Crystal structure and luminescence of a terbium complex with <Emphasis Type="Italic">p</Emphasis>-methyl benzoate and 1,10-phenanthroline

A terbium p-methyl benzoate complex with 1,10-phenanthroline, [Tb(p-MBA)₃(Phen)]₂ (p-MBA = p-methyl benzoate and Phen = 1,10-phenanthroline), has been prepared and structurally characterized by X-ray diffraction. It crystallizes in triclinic system, space group P \(\bar 1\) with a = 12.8064(12), b = 13.3589(12), c = 19.8277(19) Å, α = 91.668(2)°, β = 97.775(2)°, γ = 106.312(2)°, C₇₂H₅₈N₄O₁₂Tb₂, M _r = 1489.06, V = 3217.6(5) ų, Z = 2, ρ _c = 1.537 g/cm³, μ(MoK _α) = 2.246 mm^?1, F(000) = 1488, the final R = 0.0622 and wR = 0.0962 for 14128 independent reflections with R _int = 0.0843. It consists of two types of crystallographically independent dimeric molecules [Tb(p-MBA)₃(Phen)]₂ noted as [Tb-1] and [Tb-2]. In the dimeric molecule [Tb-1], each Tb(III) is eight-coordinated with one Phen molecule, two bridging carboxylate groups, and two bidentate chelating carboxylate groups, while in [Tb-2] each Tb(III) is eight-coordinated with one Phen molecule, four bridging carboxylate groups, and one bidentate chelating carboxylate group. The title complex shows intense green luminescence under UV light at room temperature.     

Clifford分析中κ-双正则函数的一些性质(英文)

k-双正则函数是双正则函数的推广。尽管许多k-双正则函数不是双正则函数,双正则函数的许多性质可以推广到k-双正则函数。本文研究了k-双正则函数的一些性质,包括Cauchy-Pompeiu公式,高阶Cauchy积分公式,平均值定理和级数的收敛定理。     

若干并图的优美标号

证明了,对任意大于1的自然数m,n,p,非连通图(■ V ■)∪K_(n,p)是优美图;当k≤p,m=kn+3或m=kn+1时,非连通图(P_2 V ■)∪K_(n,p)是优美图;当p≥2,m=3k+1时,非连通图(P_2 V ■)∪K_(3,p)是优美图;对任意正整数n,p,非连通图(P_1 V P_(2n+2))∪_(n,p)是优美图.     

辛空间的排列问题及具有容错能力的pooling设计的紧界

该文利用辛空间上的子空间构造了一类新的d ^z析取矩阵,然后研究了如下排列问题：对于给定的整数m, r, s,ν, d, q 和辛空间F^2ν _q中的一个(m, s) 型子空间S, 这里ν+s≥ m>r≥2s-1≥1, d≥2,q 是一个素数的幂, 作者从S中找到d个(m-1, s-1) 型子空间H₁,… H_d, 使包含在这些(m-1, s-1) 型子空间中的(r, s-1)型子空间个数达到最大. 然后利用这个排列的有关结论, 给出了一类pooling设计的紧界.     

Dynamics of a nonstandard finite-difference scheme for delay differential equations with unimodal feedback

In this article, by a nonstandard finite-difference (NSFD) scheme we study the dynamics of the delay differential equation with unimodal feedback. First, under three cases local stability of the equilibria is discussed according to Schur polynomial and Hopf bifurcation theory of discrete system. Then, the explicit algorithms for determining the direction of the Hopf bifurcation and the stability of the bifurcating periodic solutions are derived, using the normal form method and center manifold theorem. In Section 4, numerical example using Nicholson’s blowflies equation is provided to illustrate the theoretical results. Finally, it demonstrates significant superiority of nonstandard finite-difference scheme than Euler method under the means of describing approximately the dynamics of the original system.     

Indecomposable large sets of Steiner triple systems with indices 5, 6

A family ( X, B1 ), (X, B2 ), . . . , (X, Bq ) of q STS(v)s is a λ-fold large set of STS(v) and denoted by LSTS λ (v) if every 3-subset of X is contained in exactly λ STS(v)s of the collection. It is indecomposable and denoted by IDLSTS λ (v) if there does not exist an LSTS λ'(v) contained in the collection for any λ' λ. In this paper, we show that for λ = 5, 6, there is an IDLSTS λ (v) for v ≡ 1 or 3 (mod 6) with the exception IDLSTS6 (7).     

Tunable double-clad ytterbium-doped fiber laser based on a double-pass Mach-Zehnder interferometer

We have demonstrated an adjustable double-clad Yb³⁺-doped fiber laser using a double-pass Mach-Zehnder interferometer. The laser is adjustable over a range of 40 nm from 1064 nm to 1104 nm. By adjusting the state of the polarization controller, which is placed in the double-pass Mach-Zehnder interferometer, we obtained central lasing wavelengths that can be accurately tuned with controllable spacing between different tunable wavelengths. The laser has a side mode suppression ratio of 42 dB, the 3 dB spectral width is less than 0.2 nm, and the slope efficiencies at 1068 nm, 1082 nm and 1098 nm are 23%, 32% and 26%, respectively. In addition, we have experimentally observed tunable multi-wavelengths lasing output.