On the product system of a completely positive semigroup

Given a W∗-continuous semigroup φ of unital, normal, completely positive maps of B(H), we introduce its continuous tensor product system . If α is a minimal dilation E₀-semigroup of φ with Arveson product system F, then is canonically isomorphic to F. We apply this construction to a class of semigroups of arising from a modified Weyl-Moyal quantization of convolution semigroups of Borel probability measures on . This class includes the heat flow on the CCR algebra studied recently by Arveson. We prove that the minimal dilations of all such semigroups are completely spatial, and additionally, we prove that the minimal dilation of the heat flow is cocyle conjugate to the CAR/CCR flow of index two.     

Tame kernels and further 4-rank densities

There has been recent progress on computing the 4-rank of the tame kernel for F a quadratic number field. For certain quadratic number fields, this progress has led to “density results” concerning the 4-rank of tame kernels. These results were first mentioned in Conner and Hurrelbrink (J. Number Theory 88 (2001) 263) and proven in Osburn (Acta Arith. 102 (2002) 45). In this paper, we consider some additional quadratic number fields and obtain further density results of 4-ranks of tame kernels. Additionally, we give tables which might indicate densities in some generality.     

Synthesis ofS-(+)-hydroprene

A novel path toS-(+)-hydroprene (1) starting from the technical gradeS-(+)-dihydromyrcene (2, e.e. 50%) is proposed. The latter was selectively transformed intoS-3,7-dimethyloctanal (5) in three steps including hydroalumination. The reactions of5 with allyl- or methallylmagnesium chloride followed, respectively, either by oxygenation in the presence of PdCl₂/CuCl or by ozonolysis, affordS,E-6,10-dimethyl-3-undecen-2-one (7) which was treated with ethoxyethynylmagnesium bromide to give the title juvenile hormone analogue in 23% overall yield.Translated fromIzvestiya Akademii Nauk. Seriya Khimicheskaya, No 1, pp. 110–112, January, 1993.     

Infrared investigation of aluminum- and chromium-substituted magnetites and of the lacunar spinels resulting from their oxidation

When Fe³⁺ ions are substituted by aluminum or chromium on magnetite octahedral sites, the ir spectrum shows the conversion of an inverse spinel to a normal spinel. Both broad bands of magnetite are gradually replaced by the four characteristic bands of normal spinels II–III. They are also observed for solid solutions, FeCr₂O₄FeAl₂O₄, with, however, a further band at 780 cm^?1 which may be assigned to Al³⁺ ions on tetrahedral sites. Low-temperature (<400°C) oxidation of these compounds whose sizes are less than 2000 Å results in lacunar spinels III–III. The ir spectrum of these solids is characterized by two absorption bands (as for inverse spinels II–III) except for compounds close to pure γFe₂O₃ in which an order of vacancies could be put in evidence.     

Potentiometric studies of dithiooxamide with a sulphide-selective membrane electrode

The sulphide-selective electrode is applicable to the determination of dithiooxamide by titration with silver nitrate. The effect of the alkali content of the solutions on the reaction has been studied. The reaction products are silver sulphide, oxalic acid, and nitric acid. If the alkali concentration of the solution is lower than that equivalent to the acid formed during the titration, the amount of sulphide produced by hydrolysis decreases and the equilibrium potential is established more slowly.The determination is rapid and accurate in the presence of 1 M sodium hydroxide.     

Chromatographic retention prediction and octanol-water partition coefficient determination of monobasic weak acidic compounds in ion-suppression reversed-phase liquid chromatography using acids as ion-suppressors

Although simple acids, replacing buffers, have been widely applied to suppress the ionization of weakly ionizable acidic analytes in reversed-phase liquid chromatography (RPLC), none of the previously reported works focused on the systematic studies about the retention behavior of the acidic solutes in this ion-suppression RPLC mode. The subject of this paper was therefore to investigate the retention behavior of monobasic weak acidic compounds using acetic, perchloric and phosphoric acids as the ion-suppressors. The apparent octanol-water partition coefficient (K^″ow) was proposed to calibrate the octanol-water partition coefficient (Kow) of these weak acidic compounds, which resulted in a better linear correlation with log kw, the logarithm of the hypothetical retention factor corresponding to neat aqueous fraction of hydroorganic mobile phase. This log K^″ow−log kw linear correlation was successfully validated by the results of monocarboxylic acids and monohydrating phenols, and moreover by the results under diverse experimental conditions for the same solutes. This straightforward relationship not only can be used to effectively predict the retention values of weak acidic solutes combined with Snyder-Soczewinski equation, but also can offer a promising medium for directly measuring Kow data of these compounds via Collander equation. In addition, the influence of the different ion-suppressors on the retention of weak acidic compounds was also compared in this RPLC mode.     

Photochemical degradation of hyaluronic acid by singlet oxygen

Changes of the rheological properties of hyaluronic acid (sodium-magnesium salt) solutions after exposure to UV radiation indicate a vigorous decrease in their viscosity, but its still strong shear rate dependence. Whereas the presence of the singlet oxygen sensitizer (anthracene-1-sulphonic acid) brings about a loss of shear dependence; the studied solutions show newtonian behavior.     

Time-resolved spectra of excited-state absorption in Er3+ doped YAlO3

A pump- and probe-beam technique is used for measuring time-resolved excited-state absorption (ESA) and stimulated-emission (SE) spectra of Er³⁺ doped YAlO₃. The Er^{3+ 4} I _15/2 ⁴ F _7/2 transition of the sample is excited at 488 nm by an excimer laser pumped dye laser. The ESA and SE of broadband xenon flashlamp light is monitored between 300 and 860 nm by an optical multichannel analyzer (OMA). The analysis of the experimental results provides information on the effective cross sections _ESA and _SE originating from several levels and on the populations of these levels. To our knowledge this represents the first detailed investigation of time-resolved ESA and SE over a broad spectral range in rare-earth doped materials.     

Why is space three-dimensional and how may groups be seen?

First we propose a model of visual perception essentially based on the Keldysh-Chernavsky-Sossinsky three-channel theorem, from which three-dimensionality of space follows. Second, we associate with a system of subgroups H ₁, ..., H_s of a given group G a geometric object, called a group crystal, in order to visualize G. How this notion works is illustrated via the Burnside problem.     

Identification and determination of major flavonoids in rat urine by HPLC-UV and HPLC-MS methods following oral administration of Dalbergia odorifera extract

Flavonoids are the main active constituents of Dalbergia odorifera. The excretion of the major flavonoids in rat urine after oral administration of D. odorifera extract was investigated by HPLC-UV and HPLC-MS methods. Utilizing the HPLC-MS technique, 18 flavonoids, including five isoflavones, four isoflavanones, four neoflavones, two flavanones, two chalcones and one isoflavanonol were identified in free form in a urine sample based on the direct comparison of the corresponding tR, UV maximum absorbance (lambda(max)) values and MS data with the authentic standards. The amounts of the prominent flavonoids, (3R)-4'-methoxy-2',3,7-trihydroxyisoflavanone and vestitone, were determined by HPLC-UV with the internal standard method, and the validation procedure confirmed that it afforded reliable analysis of these two analytes in urine after oral administration of D. odorifera extract.