一种通过梯形PPMgLN波导倍频实现带宽可调谐光源的理论研究

本文设计了一种梯形的周期极化掺镁铌酸锂(PPMgLN)波导,并通过在传播方向上引入温度梯度来拓宽其倍频(SHG)过程的泵浦光源可接收带宽。通过有限差分的光束传输法,计算波导的有效折射率,并进行波导尺寸的设计。结果表明,通过改变梯形波导不同位置的温度,使其形成一个温度梯度,可拓宽泵浦光源的波长可接收带宽。本文所设计的PPMgLN波导最大泵浦光源可接收带宽为C波段,即1 530~1 565 nm,该波导可倍频C波段,得到输出波段带宽为765~782.5 nm,温度调谐范围为30~150 ℃。     

On the Brauer p-dimension of Henselian discrete valued fields of residual characteristic p > 0

Let $(K,v)$ be a Henselian discrete valued field with residue field $\stackrel{?}{K}$ of characteristic $p>0$, and ${\text{Brd}}_p(K)$ be the Brauer p-dimension of K. This paper shows that ${\text{Brd}}_p(K)\ge n$ if $[\stackrel{?}{K}:{\stackrel{?}{K}}^p]=p^n$, for some $n\in \mathbb{N}$. It proves that ${\text{Brd}}_p(K)=\infty$ if and only if $[\stackrel{?}{K}:{\stackrel{?}{K}}^p]=\infty$.     

On the nature of phase separation of polymer solutions at high extension rates

Experiments with stretching moderately concentrated polymer solutions have been carried out. Model experiments were carried out for poly(acrylonitrile) solutions in dimethyl siloxane. Just the choice of concentrated solutions allowed for a clear demonstration of a demixing effect with the formation of two separate phases—an oriented polymer fiber and solvent drops sitting on its surface. An original experimental device for following all subsequent stages in the demixing process was built. It combined two light beams, one transverse to the fiber and a second directed along (inside) the fiber, the latter played the role of an optical line. This gives a unique opportunity to observe processes occurring inside a fiber. The process of demixing starts from the volume phase separation across the whole cross section of a fiber at some critical deformation and the propagation of the front of demixing along the fiber. Then a solvent cylindrical skin appears which transforms into a system of separate droplets. New experimental data are discussed based on a comparison of the current different points of view on the phenomenon of deformation‐induced phase separation: thermodynamic shift of the equilibrium phase transition temperature, growth of stress‐induced concentration fluctuations in two‐component fluids, and mechanically pressing a solvent out from a polymer network. The general belief is that a rather specific (so‐called “beads‐on‐a‐string”) structure of a filament is realized in stretching dilute solutions: beads of a polymer solution connected by oriented polymer bridges forming a single object. The situation in stretching moderately concentrated solutions appears quite different: real phase separation was observed. So, the alternative phenomenon to the formation of the “beads‐on‐a‐string” structure has been experimentally proven. © 2015 Wiley Periodicals, Inc. J. Polym. Sci., Part B: Polym. Phys. 2015 , 53, 559–565     

Gorenstein平坦模与Frobenius扩张

设R■A是环的Frobenius扩张,其中A是右凝聚环,M是任意左A-模.首先证明了_AM是Gorenstein平坦模当且仅当M作为左R-模也是Gorenstein平坦模.其次,证明了Nakayama和Tsuzuku关于平坦维数沿着Frobenius扩张的传递性定理的"Gorenstein版本":若_AM具有有限Gorenstein平坦维数,则Gfd_A(M)=Gfd_R(M).此外,证明了若R■S是可分Frobenius扩张,则任意A-模(不一定具有有限Gorenstein平坦维数),其Gorenstein平坦维数沿着该环扩张是不变的.     

Cofinal elementary extensions

We investigate some properties of ordered structures that are related to their having cofinal elementary extensions. Special attention is paid to models of some very weak fragments of Peano Arithmetic.     

The structures of the isomorphous potassium and rubidium salts of 4‐nitrobenzoic acid and an overview of the metal complex stereochemistries of the alkali metal salt series with this ligand

4‐Nitrobenzoic acid (PNBA) has proved to be a useful ligand for the preparation of metal complexes but the known structures of the alkali metal salts of PNBA do not include the rubidium salt. The structures of the isomorphous potassium and rubidium polymeric coordination complexes with PNBA, namely poly[μ₂‐aqua‐aqua‐μ₃‐(4‐nitrobenzoato)‐potassium], [K(C₇H₄N₂O₂)(H₂O)₂]_n, (I), and poly[μ₃‐aqua‐aqua‐μ₅‐(4‐nitrobenzoato)‐rubidium], [Rb(C₇H₄N₂O₂)(H₂O)₂]_n, (II), have been determined. In (I), the very distorted KO₆ coordination sphere about the K⁺ centres in the repeat unit comprise two bridging nitro O‐atom donors, a single bridging carboxylate O‐atom donor and two water molecules, one of which is bridging. In Rb complex (II), the same basic MO₆ coordination is found in the repeat unit, but it is expanded to RbO₉ through a slight increase in the accepted Rb—O bond‐length range and includes an additional Rb—O_carboxylate bond, completing a bidentate O,O′‐chelate interaction, and additional bridging Rb—O_nitro and Rb—O_water bonds. The comparative K—O and Rb—O bond‐length ranges are 2.7352 (14)–3.0051 (14) and 2.884 (2)–3.182 (2) Å, respectively. The structure of (II) is also isomorphous, as well as isostructural, with the known structure of the nine‐coordinate caesium 4‐nitrobenzoate analogue, (III), in which the Cs—O bond‐length range is 3.047 (4)–3.338 (4) Å. In all three complexes, common basic polymeric extensions are found, including two different centrosymmetric bridging interactions through both water and nitro groups, as well as extensions along c through the para‐related carboxylate group, giving a two‐dimensional structure in (I). In (II) and (III), three‐dimensional structures are generated through additional bridges involving the nitro and water O atoms. In all three structures, the two water molecules are involved in similar intra‐polymer O—H...O hydrogen‐bonding interactions to both carboxylate and water O‐atom acceptors. A comparison of the varied coordination behaviour of the full set of Li–Cs salts with 4‐nitrobenzoic acid is also made.