Tverberg’s Theorem and Graph Coloring

The topological Tverberg theorem has been generalized in several directions by setting extra restrictions on the Tverberg partitions. Restricted Tverberg partitions, defined by the idea that certain points cannot be in the same part, are encoded with graphs. When two points are adjacent in the graph, they are not in the same part. If the restrictions are too harsh, then the topological Tverberg theorem fails. The colored Tverberg theorem corresponds to graphs constructed as disjoint unions of small complete graphs. Hell studied the case of paths and cycles. In graph theory these partitions are usually viewed as graph colorings. As explored by Aharoni, Haxell, Meshulam and others there are fundamental connections between several notions of graph colorings and topological combinatorics. For ordinary graph colorings it is enough to require that the number of colors q satisfy q>Δ, where Δ is the maximal degree of the graph. It was proven by the first author using equivariant topology that if q>Δ ² then the topological Tverberg theorem still works. It is conjectured that q>KΔ is also enough for some constant K, and in this paper we prove a fixed-parameter version of that conjecture. The required topological connectivity results are proven with shellability, which also strengthens some previous partial results where the topological connectivity was proven with the nerve lemma.     

Sonochemical Synthesis of Gold Nanoparticles by Using High Intensity Focused Ultrasound

The sonochemical synthesis of gold nanoparticles (GNPs) with different shapes and size distributions by using high‐intensity focused ultrasound (HIFU) operating at 463 kHz is reported. GNP formation proceeds through the reduction of Au³⁺ to Au⁰ by radicals generated by acoustic cavitation. TEM images reveal that GNPs show irregular shapes at 30 W, are primarily icosahedral at 50 W and form a significant amount of nanorods at 70 W. The size of GNPs decreases with increasing acoustic power with a narrower size distribution. Sonochemiluminescence images help in the understanding of the effect of HIFU in controlling the size and shapes of GNPs. The number of radicals that form and the mechanical forces that are generated control the shape and size of the GNPs. UV/Vis spectra and TEM images are used to propose a possible mechanism for the observed effects. The results presented demonstrate, for the first time, that the HIFU system can be used to synthesise size‐ and shape‐controlled metal nanoparticles.     

Effect of tellurium promoter on vanadium phosphate catalyst for partial oxidation of n-butane

Te-promoted (1%) vanadium phosphate catalyst (VPDTe) was prepared via VOPO4·2H2O by calcining its precursor VOHPO4·0.5H2O in a flow of n-butane/air.VPDTe catalyst has resulted a higher existence of V5+ phase with V5+/V4+ ratio of 0.23.SEM micrographs show that Te addition altered the arrangement of the platelets from "rose-like" clusters to layer with irregular shape.Te addition has also markedly lowered the reduction activation energies of the vanadium phosphate catalyst as revealed by TPR profile.The amount of active oxygen species associated with V4+ phase of the Te promoted catalyst was significantly higher than those of the unpromoted catalyst.These observations suggest that high mobility and availability of reactive oxygen species contributed to the enhancement of n-butane conversion up to 80% at 673 K,while only 47% over unpromoted catalyst (2400 h-1,1.7% n-butane in air).     

Chemical compositions of the rhizome oils of two Alpinia species of Malaysia

The essential oils obtained by hydrodistillation of the rhizomes of Alpinia aquatica Rosc. syn. Alpinia melanocarpa and Alpinia malaccensis Roscoe were analysed by capillary gas chromatography and gas chromatography-mass spectrometry. Eighteen compounds, representing 98.4% of the essential oil were identified in A. aquatica rhizome oil, with β-sesquiphellandrene in 36.5% being the major constituent, while 20 compounds representing 99.7% of the rhizome oil of A. malaccensis were identified, among which methyl (E)-cinnamate (78.2%) was the major constituent.     

