Demonstration of the stability or instability of multibreathers at low coupling

Whereas there exists a mathematical proof for one-site breathers stability, and an unpublished one for two-site breathers, the methods for determining the stability properties of multibreathers rely on numerical computation of the Floquet multipliers or on the weak nonlinearity approximation leading to discrete nonlinear Schrödinger equations. Here we present a set of multibreather stability theorems (MST) that provides a simple method to determine multibreathers stability in Klein–Gordon systems. These theorems are based in the application of degenerate perturbation theory to Aubry’s band theory. We illustrate them with several examples.     

Strategic commitment to price to stimulate downstream innovation in a supply chain

It is generally in a firm’s interest for its supply chain partners to invest in innovations. To the extent that these innovations either reduce the partners’ variable costs or stimulate demand for the end product, they will tend to lead to higher levels of output for all of the firms in the chain. However, in response to the innovations of its partners, a firm may have an incentive to opportunistically increase its own prices. The possibility of such opportunistic behavior creates a hold-up problem that leads supply chain partners to underinvest in innovation. Clearly, this hold-up problem could be eliminated by a pre-commitment to price. However, by making an advance commitment to price, a firm sacrifices an important means of responding to demand uncertainty. In this paper we examine the trade-off that is faced when a firm’s channel partner has opportunities to invest in either cost reduction or quality improvement, i.e. demand enhancement. Should it commit to a price in order to encourage innovation, or should it remain flexible in order to respond to demand uncertainty. We discuss several simple wholesale pricing mechanisms with respect to this trade-off.     

二茂铁有机锡衍生物的13C,119Sn NMR研究

本文测定了几种二茂铁有机锡衍生物的¹¹⁹Sn,¹³C NMR谱。对其中几种衍生物的¹³C NMR谱进行了归属,从而进一步验证了这类化合物的结构。着重讨论了结构如化合物中取代基X的改变对¹¹⁹Sn化学位移的影响。并对结构如 类化合物N→Sn异侧配位的问题进行了讨论。     

Protonation constant of salicylidene (N-benzoyl)glycyl hydrazone and its coordination behaviour towards some bivalent metal ions

Protonation constant of an unsymmetrical Schiff base, salicylidene(N-benzoyl)glycyl hydrazone (SalBzGH), and formation constants of its complexes have been determined potentiometrically at different temperatures in aqueous dioxane medium. Complexes of SalBzGH with VO(IV), Mn(II), Co(II), Ni(II), Cu(II), Zn(II), Cd(II) and Hg(II) have been prepared. Elemental analyses, pH-metric, molar conductance, magnetic susceptibility, electronic, IR, ESR, XRD (powder) and NMR studies have been carried out to study the coordination behaviour of SalBzGH toward these metal ions. pH-metric and 1H NMR studies show the presence of two dissociable protons in the ligand. IR and NMR spectra suggest the tridentate nature of the ligand, coordinating as a uninegative species in the Mn(II) complex and as a dinegative species in all the other complexes. Presence of two different conformers of the ligand at room temperature and stabilization of a single conformer upon complex formation have been established from¹H NMR spectra of the metal-free ligand, Zn(II) and Hg(II) complexes recorded at 296 K. Electronic and ESR spectra indicate highly distorted tetragonal geometry for VO(IV) and Cu(II) complexes. XRD powder patterns of the Zn(II) complexes are indexed for an orthorhombic crystal system.     

一维螺旋状3，6-哒嗪二甲酸镉(Ⅱ)配位聚合物的合成与结构

Using the ligand pyridazine-3，6-dicarboxylate (H₂pzdc)， a coordination polymer [Cd₂(pzdc)₂(H₂O)₄] was synthesized and characterized by elemental analysis， thermal analysis， IR and single-crystal X-ray diffraction. The complex crystallizes in the tetragonal system with space group I4₁/a. The crystallographic data are: a=1.470 6(4) nm， c=1.489 8(6) nm， V=3.222 0(19) nm³， Z=16， μ=2.725 mm^-1， D_c=2.594 g·cm^-3， R₁=0.017 8， wR₂=0.044 6. In the complex， the cadmium(Ⅱ) ions with the eight-coordinated dodecahedral geometry are linked by the pzdc ligands to generate one-dimensional chains， which are associated into the three-dimensional architecture via O-H…O hydrogen bonding. CCDC: 658853.     

Multinuclear magnetic resonance studies on intramolecular chalcogen-tin coordination in compounds of the type Me2Sn(X)CH2CH2P(E)Ph2 (X = Halogen, E = Chalcogen)

Multinuclear magnetic resonance data for the title compounds are presented and discussed. The intramolecular coordination observed in the solid state is shown to be retained in solution. The best probes for the presence or absence of pentacoordination at tin are provided by the various tin-element coupling constants, although chemical shifts are in some cases also informative. A selenium-proton correlated spectrum indicated that the coupling constant ¹J(Sn,Se) has a positive sign.     

糠醛缩氨基硫脲合镍配合物的合成、晶体结构及表征

合成了糠醛缩氨基硫脲的Ni(Ⅱ)单核配合物,通过红外光谱、紫外光谱、X射线单晶衍射和热重-差热分析等手段对其结构进行了表征.单晶结构解析结果表明,标题化合物属于三方晶系,R3-空间群,晶胞参数为:a=1.4097(1)nm,b=1.4097(1)nm,c=2.0952(2)nm,α=90°,β=90°,γ=120°,V=3.6059(4)nm3,Z=9,Dc=1.638Mg/m3,μ=1.488mm-1,F(000)=1818,R1=0.0231,wR2=0.0619.配合物中镍离子采用4配位的平面正方形配位构型,晶体堆积中通过分子间氢键形成三维网状结构.     

具有六重穿插非中心对称金刚石网络结构的Cd(Ⅱ)和Zn(Ⅱ)的配位高聚物(英)

利用1，4-二-(4-羧基吡啶基)丁烷(L)合成了两个新的三维配位聚合物{(CdL₂)·4H₂O·2ClO₄}_n 1和{(ZnL₂)·4H₂O·2ClO₄}_n 2。单晶X-射线结构分析表明，1和2具有相同的计量式，但其晶体属于不同的空间群(1属于P4n2，2属于P4₂22)。两种配合物中，每个金属离子分别由配体与四个相邻的金属离子连接，从而形成具有六重穿插的金刚石网络结构，其网络中大的空腔被高氯酸根离子和(H₂O)₄分子簇所占据。     

三硼酸锂晶体的生长形态

用自由生长系统研究了三硼酸锂ＬｉＢ_３Ｏ_５（ＬＢＯ）晶体的实际生长形态。实验表明，它的各晶面簇的重要性的顺序为：｛１１０｝＞｛０１１｝＞｛２０１｝＞｛１１１｝。讨论了ＬＢＯ晶体的生长习性与内部结构之间的关系并应用负离子配位多面体理论模型解释了ＬＢＯ晶体的生长形态。