Analytic study of power spectra of the tent maps near band-splitting transitions

Successive band-splitting transitions occur in the one-dimensional map x_i+1=g(x_i),i=0, 1, 2,... withg(x)=x, (0 x 1/2) –x +, (1/2 <x 1) as the parameter is changed from 2 to 1. The transition point fromN (=2ⁿ) bands to 2Nbands is given by=(2)^1/N (n=0, 1,2,...). The time-correlation function _i=x_ix₀/(x₀)²,x_i x_i–x_i is studied in terms of the eigenvalues and eigenfunctions of the Frobenius-Perron operator of the map. It is shown that, near the transition point=2, _i–[(10–42)/17] _i,0-[(102-8)/51]_i,1 + [(7 + 42)/17](–1)ⁱe^–yi, where2(–2) is the damping constant and vanishes at=2, representing the critical slowing-down. This critical phenomenon is in strong contrast to the topologically invariant quantities, such as the Lyapunov exponent, which do not exhibit any anomaly at=2. The asymptotic expression for _i has been obtained by deriving an analytic form of _i for a sequence of which accumulates to 2 from the above. Near the transition point=(2)^1/N, the damping constant of _i fori N is given by _N=2(^N-2)/N. Numerical calculation is also carried out for arbitrary a and is shown to be consistent with the analytic results.     

Photolysis of organopolysilanes. The reaction of photochemically generated methylphenylsilylene with conjugated dienes

Photolysis of 2-phenylheptamethyltrisilane (I) in the presence of acyclic and cyclic conjugated dienes has been investigated using both a high-pressure mercury lamp with a quartz filter and a low-pressure mercury lamp with a Vycor filter. Irradiation of I in the presence of 1,3-butadiene, isoprene or 2,3-dimethylbutadiene with a high-pressure mercury lamp gave a product arising from photochemical isomerization of a silacyclopropane derivative and a compound apparently formed by 1,4-silylene addition, along with a 1/1 “ene” adduct of the diene to a photo-rearranged intermediate containing the silicon—carbon double bond. Irradiation of I in the presence of the conjugated diene with a low-pressure mercury lamp, followed by treatment of the product with methanol, afforded a methoxysilane arising from methanolysis of the corresponding silacyclopropane, together with the isomerization product, silacyclopentene and rearranged addition product. Irradiation of I in the presence of cyclopentadiene with a high-pressure mercury lamp produced methylphenylsilylcyclopentadiene, while irradiation of a similar mixture with a low-pressure mercury lamp followed by treatment with methanol gave 4-(methoxymethylphenylsilyl)-1-cyclopentene. With 1,3-cyclooctadiene, the photochemically generated methylphenylsilylene afforded many types of addition product. Photolysis of I in the presence of 1,3-cyclohexadiene, however, afforded none of the silylene addition products.     

The study in the relationship between serum calcium and serum parathyroid hormone (PTH) by employing the various kits of PTH assay

In order to evaluate the influences of serum PTH assay in the various concentrations of serum calcium, we divided into three groups which serum calcium had below 8.0 mg/dl, 8.2 mg/dl to 9.8 mg/dl and above 10.0 mg/dl at random samples and assayed PTH in serum sample, using various kits of PTH assay obtained from commercial sources. Our results suggested that the measurement of serum PTH influenced by the concentration of serum calcium and therefore, should be taken an attention of serum calcium in each sample.     

A new approach to the synthesis of pyridazino[4,5-c]pyridazinones

The reaction of 5-hydrazinopyridazin-3(2H)-ones 1 with α-keto diester 2 in acetic acid afforded the corresponding 4,6-dihydropyridazino[4,5-c]pyridazin-5(1H)-ones 3 and pyrrolo[2,3-d)pyridazin-4(5H)-ones 4 . Compounds 3 were also obtained from 4-bromo-5-hydrazinopyridazin-3(2H)-ones 8 and 2 under milder conditions. 5-Bromo-4-hydrazinopyridazin-3(2H)-one 9 , the regioisomer of 8b , also reacted readily with 2a to give 4,7-dihydropyridazino[4,5-c]pyridazin-8(1H)-one 10b , the regioisomer of 3b .     

Ti(II)-mediated domino cyclization of 2-functionalized 1-halo-2,n-enynes (n = 7, 8) to bicyclic compounds

The reaction of 2-functionalized 1-halo-2,n-enynes (n = 7 or 8) with a divalent titanium reagent, Ti(O-i-Pr)₄/2i-PrMgCl, proceeded in a domino fashion to afford bicyclic compounds in good yields.     

Stereochemically stable double-helicate dinuclear complexes of bis(dipyrromethene)s: a chiroptical study

Helical zinc(II) complexes of bis(dipyrromethene)s bearing homochiral amide substituents were synthesized. Analysis of the products by chiral HPLC showed two diastereomeric major products and showed that dipyrromethene double-nuclear helicates are stereochemically stable and do not interconvert. Circular dichroism (CD) studies showed that the complexation reactions had proceeded with modest diastereomeric excesses. Analysis of an analogous symmetric zinc(II) bis(dipyrromethene) lacking homochiral substituents that could act as chromophores discounted induced CD by the chiral auxiliaries.     

