Binary decompositions and acyclic schemes

It is well known that the notions of normal forms and acyclicity capture many practical desirable properties for database schemes. The basic schema design problem is to develop design methodologies that strive toward these ideals. The usual approach is to first normalize the database scheme as far as possible. If the resulting scheme is cyclic, then one tries to transform it into an acyclic scheme. In this paper, we argue in favor of carrying out these two phases of design concurrently. In order to do this efficiently, we need to be able to incrementally analyze the acyclicity status of a database scheme as it is being designed. To this end, we propose the formalism of "binary decompositions". Using this, we characterize design sequences that exactly generate theta-acyclic schemes, for theta = agr,beta. We then show how our results can be put to use in database design. Finally, we also show that our formalism above can be effectively used as a proof tool in dependency theory. We demonstrate its power by showing that it leads to a significant simplification of the proofs of some previous results connecting sets of multivalued dependencies and acyclic join dependencies.

Regiospecific hydroxylation of acyclic monoterpene alcohols by aspergillus_niger

Aspergillus niger was shown to carry out the regiospecific hydroxylation of acyclic monoterpene alcohols.

Transformations of acetates of citronellol, geraniol, and linalool by Aspergillus niger: regiospecific hydroxylation of citronellol by a cell-free system

Incubation of acetates of geraniol, citronellol and linalool with Aspergillus niger resulted in their hydrolysis to corresponding alcohols which were further hydroxylated to their respective 8-hydroxy derivatives. In the case of linalyl acetate, besides linalool and 8-hydroxylinalool, small amounts of geraniol and agr-terpineol were also formed. Microsomes (105 000xg sediment) prepared from induced cells of A. niger were found to convert (1-3H)citronellol to 8-hydroxy citronellol in the presence of NADPH and O2. The pH optimum for the hydroxylase was found to be 7.6.

A regiospecific radical annulation strategy to functionalised chiral bicyclo[3.3.l]nonanes

A radical annulation, i.e. an intermolecular radical Michael addition followed by an intramolecular Michael addition of the resultant radical (radical cyclisation) has been employed for the construction of chiral functionalised bicyclo[3.3,1]-nonanes. Thus reaction of carvone hydrohalides 7 with (n)Bu(3)SnH and AIBN in the presence of excess of radicophiles 4 furnished, regiospecifically bicyclo[3.3.1]nonanes 8-14, introducing three new chiral centres in a stereoselective manner. Analogously the bromide 18 generated the bridgehead substituted bicyclo[3.3.1]-nonanes 19-21.

Two regiospecific alternative strategies in the synthesis of (-)-valeranone

Two regiospecific modifications have been developed in the synthesis of valeranone. The first one is based on the regiospecific protection of a diol and the second is based on the Wittig reaction of a hemiacetal.

Polynomial Decompositions in Polynomial Time

Fix a prime p. Given a positive integer k, a vector of positive integers Delta = (Delta(1), Delta(2), ... , Delta(k)) and a function Gamma : F-p(k) -> F-p, we say that a function P : F-p(n) -> F-p is (k, Delta, Gamma)-structured if there exist polynomials P-1, P-2, ..., P-k : F-p(n) -> F-p with each deg(P-i) <= Delta(i) such that for all x is an element of F-p(n), P(x) = Gamma(P-1(x), P-2(x), ..., P-k(x)). For instance, an n-variate polynomial over the field Fp of total degree d factors nontrivially exactly when it is (2, (d - 1, d - 1), prod)- structured where prod(a, b) = a . b. We show that if p > d, then for any fixed k, Delta, Gamma, we can decide whether a given polynomial P(x(1), x(2), ..., x(n)) of degree d is (k, Delta, Gamma)-structured and if so, find a witnessing decomposition. The algorithm takes poly(n) time. Our approach is based on higher-order Fourier analysis.

Thermal decomposition of hydrazinium hydrogen oxalate and dihydrazinium oxalate

Thermal decompositions of hydrazinium hydrogen oxalate (HHOX) and dihydrazinium oxalate (DOX) have been studied. DOX on heating is converted into HHOX and thereafter both follow the same pattern of decomposition.

Formation of Pb(Ti,Zr)O3, from thermal decomposition of oxalate precursors

Lead zir conyl oxalate hexahydrate (LZO) and lead titanyl zirconyl oxalate hydrate (LTZO) are prepared and characterized. Their thermal decompositions have been investigated by thermoanalytical and gas analysis techniques. The decomposition in air or oxygen has three steps — dehydration, decomposition of the oxalate to a carbonate and the decomposition of carbonate to PbZrO3. In non oxidising atmosphere, partial reduction of Pb(II) to Pb(0) takes place at the oxalate decomposition step. The formation of free metallic lead affects the stoichiometry of the intermediate carbonate and yields a mixture of Pb(Ti,Zr)O3 and ZrO2 as the final products. By maintaining oxidising atmosphere and low heating rate, direct preparation of stoichiometric, crystalline Pb(Ti,Zr)O3 at 550°C is possible from the corresponding oxalate precursor.

