Partitioning Boolean lattices into chains of subsets

We prove that the Boolean lattice of all subsets of an n-set can be partitioned into chains of size four if and only if n9.Research supported in part by N.S.F. grant DMS-8401281.Research supported in part by N.S.F. grant DMS-8406451.     

Submanifolds of complex space forms admitting an almost contact metric compound structure

Summary Real hypersurfaces of an almost Hermitian manifold naturally admit an almost contact metric structure and the (f, g, u, v, w, , , )-structure is defined on submanifolds of codimension 3 of an almost Hermitian manifold. We study the so-called semi-invariant submanifolds of a complex space form with almost contact metric compound structure which is a general notion of (f, g, u, v, w, , , )-structure.Dedicated to professor Eulyong Pak on his 60th birthdayThis research was partially supported by Korean Science and Engineering Foundation Grant.     

Thermodynamics of the dissociation of 2-aminopyridinium ion in synthetic seawater and a standard for pH in marine systems

Buffer solutions composed of 2-aminopyridinium chloride and 2-aminopyridine in synthetic seawater are useful as a supplement to buffers of Tris (pH 8.2) and Bis (pH 8.8) in standardizing measurements of hydrogen ion concentration (pm _H or pH(SWS)) in oceanography. The dissociation constant of 2-amino-pyridinium ion over the range of salinities (S) from 30 to 40 has now been determined from the emf of cells without liquid junction at eight temperatures (T) from 278.15 to 313.15 K. The results fit the equation pK=2498.31/T–15.3274+2.4050 lnT+S(0.012928–2.9417×10^–5T) with a standard deviation of 0.0023. Thermodynamic constants for the dissociation process and standard reference values of pm _H and pH(SWS) were derived from the data. The pm _H of the buffer consisting of 2-aminopyridinium chloride and 2-aminopyridine (each 0.04 molal) in synthetic seawater of salinity 35 varies from 7.356 at 278.15 K to 6.601 at 313.15 K.     

Synthesis and structural, spectroscopic and magnetic studies of two new polymorphs of Mn(SeO3)·H2O

Two new manganese(II) selenite polymorphs with formula Mn(SeO₃)·H₂O have been synthesized by slow evaporation from an aqueous solution. The crystal structure of both compounds (1) and (2) have been solved from X-ray diffraction data. The structure of (1) was determined from single-crystal X-ray diffraction techniques. The compound crystallizes in the Ama2 space group, with a=5.817(1), b=13.449(3), and Z=4. The structure of (2) has been solved from X-ray powder diffraction data. This phase crystallizes in the P2₁/n space group with unit-cell parameters of a=4.921(3), b=13.121(7), , β=90.03(2)° and Z=4. Both polymorphs exhibit a layered structure formed by isolated sheets of MnO₆ octahedra and (SeO₃)²⁻ trigonal pyramids in the (010) plane. These layers, which contain one manganese and selenium atom crystallographically independent, are formed by octahedra linked between them through the selenite oxoanions. The difference of both compounds consists in the stacking of the layers along the b-axis. The IR spectra show the characteristic bands of the selenite anion. Studies of luminescence performed at 6 K and diffuse reflectance spectroscopy have been carried out for both phases. The Dq and Racah (B and C) parameters, from luminescence and diffuse reflectance spectroscopy, are Dq=705, B=750, for (1) and Dq=720, B=745, for (2). The ESR spectra of both compounds are isotropic with g-values of 1.99(1). Magnetic measurements indicate the presence of antiferromagnetic couplings in both phases. The J-exchange parameters have been estimated by fitting the experimental magnetic data to a model for square-planar lattice. The values obtained are J/k=-0.83, −0.91 K and J^′/k=-0.97, −1.20 K, for polymorphs (1) and (2), respectively.     

A Pauson-Khand-type reaction between alkynes and olefinic aldehydes catalyzed by rhodium/cobalt heterobimetallic nanoparticles: an olefinic aldehyde as an olefin and CO source

Co/Rh (Co:Rh = 2:2) heterobimetallic nanoparticles derived from Co(2)Rh(2)(CO)(12) react with alkynes and alpha,beta-unsaturated aldehydes such as acrolein, crotonaldehyde, and cinnamic aldehyde and release products resulting from [2 + 2 + 1]cycloaddition of alkyne, carbon monoxide, and alkene. alpha,beta-Unsaturated aldehydes act as a CO and alkene source. These reactions produce 2-substituted cyclopentenones.     

Quantitative studies on the peroxidation of human low-density lipoprotein initiated by superoxide and by charged and neutral alkylperoxyl radicals.

