On Some Three-Color Ramsey Numbers

 In this paper we study three-color Ramsey numbers. Let K _i,j denote a complete i by j bipartite graph. We shall show that (i) for any connected graphs G ₁, G ₂ and G ₃, if r(G ₁, G ₂)≥s(G ₃), then r(G ₁, G ₂, G ₃)≥(r(G ₁, G ₂)−1)(χ(G ₃)−1)+s(G ₃), where s(G ₃) is the chromatic surplus of G ₃; (ii) (k+m−2)(n−1)+1≤r(K _1,k , K _1,m , K _n )≤ (k+m−1)(n−1)+1, and if k or m is odd, the second inequality becomes an equality; (iii) for any fixed m≥k≥2, there is a constant c such that r(K _k,m , K _k,m , K _n )≤c(n/logn), and r(C _2m , C _2m , K _n )≤c(n/logn) ^m/(m−1) for sufficiently large n. Received: July 25, 2000 Final version received: July 30, 2002 RID="*" ID="*" Partially supported by RGC, Hong Kong; FRG, Hong Kong Baptist University; and by NSFC, the scientific foundations of education ministry of China, and the foundations of Jiangsu Province Acknowledgments. The authors are grateful to the referee for his valuable comments. AMS 2000 MSC: 05C55     

Effect of preparation and metal content on the introduction of Fe in BEA zeolite, studied by DR UV-vis, EPR and Mössbauer spectroscopy

Fe-containing SiBEA zeolites were prepared by a two-step postsynthesis method: creation of vacant T-sites by dealumination of tetraethylammonium BEA zeolite with nitric acid and then impregnation of the resulting SiBEA zeolite with an aqueous solution of Fe(NO₃)₃. X-ray diffraction shows that iron is incorporated in SiBEA at lattice sites. The presence of Fe in its oxidation state +3 and at isolated tetrahedral sites for low metal content, was demonstrated by diffuse reflectance UV-vis, EPR and Mössbauer spectroscopy. For high iron content, diffuse reflectance UV-vis and Mössbauer spectra revealed the additional presence of extra-lattice FeO_x oligomers and superparamagnetic Fe-oxyhydroxide. Mössbauer spectroscopy identified superparamagnetic Fe-oxyhydroxide as the main phase when basic conditions are used for the preparation.     

Synthesis of phenothiazine-functionalized porphyrins with high fluorescent quantum yields

Two porphyrins with oligo-phenothiazine arms have been synthesized by a combination of Heck and Adler reaction, and their photophysical properties have been investigated by absorption and steady-state fluorescence spectroscopy. It is found that the excitation energy transfer occurs from the phenothiazine units to the porphyrin core, and that the porphyrins can emit intense red light with high fluorescent quantum yields.     

Two novel coordination polymers [Sm2(Pzdc)3(H2O)]x · 2xH2O and [Nd2(Pzdc)3(H2O)]x · 2xH2O: Synthesis, structure, and photoluminescent properties

Coordination polymers, [Sm₂(Pzdc)₃(H₂O)] _x · 2xH₂O (I) and [Nd₂(Pzdc)₃(H₂O)] _x · 2xH₂O (II), were obtained by hydrothermal reactions with 2,3-pyrazinedicarboxylic acid (H₂Pzdc) and the salts nitrates, and characterized by single crystal X-ray structure, thermogravimetric analysis, element analysis and infrared spectroscopy. The X-ray crystal diffraction data indicates that two complexes crystal in a monoclinic system with the space group P2₁/c, of the three dimensional framework. The Pzdc ligand in the complexes I and II adopts tetradentate, hexadentate, and heptadentate bridging modes. The influences of coordination modes of the Pzdc ligand on the superstructural diversity is discussed. The photoluminescent data suggest that the ligands act as efficient “antennas” sensitizing the luminescence of the Sm³⁺ ion. Complex I exhibits strong fluorescent emission bands in the solid state at room temperature.     

Application of step-scan FTIR to the research of quantum cascade lasers

The principle of step-scan Fourier transform infrared (FTIR) spectroscopy is introduced. Double modulation step-scan FTIR technique is used to obtain the quantum cascade laser's stacked emission spectra in the time domain. Optical property and thermal accumulation of devices due to large drive current are analyzed.