A New Lower Bound For A Ramsey-Type Problem

Let 3 ≤ r < s be fixed integers and let G be a graph on n vertices not containing a complete graph on s vertices. The main aim of this paper is to provide a new lower bound on the size of the maximum subset of G without a copy of complete graph K_r. Our results substantially improve previous bounds of Krivelevich and Bollobás and Hind. * Research supported in part by NSF grants DMS-0106589, CCR-9987845 and by the State of New Jersey. Part of this research was done while visiting Microsoft Research.     

Feasibility of determining the characteristics of the failure of fibers by electrical simulation

A feasibility study is made of the use of electrical models in a seismoacoustic study of the failure process of fibers (rods). Specific models are proposed for the case of the failure of a thin glass rod. The output signal of the electrical model is compared with the experimentally recorded elastic pulse produced upon the failure of the glass specimen. The close correspondence between the seismoacoustic pulse and the output signal of the electrical model is pointed out.     

Prediction of a linear polymer made of xenon and carbon

Electronic structure calculations predict the existence of a novel type of a chemically bound noble gas compound. The predicted species is an extended linear and periodic polymer, made of the repeat unit -(XeCC)-, where CC is the acetylenic group. The polymer has a strong partly ionic nature, with positive partial charge on the xenon atoms and a negative one on the CC groups. High energy barriers are found for the removal of a Xe atom from the chain, indicating high stability. This is the first polymer with a noble-gas-containing building block.     

To what extent can methyl derivatives be regarded as stabilized tautomers of xanthine?

Taking xanthine (Xan) as an example, validity of an approach to experimental investigations of nucleotide bases' tautomeric equilibrium, based on the use of methyl derivatives corresponding to their prototropic tautomers, was studied by (1)H NMR in dimethylsulfoxide (DMSO) and by quantum chemical calculations at the B3LYP/6-311++G(d,p) level of theory. From (1)H NMR spectra of m(7)Xan, m(9)Xan, Xan and m(3)Xan conclusion was made that the N7H tautomeric forms of the last two compounds dominate in solution, which was supported by quantum chemical data. Calculated relative energies of the N9H tautomers of Xan and m(3)Xan (8.74 and 9.57 kcal/mol, accordingly) are rather close to the m(9)Xan one (9.11 kcal/mol). Nonspecific influence of DMSO modelled by the COSMO algorithm therewith reduces these values by approximately 2-3 kcal/mol. The data obtained imply that methyl derivatives are rather good models of high-energy tautomers of nucleotide bases, if their relative energies are not less than a few kcal/mol.     

Cr(VI) adsorption mechanism on rice husk ash burned at low temperature by method of IR spectra

Boehm titration method was used to analyze functional groups on cell surface of rice husk ash burned at low temperature in the present paper. Effects of initial pH value and temperature on Cr(VI) adsorption were studied, adsorption capacity was tested with the help of kinetic models and adsorption isotherms, instruments of Fourier transform infrared spectroscopy(FTIR) and scanning electron microscope (SEM) were used to check characteristics and adsorption mechanism of Cr(VI). The results indicated that optimal removing rate was achieved at initial pH value 5, and pH values of aqueous solution changed little be fore and after adsorption process. The adsorbent of rice husk ash could remove Cr(VI) effectively, and the maximum removing rate could be 95% with Cr(VI) concentration 20 mg x L(-1) and achieve 1-2 level of state standard(GB8978-1996). The adsorption process fits pseudo-second-order kinetic model and Langmuir isotherm better, the maximum adsorption capacity of Cr(VI) was 3.2776 mg x g(-1). Results of FTIR showed that amide II band, Si--O--Si, O--Si--O were important for Cr(VI) removal. SEM micrographs revealed that series of needle-shaped precipitation appeared on cell surface, and inorganic precipitation mechanism and redox mechanism might work in the test. As a kind of low cost adsorbent, rice husk ash can be applied to remove heavy metals in environment with great potential.     

