The Boolean Prime Ideal Theorem Plus Countable Choice Do Not Imply Dependent Choice

Two Fraenkel-Mostowski models are constructed in which the Boolean Prime Ideal Theorem is true. In both models, AC for countable sets is true, but AC for sets of cardinality 2 and the 2m = m principle are both false. The Principle of Dependent Choices is true in the first model, but false in the second. Mathematics Subject Classification: 03E25, 03E35, 04A25.     

Composition and properties of freeze-dried products of nicotinic acid withβ-cyclodextrin and heptakis (2,6-0-dimethyl)-β-cyclodextrin

The purpose of the study was to examine the formation of inclusion compounds in the freeze-dried products obtained from aqueous solutions of nicotinic acid and -cyclodextrin (-CD), or heptakis (2,6-0-dimethyl)--cyclodextrin (DIMEB). The molar ratios used were 1:1 and 2:1. In addition two freezing temperatures (–40 and –196°C) and different secondary drying temperatures (+50 and +80°C) were used. Freeze-dried products with -CD obtained after low temperature freezing are of the same crystallographic structure as seen in a pure inclusion compound prepared by coprecipitation. Amorphous products were formed after fast freezing. The molar ratios of included nicotinic acid in the freeze-dried products vary — dependent on the preparation conditions — between 0.75:1 and 1:1. A factorial design proves that the included drug amount can be increased by enhancement of the amount of nicotinic acid used, by faster freezing, and by the combination of these two factors. The proof of inclusion formation was given by a combination of X-ray diffractography, differential scanning calorimetry, thermogravimetry and thermofractography.The freeze-dried preparations obtained with DIMEB were amorphous mixtures of the two components. No proof for inclusion of the nicotinic acid in the cyclodextrin cavity could be given. Higher (–40°C) or lower (–196°C) freezing temperatures and the running of the secondary drying process could not influence these results. The very low stability constant of the complex and steric reasons are responsible for this behavior.     

K3 et formules de Riemann-Hurwitzp-adiques

The well-known formula of Riemann-Hurwitz gives the change of genuses in ann-fold covering of compact connected Riemann surfaces. In Iwasawa theory, there existp-adic analogues which give the change of certain ^±-invariants in ap-extension ofCM number fields. Using functorial and arithmetical properties ofK ₃, we extend such Riemann-Hurwitzp-adic formulas to non-CM fields, assuming some restrictive hypotheses on the capitulation ofK ₂.

     

Macrocycle opening in crown ethers

Macrocycle opening in derivatives of benzocrown ethers under the action of amines is affected by the nature of the heteroatoms in the macrocycle, the nature of the functional group in the benzene ring of the crown ether, and the length, branching, and number of hydrocarbon radicals at the amine nitrogen atom. A distinguishing feature of this reaction is the template effect of MeNH₃ ⁺, Me₂NH₂ ⁺, Na⁺, and K⁺ ions.Translated fromIzvestiya Akademii Nauk. Seriya Khimicheskaya, No. 3, pp. 687–692, March, 1996.For Part I see Ref. 1.     

Synthese und Geruch von Tricyclo[6.2.2.02, 7]dodecan-Derivaten

Summary The acetale-ketone9 was synthesized as precursor for the preparation of -santalol derivatives posessing a bicyclo[2.2.2]octane nucleus. After methylenation of the keto-group the subsequent acidic hydrolysis of the acetal leads via a Prins reaction of the liberated aldehyde with the methylene group to tricyclo[6.2.2.0^{2, 7}]dodecane derivatives. Their olfactory properties are described.

     

Chemical applications of group theory and topology

The following procedure is described for investigating the qualitative dynamics of simple chemical systems: 1) A so-called influence diagram is generated representing the relationships between the reference reactants (phase-determining intermediates); 2) This influence diagram is used to generate a truth table indicating possible transitions between state vectors representing the signs of the time derivatives of of the reference reactant concentrations; 3) The truth table is used to determine a state transition diagram representing the flow topology around unstable equilibrium points; 4) The characteristic equation of the adjacency matrix of the influence diagram is solved in order to determine the presence of such unstable equilibrium points. The two types of qualitative dynamics possible for chemical systems containing two reference reactants and one feedback circuit are bifurcation between two attracting regions (bistability) and limit cycle oscillation. However, in two reference reactant systems oscillation requires an additional self-activating loop to generate the unstable equilibrium point required for its realization. Bistability and limit cycle oscillation are also two of the possible types of qualitative dynamics for chemical systems containing three reference reactants. However, chemical systems with three reference reactants and two or more feedback circuits can also contain interlocking limit cycles, which can lead to toroidal oscillations or chaos. The influence diagrams are given for the systems exhibiting these various types of dynamic behavior along with a summary of the important properties of all 729 possible influences for simple chemical systems containing three reference reactants.     