Rates of peroxidation of human LDL and rates of consumption of the LDL's alpha-tocopherol (TocH) have been measured at 37 degrees C. Peroxidation was initiated by radicals generated in the aerated aqueous phase at known rates by thermal decomposition of appropriate precursors: superoxide (O2(*-)/HOO(*)) from a hyponitrite and alkylperoxyls (ROO(*), two positively charged, one negatively charged and one neutral) from azo compounds. The efficiencies of escape from the solvent cage of the geminate pair of neutral carbon-centered radicals was found to be 0.1, but it was 0.5 for the three charged radicals, a result attributed to radical/radical Coulombic repulsion within the cage. All four alkylperoxyls initiated and terminated tocopherol-mediated peroxidation (TMP) with about equal efficiency and essentially all of these radicals that were generated were consumed in these two reactions. TMP is a radical chain process, and when initiated by the alkylperoxyls, the rate of LDL peroxidation was faster in the early stages while TocH was present than later, after all of this "antioxidant" had been consumed. In contrast, only about 3-4% of the generated superoxide radicals reacted in any measurable fashion with TocH-containing LDL at pH's from 7.6 to 6.5 and peroxidation was much slower than with a similar rate of generation of alkylperoxyls. After all the TocH had been consumed, LDL peroxidation was negligible at pH 7.6 and 7.4, but at pH 6.8 and 6.5, the peroxidation rates showed a large increase over the rates while the TocH had been present. That is, endogenous TocH behaves as an antioxidant in LDL subjected to attack by the physiologically relevant superoxide radical, whereas TocH behaves as a prooxidant in LDL subjected to attack by the probably far less physiologically important alkylperoxyls. Rates of LDL peroxidation initiated by superoxide increased as the pH was decreased, and the results are consistent with the initiation of peroxidation of fresh LDL occurring via H-atom abstraction from TocH by HOO(*) to form the Toc(*) radical and termination by reaction of O2(*-) with Toc(*), a process that occurs partly by addition leading to TocH consumption and partly by electron plus proton transfer leading to the regeneration of TocH.     

Reactions of Molecules with Two Equivalent Functional Groups. 5. Anomalous Reactivity of 1,10-Cyclooctadecanedione. Crystal and Molecular Structures of cis,cis-1,10-Diphenyl-1,10-cyclooctadiene and the Stereoisomers of 1,10-Diphenyl-1,10-cyclooctadecanediol(1)

The reaction of the title diketone (3) with phenyl Grignard produces (with rate constant k(1)) the conjugate base (6-M) of 10-hydroxy-10-phenylcyclooctadecanone (6), which is subsequently converted (with rate constant k(2)) to the conjugate base of the title diol, as a mixture of the cis (7, 55%) and trans (8, 45%) isomers. The ratio k(2)/k(1), 2.2 +/- 0.4, indicates that the carbonyl group in 6-M is 4.4 times as reactive as each carbonyl in 3. Competition experiments further demonstrate that the relative rates (per carbonyl) for addition of phenylmagnesium bromide to 3, 10-methylenecyclooctadecanone (11), and cyclopentadecanone (12) are 1.0:0.60:1.92. Possible reasons for this order of reactivity are discussed. Diols 7 and 8 undergo facile double dehydration to form the title diene 13, which is predicted by molecular mechanics calculations to be the most stable of the four possible symmetrical diene isomers. The structures of 7, 8, and 13 were secured by single-crystal X-ray studies.     

Zeb1 for RCP-induced oral cancer cell invasion and its suppression by resveratrol

Rab coupling protein (RCP) is upregulated in head and neck squamous cell carcinoma (HNSCC) and is correlated with the progression and survival of patients. However, the role of RCP in one of the aggressive types of HNSCC, oral squamous cell carcinoma (OSCC), remains elusive. In the present study, we identified the important role of Zeb1 in RCP-induced OSCC epithelial-to-mesenchymal transition (EMT) and invasion. RCP induces Zeb1 expression, and silencing Zeb1 expression significantly inhibits RCP-induced OSCC invasion. In addition, Zeb1 upregulates MT1-MMP expression to promote OSCC EMT and invasion. Furthermore, we observed that the β1 integrin/EGFR/β-catenin signaling cascade mediates RCP-induced Zeb1 expression to promote OSCC invasion. Notably, we provide evidence that resveratrol (REV) strongly inhibits RCP-induced Zeb1 expression through blocking β1 integrin endosome recycling and EGFR activation, leading to suppression of RCP-induced OSCC invasion, demonstrating the important role of RCP in OSCC invasion and its reversion by REV. Collectively, the present study provides evidence for the first time that RCP aggravates OSCC invasion through increasing Zeb1 expression and subsequently upregulating MT1-MMP expression and that this process is reversed by REV, providing novel biomarkers and indicating the therapeutic potential of REV in OSCC.Subject terms: Oral cancer, Cell invasion