Symmetric and antisymmetric tight wavelet frames

For a given set of wavelets Ψ, we provide a general, and yet simple, method to derive a new set of wavelets ${\Psi }^{\prime }$ such that each wavelet in ${\Psi }^{\prime }$ is either symmetric or antisymmetric. The affine system generated by ${\Psi }^{\prime }$ is a tight frame for the space $L_2({\mathbb{R}}^d)$ whenever the affine system generated by Ψ is so. Further, when Ψ is constructed via a multiresolution analysis, ${\Psi }^{\prime }$ can also be derived from a, but possibly different, multiresolution analysis. If moreover the multiresolution analysis for constructing Ψ is generated by a symmetric refinable function, then ${\Psi }^{\prime }$ is obtained from the same multiresolution analysis.     

1,1‐Diphenyl Ethylene‐Mediated Radical Polymerisation: A General Non‐Metal‐Based Technique For The Synthesis Of Precise Core Cross‐Linked Star Polymers

This communication details the successful synthesis of low polydispersity core cross‐linked star (CCS) polymers via DPE‐mediated polymerisation. We demonstrate the ability to produce poly(methyl methacrylate) and poly(acrylonitrile) CCS polymers that are currently inaccessible via the two most common non‐metal‐based controlled radical polymerisation techniques (NMP and RAFT polymerisations).

     

New thioether–dithiolate complexes of Cp1Ir and some reactivity features

The reaction of [Cp1IrCl₂]₂ (Cp* = η⁵ ? C₅Me₅) with the tridentate 3-thiapentane-1,5-dithiolate ligand, S(CH₂CH₂S^?)₂ (tpdt), led to the formation of [Cp1Ir(η³ ? tpdt)] (1) in 81% isolated yield. Subsequent reactions of 1 with [Cp1IrCl₂]₂ in 2:1 and 1:1 molar equiv ratios resulted in the formation of [Cp1Ir(μ ? η²:η³ ? tpdt)Cp1IrCl][PF₆] (2) and [Cp1Irμ ? η²:η³ ? tpdt)Cp1IrCl][Cp1IrCl₃] (3) in 86 and 79% yields, respectively, based on 1, whereas the reactions of 1 with [(COD)IrCl]₂ (COD = 1,5-cyclooctadiene) in 2:1 and 1:1 molar equiv ratios resulted in the formation of the homo-bimetallic derivatives Cp1Ir(μ ? η¹:η³ ? tpdt)(COD)IrCl (4) (92% yield) and [Cp1Ir(μ ? η²:η³ ? tpdt)(COD)Ir] [(COD)IrCl₂] (5) (82% yield). Reactions between 1 and [(COD)RhCl]₂, yielded the hetero-bimetallic derivatives Cp1Ir(μ ? η¹:η³ ? tpdt)(COD)RhCl (6) and [Cp1Ir(μ ? η²:η³ ? tpdt)(COD)Rh][(COD)RhCl₂] (7), in 92 and 93% yields, respectively. The reaction of 1 with methyl iodide gave mono-methylated derivative [Cp1Ir(η³-C₄H₈S₃Me)]I (8) (93% yield). All these compounds have been comprehensively characterized.     

Portfolio value-at-risk optimization for asymmetrically distributed asset returns

We propose a new approach to portfolio optimization by separating asset return distributions into positive and negative half-spaces. The approach minimizes a newly-defined Partitioned Value-at-Risk (PVaR) risk measure by using half-space statistical information. Using simulated data, the PVaR approach always generates better risk-return tradeoffs in the optimal portfolios when compared to traditional Markowitz mean–variance approach. When using real financial data, our approach also outperforms the Markowitz approach in the risk-return tradeoff. Given that the PVaR measure is also a robust risk measure, our new approach can be very useful for optimal portfolio allocations when asset return distributions are asymmetrical.     

Pre-treatment of multi-walled carbon nanotubes for polyetherimide mixed matrix hollow fiber membranes

A facile and bio-inspired route for the preparation of pure and highly crystalline metastable α-AgVO(3) is presented. Three kinds of proteins (bovine hemoglobin, bovine serum albumin, and lysozyme) were employed as inducer, which had substantial effects on the nucleation and growth of α-AgVO(3). Moreover, the amount of proteins also played a key role over the morphology and crystalline of products. The VO(3)(-)/protein complex acted as a driver to induce the formation of metastable phase, which was confirmed by resonance Rayleigh scattering and UV-vis absorption spectra. The results indicated that tailoring an interaction between protein and inorganic molecules was the key in bio-inspired selective synthesis of metastable phase, which may find applications in the design of other new functional inorganic materials.     

