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1.
2.
The q-Catalan numbers studied by Carlitz and Riordan are polynomials in q with nonnegative coefficients. They evaluate, at q = 1, to the Catalan numbers: 1, 1, 2, 5, 14,…, a log-convex sequence. We use a combinatorial interpretation of these polynomials
to prove a q-log-convexity result. The sequence of q-Catalan numbers is not q-log-convex in the narrow sense used by other authors, so our work suggests a more flexible definition of q-log convex be adopted.
Received January 2, 2007 相似文献
3.
Ian R. Butler Alfonso G. Callabero Jennifer R. Amey Dafydd A. Thomas Thomas Gelbrich 《Tetrahedron letters》2004,45(3):467-472
The synthesis of a range of ferrocene-substituted ethynylanthracenes and 1,1′-(bis-(2-ethenylanthraquinoyl)ferrocene has been achieved. The synthesis relies on the production of ferrocenylanthraquinones as key precursors. The products were obtained in the reactions of ferrocenylanthraquinones with phenylethynyllithium or trimethylsilylethynyllithium followed by reduction with tin chloride. The key products such as 1- and 2-ferrocenyl(9,10-bis-phenylethynyl)anthracenes have been characterised by X-ray single crystal diffraction. 相似文献
4.
Thin films of polystyrene (PS), poly(methyl methacrylate) (PMMA) and polystyrene-polyacrylonitrile copolymer (PS-AN), containing various embedded transition-metal complexes, have been studied by FTIR microscopy. The spatial distributions of the transition-metal carbonyl complexes throughout the thin organic polymer films have been determined by a two-dimensional IR mapping procedure. The spectral variations observed in the distribution of the metal carbonyls throughout the different polymer films are discussed. The IR data show that the technique used to prepare the organometallic-embedded thin films (viz. freeze-drying of solutions followed by hot mechanical pressing of the residues) does in general lead to homogeneous films which may eventually find industrial application, e.g. as membrane sensors for small molecules. 相似文献
5.
T. Rajagopalan J.A. Lubguban S. Gangopadhyay J. Sun S.L. Simon R. Butler 《Applied Surface Science》2006,252(18):6323-6331
Hexamethyldisilazane (HMDS) vapor treatment of plasma-damaged nanoporous organosilicate thin films has been studied as a function of treatment temperature in this work. Although, the HMDS vapor treatment facilitated incorporation of methyl (CH3) groups subsequent to the removal of free hydroxyl (OH) groups in the damaged films at treatment temperature as low as 55 °C, the bonded OH groups were not removed. More significantly, detailed analysis of the results reveals that HMDS vapor modified only the surface of the plasma-damaged samples and not the entire film as expected. This is attributed to the formation of a thin solid layer on the surface, which effectively prevents penetration of HMDS vapors into the bulk. The Fourier transform-infrared (FT-IR) absorption and dielectric constant measurements confirm that the vapor treatment assists only partial curing of the plasma-damaged films. Alternative processes of curing the films with HMDS dissolved in supercritical carbon dioxide (SCCO2) as a medium of reaction in static and pulsed modes were also attempted and the results are presented in this paper. 相似文献
6.
A series of nitrosyl complexes of empirical formula Kn[M(CN)5NO], where M = V, Cr, Mn and Co and n = 3, or M = Mo and n = 4, have been prepared which are notional analogues of the widely used vasodilator sodium nitroprusside. Their reactivity towards common nucleophiles (OH?, NH2R, NHR2, HS? and RS?), acid and photolysis has been investigated to elucidate the desired properties required of new metal nitrosyls which may have some potential as new non-cyanide-based vasodilators. 相似文献
7.
A statistic is found to combinatorially generate the cycle-counting q-hit numbers, defined algebraically by Haglund [Adv. in Appl. Math. 17 (1996) 408–459]. We then define the notion of a cycle-Mahonian pair of statistics (generalizing that of a Mahonian statistic), and show that our newly discovered statistic is part of such a pair. Finally, we note a second example of a cycle-Mahonian pair of statistics which leads us to define the stronger property of being a cycle-Euler–Mahonian pair. 相似文献
8.
W. J. Altaf O. A. Akanle L. L. Admans D. Beasley C. Butler N. M. Spyrou 《Journal of Radioanalytical and Nuclear Chemistry》2004,259(3):493-498
The elemental composition of human hair obtained from different studies at Surrey University over a period of 25 years has
been recorded and forms part of a database, for biological and environmental samples, which is being developed. Instrumental
neutron activation analysis (INAA), using reactor neutrons, was the principal method employed and from which reported data
are presented.Elemental concentrations of Br, Ca, Ce, Cl, Co, Cr, Cs, F, Fe, Hf, K, Mg, Mn, Na, Rb, Sb, Sc, Se, V and Zn were obtained and
recorded in the database. Chronological variations in two sets of subjects separated by a period of time of 16 years are also
given. Variations in the concentration values of some elements related to the state of health and disease were reported for
hair samples collected from subjects suffering from manic depression, senile dementia and breast cancer. Concentration values
of some elements with relation to the nationality of subjects from Bulgaria, England, Kenya, Nigeria and Wales are presented
and compared. This study is part of on-going research in the analysis of biomedical and bioenvironmental materials. The database
is still in its infancy.
This revised version was published online in August 2006 with corrections to the Cover Date. 相似文献
9.
We report studies of examples of reflection-asymmetric nuclei which are difficult to access using compound nucleus reactions. The octupole radium isotopes withN>132 and radon isotopes are not accessible by reactions employing stable targets and beams; we have shown that multinucleon transfer reactions can populate these nuclei with sufficient yield for their structure to be determined. We report high-spin studies in218, 220, 222Rn and222, 224, 226, 228, 230Ra: these show that the Ra isotopes withA<228 have the characteristics of octupole deformed nuclei whereas the Rn isotopes behave like octupole vibrators. Measurements of theB(E1)/B(E2) ratios indicate that the electric dipole moment in these nuclei is constant with spin. The most octupole deformed nuclei are predicted to be uranium isotopes withN≈132; measurements of the very fissile nucleus226U suggest that it is octupole deformed and has a large intrinsic electric dipole moment. Finally, we speculate that the best examples of pear shapes are the hyperdeformed minima predicted to lie low in uranium isotopes withN≈140; their signature of high-multiplicity low-energyE1 photon cascades should be detectable using present-day high-efficiency germanium arrays. 相似文献
10.
Hyperfine Interactions - Conversion electron Mössbauer spectroscopy measurements have been made on a diamond sample synthesized by chemical vapour deposition. The sample was implanted with 70... 相似文献