Surface modification by calcium ions—Effect on chromatographic properties of silica

Summary A liquid chromatographic method incorporating column-switching and fluorimetric detection for the determination of triamterene in untreated urine, is described. The urine samples (5 L) were directly introduced onto an Hypersil ODS-C18, 30 m (20 mm×2.1 mm I.D.) pre-column. Polar urinary compounds were removed by flushing the pre-column with water for 1 min, and the analyte was then switched onto an HP-LiChrospher RP C18,5 m (125 mm×4mm ID) analytical column using an acetonitrile/phosphate buffer gradient elution. Fluorescence detection was performed at 230 nm excitation and 430 nm emission wavelengths. The recovery of drug was 102±2% in the 0.10–20.0 g/mL concentration range, the limit of detection being 5 ng/mL. A validation of the usefulness of this procedure was accomplished by analysing urine extracts obtained from real samples.Hypersil ODS is not a product of Merck, Germany. Please give supplier (p. 5).     

Magnetic/Conducting Hybrid Compound Composed of 1-D Chain [Mn2Cl5(EtOH)]∞ and BEDT-TTF Stacking Layer

An assembled compound (BEDT-TTF)₂[Mn₂Cl₅(EtOH)] (1) consisting of two structural lattices of Mn(II)-Cl one-dimensional (1-D) chains and bis(ethylenedithio)tetrathiafulvalene (BEDT-TTF) stacking layers was synthesized by electrochemical crystallization. Compound 1 crystallized in triclinic space group P-1 (#2) with a=13.1628(5) Å, b=20.3985(9) Å, c=7.4966(3) Å, α=98.3498(8)°, β=104.980(1)°, γ=74.602(2)°, V=1868.3(1) ų, and Z=2. The 1-D chains and the stacking layers are aligned along the c-axis of the unit cell. The 1-D chain is described as [Mn₂Cl₅(EtOH)]_∞⁻ in which two Mn(II) ions and four Cl⁻ ions form a ladder-like chain with Kagomé (cuboidal) sublattices, and the remaining Cl⁻ ion and an ethanol molecule cap the edge-positioned Mn(II) ions of the chains. The BEDT-TTF molecules are packed between the Mn-Cl chains (ac-plane), the intermolecular S·S contacts of which are approximately found in the range 3.440(2)-3.599(2) Å. The packing feature of BEDT-TTF molecules is very similar to that of (BEDT-TTF)₂ClO₄(TCE)_0.5 (TCE=1,1,2-trichloroethane) (J. Am. Chem. Soc., 105, 297 (1983)). Regarding the electronic state of each BEDT-TTF molecule, Raman spectroscopic analysis and ESR study revealed the presence of half-valence BEDT-TTF molecules (charge delocalization) in 1. Magnetic measurements clearly demonstrated that the paramagnetic spins on the 1-D chain [Mn₂Cl₅(EtOH)]_∞⁻ arrange antiferromagnetically in the low-temperature region. Additionally, 1 exhibits metallic conductivity in the temperature range 2.0-300 K (σ=21 S cm⁻¹ at 300 K and 1719 S cm⁻¹ at 2.0 K), due to the contribution of the stacked BEDT-TTFs. Consequently, these peculiarities that correspond to antiferromagnetic/metallic conductivity demonstrate the “bi-functionality” of 1.     

Dehydrogenation versus oxygenation in two-electron and four-electron reduction of dioxygen by 9-alkyl-10-methyl-9,10-dihydroacridines catalyzed by monomeric cobalt porphyrins and cofacial dicobalt porphyrins in the presence of perchloric acid

Dehydrogenation of 10-methyl-9,10-dihydroacridine (AcrH(2)) by dioxygen (O(2)) proceeds efficiently, accompanied by the two-electron and four-electron reduction of O(2) to produce H(2)O(2) and H(2)O, which are effectively catalyzed by monomeric cobalt porphyrins and cofacial dicobalt porphyrins in the presence of perchloric acid (HClO(4)) in acetonitrile (MeCN) and benzonitrile (PhCN), respectively. The cobalt porphyrin catalyzed two-electron reduction of O(2) also occurs efficiently by 9-alkyl-10-methyl-9,10-dihydroacridines (AcrHR; R = Me, Et, and CH(2)COOEt) to yield 9-alkyl-10-methylacridinium ion (AcrR+) and H(2)O(2). In the case of R = Bu(t) and CMe(2)COOMe, however, the catalytic two-electron and four-electron reduction of O(2) by AcrHR results in oxygenation of the alkyl group of AcrHR rather than dehydrogenation to yield 10-methylacridinium ion (AcrH+) and the oxygenated products of the alkyl groups, i.e., the corresponding hydroperoxides (ROOH) and the alcohol (ROH), respectively. The catalytic mechanisms of the dehydrogenation vs the oxygenation of AcrHR in the two-electron and four-electron reduction of O(2), catalyzed by monomeric cobalt porphyrins and cofacial dicobalt porphyrins, respectively, are discussed in relation to the C(9)-H or C(9)-C bond cleavage of AcrHR radical cations produced in the electron-transfer oxidation of AcrHR.