A Wiener-Wintner theorem for 1/f power spectra

Wiener's generalized harmonic analysis (GHA) provides a theory of harmonic analysis for subspaces of tempered functions not accessible to the L¹,L², and Fourier series theories; and it does it in a way that is usually more quantitative than that provided by the theory of distributions. On the other hand, GHA does not yield an adequate spectral analysis of large classes of functions, including nonstationary processes and, in particular, 1/f noise. In this paper we adapt GHA to deal with 1/f noise by extending the Wiener-Wintner theorem to the case of 1/f power spectra.     

EFFECTS OF RHODAMINE 123 IN THE DARK AND AFTER IRRADIATION ON MITOCHONDRIAL ENERGY METABOLISM

Isolated rat liver mitochondria have been used to study the mechanism of toxicity of Rhodamine 123 (Rho 123) in the dark and after irradiation with visible light. We report an inhibition of adenosine 5'-diphosphate phosphorylation which is increased after illumination. In the dark, the first steps of the phosphorylation process (i.e. the entry of substrates into the matrix, the electron transport to oxygen and the creation of the proton gradient) as well as ATPase activity are not significantly perturbed at Rho 123 concentration below 10 micrograms/mL. In contrast, the movements of the phosphate compounds are drastically impaired. Irradiation strengthens the detrimental effects in an oxygen dependent process. The nature of the noxious transient species is not clearly established, but it is suggested that singlet oxygen could be responsible for the observed damage.     

Synthesis and Structure of New Cobalt–Carbonyl Complexes Containing Tellurium Atoms

Co₂(CO)₈ and Te₂O react to form the well known Co₄(CO)₁₀Te₂, Co₄(CO)₁₁Te₂ complexes and the two new cluster complexes CCo₆(CO)₁₂Te₂(1), and CCo₆(CO)₁₀Te₂(Te₃) (2). The structures of 1 and 2 were determined by X-ray analysis, together with the triphenylphosphine derivative of 1, CCo₆(CO)₁₁(PPh₃)Te₂(3), which was analyzed to clarify the disordered structure of the parent compound. Complex 1 is formed by a prismatic cluster of cobalt atoms with a carbon embedded in the cage; two tellurium atoms cap the triangular faces of the prism and each cobalt atom links two terminal carbonyl groups. The complex 2 has a similar prismatic cage CCo₆; two ₄-Te atoms cap two rectangular faces of the prism, while other two Te atoms bridge two edges of the triangular faces and are linked each other through a third Te atom. Electron counting gives for complex 2 92 electrons: the presence of two long Co–Co distances suggests that the two excess electrons are located on Co–Co antibonding orbitals. Crystal data for 1, space group C2/c, a = 12.845(2) Å, b = 13.449(2) Å, c = 13.246(2) Å, = 91.95(2)°, Z = 4, R = 0.097 for 2555 reflections; for 2, space group Pnna, a = 17.219(5) Å, b= 14.969(6) Å, c = 9.178(4) Å, Z = 4,R = 0.037 for 3103 reflections; for 3, space group P2₁/c, a = 9.288(2) Å, b = 14.920(6) Å, c = 26.300(9) Å, = 99.99(2)°, Z = 4, R = 0.037 for 4300 reflections. The vibrational analysis of the complex 1 was performed and most of the (CO), (₆C–Co), (Co–Co) and (Co–Co) modes were assigned. The (Co–Te) modes were interpreted on the basis of the intermolecular coupling, due to the close contact between neighboring clusters in one distinct direction in the crystal.     

1,2,3-Triazolodiazepines. I. Preparation and benzodiazepine receptor binding of 1-benzyl- and 1-phenethyl-1,2,3-triazolo-[4,5-b][1,4]diazepines

Several new 1,2,3-triazolo[4,5-b][1,4]diazepines were prepared starting from 1-benzyl-1 and 1-phenethyl-4,5-diamino-1,2,3-triazole 2 (Scheme 1), by condensation reactions with β-diketones (Scheme 2), β-ketoesters (Scheme 3), and diethyl malonates (Scheme 4). In the first case we obtained compounds 3 and 4 with basic properties, while the ester function condensations gave cyclic amide derivatives 7, 8, 10, 12 and 13 with acid properties. Some N-methyl derivatives 11, 14 and 15 were obtained from the cyclic amide compounds. Most of compounds were tested for their ability to displace [³H]flunitrazepam from bovine brain membranes but no compound showed benzodiazepine receptor binding affinity.     

Triazolylbenzimidazolthiones and derivatives of the new 1,2,3‐triazolo[ 1,5‐a][ 1,3,5]benzotriazepine heterocycle

Four new triazolylbenzimidazolthione derivatives (2a‐d), analogous to triazolylbenzimidazolone derivatives previously tested as activators of the BK_Ca potassium channels, were prepared and assayed without success. Some derivatives of a new tricyclic nitrogen heterocycle, 1,2,3‐triazolo[1,5‐a][1,3,5]benzo‐triazepine, bearing a carboxamido group in the 3 position, other substituents in the 8 position and a carbonyl (5a‐d) or thione (6a‐c) or methylthio (7a‐c) function in the 5 position were synthesised. The nucleophilic displacement of the methylthio substituent with morpholine or cyclopentylamine provided the 5‐amino‐substituted tricyclic derivatives 8a‐d. Starting from the l‐(2‐nitrophenyl)‐4‐cyano‐5‐amino‐1,2,3‐triazole (9), the 3‐cyano‐triazolobenzotriazepin‐5‐one derivative 12 was also obtained. The majority of the new compounds were tested towards the BK_Ca potassium channels, the benzodiazepine and adenosine A₁ and A_2a receptors, but no remarkable activity was detected.     

The (N=1) Supersymmetric Sine-Gordon model in two dimensions. I

In this paper and its companion (II) we prove that the SupersymmetricN=1 massless Sine-Gordon field theory, at finite (space) volume, exists and is analytic in the coupling constant . Moreover at finite (space) volume is Witten index is=1.