Structural and photoluminescence investigation on the hot-wire assisted plasma enhanced chemical vapor deposition growth silicon nanowires

High density of silicon nanowires (SiNWs) were synthesized by a hot-wire assisted plasma enhanced chemical vapor deposition technique. The structural and optical properties of the as-grown SiNWs prepared at different rf power of 40 and 80 W were analyzed in this study. The SiNWs prepared at rf power of 40 W exhibited highly crystalline structure with a high crystal volume fraction, X_C of ～82% and are surrounded by a thin layer of SiO_x. The NWs show high absorption in the high energy region (E>1.8 eV) and strong photoluminescence at 1.73 to 2.05 eV (red–orange region) with a weak shoulder at 1.65 to 1.73 eV (near IR region). An increase in rf power to 80 W reduced the X_C to ～65% and led to the formation of nanocrystalline Si structures with a crystallite size of <4 nm within the SiNWs. These NWs are covered by a mixture of uncatalyzed amorphous Si layer. The SiNWs prepared at 80 W exhibited a high optical absorption ability above 99% in the broadband range between 220 and ～1500 nm and red emission between 1.65 and 1.95 eV. The interesting light absorption and photoluminescence properties from both SiNWs are discussed in the text.     

Three-dimensional bin packing problem with variable bin height

This paper studies a variant of the three-dimensional bin packing problem (3D-BPP), where the bin height can be adjusted to the cartons it packs. The bins and cartons to be packed are assumed rectangular in shape. The cartons are allowed to be rotated into any one of the six positions that keep the carton edges parallel to the bin edges. This greatly increases the difficulty of finding a good solution since the search space expands significantly comparing to the 3D-BPP where the cartons have fixed orientations. A mathematical (mixed integer programming) approach is modified based on [Chen, C. S., Lee, S. M., Shen, Q. S., 1995. An analytical model for the container loading problem. European Journal of Operational Research 80 (1), 68–76] and numerical experiments indicate that the mathematical approach is not suitable for the variable bin height 3D-BPP. A special bin packing algorithm based on packing index is designed to utilize the special problem feature and is used as a building block for a genetic algorithm designed for the 3D-BPP. The paper also investigates the situation where more than one type of bin are used and provides a heuristic for packing a batch of cartons using the genetic algorithm. Numerical experiments show that our proposed method yields quick and satisfactory results when benchmarked against the actual packing practice and the MIP model with the latest version of CPLEX.     

On solving the chaotic Chen system: a new time marching design for the variational iteration method using Adomian’s polynomial

This paper centres on the effectiveness of the variational iteration method and its modifications for numerically solving the chaotic Chen system, which is a three-dimensional system of ODEs with quadratic nonlinearities. This research implements the multistage variational iteration method with an emphasis on the new multistage hybrid of variational iteration method with Adomian polynomials. Numerical comparisons are made between the multistage variational iteration method, the multistage variational iteration method using the Adomian’s polynomials and the classic fourth-order Runge-Kutta method. Our work shows that the new multistage hybrid provides good accuracy and efficiency with a performance that surpasses that of the multistage variational iteration method.     

A predictive gradient strategy for multiobjective evolutionary algorithms in a fast changing environment

An essential feature of a dynamic multiobjective evolutionary algorithm (MOEA) is to converge quickly to the Pareto-optimal Set before it changes. In cases where the behavior of the dynamic problem follows a certain trend, convergence can be accelerated by anticipating the characteristics of future changes in the problem. A prediction model is usually used to exploit past information and estimate the location of the new Pareto-optimal Set. In this work, we propose the novel approach of tracking and predicting the changes in the location of the Pareto Set in order to minimize the effects of a landscape change. The predicted direction and magnitude of the next change, known as the predictive gradient, is estimated based on the history of previously discovered solutions using a weighted average approach. Solutions updated with the predictive gradient will remain in the vicinity of the new Pareto-optimal Set and help the rest of the population to converge. The prediction strategy is simple to implement, making it suitable for fast-changing problems. In addition, a new memory technique is introduced to exploit any periodicity in the dynamic problem. The memory technique selects only the more promising stored solutions for retrieval in order to reduce the number of evaluations used. Both techniques are incorporated into a variant of the multi-objective evolutionary gradient search (MO-EGS) and two other MOEAs for dynamic optimization and results indicate that they are effective at improving performance on several dynamic multiobjective test problems.     

Optimal Two-commodity Flows with Non-linear Cost Functions

We consider networks in which two different commodities have to be transported across undirected arcs, subject to a shared capacity on the arcs. For each arc and commodity there is an associated non-linear cost that depends on the amount of the commodity transported across the arc. The aim is to minimize the sum of the costs over all arcs and commodities. Efficient algorithms for solving this problem for two types of objective functions will be presented: in the first the cost depends on the absolute value of the flow and in the second the cost is a quadratic function of the flow. Previous work on multi-commodity flow has concentrated on linear cost problems or tackled non-linear cost problems with Lagrangian relaxation methods and other more general techniques. The algorithms in this paper, on the other hand, provide a very efficient way of dealing with two types of non-linear two-commodity optimal flow problems.