Fourier transforms in function-space and parabolic differential equations

A Fourier transform for sufficiently bounded and regular functionals on C([0, 1], R) is introduced, which interchanges multiplication and differentiation. We define convolutions and prove a convolution theorem. Finally, we use the transform to uniquely solve the Cauchy problem for second-order parabolic equations in function-space, where the coefficients depend only on t.     

A cascade decomposition theory with applications to Markov and exchangeable cascades

A multiplicative random cascade refers to a positive -martingale in the sense of Kahane on the ultrametric space A new approach to the study of multiplicative cascades is introduced. The methods apply broadly to the problems of: (i) non-degeneracy criterion, (ii) dimension spectra of carrying sets, and (iii) divergence of moments criterion. Specific applications are given to cascades generated by Markov and exchangeable processes, as well as to homogeneous independent cascades.

     

The chemical reduction of small inorganic gases in an electrothermal plasma reactor

Chemical reduction of small inorganic gases is accomplished using an electro-thermal plasma reactor. This benchscale reactor maintains a highly reactive plasma zone in a fluidized bed of carbon particles through which an electrical current is discharged. The carbon particles function as current-controlling media, heat sinks and reaction sites. Chemicals introduced into this medium are subjected to a variety of energy sources and chemically reactive species, which result in chemical reduction. It is shown that the inorganic gases, H₂O, CO₂, NO, NO₂ and SO₂, are chemically reduced in the plasma zone of the reactor. The end products consist of hydrogen, carbon monoxide and nitrogen gases. Additionally, elemental sulfur is deposited onto the carbon particles.     

Concerning the preparations of some pyridylimidazothiazole derivatives

The preparations of some 4-pyridylimidazo[2,1-b]thiazole and -imidazo[5,1-b]thiazole derivatives are described. In some of the cyclizations to form the imidazothiazole ring systems, trifluoroacetic anhydride, the dehydration reagent employed, participated in the reaction leading to products bearing a trifluoromethyl or trifluoroacetyl substituent.     

Ring-disk electrode studies of the open-circuit dissolution of iodine films formed during the anodic oxidation of iodide on platinum

The open-circuit behavior of iodine films formed on platinum by electrooxidation of iodide was studied at rotating disk and rotating ring-disk electrodes. The potential transient and ring current transient at open circuit for c_I^?>0.012 M can be explained by assuming: (1) convective-diffusion controlled dissolution of the film; (2) establishment of the I₂+I^?→ I₃^? equilibrium; (3) establishment of the I₂ (solid) →I₂ (solution) equilibrium. The behavior at lower concentrations of c_I^? suggests that convective-diffusion control is absent.     

Chemistry of the phenoxathiins and isosterically related heterocycles. XXIX The crystal and molecular structure of 5-(3′-hydroxypyridyl-2′-thio)-4-nitro-1-methylimidazole

Reaction of the dianion of 3-hydroxypyridine-2(1H)-thione with 5-chloro-4-nitro-1-methylimidazole in N,N-dimethylformamide led to the formation of 5-(3′-hydroxypyridyl-2′-thio)-4-nitro-1-methylimidazole, which failed to cyclize to the desired pyrid[1,4]oxathiinoimidazole derivative. In an effort to determine why the intermediate phenolate sulfide had failed to cyclize, the crystal structure of the isolated product was determined. The structure refined to R = 0.036.     

Palladium assisted organic reactions: III. The preparation of di-μ-chlorobis-(N,N-dialkylbenzylamine-2,C,N)dipalladium(II) complexes

The preparation and ¹H NMR spectra of some di-μ-chloro-bis(N,N-dialkylbenzylamine-2,C,N)dipalladium(II) complexes, and the corresponding monomeric triphenylphosphine derivatives are described. A reaction sequence is presented for the cyclopalladation reaction and some improved conditions for the preparation of these complexes are presented.     

Synthesis and structures of the first bismuth-ester complexes using heterobifunctional thiolate anchored ligands and mass spectrometric identification of ligand-bridged derivatives

The first systematic series of bismuth complexes involving ester donors, Bi(SCH(2)C(O)OCH(2)CH(3))Cl(2), Bi(SCH(2)C(O)OCH(3))(2)Cl, and Bi(SCH(2)COOCH(3))(3), has been isolated and characterized by spectroscopic (IR, Raman) and X-ray crystallographic data. In addition, these and other species have been identified by electron-impact, electrospray, and atmospheric pressure chemical ionization mass spectometry. The generally applicable synthetic methodology involves the use of heterobifunctional ligands containing a thiolate moiety as an anchor to facilitate coordinate interactions between weak donors (carbonyls) and weak acids (bismuth). The bifunctional nature of the ligands is manifested in both chelating and bridging roles. Important comparisons can be made with the pharmaceutical agent "colloidal bismuth subcitrate" (CBS). The observations allow for a new appreciation of bioactive bismuth compounds, by providing an approach to study the interaction of biorelevant functional groups with bismuth.