On weak integrability and boundedness in Banach spaces

Thin and thick sets in normed spaces were defined and studied by M.I. Kadets and V.P. Fonf in 1983. In this paper, we give a new characterization of thick sets in terms of weak integrability of Banach space valued measurable functions. We also characterize thick sets in terms of boundedness of vector measures, and explain how this concept is related to the theory of barrelled spaces.     

The Dynamics of Long-Range Financial Accumulation and Crisis

A dynamic model of money stock/flow relations for a generic economic agent is developed, and employed to model and discuss the long-range (decades) impact of returns on any form of saved or invested money on a macroeconomy. It is shown that, subject to realistic assumptions about behavior of economic agents, a macro-economic system with positive returns must eventually reach a depression-like economic state. The observed disproportionate growth of financial sectors in recent years is explained by the proposed model. Simulation runs are presented. An indicator for economic fragility is proposed.     

Multistep Continuous‐Flow Synthesis in Medicinal Chemistry: Discovery and Preliminary Structure–Activity Relationships of CCR8 Ligands

A three‐step continuous‐flow synthesis system and its application to the assembly of a new series of chemokine receptor ligands directly from commercial building blocks is reported. No scavenger columns or solvent switches are necessary to recover the desired test compounds, which were obtained in overall yields of 49–94 %. The system is modular and flexible, and the individual steps of the sequence can be interchanged with similar outcome, extending the scope of the chemistry. Biological evaluation confirmed activity on the chemokine CCR8 receptor and provided initial structure–activity‐relationship (SAR) information for this new ligand series, with the most potent member displaying full agonist activity with single‐digit nanomolar potency. To the best of our knowledge, this represents the first published example of efficient use of multistep flow synthesis combined with biological testing and SAR studies in medicinal chemistry.     

A generating set search method using curvature information

Direct search methods have been an area of active research in recent years. On many real-world problems involving computationally expensive and often noisy functions, they are one of the few applicable alternatives. However, although these methods are usually easy to implement, robust and provably convergent in many cases, they suffer from a slow rate of convergence. Usually these methods do not take the local topography of the objective function into account. We present a new algorithm for unconstrained optimisation which is a modification to a basic generating set search method. The new algorithm tries to adapt its search directions to the local topography by accumulating curvature information about the objective function as the search progresses. The curvature information is accumulated over a region thus smoothing out noise and minor discontinuities. We present some theory regarding its properties, as well as numerical results. Preliminary numerical testing shows that the new algorithm outperforms the basic method most of the time, sometimes by significant relative margins, on noisy as well as smooth problems. This work was supported by the Norwegian Research Council (NFR).     

Communication: thermodynamics of condensed matter with strong pressure-energy correlations

We show that for any liquid or solid with strong correlation between its NVT virial and potential-energy equilibrium fluctuations, the temperature is a product of a function of excess entropy per particle and a function of density, T = f(s)h(ρ). This implies that (1) the system's isomorphs (curves in the phase diagram of invariant structure and dynamics) are described by h(ρ)/T = Const., (2) the density-scaling exponent is a function of density only, and (3) a Gru?neisen-type equation of state applies for the configurational degrees of freedom. For strongly correlating atomic systems one has h(ρ) = ∑(n)C(n)ρ(n/3) in which the only non-zero terms are those appearing in the pair potential expanded as ν(r) = ∑(n)ν(n)r(-n). Molecular dynamics simulations of Lennard-Jones type systems confirm the theory.     

Micropump based on electroosmosis of the second kind

A microfluidic pump based on electroosmosis of the second kind was designed and fabricated. Experimental results using DC and AC voltages showed a close to second‐order relationship between flow and voltage, in good agreement with theory. The experimental flow rates were considerably lower than the predicted maximum for the micropumps, which can be attributed to the hydrodynamic resistance of the channel network. This also indicates that higher flow velocities are obtainable for modified pump designs.     

Recent experimental and theoretical developments towards the observation of parity violation (PV) effects in molecules by spectroscopy

Parity violation (PV) at the molecular level is known to be responsible for a tiny energy difference between the two enantiomers of a chiral molecule. This parity violation energy difference (PVED) has not yet been detected by experiment. In the last few years, the search for PV effects in molecules has made important steps ahead for several reasons. On one hand, very accurate infra-red spectroscopy measurements were performed by metrologists on bromochlorofluoromethane (CHFClBr) with a 10 Hz accuracy, which so far is the most precise. On the other hand, relativistic calculations were used for the evaluation of DeltaE(PV) allowing for a screening of favorable molecules for future measurements. The synthesis of such chiral molecules with high parity violation effects is currently being investigated. In memory of Professor Jean-Bernard Robert.     

Near-IR spectroscopy as a method for studying the formation of calcium naphthenate

A method for studying the precipitation of calcium naphthenate particles by means of near-IR spectroscopy is presented. Naphthenic or fatty acids were dissolved in water at high pH (11.2–11.5). Upon addition of a Ca²⁺ solution the nucleation period and particle growth were monitored. The near-IR spectra experience a baseline elevation owing to the formation and growth of calcium naphthenate particles. The resulting change in optical density over time is discussed on the basis of supersaturation, particle sizes, agglomeration, Ca²⁺-to-carboxylic acid ratio and nucleation process. Solubility products, defined as the ion concentration products where no particle growth was detected, were estimated for the calcium soaps. The method showed some quantitative limitations since the particle sizes changed with supersaturation. Smaller particles will have less influence on the optical density and the larger particle will dominate the resulting scattering contribution. However, it is obvious that the method has qualitative value, for example, to study the efficiency of different calcium naphthenate inhibitors.     

Syntheses of two cytotoxic polyunsaturated pyrrole metabolites of the marine sponge Mycale micracanthoxea

Starting from eicosapentaenoic acid (EPA) the marine, naturally occurring, pyrrole derivatives, mycalazol 5 and mycalazal 2 have been synthesized. The Stille coupling reaction is a key step in the syntheses.     

One-pot synthesis of substituted catechols from the corresponding phenols

Phenols are converted to salicylaldehydes with paraformaldehyde, MgCl₂-Et₃N in THF, and when subsequently treated with aqueous NaOH and H₂O₂ afford the corresponding catechols. The sequence is conveniently carried out as a one-pot procedure.