Shape control of nickel selenides synthesized by a simple hydrothermal reduction process

Nickel selenide (NiSe) nanoparticles were prepared from the reaction of a SeCl₄ aqueous solution with a NiCl₂·6H₂O aqueous solution in the presence of polyvinyl alcohol (PVA) as a capping agent and hydrazine hydrate (N₂H₄·H₂O) as a reductant through a hydrothermal method. The size, morphology, chemical composition and purity of these nanoparticles depend on the capping agent, reductant, reaction temperature and time.     

线型缩聚反应的计算机模拟

缩聚反应是一类重要的高分子合成方法。其中最简单的反应为线型缩聚体系,它可分为两类,分别是含有两个可缩合的官能团的单体或单体对进行的相互缩合的体系。Flory在上世纪四十年代采用统计方法对该缩聚体系做过系统的理论研究,并在官能团等活性的假定下提出了著名的Flory分布函数,由此揭示了反应体系中数均聚合度xn、重均聚合度xw、不同聚合度分子的分布情况与反应程度p的关系。本文利用计算机模拟的方法,同样在官能团等活性的假定下模拟了线性缩聚反应的全反应过程,所得到的结果与用统计方法所得到的结果完全一致。本方法是对整个真实反应过程的直观模拟,对研究相似的以逐步聚合反应机理进行的反应具有普适性,并具有可拓展到模拟更真实的粘性聚合体系以及研究反应动力学的潜力。     

Singularities of slice regular functions

Beginning in 2006, G. Gentili and D. C. Struppa developed a theory of regular quaternionic functions with properties that recall classical results in complex analysis. For instance, in each Euclidean ball B(0, R) centered at 0 the set of regular functions coincides with that of quaternionic power series $\sum _{n \in {\mathbb {N}}} q^n a_n$ converging in B(0, R). In 2009 the author proposed a classification of singularities of regular functions as removable, essential or as poles and studied poles by constructing the ring of quotients. In that article, not only the statements, but also the proving techniques were confined to the special case of balls B(0, R). Quite recently, F. Colombo, G. Gentili and I. Sabadini (2010) and the same authors in collaboration with D. C. Struppa (2009) identified a larger class of domains, on which the theory of regular functions is natural and not limited to quaternionic power series. The present article studies singularities in this new context, beginning with the construction of the ring of quotients and of Laurent‐type expansions at points p other than the origin. These expansions, which differ significantly from their complex analogs, allow a classification of singularities that is consistent with the one given in 2009. Poles are studied, as well as essential singularities, for which a version of the Casorati‐Weierstrass Theorem is proven.     

Duality theorems on an infinite network *

We study conjugate duality for optimization problems on an infinite, but locally finite network with countable node set X and countable are set Y In contrast to earlier approaches we do not employ Hilbert or Banach space methods. Instead we work in the spaces R^X and R^Y which are siven their Droduct toDolosv, As an application we obtain generalizations of some basic inverse relations from discrete potential theory     

Optimality conditions and duality models for generalized fractional programming problems containing locally subdifferentiable and ρ:-convex functions

Both parametric and nonparametric necessary and sufficient optimality conditions are established for a class of nonsmooth generalized fractional programming problems containing ρ-convex functions. Subsequently, these optimality criteria are utilized as a basis for constructing two parametric and four parameter-free duality models and proving appropriate duality theorems. Several classes of generalized fractional programming problems, including those with arbitrary norms, square roots of positive semidefinite quadratic forms, support functions, continuous max functions, and discrete max functions, which can be viewed as special cases of the main problem are briefly discussed. The optimality and duality results developed here also contain, as special cases, similar results for nonsmooth problems with fractional, discrete max, and conventional objective functions which are particular cases of the main problem considered in this paper     

Defect generation of rutile-type SnO2 nanocondensates: Imperfect oriented attachment and phase transformation

The rutile-type SnO₂ nanocondensates as condensed by Nd-YAG laser ablation on Sn target under oxygen background gas were characterized by analytical electron microscopy to have {110}, {100} and {101} facets, which are beneficial for {∼hkl} vicinal attachment to form edge dislocations, faults and twinned bicrystals. The {011}-interface relaxation, by shearing along 〈011〉 directions, accounts for a rather high density of edge dislocations near the twin boundary thus formed. The rutile-type SnO₂ could be alternatively transformed from orthorhombic CaCl₂-type structure (denoted as o) following parallel crystallographic relationship, ()_r//()_o; [111]_r//[111]_o, and full of commensurate superstructures and twins parallel to (011) of both phases.     

Identification of target-specific bioisosteric fragments from ligand–protein crystallographic data

Bioisosteres are functional groups or atoms that are structurally different but that can form similar intermolecular interactions. Potential bioisosteres were identified here from analysing the X-ray crystallographic structures for sets of different ligands complexed with a fixed protein. The protein was used to align the ligands with each other, and then pairs of ligands compared to identify substructural features with high volume overlap that occurred in approximately the same region of geometric space. The resulting pairs of substructural features can suggest potential bioisosteric replacements for use in lead-optimisation studies. Experiments with 12 sets of ligand–protein complexes from the Protein Data Bank demonstrate the effectiveness of the procedure.     

Inscribing an axially symmetric polygon and other approximation algorithms for planar convex sets

Given a planar convex set C, we give sublinear approximation algorithms to determine approximations of the largest axially symmetric convex set S contained in C, and the smallest such set S^′ that contains C. More precisely, for any >0, we find an axially symmetric convex polygon QC with area |Q|>(1−)|S| and we find an axially symmetric convex polygon Q^′ containing C with area |Q^′|<(1+)|S^′|. We assume that C is given in a data structure that allows to answer the following two types of query in time T_C: given a direction u, find an extreme point of C in direction u, and given a line ℓ, find C∩ℓ. For instance, if C is a convex n-gon and its vertices are given in a sorted array, then T_C=O(logn). Then we can find Q and Q^′ in time O(^−1/2T_C+^−3/2). Using these techniques, we can also find approximations to the perimeter, area, diameter, width, smallest enclosing rectangle and smallest enclosing circle of C in time O(^−1/2T_C).     

Bernstein-type operators in Chebyshev spaces

We prove that it is possible to construct Bernstein-type operators in any given Extended Chebyshev space and we show how they are connected with blossoms. This generalises and explains a recent result by Aldas/Kounchev/Render on exponential spaces. We also indicate why such operators automatically possess interesting shape preserving properties and why similar operators exist in still more general frameworks, e.g., in Extended Chebyshev Piecewise spaces. We address the problem of convergence of infinite sequences of such operators, and we do prove convergence for special instances of Müntz spaces.