Singular perturbed Markov chains and exact behaviors of simulated annealing processes

We study asymptotic properties of discrete and continuous time generalized simulated annealing processesX(·) by considering a class of singular perturbed Markov chains which are closely related to the large deviation of perturbed diffusion processes. Convergence ofX(t) in probability to a setS ₀ of desired states, e.g., the set of global minima, and in distribution to a probability concentrated onS ₀ are studied. The corresponding two critical constants denoted byd and withd are given explicitly. When the cooling schedule is of the formc/logt, X(t) converges weakly forc>0. Whether the weak limit depends onX(0) or concentrates onS ₀ is determined by the relation betweenc, d, and . Whenc>, the expression for the rate of convergence for each state is also derived.     

Synthesis and structure of a novel three-dimensional metal selenite containing multidirectional intersecting double helical chains: [Fe2(H2O)4(SeO3)2]

A novel three-dimensional metal selenite [Fe₂(H₂O)₄(SeO₃)₂] (1) has been hydrothermally synthesized and characterized by the elemental analyses, IR spectrum, TG analysis and the single crystal X-ray diffraction. Compound 1 crystallizes in the monoclinic system, space group P21/n, with a=6.5283(13) Å, b=8.8754(18) Å, c=7.6798(15) Å, (=98.82(3)β, V=439.71(15) Å3, and Z=2. Compounds 1 exhibits interesting three-dimensional structure constructed from {FeO₆} octahedra and {SeO₃} pyramids linked via the corner- and/or edge-sharing mode. The most interesting structural feature of compound 1 is that the existence of multidirectional intersecting double helical chains in one compound.     

Synthesis of thiol chelating resins and their adsorption properties toward heavy metal ions

A series of chelating resins, derived from a macroreticular styrene-divinylbenzene (2%) copolymer beads grafted with various poly(ethylene glycols) HO? (? CH₂? CH₂? O? )_n? H(n = 0, 4, 9, 13) and containing thiol groups as chelating functions, have been synthesized in a three-step reaction sequence. The structure of the functionalized resins was confirmed by IR spectrophotometry, elemental analysis, and differential scanning calorimetry. The complexation behavior of these thiol resins was investigated towards Hg(II), Cu(II), and Pb(II) ions in aqueous solution by a batch equilibration technique. The influence of pH on adsorption capacity was also examined. The adsorption values for metal ions' intake followed the order Hg(II) > Cu(II) > Pb(II). The affinity of these polymers towards Hg(II) ions was so high that the total mercury level in the liquid decreased from 20 ppm to below 10 ppb after 2 h of treatment. Polymers can be regenerated by washing with a solution of hydrochloric acid (6N) and 10% by weight of an aqueous solution of thiourea. © 1994 John Wiley & Sons, Inc.     

Syntheses and Crystal Structures of Two Metal Succinates Modified by Bipyridines

Two new metal succinates modified by rigid bipyridines, Cd(4, 4′‐bpy)(C₄H₄O₄)·1/4H₂O ( 1 ) and Cu(2, 2′‐bpy)(C₄H₄O₄)_0.5(NO₃)(H₂O) ( 2 ) (bpy = bipyridine), have been synthesized by hydrothermal reactions and structurally determined. Complex 1 crystallizes in the orthorhombic space group Cmca with the cell parameters a = 11.696(2), b = 15.554(2), c = 15.874(3) Å, α = β = γ = 90.00°, V = 2888(3) ų, Z = 8. Complex 2 crystallizes in the triclinic space group with a = 7.077(1), b = 9.838(2), c = 10.461(2) Å, α = 71.941(3)°, β = 73.078(3)°, γ = 74.502(3)°, V = 649.8(2) ų, Z = 2. In complex 1 , a 2‐D network was formed by Cd‐succinato bonding. The 2‐D networks are pillared by 4, 4′‐bpy ligands, forming a 3‐D grid framework. The 2‐fold interpenetration of the resulting 3‐D frameworks completes the molecular structure. In complex 2 , the Cu^II atom adopts a distorted octahedral in which the Cu^II atoms are bridged by two H₂O molecules into an infinite zigzag chain, [Cu₂(H₂O)₂(C₄H₄O₄)]_n. The neighboring chains are further linked by π‐π stacking interactions into a 2‐D network, and the interlayer hydrogen bonds lead to the final 3‐D crystal structure.     

基于电子商务的集群式供应链跨链库存控制

以电子商务环境下集群式供应链库存控制为对象,建立了时变需求下跨链合作的交叉库存模型,并用H∞控制中抑制外部干扰的对策理论来寻求最优订货策略,以减小库存、订货波动和提高供需网快速响应市场的能力.文中采用对比分析方法分别针对供应链间有合作与无合作情形对模型做了仿真实验,仿真表明,实施H∞控制和交叉紧急库存补充策略可以有效避免货物积压或缺货现象,提高供应链及集群的竞争力.     

One-pot ligation strategy for atypical ubiquitin chains synthesis by using the trifluoroacetamidomethyl-protected isopeptide-linked Ub (Tfacm-isoUb) unit

Protein chemical synthesis can provide the homogeneous atypical ubiquitin chains that are usually difficult to obtain by other methods. Herein, we report a new one-pot ligation approach for the synthesis of atypical Ub chains based on the Tfacm-protected isoUb building block with operational simplicity and high efficiency. The key intermediate, the Tfacm-protected isoUb building block can be readily prepared by Fmoc SPPS. The practicality and efficiency of the new method is demonstrated by the successful preparation of K11-linked di-Ub.     

Direct Proof of Determinant Representation for Scalar Products of the XXZ Gaudin Model with Generic Non-Diagonal Boundary Terms

After constructing the Bethe state of the XXZ Gaudin model with generic non-diagonal boundary terms,we analyze the properties of this state and obtain the determinant representations of the scalar products for this XXZ Gaudin model.