Nonlinear Maps Preserving the Jordan Triple *-Product on Factor von Neumann Algebras

Let A and B be two factor von Neumann algebras. For A, B ∈ A, define by [A, B]_*= AB-BA~*the skew Lie product of A and B. In this article, it is proved that a bijective map Φ : A → B satisfies Φ([[A, B]_*, C]_*) = [[Φ(A), Φ(B)]_*, Φ(C)]_*for all A, B, C ∈ A if and only if Φ is a linear *-isomorphism, or a conjugate linear *-isomorphism, or the negative of a linear *-isomorphism, or the negative of a conjugate linear *-isomorphism.     

Fuzzy similarity-based nearest-neighbour classification as alternatives to their fuzzy-rough parallels

Fuzzy-rough sets have enjoyed much attention in recent years as an effective way in which to extend rough set theory such that it can deal with real-valued data. More recently, fuzzy-rough sets have been employed for the task of classification. This has led to the development of approaches such as fuzzy-rough nearest-neighbour (FRNN) and its extension based on vaguely-quantified rough sets (VQNN). These methods perform well and experimental evaluation demonstrates that VQNN in particular is very effective for dealing with data in the presence of noise. In this paper, the underlying mechanisms of FRNN and VQNN are investigated and analysed. The theoretical proof and empirical evaluation show that the resulting classification of FRNN and VQNN depends only upon the highest similarity and greatest summation of the similarities of each class, respectively. This fact is exploited in order to formulate the novel methods proposed in this paper: similarity nearest-neighbour (SNN) and aggregated-similarity nearest-neighbour (ASNN). These two novel approaches are equivalent to FRNN and VQNN, but do not employ the concepts or framework of fuzzy-rough sets. Instead only fuzzy similarity is used. Experimental evaluation confirms the observation that these new methods maintain the classification performance of the existing advanced fuzzy-rough nearest-neighbour-based classifiers. In addition, the underlying mathematical foundation is simplified.     

New Double Wronskian Solutions of the Whitham-Broer-Kaup System: Asymptotic Analysis and Resonant Soliton Interactions

In this paper, by the Darboux transformation together with the Wronskian technique, we construct new double Wronskian solutions for the Whitham-Broer-Kaup (WBK) system. Some new determinant identities are developed in the verification of the solutions. Based on analyzing the asymptotic behavior of new double Wronskian functions as t → ±∞, we make a complete characterization of asymptotic solitons for the non-singular, non-trivial and irreducible soliton solutions. It turns out that the solutions are the linear superposition of two fully-resonant multi-soliton configurations, in each of which the amplitudes, velocities and numbers of asymptotic solitons are in general not equal as t → ±∞. To illustrate, we present the figures for several examples of soliton interactions occurring in the WBK system.     

Effect of sulfate in mineral precursor on capacitance behavior of prepared activated carbon

Journal of Solid State Electrochemistry - Analog sulfur-containing precursors (ASCPs) were employed to prepare activated carbon (AC) for supercapacitor by potassium hydroxide (KOH) chemical...     

一类0-1背包问题算法程序的形式化推导

0-1背包问题是经典的组合优化问题与NP完全问题,具有重要的应用价值与理论意义.本文使用PAR(Partition and Recurrence)方法形式化推导了0-1背包问题的高效动态规划箅法程序.通过类比分析.该问题的若干变形问题的算法也可推导得到.算法通过PAR平台的自动生成系统转换成可执行语言程序并运行通过,保证了该类0-1背包问题算法的正确性和可靠性.本文主要的贡献是将PAR方法推广到能处理带约束条件的组合优化类问题,大大扩展了PAR方法的应用范围,为形式化开发高效高可信组合优化类算法开辟了一条新途径.     

Study of trace-element metabolism during the formation of rat's cataract

A cataract in the lenses of Wistar rats was induced by injecting Na₂SeO₃ into their bodies; they exhibited various kinds of cataract between 8 and 28 days. Samples were prepared using the method of low temperature ashing. The trace-element analyses of samples of different kinds of lenses were carried out by PIXE method. From the results obtained we have studied the ratio of their concentrations relative to the control values in relation to the formation time of cataract. It was found that the metabolites, of most trace-elements in the control lenses are stable, but in various kinds of cataractous lenses they display certain changes. Elements are clearly divided into two types. Elements of the first type are S, Cl, Ca, Fe and Zn. They appear to accumulate relative to the controls, while the second type, P, K and Rb, shows deficiency. The functions of trace-element metabolism during the formation of cataract are also discussed.     

2-Local {*}-Lie isomorphisms of operator algebras

Let \({H}\) be a complex Hilbert space of dimension greater than \({3}\). We show that every surjective 2-local \({*}\)-Lie isomorphism \({\Phi}\) of \({B(H)}\) has the form \({\Phi=\Psi+\tau}\), where \({\Psi}\) is a \({*}\)-isomorphism or the negative of a \({*}\)-anti-isomorphism of \({B(H)}\), and \({\tau}\) is a homogeneous map from \({B(H)}\) into \({\mathbb{C}I}\) vanishing on every sum of commutators.     

Lie Triple Derivable Mappings on Rings

Let ? be a ring containing a nontrivial idempotent. In this article, under a mild condition on ?, we prove that if δ is a Lie triple derivable mapping from ? into ?, then there exists a Z _{A, B} (depending on A and B) in its centre 𝒵(?) such that δ(A + B) = δ(A) + δ(B) + Z _{A, B} . In particular, let ? be a prime ring of characteristic not 2 containing a nontrivial idempotent. It is shown that, under some mild conditions on ?, if δ is a Lie triple derivable mapping from ? into ?, then δ = D + τ, where D is an additive derivation from ? into its central closure T and τ is a mapping from ? into its extended centroid 𝒞 such that τ(A + B) = τ(A) + τ(B) + Z _{A, B} and τ([[A, B], C]) = 0 for all A, B, C ∈ ?.     

Copper-catalyzed ortho-Monofluorination of Aniline Derivatives with Selectfluor Directed by Picolinic Acid Amides

A novel and facile method for selective ortho-C-H monofluorination of aniline derivatives was achieved using Selectfluor/Cu(OAc)₂/HOAc system. The reaction proceeded via electrophilic process with diverse substrates in acceptable moderate to high yields. The position selectivity was controlled by bidentate coordination of picolinic acid amides with copper.