Covering point sets with two disjoint disks or squares

We study the following problem: Given a set of red points and a set of blue points on the plane, find two unit disks C_R and C_B with disjoint interiors such that the number of red points covered by C_R plus the number of blue points covered by C_B is maximized. We give an algorithm to solve this problem in O(n^8/3log²n) time, where n denotes the total number of points. We also show that the analogous problem of finding two axis-aligned unit squares S_R and S_B instead of unit disks can be solved in O(nlogn) time, which is optimal. If we do not restrict ourselves to axis-aligned squares, but require that both squares have a common orientation, we give a solution using O(n³logn) time.     

Highly luminescent Cu(I)-phenanthroline complexes in rigid matrix and temperature dependence of the photophysical properties.

We synthesized new [Cu(NN)(2)](+)-type complexes where NN = 2-5 and denotes a 2,9-disubstituted-1,10-phenanthroline ligand (related complexes of 1 and 6 ligands are used for reference purposes). For 2, 3, and 4 the ligand substituents are long alkyl-type fragments, whereas in 5 a phenyl ring is directly attached to the chelating unit. At 298 K the four complexes display relatively intense metal-to-ligand-charge-transfer (MLCT) emission bands with maxima around 720 nm, Phi(em) approximately 1 x 10(-)(3) and tau > 100 ns in deaerated CH(2)Cl(2). The emission behavior at 77 K in a CH(2)Cl(2)/MeOH matrix is quite different for complexes of alkyl- (2-4) versus phenyl-substituted (5) ligands. The former exhibit very intense emission bands centered around 642 nm and hypsochromically shifted with respect to 298 K, whereas the luminescence band of [Cu(5)(2)](+) is faint and shifted toward the infrared side. These results prompted us to study in detail the temperature dependence of luminescence properties of [Cu(2)(2)](+) and [Cu(5)(2)](+) in the 300-96 K range. For both complexes the excited state lifetimes increase monotonically by decreasing temperatures, and the trend is well described by an Arrhenius-type treatment involving two equilibrated MLCT excited levels. The emission bands show a similar behavior for the two compounds (intensity decrease and red-shift) only in the 300-120 K range, when the solvent is fluid. In the frozen regime (T 相似文献   

On the structure, infrared and Raman spectra of the 2:1 cysteine–Zn complex

A recent study on the Raman spectrum of the cysteine zwitterion and anion, and the 2:1 (Cys)₂Zn complex was reanalyzed employing B3LYP/6-311++G(3df,2pd) calculations in a simulated water environment. The spectra were rediscussed in light of the apparent incorrect structure determined in the original paper for this complex. The complex turns out to be tetrahedral and tetracoordinated instead of octahedral hexacoordinated, as initially proposed. The calculated Raman spectrum of the complex agrees very well with the experimental data, showing that both the geometrical and electronic structures are well represented. Three metal–ligand bands are found, two of them involving mostly the symmetrical and asymmetrical stretching of the Zn–N and Zn–S bonds. They were measured at 334 and 296 cm^?1 and calculated at 319 and 249 cm^?1, respectively. The third band involves the stretching of Zn–S bonds but also skeletal vibrations of the ligand. This band, measured at 399 cm^?1 and calculated at 444 cm^?1, has been previously assigned incorrectly to a Zn–O bond which does not actually exists since the CO ₂ ^?1 fragments are located away from the Zn ion.     

Extraction of antioxidants from plants using ultrasonic methods and their antioxidant capacity

The analytical method based on the HPLC coupled with UV detection (HPLC‐UV) for the determination of selected antioxidants (i.e. esculetin, scopoletin, 7‐hydroxycoumarine, rutin, xanthotoxin, 5‐methoxypsoralen and quercetin) in plant material was developed. Two ultrasonic extraction methods for the isolation of these compounds from the plants such as Mentha longifolia L., Mentha spicata L., Ruta graveolens L., Achyllea millefolium L., Plantago lanceolata L. and Coriandrum sativum L. were used. Both of these methods, i.e. ultrasonic probe and ultrasonic bath, were optimised and compared to each other. For the proposed HPLC‐UV method LOQ values in the range from 22.7 (xanthotoxin) up to 97.2 ng/mL (rutin) were obtained. For all extracts the antioxidant capacity based on the reduction of free 2,2‐diphenyl‐1‐picrylhydrazyl (DPPH) radical was also determined. Obtained results ranged from 10.11 up to 73.50% of DPPH radical inhibition.     

