On the convergence of an inexact Newton-type method

In this paper we give local convergence results of an inexact Newton-type method for monotone equations under a local error bound condition. This condition may hold even for problems with non-isolated solutions, and it therefore is weaker than the standard non-singularity condition.     

Electrochemically programmed, spatially selective biofunctionalization of silicon wires

A method for the spatially selective biofunctionalization of silicon micro- and nanostructures is reported, and results are presented for both single-crystal silicon (111) or (100) surfaces. An electroactive monolayer of hydroquinone was formed on the surface of H-terminated silicon working electrodes via an olefin reaction with UV-generated surface radicals. Molecules presenting either cyclopentadiene or a thiol group can be immobilized onto the regions where the hydroquinone has been oxidized. Molecular size and crystal orientation are evaluated as important factors that dictate the electrode stability in aqueous solution under anodic potentials. Monolayers composed of smaller molecules on (111) surfaces exhibit the highest packing density and are more effective in preventing anodic oxidation of the underlying substrate. Voltammetry, X-ray photoelectron spectroscopy, and atomic force and fluorescence microscopy are utilized to interrogate the kinetic rates of biofunctionalization, the extent of surface coverage, monolayer quality, and the spatial selectivity of the process.     

Efficient Algorithms for the Smallest Enclosing Ball Problem

Consider the problem of computing the smallest enclosing ball of a set of m balls in ⁿ. Existing algorithms are known to be inefficient when n > 30. In this paper we develop two algorithms that are particularly suitable for problems where n is large. The first algorithm is based on log-exponential aggregation of the maximum function and reduces the problem into an unconstrained convex program. The second algorithm is based on a second-order cone programming formulation, with special structures taken into consideration. Our computational experiments show that both methods are efficient for large problems, with the product mn on the order of 10⁷. Using the first algorithm, we are able to solve problems with n = 100 and m = 512,000 in about 1 hour.His work was supported by Australian Research Council.Research supported in part by the Singapore-MIT Alliance.     

Simulated annealing with a potential function with discontinuous gradient on Rd

In this paper, we have proven that the simulated annealing processdX _t = −β(t) ∇U (X _t ) + √2dW _tt with a potential function on R^d, of which the gradient is discontinuous, converges in probability to a neighborhood of the global minima of the potential function.     

An efficient alternating minimization method for fourth degree polynomial optimization

Journal of Global Optimization - In this paper, we consider a class of fourth degree polynomial problems, which are NP-hard. First, we are concerned with the bi-quadratic optimization problem...     

肋片板式蒸发冷凝器传热性能及优化研究

提出一种肋片板式蒸发冷凝器,主要研究肋片间距和肋片高度对工质强化传热和阻力性能的影响。计算与优化结果表明:肋片高度从12 mm增大到20 mm时,出口温度降低8.98 K,压降却增大三倍;肋片间距从40 mm增大到7 mm,温度下降1 K左右,压降减小27 Pa。应用多目标遗传算法,将"出口温度低,压降小"作为优化目标函数,研究肋片板式蒸发冷凝器的结构优化,得到优化结果的Pareto front分布,同时得到肋片间距和肋片高度分别为69.275 mm和15.71 mm,为板式蒸发冷凝器的改进和发展提供一定的指导意义。     

Preparation and up-conversion fluorescence of rare earth (Er or Yb/Er)-doped TiO2 nanobelts

Anatase TiO₂ nanobelts doped with rare earth (RE) ions Yb³⁺, Er³⁺ or Yb³⁺/Er³⁺ have been prepared using layered titanate nanobelts (LTO NBs) with RE ions as the precursor obtained by ion-exchange between LTO NBs and RE ions under hydrothermal process. Various measurement results demonstrate that the RE ions have doped into the lattice of TiO₂, and the Er³⁺ or Yb³⁺/Er³⁺ doped nanobelts show strong visible up-conversion (UC) fluorescence under 980 nm excitation. The UC emission intensity of LTO NBs embedded with Er³⁺ or Yb³⁺/Er³⁺ is slightly higher than that of the corresponding TiO₂ nanobelts doped with RE ions, whereas higher RE doping content leads to the decrease of UC emission intensity due to the concentration-quenching effect.     

Sorbitol-based supramolecular organogelators with effective phase-selective gelation and significant self-healing property

Several effective phase-selective gelators (PSGs) have been developed from a series of cheap and easy-to-make sorbitol-based compounds for the removal of many oils from their biphasic mixtures with water. The dominant factors that drive gelation have been studied using FTIR and temperature-dependent ¹H NMR spectra. Additionally, the case of PSGs exhibit significant self-healing properties that can recover the gelatin block and hence provide a more flexible approach for oil-spill recovery. The highly effective phase-selective performance and self-healing properties of these organogelators indicate the potential and promising applicability in oil-spill recovery.