On large sets of almost Hamilton cycle decompositions

A large set of CS(v, k, λ), k‐cycle system of order v with index λ, is a partition of all k‐cycles of K_v into CS(v, k, λ)s, denoted by LCS(v, k, λ). A (v ? 1)‐cycle is called almost Hamilton. The completion of the existence spectrum for LCS(v, v ? 1, λ) only depends on one case: all v ≥ 4 for λ = 2. In this article, it is shown that there exists an LCS(v, v ? 1,2) for any v ≡ 0,1 (mod 4) except v = 5, and for v = 6,7,10,11. © 2006 Wiley Periodicals, Inc. J Combin Designs 16: 53–69, 2008     

参数曲线的全局凸性判别条件

基于平面曲线的二次微商,导出了二重点的判别条件,结合参数曲线的局部凸性条件,得到了参数闭曲线的充要条件。给出了参数曲线的拐点判别条件,从而得到了参数曲线局部凸的充要条件。     

Construction and performance characteristics of new fentanyl-selective plastic membrane electrode.

The construction and performance characteristics of an ion-selective electrode for fentanyl-drug cation, based on an ion-pair complex with tetrakis[3,5-bis-(trifluoromethyl)phenyl]borate anion in a PVC matrix were studied. A linear response for 1 x 10(-5) mol dm-3 to 1 x 10(-2) mol dm-3 drug with a slope of 57.9 +/- 0.5 mV/decade was established. The optimum pH range was 2 to 6. The lower detection limit was 6.29 x 10(-6) mol dm-3 fentanyl citrate (2.1165 micrograms cm-3 fentanyl). There were negligible interferences from a number of inorganic cations, structural analogues, and some common drug additives in injections. The electrode proposed has been successfully applied to determine fentanyl citrate in injections. The results correlated well with those obtained by the United States Pharmacopoeia standard procedure.     

Upconversion fluorescence property of Er/Yb-codoped novel bismuth-germanium glass

Infrared-to-visible upconversion fluorescence property of Er³⁺/Yb³⁺-codoped novel bismuth-germanium glass under 975 nm LD excitation has been studied. Intense green and red emissions centered at 525, 546 and 657 nm, corresponding to the transitions ²H_11/2→⁴I_15/2, ⁴S_3/2→⁴I_15/2, and ⁴F_9/2→⁴I_15/2, respectively, were observed at room temperature. The quadratic dependence of the 525, 546 and 657 nm emissions on excitation power indicates that a two-photon absorption process occurs. The structure of the bismuth-germanium glass has been investigated by peak-deconvolution of FT-Raman spectrum, and the structural information was obtained from the peak wavenumbers. This novel bismuth-germanium glass with low maximum phonon energy (∼750 cm⁻¹) can be used as potential host material for upconversion lasers.     

Comparative investigation of up-conversion luminescence in Tm-doped oxide-chloride germanate and tellurite glasses

Tm³⁺-doped oxide-chloride germanate and tellurite glasses have been synthesized by conventional melting method. Intense up-conversion luminescence emissions were simultaneously observed at room temperature in these glasses. The possible up-conversion mechanisms are discussed and estimated. However, in these Tm³⁺-doped glasses, tellurite glass showed weaker up-conversion emissions than germanate glass, which is inconsistent with the prediction from the difference of maximum phonon energy between tellurite and germanate glasses. In this paper, Raman spectroscopy was employed to investigate the origin of the difference in up-conversion luminescence in the two glasses. Our results confirm that, besides the maximum phonon energy, the phonon density of host glasses is also an important factor in determining the up-conversion efficiency.     

Dynamics of a small vibro-impact pile driver

A mathematical model is developed to study periodic-impact motions and bifurcations in dynamics of a small vibro-impact pile driver. Dynamics of the small vibro-impact pile driver can be analyzed by means of a three-dimensional map, which describes free flight and sticking solutions of the vibro-impact system, between impacts, supplemented by transition conditions at the instants of impacts. Piecewise property and singularity are found to exist in the Poincaré map. The piecewise property is caused by the transitions of free flight and sticking motions of the driver and the pile immediately after the impact, and the singularity of map is generated via the grazing contact of the driver and the pile immediately before the impact. These properties of the map have been shown to exhibit particular types of sliding and grazing bifurcations of periodic-impact motions under parameter variation. The influence of piecewise property, grazing singularities and parameter variation on the performance of the vibro-impact pile driver is analyzed. The global bifurcation diagrams for the impact velocity of the driver versus the forcing frequency are plotted to predict much of the qualitative behavior of the actual physical system, which enable the practicing engineer to select excitation frequency ranges in which stable period one single-impact response can be expected to occur, and to predict the larger impact velocity and shorter impact period of such response.     

Study on Chromium‐Containing Aluminophosphate CrAPO‐5 via Density Functional Theory

Various structures of CrAPO‐5 clusters are studied via density functional B3LYP exchange‐correlation method. The optimized structures are compared with data from X‐ray absorption. Their total energies and atomic net charges are also analyzed. Results indicate that the substitution of the aluminum site of an AFI framework by chromium is in general not feasible. The chromium ion is more likely docked in between two neighboring 12‐membered rings of the framework of AFI. To further verify our claim, the excitation energies of the representative chromium structures of CrAPO‐5 clusters are calculated via the TDDFT method. The results for excitation energies further support that Cr³⁺ is not incorporated into the framework.     

Synthesis, structure and physicochemical characterization of a noncentrosymmetric, quaternary thiostannate: EuCu2SnS4

EuCu₂SnS₄ was prepared by a stoichiometric combination of the elements heated to 700 °C for 125 h. The structure was determined by single crystal X-ray diffraction methods. The compound crystallizes in the noncentrosymmetric, orthorhombic space group Ama2 with a=10.4793(1) Å, b=10.3610(2) Å, c=6.4015(1) Å, Z=4, R1=0.99% and wR2=2.37%. The structure type is that of SrCu₂GeSe₄. The structure can be described as a three-dimensional network built from near perfect SnS₄ and distorted CuS₄ tetrahedra together with EuS₈ square antiprisms. The dark red compound is a semiconductor with an optical bandgap of 1.85 eV.