Decomposition methods based on articulation vertices for degree-dependent spanning tree problems

Decomposition methods for optimal spanning trees on graphs are explored in this work. The attention is focused on optimization problems where the objective function depends only on the degrees of the nodes of the tree. In particular, we deal with the Minimum Leaves problem, the Minimum Branch Vertices problem and the Minimum Degree Sum problem. The decomposition is carried out by identifying the articulation vertices of the graph and then its blocks, solving certain subproblems on the blocks and then bringing together the optimal sub-solutions following adequate procedures. Computational results obtained using similar Integer Programming formulations for both the original and the decomposed problems show the advantage of the proposed methods on decomposable graphs.     

Laser ablation synthesis of new gold phosphides using red phosphorus and nanogold as precursors. Laser desorption ionisation time‐of‐flight mass spectrometry

Gold phosphides show unique optical or semiconductor properties and there are extensive high technology applications, e.g. in laser diodes, etc. In spite of the various AuP structures known, the search for new materials is wide. Laser ablation synthesis is a promising screening and synthetic method. Generation of gold phosphides via laser ablation of red phosphorus and nanogold mixtures was studied using laser desorption ionisation time‐of‐flight mass spectrometry (LDI TOFMS). Gold clusters Au_m⁺ (m = 1 to ~35) were observed with a difference of one gold atom and their intensities were in decreasing order with respect to m. For P_n⁺ (n = 2 to ~111) clusters, the intensities of odd‐numbered phosphorus clusters are much higher than those for even‐numbered phosphorus clusters. During ablation of P‐nanogold mixtures, clusters Au_m⁺ (m = 1‐12), P_n⁺ (n = 2‐7, 9, 11, 13–33, 35–95 (odd numbers)), AuP_n⁺ (n = 1, 2–88 (even numbers)), Au₂P_n⁺ (n = 1‐7, 14–16, 21–51 (odd numbers)), Au₃P_n⁺ (n = 1‐6, 8, 9, 14), Au₄P_n⁺ (n = 1‐9, 14–16), Au₅P_n⁺ (n = 1‐6, 14, 16), Au₆P_n⁺ (n = 1‐6), Au₇P_n⁺ (n = 1‐7), Au₈P_n⁺ (n = 1‐6, 8), Au₉P_n⁺ (n = 1‐10), Au₁₀P_n⁺ (n = 1‐8, 15), Au₁₁P_n⁺ (n = 1‐6), and Au₁₂P_n⁺ (n = 1, 2, 4) were detected in positive ion mode. In negative ion mode, Au_m^– (m = 1–5), P_n^– (n = 2, 3, 5–11, 13–19, 21–35, 39, 41, 47, 49, 55 (odd numbers)), AuP_n^– (n = 4–6, 8–26, 30–36 (even numbers), 48), Au₂P_n^– (n = 2–5, 8, 11, 13, 15, 17), Au₃P_n^– (n = 6–11, 32), Au₄P_n^– (n = 1, 2, 4, 6, 10), Au₆P₅^–, and Au₇P₈^– clusters were observed. In both modes, phosphorus‐rich Au_mP_n clusters prevailed. The first experimental evidence for formation of AuP₆₀ and gold‐covered phosphorus Au₁₂P_n (n = 1, 2, 4) clusters is given. The new gold phosphides generated might inspire synthesis of new Au‐P materials with specific properties. Copyright © 2012 John Wiley & Sons, Ltd.     

Real-Time In Vivo Detection of Cellular Senescence through the Controlled Release of the NIR Fluorescent Dye Nile Blue

In vivo detection of cellular senescence is accomplished by using mesoporous silica nanoparticles loaded with the NIR-FDA approved Nile blue (NB) dye and capped with a galactohexasaccharide ( S3 ). NB emission at 672 nm is highly quenched inside S3 , yet a remarkable emission enhancement is observed upon cap hydrolysis in the presence of β-galactosidase and dye release. The efficacy of the probe to detect cellular senescence is tested in vitro in melanoma SK-Mel-103 and breast cancer 4T1 cells and in vivo in palbociclib-treated BALB/cByJ mice bearing breast cancer tumor.     

‘One‐Touch’ Voltammetry of Microparticles for the Identification of Corrosion Products in Archaeological Lead

Voltammetry of microparticles is applied to the identification of lead corrosion products by means of an essentially non‐invasive ‘one‐touch’ technique based on the use of graphite pencil. This methodology permits the mechanical attachment of few nanograms of sample from the surface of lead archaeological artefacts to a paraffin‐impregnated graphite electrode, which, upon immersion in aqueous electrolytes, provides distinctive voltammetric responses for litharge and cotunnite‐ anglesite‐, cerusite‐based corrosion products. The reported method is applied to the identification of corrosion products in archaeological lead pieces from different Iberian sites in Valencia (Spain).     

Solving Nonlinear p-Adic Pseudo-differential Equations: Combining the Wavelet Basis with the Schauder Fixed Point Theorem

We consider the pointwise convergence problem for the solution of Schrödinger-type equations along directions determined by a given compact subset of the real line. This problem contains Carleson’s problem as the simplest case and was studied in general by Cho et al. We extend their result from the case of the classical Schrödinger equation to a class of equations which includes the fractional Schrödinger equations. To achieve this, we significantly simplify their proof by completely avoiding a time localization argument.     

Stepwise Oxidations in a Cofacial Copper(II) Porphyrin Dimer: Through-Space Spin-Coupling and Interplay between Metal and Radical Spins

cis and trans-copper(II) porphyrin dimers have been synthesized, in which two Cu^II porphyrin macrocycles are bridged through a rigid ethene linker for possible through-space and through-bond spin-couplings between the paramagnetic Cu^II centers. It has been found that the two macrocycles come closer after 1 e⁻ oxidation, however, they move far apart upon further 1 e⁻ oxidation leading to transformation of the cis to the trans isomer. Detailed investigations are performed here on the interactions between the two porphyrin macrocycles, between two unpaired spins of closely spaced Cu^II centers, and also between the unpaired spins of metal and porphyrin π–cation radicals. Spectroscopic investigations along with the X-ray structure of the 2 e⁻-oxidized complex displayed strong electronic communications through the bridge between two porphyrin π–cation radicals. The counterion I₉⁻ is stabilized in an unusual trigonal-pyramidal structure in the 2 e⁻-oxidized complex in which the central iodide ion is bound with four iodine (I₂) molecules. Variable-temperature magnetic study revealed strong antiferromagnetic coupling between the two porphyrin π–cation radical spins (J_r–r) in the 2 e⁻-oxidized complex. DFT calculations suggest stabilization of the triplet state, which is also in good agreement with the experiment. Ab initio molecular dynamics allowed the variation of the structural details to be followed upon stepwise oxidations and also the final isomerization process including its associated energy barrier.     

Kinetic Study on Models of the Tetrabutqxyzirconium-Catalyzed Reaction Between α, ω -Dicarboxypolyamide-11 and α, ω -Dihydroxypolyoxyethylene

The kinetics of the tetrabutoxyzirconium-catalyzed esterifications between 11-dodecylamideundecanoic acid and 1-dodecanol, 2-tridecanol, a-dodecyl-ω-hydroxypolyoxyethylene are studied and compared to that of α, ω-dicarboxypolyamide-l 1 and α, ω-dihydroxypolyoxyethylene. The reaction with 2-tridecanol is characterized by an autoacceleration phenomenon. In the other cases the reaction rate is not greatly affected by catalyst concentration. An explanation involving the formation of catalyst condensates at the very beginning of the reaction is put forward.