A finiteness theorem for maximal independent sets

Denote bymi(G) the number of maximal independent sets ofG. This paper studies the setS(k) of all graphsG withmi(G) = k and without isolated vertices (exceptG K ₁) or duplicated vertices. We determineS(1), S(2), andS(3) and prove that |V(G)| 2 ^k–1 +k – 2 for anyG inS(k) andk 2; consequently,S(k) is finite for anyk. Supported in part by the National Science Council under grant NSC 83-0208-M009-050     

Intramolecular 1,3-dipolar cycloaddition of cyclo-1,3-diene-tethered nitrile oxides

Intramolecular 1,3-dipolar cycloaddition of cyclo-1,3-diene- and -1,3,5-triene-tethered nitrile oxides gave tricyclic isoxazolines as a single stereoisomer in most cases. The relative stereochemistry of tricycle-fused isoxazolines resulting from 1,3-dipolar cycloaddition of cyclo-1,3-diene-tethered nitrile oxides is cis-cis, whereas from cyclohepta-1,3,5-triene-tethered nitrile oxides the cis-trans isomer predominates.     

Relationship between T c and electronegativity differences in compound superconductors

The electronegativity differences, N, between the anions and the cations in suggested resonating elements of some representative high-temperature superconductors with T _c - 10 K are evaluated adopting Pauling's scale. The relationship between N and T _c was found to separate all the examined high-T _csuperconductors onto two curves: One for the cuprate superconductors having two-dimensional layered structures was a straight line, T _c=29.8+4.1N; the other correlation curve representing the remaining compound superconductors including the doped 113 perovskite and the perovskite-related 214 structures was at lower T _c values but also suggested that increasing electronegativity differences was related to increasing T _c.This work was supported by the Director, Office of Energy Research, Office of Basic Energy Sciences, Materials Sciences Division of the U.S. Department of Energy under Contract No. DE-AC03-76SF00098     

Diagnosing the miR-141 prostate cancer biomarker using nucleic acid-functionalized CdSe/ZnS QDs and telomerase

The microRNA, miR-141, is a promising biomarker for prostate cancer. We implement here a two-step sensing platform for the sensitive detection of miR-141. The first step involves the use of semiconductor CdSe/ZnS quantum dots (QDs) modified by FRET quencher-functionalized nucleic acids, that include the recognition sequence for miR-141 and a telomerase primer sequence for the second step of the analytical platform. Subjecting the probe-modified QDs to miR-141, in the presence of duplex specific nuclease, DSN, leads to the formation of a miR-141/probe duplex and to its DSN-mediated cleavage, while regenerating the miR-141. The DSN-induced cleavage of the quencher units leads to the activation of the fluorescence of the QDs, thus allowing the optical detection of miR-141 with a sensitivity corresponding to 1.0 × 10^–12 M. The nucleic acid residues associated with the QDs after cleavage of the probe nucleic acids by DSN act as primers for telomerase. The subsequent telomerase/dNTPs-stimulated elongation of the primer units forms G-quadruplex telomer chains. Incorporation of hemin in the resulting G-quadruplex telomer chains yields horseradish peroxidase-mimicking DNAzyme units, that catalyze the generation of chemiluminescence in the presence of luminol/H₂O₂. The resulting chemiluminescence intensities provide a readout signal for miR-141, DL = 2.8 × 10^–13 M. The first step of the sensing platform is non-selective toward miR-141 and the resulting fluorescence may be considered only as an indicator for the existence of miR-141. The second step in the sensing protocol, involving telomerase, provides a selective chemiluminescence signal for the existence of miR-141. The two-step sensing platform is implemented for the analysis of miR-141 in serum samples from healthy individuals and prostate cancer carriers. Impressive discrimination between healthy individuals and prostate cancer carriers is demonstrated.     

Pyrenoimidazole‐Based Deep‐Blue‐Emitting Materials: Optical,Electrochemical, and Electroluminescent Characteristics

A series of pyrenoimidazoles that contained various functional chromophores, such as anthracene, pyrene, triphenylamine, carbazole, and fluorene, were synthesized and characterized by optical, electrochemical, and theoretical studies. The absorption spectra of the dyes are dominated by electronic transitions that arise from the pyrenoimidazole core and the additional chromophore. All of the dyes exhibited blue‐light photoluminescence with moderate‐to‐high quantum efficiencies. They also displayed high thermal stability and their thermal‐decomposition temperatures fell within the range 462–512 °C; the highest decomposition temperature was recorded for a carbazole‐containing dye. The oxidation propensity of the dyes increased on the introduction of electron‐rich chromophores, such as triphenylamine or carbazole. The application of selected dyes that featured additional chromophores such as pyrene, carbazole, and triphenylamine as blue‐emissive dopants into multilayered organic light‐emitting diodes with a 4,4′‐bis(9H‐carbazol‐9‐yl)biphenyl (CBP) host was investigated. Devices that were based on triphenylamine‐ and carbazole‐containing dyes exhibited deep‐blue emission (CIE 0.157, 0.054 and 0.163, 0.041), whereas a device that was based on a pyrene‐containing dye showed a bright‐blue emission (CIE 0.156, 0.135).     

