Countable network weight and multiplication of Borel sets

A space Borel multiplies with a space if each Borel set of is a member of the -algebra in generated by Borel rectangles. We show that a regular space Borel multiplies with every regular space if and only if has a countable network. We give an example of a Hausdorff space with a countable network which fails to Borel multiply with any non-separable metric space. In passing, we obtain a characterization of those spaces which Borel multiply with the space of countable ordinals, and an internal necessary and sufficient condition for to Borel multiply with every metric space.

     

Prox-regular functions in variational analysis

The class of prox-regular functions covers all l.s.c., proper, convex functions, lower- functions and strongly amenable functions, hence a large core of functions of interest in variational analysis and optimization. The subgradient mappings associated with prox-regular functions have unusually rich properties, which are brought to light here through the study of the associated Moreau envelope functions and proximal mappings. Connections are made between second-order epi-derivatives of the functions and proto-derivatives of their subdifferentials. Conditions are identified under which the Moreau envelope functions are convex or strongly convex, even if the given functions are not.

     

Flow injection analysis of potassium using an all-solid-state potassium-selective electrode as a detector

The concentration of potassium was determined by a combination of flow injection analysis (FIA) with an all-solid-state potassium sensor detection. The all-solid-state potassium-selective electrode possessing long-term potential stability was fabricated by coating an electroactive polypyrrole/poly(4-styrenesulfonate) film electrode with a plasticized poly(vinyl chloride) membrane containing valinomycin. The simple FIA system developed in this laboratory demonstrated sensitivity identical to that in the batch system and achieved considerably rapid assay (150 samples h⁻¹). Analyses of soy sauce and control serum samples by this FIA system yielded results in good agreement with those obtained by conventional measurements.     

Interactions between naproxen and maltoheptaose,the non-cyclic analog ofβ-cyclodextrin

The crystallinity of naproxen in solid combinations with amorphous maltoheptaose, the non-cyclic analog of -cyclodextrin, was assessed using differential scanning calorimetry supported by X-ray powder diffractometry. Cogrinding induced a decrease in drug crystalinity to an extent which depended on the grinding time, and was most pronounced for the combination of equimolecular composition. Thermal analysis showed that the mechanism behind the conversion of crystalline naproxen into the amorphous state by cogrinding with maltoheptaose differed from that with randomly substituted, amorphous -cyclodextrins. Interactions of naproxen with maltoheptaose in aqueous solution were studied by means of fluorescence spectroscopy, phase-solubility analysis, and computeraided molecular modelling. Maltoheptaose can wrap up naproxen, taking on a cyclic conformation and forming a pseudo inclusion complex (apparent binding constant K_{1: 1} = 1.0 × 10³ (–20%) L mol^–1 at 25 °C) which is about as stable as the true inclusion complex with -cyclodextrin in the lowest temperature range (0-100 K). A better complexing ability for naproxen in terms of binding constant values, however, was displayed by both native and derivatized -cyclodextrins, the hosts with covalently-bound cyclic structures.     

High-temperature TG/DSC/QMS applications in environmental protection

The decomposition reactions of polystyrene, phenolic resin and a protective undercoating material for automobiles which contains PVC were tested using a new type of thermal analysis — mass spectrometry coupling system for measurements to 1500C or 2000C, which is based on the principle of a two-step skimmer orifice system. The results will be presented, with particular emphasis on the detection sensitivity of the new system for the products of decomposition.The capability of this coupling system to detect even heavy metals such as lead and silver in the waste gases from decomposition or after evaporation at high temperatures will also be demonstrated.     

