in adsorbed amount around the point of zero potential of the gold.     

Dynamics of curved DNA molecules: prediction and experiment

We have developed a quantitative predictive model capable of describing the dynamics of migration of intrinsically curved DNA fragments on polyacrylamide gels. The model takes into account structural features of DNA, end-to-end distance, screening of hydrodynamic interactions, ionic strength of buffer, electrostatic persistence length, structural fluctuations of the macromolecule, counter condensation, and variation of dielectric constant and viscosity of water with MPD. In doing so, we have also addressed a decade old issue on the effect of the organic solvent 2-methyl-2,4-pentanediol on gel migration of phased A-tracts. We show here that A-tract-solvent interactions are less favored compared with A-tract-A-tract and solvent-solvent interactions.     

Superoxes,high temperature universal phases in (GC)2

Most of the common classes of organic compounds chromatograph normally on Superoxes. There is no tailing or adverse effect from excessively different activity different activity coefficients. Superoxes are therefore universal phases for gas chromatography. This is also expressed by a wide useful temperature range from ～50° to ～300°. High MW Superox-4 has a MAOT about 20° higher than the lower MW Superox-0.1. Several applications illustrating the versatility of Superox phases in (GC)² are presented.     

Generating M-Indeterminate Probability Densities by Way of Quantum Mechanics

Probability densities that are not uniquely determined by their moments are said to be “moment-indeterminate,” or “M-indeterminate.” Determining whether or not a density is M-indeterminate, or how to generate an M-indeterminate density, is a challenging problem with a long history. Quantum mechanics is inherently probabilistic, yet the way in which probability densities are obtained is dramatically different in comparison with standard probability theory, involving complex wave functions and operators, among other aspects. Nevertheless, the end results are standard probabilistic quantities, such as expectation values, moments and probability density functions. We show that the quantum mechanics procedure to obtain densities leads to a simple method to generate an infinite number of M-indeterminate densities. Different self-adjoint operators can lead to new classes of M-indeterminate densities. Depending on the operator, the method can produce densities that are of the Stieltjes class or new formulations that are not of the Stieltjes class. As such, the method complements and extends existing approaches and opens up new avenues for further development. The method applies to continuous and discrete probability densities. A number of examples are given.

     

Correction to: Preface

Foundations of Computational Mathematics -     

Constructing banking networks under decreasing costs of link formation

The structure of networks plays a central role in the behavior of financial systems and their response to policy. Real-world networks, however, are rarely directly observable: banks’ assets and liabilities are typically known, but not who is lending how much and to whom. This paper adds to the existing literature in two ways. First, it shows how to simulate realistic networks that are based on balance-sheet information. To do so, we introduce a model where links cause fixed-costs, independent of contract size; but the costs per link decrease the more connected a bank is (scale economies). Second, to approach the optimization problem, we develop a new algorithm inspired by the transportation planning literature and research in stochastic search heuristics. Computational experiments find that the resulting networks are not only consistent with the balance sheets, but also resemble real-world financial networks in their density (which is sparse but not minimally dense) and in their core-periphery and disassortative structure.

     

New results for diffusion in Lorentz lattice gas cellular automata

New calculations to over ten million time steps have revealed a more complex diffusive behavior than previously reported of a point particle on a square and triangular lattice randomly occupied by mirror or rotator scatterers. For the square lattice fully occupied by mirrors where extended closed particle orbits occur, anomalous diffusion was still found. However, for a not fully occupied lattice the superdiffusion, first noticed by Owczarek and Prellberg for a particular concentration, obtains for all concentrations. For the square lattice occupied by rotators and the triangular lattice occupied by mirrors or rotators, an absence of diffusion (trapping) was found for all concentrations, except on critical lines, where anomalous diffusion (extended closed orbits) occurs and hyperscaling holds for all closed orbits withuniversal exponentsd _f =7/4 and =15/7. Only one point on these critical lines can be related to a corresponding percolation problem. The questions arise therefore whether the other critical points can be mapped onto a new percolation-like problem and of the dynamical significance of hyperscaling.