An enantiospecific approach to thapsanes from R-carvone: synthesis of (−)-thaps-8-en-5-ol†

The first enantiospecific synthesis of a thapsane, containing three contiguous quaternary carbon atoms, is accomplished starting from R-carvone. An intramolecular alkylation and an intramolecular diazoketone cyclopropanation reaction were employed for the stereo- and regiospecific generation of three contiguous quaternary carbon atoms present in the thapsane framework.

Photochemistry of .alpha.,.beta.-unsaturated thiones: addition to electron-rich olefins from T1

1,1,3-Trimethyl-2-thioxo-1,2-dihydronaphthale(1n)e adds to electron-rich olefins upon excitation to either Sz (PP*) or Sl (ns*) states. Excitation to S2 level resulted in the same mixture of products, namely thietane and 1,4-dithiane, as on excitation to S1 level. Addition occurs to the thiocarbonyl function and not to the carbon-carbon double bond. The addition is site-specific, and the formation of thietane is regiospecific. The ratio of thietane to 1,4-dithiane in the product mixture is dependent on the concentration of the thioenone. The addition is suggested to originate from the lowest triplet state (Tl) and involves diradical intermediates.

Vinyl radical induced Michael additions: Total synthesis of (±)-seychellene

A new strategy for the total synthesis of (±)-seychellene which involves (i) a regiospecific construction of a bicyclo(2.2.2)octene moiety having a methyl group at the bridgehead and (ii) a vinyl radical induced intramolecular Michael addition is described.

Synthetic investigations on illudinine: a new synthesis of methyl 8-methoxy-2,2-dimethyl-7-oxo-1,2,3,5,6,7-hexahydro-s-indacene-4-carboxylate

A new strategy for the total synthesis of methyl 8-methoxy-2,2-dimethyl-7-oxo-1,2,3,5,6,7-hexahydro-s-indacene-4-carboxylate 4, a key intermediate in the synthesis of illudalanes, is reported. The key step in this strategy is a new method of preparation of indanones from tetralones. Thus, the furfurylidene derivative of 6-methoxy-3,4-dihydronaphthalen-1-(2H)-one is oxidised to the dicarboxylic acid 9a which is cyclodehydrated to methyl 7-methoxy-1-oxoindan-4-carboxylate 10. Similar reactions on the tetrahydronaphthalenone 25, obtained from 6-methoxy-1,2,3,4-tetrahydronaphthalene-7-carbaldehyde 11 by sequential transformations including a regiospecific benzylic oxidation resulted in the hexahydro-s-indacenone 4, thus completing a formal synthesis of illudinine 1.

Kinetics of propellant decomposition

Equations for solid-state decompositions which are controlled by the phase-boundary movement and nucleation have been examined using ammonium perchlorate/polystyrene propellant decomposition at 503 K and 533 K. It was found that 3 different equations governed by the nucleation process show a good fit of data at these temperatures. However, the best fit was obtained for the following Avrami-Erofeev equation, [-In (1 - α]1/4=kt.

Radical Annulation Strategy to Chiral Pupukeanones: Total Synthesis of (+)-10-ex&l(- Naphthyl)pupukean-9-onea nd (+)-lO-exo-l(- Naphthyl)-5-epipupukean-9-ones1

Intramolecular alkylation reaction of the bromoenone 12, obtained from S-carvone in three steps, furnished the bicyclo[2.2.2]octenone 13. Contrary to the anticipated radical annulation reaction, the bicyclic bromides 14 and 15, obtained from the enone 13, generated exclusively the cyclopropane product 18 via a 3-exo-trig radical cyclization on reaction with nBu3SnH and AIBN, even in the presence of a large excess of a radicophile. On the other hand, bromoenone 24, synthesized from R-carvone via S-naphthylcarvone 21, underwent radical annulation reaction in the presence of radicophiles to furnish the isotwistanes 25-28 in a regio- and stereospecific manner. Hydrogenation of the olefin 34, obtained from the diketone 27 via a regiospecific Wittig reaction, furnished the naphthyl-5-epipupukean-9-one 33, whereas stereoselective hydrogenation of the enone 36, prepared from the keto ester 25 via a Grignard reaction and dehydration sequence, generated the naphthylpupukeanone 32.