Limit cycle analysis of a class of strongly nonlinear oscillation equations

The limit cycle of a class of strongly nonlinear oscillation equations of the form % MathType!MTEF!2!1!+-% feaafeart1ev1aaatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn% hiov2DGi1BTfMBaeXafv3ySLgzGmvETj2BSbqefm0B1jxALjhiov2D% aebbfv3ySLgzGueE0jxyaibaiGc9yrFr0xXdbba91rFfpec8Eeeu0x% Xdbba9frFj0-OqFfea0dXdd9vqaq-JfrVkFHe9pgea0dXdar-Jb9hs% 0dXdbPYxe9vr0-vr0-vqpWqaaeaabiGaciaacaqabeaadaqaaqGaaO% qaaiqadwhagaWaaiabgUcaRmXvP5wqonvsaeHbbjxAHXgiofMCY92D% aGqbciab-DgaNjab-HcaOiaadwhacqWFPaqkcqWF9aqpcqaH1oqzca% WGMbGaaiikaiaadwhacaGGSaGabmyDayaacaGaaiykaaaa!50B8!\[\ddot u + g(u) = \varepsilon f(u,\dot u)\] is investigated by means of a modified version of the KBM method, where is a positive small parameter. The advantage of our method is its straightforwardness and effectiveness, which is suitable for the above equation, where g(u) need not be restricted to an odd function of u, provided that the reduced equation, corresponding to =0, has a periodic solution. A specific example is presented to demonstrate the validity and accuracy of our 09 method by comparing our results with numerical ones, which are in good agreement with each other even for relatively large .     

Structures of boron chelates of mono- and diacylketene aminals

The molecular and crystal structures of diphenylboron chelates of acetylketeneN-benzoylaminal and 2-(N-benzoyl)diaminomethylene-4-dimethylaminomethylenecyclohexane-1,3-dione and the structure of the difluoroboron complex of diacetylketeneN-benzoylaminal were established. It was found that the aminovinylcarbonyl fragment of the ligand is involved in the formation of a boron-containing ring. A delocalized -electron system over the NCCCO fragment of the chelate ring is characteristic of the molecules studied both in crystals and solutions.Translated fromIzvestiya Akademii Nauk. Seriya Khimicheskaya, No. 10, pp. 2541–2546, October, 1996.     

Approximate minimum-cost multicommodity flows in\tilde O(ɛ −2 KNM) timetime

We show that an ε-approximate solution of the cost-constrainedK-commodity flow problem on anN-nodeM-arc network,G can be computed by sequentially solving O(K(? ^?2+logGK) logGM log (G? ^?1 GK)) single-commodity minimum-cost flow problems on the same network. In particular, an approximate minimum-cost multicommodity flow can be computed in $\tilde O$ (G? ^?2 GKNM) running time, where the notation Õ(·) means “up to logarithmic factors”. This result improves the time bound mentioned by Grigoriadis and Khachiyan [4] by a factor ofM/N and that developed more recently by Karger and Plotkin [8] by a factor of? ^?1. We also provide a simple $\tilde O$ (NM)-time algorithm for single-commodity budget-constrained minimum-cost flows which is $\tilde O$ (? ^?3) times faster than the algorithm developed in the latter paper.     

Determination of pyrene and benzo(a)pyrene residues in water by derivative synchronous solid-phase spectrofluorimetry

Benzo(a)pyrene (BaP) and pyrene (Pyr) are two polycyclic aromatic hydrocarbons (PAHs) showing native fluorescence in solution. Both compounds have been determined in water at trace levels by solid-phase spectrofluorimetry, in which BaP and Pyr are fixed on Sephadex G-25 gel and the relative fluorescence intensity is measured after the system is packed in a 1-mm silica cell. First-derivative synchronous spectra obtained at =38 nm were used to determine BaP and Pyr in the presence of other potentially interferent PAHs. The spectral characteristics of the PAHs-gel system are described, the applicable concentration ranges being 0.4–2.5 ng/ml for BaP and 0.7–4.5 ng/ml for Pyr. The relative standard deviations were 1.1% and 1.4% for BaP and Pyr respectively. The detection limits were 0.04 ng/ml for BaP and 0.1 ng/ml for Pyr. The method was applied to the analysis of both compounds in water at trace levels and a recovery study on tap, natural and sea waters was carried out.     

The matched queueing network PH/M/c→oPH/PH/1

We consider a matched queueing network PH/M/coPH/PH/1, where the output of the first subsystem PH/M/c is regarded as one of the inputs of the second subsystem and matched with another input of PH-renewal process, and they are served by a single server with PH-service-distribution. The stationary state probabilities, the distribution of the virtual waiting times in the two subsystems, and the distribution of the total virtual waiting time are derived.The work was supported by the Max-Planck-Gesellschaft, Germany, and the Chinese Academy ofSciences.