Countable network weight and multiplication of Borel sets

A space Borel multiplies with a space if each Borel set of is a member of the -algebra in generated by Borel rectangles. We show that a regular space Borel multiplies with every regular space if and only if has a countable network. We give an example of a Hausdorff space with a countable network which fails to Borel multiply with any non-separable metric space. In passing, we obtain a characterization of those spaces which Borel multiply with the space of countable ordinals, and an internal necessary and sufficient condition for to Borel multiply with every metric space.

     

Chains of strongly non-reflexive dual groups of integer-valued continuous functions

Answering a question of Eklof-Mekler (Almost free modules, set-theoretic methods, North-Holland, Amsterdam, 1990), we prove: (1) If there exists a non-reflecting stationary set of consisting of ordinals of cofinality for each , then there exist abelian groups such that and for each . (2) There exist abelian groups such that for each and for each . The groups are the groups of -valued continuous functions on a topological space and their dual groups.

     

Abstract functions with continuous differences and Namioka spaces

Let be a semigroup and a topological space. Let be an Abelian topological group. The right differences of a function are defined by for . Let be continuous at the identity of for all in a neighbourhood of . We give conditions on or range under which is continuous for any topological space . We also seek conditions on under which we conclude that is continuous at for arbitrary . This led us to introduce new classes of semigroups containing all complete metric and locally countably compact quasitopological groups. In this paper we study these classes and explore their relation with Namioka spaces.

     

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.

     

Optimization of inoculum to substrate ratio for enhanced methane yield from leather fleshings in a batch study

One of the most significant issues of the last few decades has been tracing for renewable energy sources. Animal fleshing (ANFL) is the most common proteinaceous solid waste accured during the production of leather and it must be disposed of in an environmentally responsible manner. This paper is attempts to assess the biogas production from solid waste originating from the chrome based tannery. Anaerobic digestion of these wastes will be a viable option for waste stabilization and energy production in the form of biogas to be utilized in the industry. The bio-methane potential of the wastes were examined by mixing these wastes with various sources of inoculum and different inoculum to substrate (I/S) ratio considered. The batch experiments were carried out in 2.5 l glass reactors with a various source of inoculumviz., Cow Dung (CD), Elephant Dung (ED) and Bio-Digested Slurry (BDS) with varied inoculum to substrate (LFs) ratios for a retention time of 50 days with replications. The results obtained from the experiments showed that BDS:LF (25:75) had the highest gas production of 14505 ml (651.85 ml CH₄g^?1 VS) followed by CD:LF (50:50) produced 12072.5 ml (789.36 ml CH₄g^?1 VS) and ED:LF (75:25) produced 11252.5 ml (1492.08 ml CH₄g^?1 VS)with a methane content of 63.77, 61.92 and 62.72%, respectively.     

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.