Seabed classification from acoustic profiling data using the similarity index

We introduce the similarity index (SI) for the classification of the sea floor from acoustic profiling data. The essential part of our approach is the singular value decomposition of the data to extract a signal coherent trace-to-trace using the Karhunen-Loeve transform. SI is defined as the percentage of the energy of the coherent part contained in the bottom return signals. Important aspects of SI are that it is easily computed and that it represents the textural roughness of the sea floor as a function of grain size, hardness, and a degree of sediment sorting. In a real data example, we classified a section of the sea floor off Cheju Island south of the Korean Peninsula and compared the result with the sedimentology defined from direct sediment sampling and side scan sonar records. The comparison shows that SI can efficiently discriminate the bottom properties by delineating sediment-type boundaries and transition zones in more detail. Therefore, we propose that SI is an effective parameter for geoacoustic modeling.     

Structure,transport and magnetic properties of the double perovskite (Ca<Subscript>2-2x</Subscript>Sr<Subscript>2x</Subscript>)FeMoO<Subscript>6</Subscript>

In this paper we report the results of a detailed investigation of the double perovskite (Ca_2-2xSr_2x)FeMoO₆ system. Chemical size effects on structural, electrical, and magnetic properties caused by the substitution of isovalent, larger Sr ions into the smaller Ca sites, resulting in (Ca_2-2xSr_2x)FeMoO₆, have been examined. The compounds crystallize in the monoclinic space group P2₁/n for 0.0x<0.2, the orthorhombic space group Pbnm for 0.2x<0.4, and the tetragonal space group I4/m and I4/mmm for x0.4. Examination of the resistivity of all compounds reveals a metallic behavior which is well described by a Tⁿ dependence except for x=1.0. These n values change from 1 to 2 as T decreases lower than T_c. This is indicative of a variation in the transport mechanism at T_c. The ferrimagnetic transition temperature T_c increases with increasing x from 318 (x=0.0) to 393 K (x=1.0). For all samples, the saturation magnetization at 82 K obeys M_s3.5_B/(formula unit), compared to a theoretical spin-only moment of 4_B/(formula unit) for a perfectly ordered compound. PACS 74.25.Fy; 74.25.Ha     

Self‐assembly of H‐bonded side‐chain and cross‐linking copolymers containing diblock‐copolymeric donors and single/double H‐bonded light‐emitting acceptors

A series of diblock‐copolymers were synthesized through anionic polymerization of styrene and tert‐butyl methacrylate (tBuA) with different monomer ratios, and analogous block‐copolymeric derivatives (PS‐b‐PAA)s with monofunctional carboxylic acid groups were obtained by further hydrolyzation as hydrogen‐bonded (H‐bonded) proton donors. Via H‐bonded interaction, these diblock‐coplymeric donors (PS‐b‐PAA)s were incorporated with luminescent mono‐pyridyl/bis‐pyridyl acceptors to form single/double H‐bonded supramolecules, that is, H‐bonded side‐chain/cross‐linking copolymers, respectively. The supramolecular architectures formed by donor polymers and light‐emitting acceptors were influenced by the ratio of acid blocks in the diblock copolymeric donors and the type of single/double H‐bonded light‐emitting acceptors. Their thermal and luminescent properties can be adjusted by H‐bonds, and more than 100 nm of red‐shifted photoluminescence (PL) emissions were observed, which depend on the degrees of the H‐bonding interactions. Self‐assembled phenomena of amphiphilic dibolck copolymers and their H‐bonded complexes were confirmed by TEM micrographs, and supramolecular microphase separation of spherical micelle‐like morphology was demonstrated to affect the photophysical properties. Polymer light‐emitting diode (PLED) devices containing H‐bonded complexes showed electroluminescence (EL) emissions of 503–560 nm under turn‐on voltages of 7.5–9.0 V, maximum power efficiencies of 0.23–0.37 cd/A (at 100 mA/cm²), and maximum luminances of 318–519 cd/m² (around 25 V). © 2009 Wiley Periodicals, Inc. J Polym Sci Part A: Polym Chem 47: 4685–4702, 2009