Partitioning Boolean lattices into chains of subsets

We prove that the Boolean lattice of all subsets of an n-set can be partitioned into chains of size four if and only if n9.Research supported in part by N.S.F. grant DMS-8401281.Research supported in part by N.S.F. grant DMS-8406451.     

Element neighbourhoods in twofold triple systems

The method of differences is used to establish that every 2-regular multigraph onv– 10,2 (mod 3) points occurs as the neighbourhood graph of an element in a twofold triple system of orderv, with two exceptions: C₂C₃and C₃C₃.Dedicated to Professor Hanfried Lenz on the occasion of his seventieth birthday     

On the nature and origin of complexity in discrete,homogeneous, locally-interacting systems

The observed complexity of nature is often attributed to an intrinsic propensity of matter to self-organize under certain (e.g., dissipative) conditions. In order better to understand and test this vague thesis, we define complexity as logical depth, a notion based on algorithmic information and computational time complexity. Informally, logical depth is the number of steps in the deductive or causal path connecting a thing with its plausible origin. We then assess the effects of dissipation, noise, and spatial and other symmetries of the initial conditions and equations of motion on the asymptotic complexity-generating abilities of statistical-mechanical model systems. We concentrate on discrete, spatially-homogeneous, locally-interacting systems such as kinetic Ising models and cellular automata.     

Fortran IV programs for the penultimate copolymerization model

Three programs have been written for calculations involving use of the penultimate copolymerization model. The first computes the penultimate reactivity ratios from composition-conversion data, without constraints, at any conversion. A nonlinear leastsquares technique using Marquardt's algorithm is employed. The second program computes the four optimum starting monomer feed ratios, M₁⁰/M₂⁰ which should be used by the experimenter from the penultimate reactivity ratios. These optimum feed ratios are obtained by choosing the conditions necessary to minimize the determinant of the variance-covariance matrix. The input for the first program includes estimates of known values of the penultimate reactivity ratios. By using these two programs sequentially the experimenter has an optimized experimental approach toward evaluating penultimate reactivity ratios at any conversion. Finally, a program has been provided to calculate composition–conversion data, given penultimate reactivity ratios.     

Physico-chemical characterization of nanofiltration membranes.

This study presents a methodology for an in-depth characterization of six representative commercial nanofiltration membranes. Laboratory-made polyethersulfone membranes are included for reference. Besides the physical characterization [molecular weight cut-off (MWCO), surface charge, roughness and hydrophobicity], the membranes are also studied for their chemical composition [attenuated total reflectance Fourier spectroscopy (ATR-FTIR) and X-ray photoelectron spectroscopy (XPS)] and porosity [positron annihilation spectroscopy (PAS)]. The chemical characterization indicates that all membranes are composed of at least two different layers. The presence of an additional third layer is proved and studied for membranes with a polyamide top layer. PAS experiments, in combination with FIB (focused ion beam) images, show that these membranes also have a thinner and a less porous skin layer (upper part of the top layer). In the skin layer, two different pore sizes are observed for all commercial membranes: a pore size of 1.25-1.55 angstroms as well as a pore size of 3.20-3.95 angstroms (both depending on the membrane type). Thus, the pore size distribution in nanofiltration membranes is bimodal, in contrast to the generally accepted log-normal distribution. Although the pore sizes are rather similar for all commercial membranes, their pore volume fraction and hence their porosity differ significantly.     

Synthesis of an azacrown template for phosphatidylinositol-4,5-bis(phosphate) recognition

An azacrown system has been developed for selective membrane binding of phosphatidylinositol-4,5-bis(phosphate) recognition. Neutral and cationic forms of the metacyclophane macrocycles have been synthesized by divergent routes in acceptable yields. Such diversity will be useful in identifying anion receptors that operate best at membrane interfaces.     

Bipolar pulse conductometric monitoring of ion-selective electrodes: Part 1. Method development with a calcium-selective electrode and elucidation of the basic principles involved

The potential generated by a plastic-membrane calcium ion-selective electrode (i.s.e.) is shown to be indirectly measurable by a non-zero current method based on bipolar pulse conductance. Linear current—voltage curves are obtained using 0–5-V pulses; the current axis intercept is related to the i.s.e. potential. A simple electrical contact (e.g., platinum or stainless steel) can be used instead of a poised reference electrode as the counter electrode in this two-electrode system. Long-term exposure of the i.s.e. to calcium solutions causes an upward drift in the measured current. This drift is minimized by avoiding long exposure times to solution, rinsing the electrode between measurements, and constructing current—voltage curves for determination of the current axis intercepts. Voltage pulses lasting 100 μs are optimum for this method. Shorter pulses are subject to error from capacitive charging currents, and longer pulses yield poorer precision, and degrade the electrode through faradaic reactions. The measured signal is dependent upon Ca²⁺ concentration (rather than activity), making ionic strength adjustment unnecessary. The concentration dependence is induced by application of voltage pulses greater than ~ 15 mV in amplitude. Selectivities of the potentiometric and conductometric methods are shown to be comparable for a variety of interfering monovalent and divalent cations. The conductometric method yields a fast i.s.e. response because of induced migration of Ca²⁺ into the membrane. Response time decreases as the pulse height increases. Pulses greater than 2 V in magnitude yield response times limited by the solution mixing time rather than by the electrode.     

Base- and light-assisted synthesis of anthracenes from 3-allylnaphthalene-2-carbaldehydes

The synthesis of substituted anthracenes from naphthalene precursors is described. The key step involved heating ortho-allyl substituted naphthalene-2-carbaldehydes and potassium t-butoxide in DMF with concomitant irradiation from a high pressure mercury lamp to afford anthracenes in yields of 76-98%.     

Concise synthesis of anhydrovinblastine from leurosine

[reaction: see text] The Cp(2)TiCl-mediated deoxygenation of leurosine (1) afforded anhydrovinblastine (4) in good yield. Furthermore, as the reaction proceeded via a carbon-centered radical intermediate, this transient was also trapped by a hydrogen-atom donor to afford selectively reduced alkaloid 10.