In Situ IR Spectroscopic Studies on Molybdenum Nitride Catalysts: Active Sites and Surface Reactions

Recent IR spectroscopic studies on the surface properties of fresh Mo₂N/-Al₂O₃ catalyst are presented in this paper. The surface sites of fresh Mo₂N/-Al₂O₃, both Mo⁺ (0<<2) and N sites, are probed by CO adsorption. Two characteristic IR bands were observed at 2045 and 2200 cm^-1, due to linearly adsorbed CO on Mo and N sites, respectively. The surface N sites are highly reactive and can react with adsorbed CO to form NCO species. Unlike adsorbed CO on reduced passivated one, the adsorbed CO on fresh Mo₂N/-Al₂O₃ behaves similarly to that of group VIII metals, suggesting that fresh nitride resembles noble metals. It is found that the surface of Mo nitrides slowly transformed into sulfide under hydrotreating conditions, which could be the main reason for the activity drop of molybdenum nitride catalysts in the presence of sulfur-containing species. Some surface reactions, such as selective hydrogenation of 1,3-butadiene, isomerization of 1-butene, and hydrodesulfurization of thiophene, were studied on both fresh and reduced passivated Mo₂N/-Al₂O₃ catalysts using IR spectroscopy. The mechanisms of these reactions are proposed. The adsorption and reaction behaviors of these molecules on fresh molybdenum nitride also resemble those on noble metals, manifesting the unique properties of fresh molybdenum nitride catalysts. Mo and N sites are found to play different roles in the adsorption and catalytic reactions on the fresh Mo₂N/-Al₂O₃ catalyst. Generally, Mo sites are the main active sites for the adsorption and reactions of adsorbates; N sites are not directly involved in catalytic reactions but they modify the electronic properties of Mo sites.     

Highly conformationally constrained halogenated 6-spiroepoxypenicillins as probes for the bioactive side-chain conformation of benzylpenicillin

Summary The halogenated 6-spiroepoxypenicillins are a series of novel semisynthetic-lactam compounds with highly conformationally restricted side chains incorporating an epoxide. Their biological activity profiles depend crucially on the configuration at position C-3 of that epoxide. In derivatives with aromatic-containing side chains, e.g., anilide, the 3R-compounds possess notable Gram-positive antibacterial activity and potent-lactamase inhibitory properties. The comparable 3S-compounds are antibacterially inactive, but retain-lactamase inhibitory activity.Using the molecular simulation programs COSMIC and ASTRAL, we attempted to map a putative, lipophilic accessory binding site on the PBPs that must interact with the side-chain aromatic residue. Comparative computer-assisted modelling of the 3R, and 3S-anilides, along with benzylpenicillin, indicated that the available conformational space at room temperature for the side chains of the 3R and the 3S-anilides was mutually exclusive. The conformational space for the more flexible benzylpenicillin could accommodate the side chains ofboth the constrained penicillin derivatives. By a combination of van der Waals surface calculations and a pharmacophoric distance approach, closely coincident conformers of the 3R-anilide and benzylpenicillin were identified. These conformers must be related to the antibacterial, bioactive conformer for the classical-lactam antibiotics. From these proposed bioactive conformations, a model for the binding of benzylpenicillin to the PBPs relating the three-dimensional arrangement of a putative lipophilic S₂-subsite, specific for the side-chain aromatic moiety, and the 3-carboxylate functionality is presented.This work has been reported in preliminary form at the 4th Royal Society of Chemistry International Symposium on Recent Advances in the Chemistry of-lactam Antibiotics, Churchill College, Cambridge, U.K., 3–6 July 1988.     

RNA Methylation m6A: A New Code and Drug Target?

The m⁶A‐RNA modification is a dynamic and reversible process, which has emerged as a new RNA code for the regulation of gene expression. The functional network of methyltransferases (writers), demethylases (erasers), and binding proteins (readers) modulate the level of m⁶A modification. Dysfunction of RNA methylation has been associated with various fundamental biological processes and human diseases. Herein, we briefly introduce an understanding‐enabled manipulation on m⁶A‐RNA modification with an emphasis on the use of small‐molecule intervention.      

Reaction of 4,4′-dimethyldiphenyl ether with phosphorus trichloride in the presence of anhydrous aluminum chloride

The reaction of 4,4-dimethyldiphenyl ether with phosphorus trichloride in the presence of anhydrous aluminum chloride was studied. This reaction affords 2,8-dimethyl-10H-10⁵-phenoxaphosphine 10-oxide as virtually the only product. In air, the latter in an alkaline solution is quantitatively transformed into 10-hydroxy-2,8-dimethyl-10H-10⁵-phenoxaphosphine 10-oxide.__________Published in Russian in Izvestiya Akademii Nauk. Seriya Khimicheskaya, No. 12, pp. 2762–2765, December, 2004.