A Kantorovich-type analysis of Broyden’s method using recurrent functions

We provide a semilocal convergence analysis for Broyden’s method for approximating locally unique solutions of nonlinear operator equations. Using the majorant principle we show that under the same or weaker hypotheses, in combination with our new idea of recurrent functions, we can find weaker sufficient conditions for the convergence of Broyden’s method as well as finer error bounds on the distances involved, and a more precise information on the location of the solution than before (Broyden, Math. Comput. 19:577–593, 1965; Chen, Ann. Inst. Stat. Math. 42:387–401, 1990; Dennis, Nonlinear Functional Analysis and Applications, pp. 425–472, Academic Press, San Diego, 1971; Li and Fukushima, Ann. Oper. Res. 103:71–97, 2001). Numerical examples are also provided involving polynomial, integral, and differential equations.     

掺银氧化锌纳米棒的水热法制备研究

利用水热法在直流磁控溅射制备的掺铝氧化锌 (AZO) 种子层上制备了不同形貌和光学性能的掺银ZnO纳米棒, 并采用XRD、扫描电镜、透射谱、光发射谱和EDS谱详细研究了Ag离子与Zn离子的摩尔百分比 (R_Ag/Zn) 及AZO种子层对掺银ZnO纳米棒的结构和光学性质的影响. 随着R_Ag/Zn的增加, 掺银ZnO 纳米棒的微结构和光学性质的变化与银掺杂诱导的纳米棒的端面尺寸变化有关. 平均端面尺寸的变化归结于种子层颗粒大小和颗粒数密度不同导致掺入的Ag离子的相对比例不同. 溅射15 min的AZO种子层上生长的ZnO纳米棒由于缺陷增多导致在可见光区的发光峰明显强于溅射10 min 的AZO种子层上、相同R_Ag/Zn 条件下生长的ZnO纳米棒. Ag掺杂产生的点缺陷增多导致可见光区PL波包较宽. 纯ZnO纳米棒的微结构与种子层厚度导致的结晶度和颗粒大小有关. 关键词： ZnO纳米棒 水热法 Ag掺杂 直流磁控溅射     

High Pressure Theoretical Studies of Actinide Dioxides

Actinide dioxides (ThO 2 , UO 2 , Pu 2 etc.) compounds have the CaF 2 -type structure at ambient pressure and temperature. Under high pressure, they exist in the PbCl 2 -type structure, belonging to space group Pnma [1]. We have studied crystal structures under high pressure in actinide dioxides by means of first-principles self-consistent total-energy calculations with the non-local Perdew, Burke and Ernzerhof (PBE) exchange correlation using the full-potential linear-muffin-tin-orbital (FPLMTO) method. The atomic equilibrium volume, bulk modulus and transition pressure for actinide dioxides were calculated, covering the full pressure range for which the mentioned experiments have been done [2].     

The effect of ligands on the first hyperpolarizabilities of rich d electron molecular system: iridium clusters,a TDDFT study

A systematically varied series of tetrahedral iridium clusters have been studied using a TDDFT method focusing on their electronic and nonlinear optical properties. The clusters W₂Ir₂(CO)₁₀(η⁵-C₅H₄Me)₂ (1), WIr₃(μ-dppe)(CO)₉(η⁵-C₅H₄Me (2), W₂Ir₂(μ-L)(CO)₈(η⁵-C₅H₄Me)₂(L = dppe 3, dppf 4), Ir₄(μ-L)(CO)₁₀(L = dppm 5, dppe 6, Ph₂P(CH₂)₃PPh₂ 7, Ph₂P(CH₂)₄PPh₂ 8, (Ph₂P)₂CHMe 9), Ir₄(CO)₁₀(phen)(phen = 1,10-phenanthroline) (10) exhibit the first static hyperpolarizabilities of medium magnitude (β _tot ～ 10 × 10^?30esu). The origination of β is discussed in terms of the electronic structure calculation and the expanded orbital decomposition scheme. The result suggests the origination of β for all the clusters are mainly d–d electron transitions intra metal skeleton, and d–π* electron transitions from metals to carbonyls. For cluster 5, which contains the ferrocenyl group, the main origination of β involves charge transfer from d orbitals of ferrocene to d orbirals of Ir and W.     

On extension and refinement of the Poincaré inequality

The aim of this paper is to analyze the heat semigroup ${(\mathcal{N}_{t})_{t >0 } = \{e^{t \Delta}\}_{t >0 }}$ generated by the usual Laplacian operator Δ on ${\mathbb{R}^{d}}$ equipped with the d-dimensional Lebesgue measure. We obtain and study, via a method involving some semigroup techniques, a large family of functional inequalities that does not exist in the literature and with the local Poincaré and reverse local Poincaré inequalities as particular cases. As a consequence, we establish in parallel a new functional and integral inequality related to the Ornstein–Uhlenbeck semigroup.     

One-level reformulation of the bilevel Knapsack problem using dynamic programming

In this paper, we consider the Bilevel Knapsack Problem (BKP), which is a hierarchical optimization problem in which the feasible set is determined by the set of optimal solutions for a parametric Knapsack Problem. We introduce a new reformulation of the BKP into a one-level integer programming problem using dynamic programming. We propose an algorithm that allows the BKP to be solved exactly in two steps. In the first step, a dynamic programming algorithm is used to compute the set of follower reactions to leader decisions. In the second step, an integer problem that is equivalent to the BKP is solved using a branch-and-bound algorithm. Numerical results are presented to show the performance of our method.     

Landau theory of ferroelectric transition in long cylindrical nanoparticles

Using a phenomenological Landau theory, the size dependence on ferroelectric transition for free-standing long cylindrical nanoparticles is discussed. We derive the size dependence of the transition temperature, polarization profile as well as the static susceptibility. The transition temperature vanishes below a critical size where the static susceptibility shows divergence obeying Curie-Weiss law. In order to make this result compared with experiments, the average polarization and the susceptibility is computed with a Gaussian particle size distribution. The average polarization in such a case shows smearing with respect to the particle size whereas the divergence in the susceptibilty gets rounded. This might correspond to a size dependent soft mode which can be observed in Raman measurement.     

Glycopolymers Made from Polyrotaxanes Terminated with Bile Acids: Preparation,Self‐Assembly,and Targeting Delivery

The use of natural compounds to construct biomaterials, including delivery system, is an attractive strategy. In the present study, through threading functional α‐cyclodextrins onto the conjugated macromolecules of poly(ethylene glycol) (PEG) and natural compound bile acid, glycopolymers of polyrotaxanes with the active targeting ability are obtained. These glycopolymers self‐assemble into micelles as evidenced by dynamic light scattering and transmission electron microscopy, in which glucosamine, as an example of targeting groups, is introduced. These micelles after loading doxorubicin (DOX) exhibit the selective recognition with cancer cells 4T1. Meanwhile, the maximal half inhibitory concentration is determined to be ≈2.5 mg L^?1 for the DOX‐loaded micelles, close to the value of free DOX·HCl (1.9 mg L^?1). The cumulative release of DOX at pH 5.5 is faster than at pH 7.4, which may be used as the controlled release system. This drug delivery system assembled by glycopolymers features high drug loading of DOX, superior biocompatibility. The strategy not only utilizes the micellization induced by bile acids, but also overcomes the major limitation of PEG such as the lack of targeting groups. In particular, this drug delivery platform can extend to grafting the other targeting groups, rendering this system more versatile.