混合范数空间中函数的Taylor系数

本文研究了混合范数空间Ｈ（ｐ，ｑ，ａ）中解析函数ｆ的Ｔａｙｌｏｒ系数，对０＜ｐ≤２，０＜ｑ＜∞，ａ＞０和２≤ｐ＜∞，０＜ｑ＜∞，ａ＞０两种情形，分别给出了ｆ属于Ｈ（ｐ，ｑ，ａ）的必要条件和充分条件。用上述结果我们还得到了几个关于混合范数空间的乘子定理，这些结果也推广了Ｈａｒｄｙ和Ｌｉｔｔｌｅｗｏｏｄ关于Ｈ＾ｐ空间的相应结论。     

Low-dimensional Compounds Containing Cyano Groups. XIII. Structural–spectral Correlation of Copper Dicyanoargentates

The new mixed-valence mixed-metal complex Cu(py)₆Cu₂Ag₂(CN)₆ (py = pyridine) possesses a three dimensional polymeric crystal structure. The Cu(I) atom is tetrahedrally coordinated by two nitrogen atoms of pyridine molecules, by one nitrogen atom of the dicyanoargentate anion and by one carbon atom of the cyano group. Both the dicyanoargentate anion and the cyano group bridge the Cu(I) atom with neighboring Cu(II) atoms. These are hexacoordinated in the form of an elongated tetragonal bipyramid. The equatorial plane is formed by two nitrogen atoms from two pyridine molecules and two nitrogen atoms from bridging cyano groups. Axial positions are occupied by nitrogen atoms of the bridging [Ag(CN₂]⁻ anions. Correlation between structures of the title compound and seven other dicyanoargentates with their i.r. spectra has been studied. The coordination mode of [Ag(CN₂]⁻ anions in compounds Cu_8-xAg_x(tn)₃(CN)₁₀ x = 0.25, Cu(3-Mepy)₂Ag₂(CN)₄, Cu(py)₂Ag₂(CN)₄ and Cu(py)₄Ag₂(CN)₄ (tn is 1,3-diaminopropane, 3-Mepy is 3-methylpyridine) is predicted based on this correlation.     

Solutions of logarithmic type for elliptic and hypoelliptic equations

LetK be an algebraically closed field withp:=char (K)>0 andX a bielliptic curve over Spec(K) with genus≥6 and such that the canonical model ofX is ordinary. In this paper we determine all the possible gap sequences of Weierstrass points on such curves.     

Processes associated with ionic current rectification at a 2D-titanate nanosheet deposit on a microhole poly(ethylene terephthalate) substrate

Films of titanate nanosheets (approx. 1.8-nm layer thickness and 200-nm size) having a lamellar structure can form electrolyte-filled semi-permeable channels containing tetrabutylammonium cations. By evaporation of a colloidal solution, persistent deposits are readily formed with approx. 10-μm thickness on a 6-μm-thick poly(ethylene-terephthalate) (PET) substrate with a 20-μm diameter microhole. When immersed in aqueous solution, the titanate nanosheets exhibit a p.z.c. of − 37 mV, consistent with the formation of a cation conducting (semi-permeable) deposit. With a sufficiently low ionic strength in the aqueous electrolyte, ionic current rectification is observed (cationic diode behaviour). Currents can be dissected into (i) electrolyte cation transport, (ii) electrolyte anion transport and (iii) water heterolysis causing additional proton transport. For all types of electrolyte cations, a water heterolysis mechanism is observed. For Ca²⁺ and Mg²⁺ions, water heterolysis causes ion current blocking, presumably due to localised hydroxide-induced precipitation processes. Aqueous NBu₄⁺ is shown to ‘invert’ the diode effect (from cationic to anionic diode). Potential for applications in desalination and/or ion sensing are discussed.

     

On the derivation of the entropy of ideal quantum gases confined in a three-dimensional harmonic potential

In this work,the entropy functions of ideal quantum gases in a three-dimensional harmonic trap are analytically calculated using temperature as an explicit variable.Afterward,the applicability of the analytical formulas is validated by comparison with the numerical calculation.The results illustrate that the obtained functions could be applied for the whole temperature regime with a maximum relative deviation of less than 7.5%in the vicinity of the critical temperature Tcin the case of Bose gases.Meanwhile,for Fermi gases,although the analytical formula fits well at very low-and high-temperature regimes,it cannot be applied at temperature in the range[0.3-0.5]T_F,where T_F is the Fermi temperature.In addition,the consistency between our formulas and classical ones at significantly high temperatures is also discussed.     

Generating Function of the Tilings of an Aztec Rectangle with Holes

We consider a generating function of the domino tilings of an Aztec rectangle with several unit squares removed from the boundary. Our generating function involves two statistics: the rank of the tiling and half number of vertical dominoes as in the Aztec diamond theorem by Elkies, Kuperberg, Larsen and Propp. In addition, our work deduces a combinatorial explanation for an interesting connection between the number of lozenge tilings of a semihexagon and the number of domino tilings of an Aztec rectangle.     