Electrochemical Studies on Effects of Psychostimulants,Opioids and Alcohol Intake Towards Level of Hydrogen Peroxide in the Brain Striatum

Hydrogen peroxide (H₂O₂) was the main types of many peroxides produced in living mammalian cells that consumed oxygen. In the brain, the main source of H₂O₂ was the superoxide dismutase (SOD)‐catalyzed reaction in mitochondria. However, the level of H₂O₂ would be elevated through administration of control drugs and alcohol by dopamine metabolism of monoamine oxidase. In this study, a H₂O₂ microsensor was used to investigate the level of H₂O₂ in the brain striatum after administration of methamphetamine (MAP), morphine (MrP) or ethanol (Eth). The placement of microsensor in the brain was done at coordinates A/P 1.1 from bregma, M/L+2.6 and D/V‐1.5. A working potential of +0.05 V vs. Ag/AgCl was applied. The H₂O₂ concentration was measured direct from the current generated by its catalytic reaction at the electro active surface of the electrode. A significant increase of H₂O₂ level was observed after 7 successive injections of the controlled drugs or alcohol. The initial measurement of H₂O₂ is essential as excess dosage of H₂O₂ during treatment will contribute to the formation of neurotoxin oxygenated radicals. The H₂O₂ was the precursor of O_2? and OH radicals. Thus, this study provided a mean to monitor H₂O₂ level in the brain.     

Effect of calcination temperature on the photocatalytic activity of carbon‐doped titanium dioxide revealed by photoluminescence study

Carbon‐doped titania (C‐TiO₂) nanoparticles were synthesized by the sol–gel method at different calcination temperatures (300–600°C) employing titanium tetraisopropoxide (TTIP) as the titanium source and polyoxyethylene sorbitan monooleate (Tween 80) as the carbon source. The physical properties of C‐TiO₂ samples were characterized by X‐ray diffraction (XRD) and scanning electron microscopy (SEM). The photocatalytic activities were checked through the photodegradation of phenolphthalein (PHP) under ultraviolet irradiation. The UV spectrum showed that the carbon doping extends the absorption range of TiO₂ to the visible region. However, the photocatalytic activity is affected by the electron–hole recombination phenomenon, as revealed by the photoluminescence (PL) study. According to the PL spectra, carbon doping reduces the edge‐to‐edge electron–hole recombination. Nevertheless, the number of defect sites is greatly influenced by the calcination temperature of C‐TiO₂. C‐TiO₂ that was calcined at 400°C showed the highest photodegradation percentage of PHP, which was mainly attributed to the synergic effect of the low direct edge‐to‐edge electron–hole recombination, high content of defect sites, and retention of active electrons on the surface hydroxyl group.     

In reply to “A query on the Mg2p of MgO”

Research on Chemical Intermediates -     

Ab initio calculation of vibrational frequencies of GexSe1−x glass

We have used the density functional theory to make the models of Ge_xSe_1?x glass for which the energy is a minimum. The clusters, Ge₂Se₂, Ge₂Se₃, Ge₃Se, Ge₃Se₂, Ge₄Se, GeSe₃, GeSe₄, chain mode zig-zag Ge₄Se₃, corner sharing GeSe₄, and edge sharing Ge₂Se₆, have been made successfully and their vibrational spectra have been calculated from the first principles. We are able to optimize the bond distances as well as the bond angles. The calculated values of the frequencies of vibrations of the various clusters have been compared with those obtained from the experimental Raman spectra of actual glasses, Ge_xSe_1?x(0 < x < 0.3). The local concentration, x within 0.25 nm is nonuniform in the amorphous material. When the same cluster occurs in two stable configurations, low frequency vibrations of frequency, ν < 100 cm^?1, are found. The corner sharing GeSe₄ has low frequency modes at 54 cm^?1 and 93 cm^?1 whereas these modes disappear in the pyramidal configuration. The low frequency modes are therefore associated with the breaking of C₄ symmetry of the pyramidal configuration. The computed vibrational frequencies of clusters Ge₃, Ge₄Se₃, Ge₂Se₃, GeSe₃ and Ge₃Se₂ are actually present in the Raman spectra of the glass, Ge_xSe_1?x(0 < x < 0.3).