Investigation into factors influencing stereoselectivity in the reactions of heterocycles with donor-acceptor-substituted rhodium carbenoids

Rhodium-catalyzed decomposition of aryldiazoacetates in the presence of pyrroles or furans results in mono- or biscyclopropanation of the heterocycle, but with opposite enantioinduction. In the absence of sterically encumbering groups, the cyclopropanation of furan occurs with initial bond formation at the 2-position. If this pathway is sterically blocked, cyclopropanation can occur with initial bond formation at the 3-position of the furan ring; in this case, the cyclopropanation reaction takes place on the opposite face of the heterocycle, and the opposite enantioinduction is observed. Upon extension of this methodology to benzofurans, a highly enantioselective monocyclopropanation reaction occurs to furnish a product derived from initial bond formation at the 2-position of the benzofuran. When this reaction pathway is inhibited by sterically encumbering substituents on the benzofuran, no cyclopropanation of the furan ring is observed, and instead, double cyclopropanation of the benzene ring occurs. Double cyclopropanation of the benzene ring was also observed in reactions with indoles.     

Analysis of odorous trichlorobromophenols in water by in-sample derivatization/solid-phase microextraction GC/MS

The simultaneous determination of several odorous trichlorobromophenols in water has been carried out by an in-sample derivatization headspace solid-phase microextraction method (HS-SPME).The analytical procedure involved their derivatization to methyl ethers with dimethyl sulfate/NaOH and further HS-SPME and gas chromatography-mass spectrometry (GC/MS) determination. Parameters affecting both the derivatization efficiency and headspace SPME procedures, such as the selection of the SPME fiber coating, derivatization–extraction time and temperature, were studied. The commercially available polydimethylsiloxane (PDMS) 100 μm and Carboxen-polydimethylsiloxane-divinylbenzene (CAR-PDMS-DVB) fibers appeared to be the most suitable for the simultaneous determination of these compounds. The precision of the HS-SPME/GC/MS method gave good relative standard deviations (RSDs) run-to-run between 9% and 19% for most of them, except for 2,5-diCl-6-Br-phenol, 2,6-diCl-3-Br-phenol and-2,3,6-triBr-phenol (22%, 25% and 23%, respectively). The method was linear over two orders of magnitude, and detection limits were compound dependent but ranged from 0.22 ng/l to 0.95 ng/l. The results obtained for water samples using the proposed SPME procedure were compared with those found with the EPA 625 method, and good agreement was achieved. Therefore, the in-sample derivatization HS-SPME/GC/MS procedure here proposed is a suitable method for the simultaneous determination of odorous trichlorobromophenols in water.     

Simultaneous electrophoretic analysis of proteins of very high and low molecular mass using Tris‐acetate polyacrylamide gels

To separate and analyze giant and small proteins in the same electrophoresis gel, we have used a 3–15% polyacrylamide gradient gel containing 2.6% of the crosslinker bisacrylamide and 0.2 M of Tris‐acetate buffer (pH 7.0). Samples were prepared in a sample buffer containing lithium dodecyl sulphate and were run in the gel described above using Tris‐Tricine‐SDS‐sodium bisulfite buffer, pH 8.2, as electrophoresis buffer. Here, we show that this system can be successfully used for general applications of SDS‐PAGE such as CBB staining and immunoblot. Thus, by using Tris‐acetate 3–15% polyacrylamide gels, it is possible to simultaneously analyze proteins, in the mass range of 10–500 kDa, such as HERC1 (532 kDa), HERC2 (528 kDa), mTOR (289 kDa), Clathrin heavy chain (192 kDa), RSK (90 kDa), S6K (70 kDa), β‐actin (42 kDa), Ran (24 kDa) and LC3 (18 kDa). This system is highly sensitive since it allows detection from as low as 10 μg of total protein per lane. Moreover, it has a good resolution, low cost, high reproducibility and allows for analysis of proteins in a wide range of weights within a short period of time. All these features together with the use of a standard electrophoresis apparatus make the Tris‐acetate‐PAGE system a very helpful tool for protein analysis.     

Application of micro-FTIR imaging in the Earth sciences

In this paper we describe recent applications of micro-infrared imaging in the Earth sciences. We address, in particular, the use of Fourier-transform infrared (FTIR) spectroscopy in characterizing the zoning and speciation of H and C in a variety of geological materials, including microporous minerals, nominally anhydrous volcanic minerals (NAMs), and crystal inclusions. These investigations show that use of the modern techniques of FTIR imaging enables detection of the zoning of volatile species across the studied samples, and possible configuration changes of structurally-bound carbon molecular species (e.g., CO₂ vs CO₃) during crystal growth. Such features, which are not accessible with other micro-analytical techniques, may provide information about the physicochemical properties which act as constraints in the genesis of the samples, and important information about the evolution of the geological system. Tests performed with focal-plane-array detectors (FPA) show that resolution close to the diffraction limit can be achieved if the amounts of the target molecules in the sample are substantially different. We also point out the possibility of using FTIR imaging for investigations under non-ambient conditions.