Synthesis and Evaluation of Chalcone Derivatives as Novel Sunscreen Agent

Ultraviolet (UV) irradiation is a serious problem for skin health thus the interest in the research to develop sunscreen agent has been increasing. Chalcone is a promising compound to be developed as its chromophore absorbs in the UV region. Therefore, in the present work, we synthesized eight chalcone derivatives through Claisen–Schmidt condensation at room temperature. The evaluation of the optical properties of each chalcone derivatives in the UV region was conducted through spectroscopic and computational studies. The synthesized chalcones were obtained in good yields and they were active in the UV region. The results revealed that more methoxy substituents to chalcone leads toward red shift. All chalcone derivatives have high molar absorptivity value (21,000–56,000) demonstrating that they have the potential to be used as the sunscreen agent. The cytotoxicity assay showed that chalcone derivatives were demonstrating low toxicity toward normal human fibroblast cell, which is remarkable. Therefore, we concluded that the synthesized chalcones in this work were potential to be developed as novel sunscreen agents in real application.     

Electronic structures of NbGen−/0/+ (n = 1–3) clusters from multiconfigurational CASPT2 and density matrix renormalization group-CASPT2 calculations

Density functional theory and multiconfigurational CASPT2 and density matrix renormalization group DMRG-CASPT2 have been employed to study the low-lying states of NbGe_n^−/0/+ (n = 1–3) clusters. With the DMRG-CASPT2 method, the active spaces are extended to a size of 20 orbitals. For most of the states, the CASPT2 relative energies are comparable with the DMRG-CASPT2 results. The leading configuration, bond distances, vibrational frequencies, and relative energies of the low-lying states of these clusters were calculated. The ground states of these clusters were computed to be ³Δ, ⁴Φ, and ⁵Φ of NbGe^−/0/+; ³A₂, ⁴B₁, and ³B₁ of cyclic-NbGe₂^−/0/+; and ¹A′, 1²A″ and 1²A′′ (²E), and ³A″ of tetrahedral-NbGe₃^−/0/+ isomers. For NbGe cluster, our calculations proposed that the ⁶∑ is almost degenerate with the ⁴Φ with the CASPT2 and DMRG-CASPT2 relative energies of 0.05 and 0.06 eV. The adiabatic detachment energies of NbGe_n⁻ (n = 1–3) clusters were estimated to be 1.46, 1.55, and 2.18 eV by the CASPT2 method. The relevant detachment energies of the anionic ground state and the ionization energies of the neutral ground states are evaluated at the CASPT2 level.     

Fourier transform and smoothness of solutions of a class of semilinear elliptic degenerate equations with double characteristics

This paper is a continuation of our earlier note [V. T. T. Hien and N. M. Tri, “Analyticity of Solutions of Semililnear Equations with Double Characteristics,” J. Math. Anal. Appl. 337, 1249–1260 (2008)]. Here we prove the analyticity of solutions of a class of semilinear elliptic degenerate equations with double characteristics by using the Fourier transform.     

Metallabis(phosphonate) als Chelatliganden. II. Synthese und Reaktivität ein- und zweikerniger Palladiumbis(phosphonat)-Komplexe mit OHO- und OBF2O-Brückenbindungen

Metallabisphosphonates as Chelating Ligands. II. Synthesis and Reactivity of Mono- and Binuclear Palladiumbisphosphonate Complexes Containing OHO and OBF₂O Bridges The complexes C₅H₅Pd[{P(OR)₂O}₂H] ( 1 : R = Me; 2 : R = Et) are formed either by reaction of C₅H₅Pd(2-MeC₃H₄) with dimethyl- and diethylphosphite or by reaction of [ClPd{P(OR)₂O}₂H]₂ ( 3 : R = Me; 4 : R = Et) with TlC₅H₅. With excess HP(O)(OMe)₂, the π-allyl complex (2-MeC₃H₄)Pd[{P(OMe)₂O}₂H] ( 5 ) is also formed (besides 1 ) from C₅H₅Pd(2-MeC₃H₄). The ¹H and ³¹P n.m.r. spectra indicate that in 1 – 5 the PdP₂O₂H chelate ring presumably contains a symmetrical OHO-hydrogen bond. The reaction of 3 with BF₃ etherate leads to the binuclear complex [ClPd{P(OMe)₂O}₂BF₂]₂ ( 6 ) which reacts with TlC₅H₅ to yield C₅H₅Pd[{P(OMe)₂O}₂BF₂] ( 7 ). From C₅H₅Pd[{P(OR)₂O}₂H] ( 1 , 2 ) and NH₃ the bisamminepalladium bisphosphonates(NH₃)₂Pd[P(OR)₂O]₂ ( 8 , 9 ) are formed which probably possess a trans-configuration. The reaction of 8 , 9 with CF₃COOH does not lead to a corresponding Pd[{P(OR)₂O}₂H] chelate complex but instead gives by elimination of NH₃ polymeric palladium bisphosphonates [Pd{P(OR)₂O}₂]_n ( 10 , 11 ). 1 reacts with thallium acetylacetonate to give C₅H₅Pd[P(OMe)₂O]₂Tl ( 12 ).