On Krull's Separation Lemma

We show that Krull's Separation Lemma for arbitrary rings and a certain lattice-theoretical generalization of it are equivalent to the classical Prime Ideal Theorem for Boolean algebras. As an application, we derive the intersection theorem for Baer radicals from choice principles weaker than the Axiom of Choice. A central tool for our considerations are Scott-openm-filters in quantales.     

Simulated vibrational spectra of aflatoxins and their demethylated products and the estimation of the energies of the demethylation reactions

The structure of four natural mycotoxins, the aflatoxin B1, B2, G1 and G2 and their demethylated products were optimized with quantum chemical method. The energies and the thermodynamic functions of the molecules were calculated and applied to calculation of the reaction energies of the demethylations. Further results of the calculations are the vibrational force constants, the infrared spectra of the molecules and the assignments of the spectral bands.     

The stability of radio-frequency plasma-treated polydimethylsiloxane surfaces

Polydimethylsiloxane (PDMS) is a widely used material for manufacturing lab-on-chip devices. However, the hydrophobic nature of PDMS is a disadvantage in microfluidic systems. To transform the hydrophobic PDMS surface to hydrophilic, it was treated with radio-frequency (RF) air plasma at 150, 300, and 500 mTorr pressures for up to 30 min. Following the surface treatment, the PDMS specimens were stored in air, deionized water, or 0.14 M NaCl solution at 4 degrees C, 20 degrees C, and 70 degrees C. The change in the hydrophilicity (wettability) of the PDMS surfaces was followed by contact angle measurements and Fourier transform infrared attenuated total reflectance (FTIR-ATR) spectroscopy as a function of time. As an effect of the RF plasma treatment, the contact angles measured on PDMS surfaces dropped from 113 +/- 4 degrees to 9 +/- 3 degrees . The chamber pressure and the treatment time had no or negligible effect on the results. However, the PDMS surface gradually lost its hydrophilic properties in time. The rate of this process is influenced by the difference in the dielectric constants of the PDMS and its ambient environment. It was the smallest at low temperatures in deionized water and largest at high temperatures in air. Apparently, the OH groups generated on the PDMS surface during the plasma treatment tended toward a more hydrophilic/less hydrophobic environment during the relaxation processes. The correlation between the FTIR-ATR spectral information and the contact angle data supports this interpretation.     

Comparison of Fe-AlPILC and Fe-ZSM-5 catalysts used for degradation of methomyl

Catalytic performances of Fe-AlPILC (14 wt.% Fe) and Fe-ZSM-5 (5 wt.% Fe) catalysts are compared in the wet oxidative degradation of methomyl. Fe-ZSM-5 exhibits outstanding whereas Fe-AlPILC shows only mediocre activity. Positions of iron are analysed in the two catalysts by Mössbauer spectroscopy. Iron is in highly dispersed state in Fe-AlPILC whereas in the other case a hematite/ZSM-5 composite is formed. The catalytic activity is attributed to iron located and stabilized in ionic dispersion.     

Sedimentation equilibria of ferrofluids: II. Experimental osmotic equations of state of magnetite colloids

The first experimental osmotic equation of state is reported for well-defined magnetic colloids that interact via a dipolar hard-sphere potential. The osmotic pressures are determined from the sedimentation equilibrium concentration profiles in ultrathin capillaries using a low-velocity analytical centrifuge, which is the subject of the accompanying paper I. The pressures of the magnetic colloids, measured accurately to values as low as a few pascals, obey Van 't Hoff's law at low concentrations, whereas at increasing colloid densities non-ideality appears in the form of a negative second virial coefficient. This virial coefficient corresponds to a dipolar coupling constant that agrees with the coupling constant obtained via independent magnetization measurements. The coupling constant manifests an attractive potential of mean force that is significant but yet not quite strong enough to induce dipolar chain formation. Our results disprove van der Waals-like phase behavior of dipolar particles for reasons that are explained.     

Completions for partially ordered semigroups

A standard completion γ assigns a closure system to each partially ordered set in such a way that the point closures are precisely the (order-theoretical) principal ideals. If S is a partially ordered semigroup such that all left and all right translations are γ-continuous (i.e., Y∈γS implies {x∈S:y·x∈Y}∈γS and {x∈S:x·y∈Y}∈γS for all y∈S), then S is called a γ-semigroup. If S is a γ-semigroup, then the completion γS is a complete residuated semigroup, and the canonical principal ideal embedding of S in γS is a semigroup homomorphism. We investigate the universal properties of γ-semigroup completions and find that under rather weak conditions on γ, the category of complete residuated semigroups is a reflective subcategory of the category of γ-semigroups. Our results apply, for example, to the Dedekind-MacNeille completion by cuts, but also to certain join-completions associated with so-called “subset systems”. Related facts are derived for conditional completions. A first draft of this paper by the second author, containing parts of Section 2, was received on August 9, 1985.     

Posets isomorphic to their extensions

A standard extension for a poset P is a system Q of lower ends (descending subsets) of P containing all principal ideals of P. An isomorphism between P and Q is called recycling if [Y]Q for all YQ. The existence of such an isomorphism has rather restrictive consequences for the system Q in question. For example, if Q contains all lower ends generated by chains then a recycling isomorphism between P and Q forces Q to be precisely the system of all principal ideals. For certain standard extensions Q, it turns out that every isomorphism between P and Q (if there is any) must be recycling. Our results include the well-known fact that a poset cannot be isomorphic to the system of all lower ends, as well as the fact that a poset is isomorphic to the system of all ideals (i.e., directed lower ends) only if every ideal is principal.