Electronic structural studies of pyrrolidinium-based ionic liquids for electrochemical application

Electrochemical stability and noncovalent interactions escorting the cyclic ammonium-based ionic liquids composed of N-alkyl-substituted N-methyl pyrrolidinium (P_yr1R) (R = methyl, ethyl, propyl, butyl, pentyl, hexyl) cations and four anions hexafluorophosphate (PF₆), tetrafluoroborate (BF₄), bis(trifluoromethylsulfonyl-imide (TFSI), and trifluoromethane sulfonate (TFO) have been analyzed using the density functional theory. Electronic structures, electrochemical window, frontier orbital energy difference (HOMO-LUMO gap), binding energies, vibrational spectra of these ion pairs were characterized. It has been established that ion pair formation is largely reigned by C H⋯F interactions between anionic fluorine for BF₄⁻ and PF₆⁻ anions and C H⋯O interactions between anionic oxygen for TFSI and TFO anions and pyrrolidinic proton, methyl, or alkyl group protons of the cations. The effect of alkyl chain length and pairing anions of the alkyl substituted N-methyl pyrrolidinium-based ionic liquids on the electrochemical window was investigated. The results revealed that the HOMO energy of pairing anions is the key factor to decide the electrochemical window. Further quantification of noncovalent interactions in terms of electrostatic and hydrogen bonding interactions has been brought out employing a novel method with the aid of Mulliken and Merz-Singh-Kollman charges, prevailed in pyrrolidinium-based ionic liquids.     

Numerical analysis of vortex dynamics and unsteady turbulent heat transfer in lid-driven square cavity

Based on the solution of unsteady Reynolds equations (URANS) closed with the aid of differential equations for shear stresses transport (MSST), the evolution of the vortex structure in a square cavity with a moving lid and an unsteady turbulent heat transfer in the air medium are computed while maintaining constant temperatures of the hot moving and cold motionless walls (Re = 5·10⁴). The phases of the development of dynamic and thermal processes are analyzed.     

Asymptotics in percolation on high‐girth expanders

We consider supercritical bond percolation on a family of high‐girth ‐regular expanders. The previous study of Alon, Benjamini and Stacey established that its critical probability for the appearance of a linear‐sized (“giant”) component is . Our main result recovers the sharp asymptotics of the size and degree distribution of the vertices in the giant and its 2‐core at any . It was further shown in the previous study that the second largest component, at any , has size at most for some . We show that, unlike the situation in the classical Erd?s‐Rényi random graph, the second largest component in bond percolation on a regular expander, even with an arbitrarily large girth, can have size for arbitrarily close to 1. Moreover, as a by‐product of that construction, we answer negatively a question of Benjamini on the relation between the diameter of a component in percolation on expanders and the existence of a giant component. Finally, we establish other typical features of the giant component, for example, the existence of a linear path.     

A 116-Nuclear Metallosupramolecular Cage-of-Cage Showing Multistep Single-Crystal-to-Single-Crystal Transformation

Here a unique single-crystal-to-single-crystal (SCSC) transformation of a 116-nuclear Au^I₇₂Cd^II₄₀Na^I₄ cage-of-cage ( 2 _CdNa) is reported, which was created from a trigold(I) metalloligand with d -penicillamine by way of a 9-nuclear Au^I₆Cd^II₃ cage ( 1 ). Cage-of-cage 2 _CdNa is composed of 12 cages of 1 that are linked by 4 Cd²⁺ and 4 Na⁺ ions, with its surface being covered by 12 NO₃⁻ ions to form a discrete, spherical molecule with a diameter ca. 4.7 nm. In crystal 2 _CdNa, the cage-of-cage molecules are packed in a cubic lattice with a huge cell volume of ca. 4.5×10⁵ ų_, so as to have large interstices with diameters of more than 3 nm. Upon soaking crystals 2 _CdNa in aqueous Cu(NO₃)₂, all Cd²⁺ and Na⁺ were quickly exchanged by Cu²⁺ to produce an analogous Au^I₇₂Cu^II₄₄ cage-of-cage ( 2 _Cu) in a SCSC manner. Prolonged soaking led to the SCSC transformation to another supramolecular structure ( 2′ _Cu) consisting of 152-nuclear Au^I₇₂Cu^II₈₀ cage-of-cages that are alternately H-bonded with the Au^I₇₂Cu^II₄₄ cage-of-cages. 2′ _Cu showed the accommodation of MoO₄²⁻ and the conversion of MoO₄²⁻ to β-Mo₈O₂₆⁴⁻ in the crystal, with retention of single-crystallinity.