Topological Space of the Chemical Elements and its Properties

We carried out a mathematical study of 72 chemical elements taking advantage of the chemotopological method. We selected 128 properties to define the elements (physico-chemical, geochemical and chemical properties). Then, we looked for correlated properties and we reduced the number of them to 90. In this way we defined each element as a 90-tuple. Afterwards, we applied principal component analysis and cluster analysis (4 similarity functions and 5 grouping methodologies). Then, we calculated a consensus tree for the 20 dendrograms generated by the CA. Afterwards, we extracted the similarity relationships from the consensus tree and built up a basis for a topology on the set of chemical elements. Finally, we calculated some topological properties (closures, derived sets, boundaries, interiors and exteriors) of several subsets of chemical elements. We found that alkali metals, alkaline earth metals and noble gases appear not related to the rest of the elements. Also, we found that the boundary of non-metals are the semimetals with a stair-shape on the periodic table     

Cobalt Ion Incorporation into Periodic Mesoporous Organosilica Materials Synthesized by Co-condensation of 1,2-Bistrimethoxysilylethane with 3-Glycidoxypropyltriethoxysilane

Bifunctional periodic mesoporous organosilica materials with and without cobalt ion incorporation were synthesized by co-condensation of 1,2-bistrimethoxysilylethane (BTME) with 3-glycidoxypropyltriethoxysilane (GPTS) in the presence of cetyltrimethylammonium bromide. Nitrogen gas adsorption on samples with varying ratios of BTME:GPTS revealed that increasing the amount of GPTS affects pore size, surface area and pore volume as well as shapes of the isotherms and hysteresis loops. The hysteresis loops of the Type IV isotherms obtained for GPTS-modified ethane silica materials (without cobalt ion) change from Type H3 to Type H4 with increasing GPTS content. There is a tendency for pore sizes to change from mesopore to micropore when the amount of GPTS is increased. Isotherms of cobalt ion incorporated GPTS-modified ethane silica materials change from Type IV to Type I with increasing GPTS content. The surface area, pore volume and pore diameter decrease with increasing loading of GPTS as well as after cobalt ion incorporation. Thermogravimetric analysis and differential thermal analysis show that the surfactant is removed by solvent extraction. Cobalt ion incorporation is confirmed by powder X-ray diffraction and Raman spectroscopy.     

Uniformly non-l n (1) Musielak-Orlicz sequence spaces

We give a necessary and sufficient condition for the uniformly non-l _n ⁽¹⁾ property of Musielak-Orlicz sequence spacesl ^Φ generated by a sequence Φ=(ϕ_n:n⩾l) of finite Orlicz functions such that for eachn∈ℕ. As a result, forn ₀⩾2, there exist spacesl ^Φ which are only uniformly non-l _n ⁽¹⁾ forn⩾n ₀. Moreover we obtain a characterization of uniformly non-l _n ⁽¹⁾ and reflexive Orlicz sequence spaces over a wide class of purely atomic measures and of uniformly non-l _n ⁽¹⁾ Nakano sequence spaces. This extends a result of Luxemburg in [19]. Submitted in memory of Professor W. Orlicz     

Uniformities for the convergence in law and in probability

The convergence (X _n, Y_n)0 is investigated and characterized for probability metrics which metrize convergence in distribution or in probability. Some related metrics are also considered.     

Rare numbers

Suppose thatX ₁,X ₂,... is a sequence of iid random variables taking values inZ ⁺. Consider the random sequenceA(X)(X ₁,X ₂,...). LetY _n be the number of integers which appear exactly once in the firstn terms ofA(X). We investigate the limit behavior ofn ^–(1–) Y _n for [0, 1].     

Properties of the random search in global optimization

From theorems which we prove about the behavior of gaps in a set ofN uniformly random points on the interval [0, 1], we determine properties of the random search procedure in one-dimensional global optimization. In particular, we show that the uniform grid search is better than the random search when the optimum is chosen using the deterministic strategy, that a significant proportion of large gaps are contained in the uniformly random search, and that the error in the determination of the point at which the optimum occurs, assuming that it is unique, will on the average be twice as large using the uniformly random search compared with the uniform grid. In addition, some of the properties of the largest gap are verified numerically, and some extensions to higher dimensions are discussed. The latter show that not all of the conclusions derived concerning the inadequacies of the one-dimensional random search extend to higher dimensions, and thaton average the random search is better than the uniform grid for dimensions greater than 6.This paper is based on work started in the Statistics Department of Princeton University when the first author was visiting as a Research Associate. Part of this research was supported by the Office of Naval Research, Contract No. 0014-67-A-0151-0017, and by the US Army Research Office—Durham, Contract No. DA-31-124-ARO-D-215.2 The authors wish to thank B. Omodei for his careful work in preparing the programs for the results of Figs. 1–2 and Table 1. The computations were performed on the IBM 360/50 of the Australian National University's Computer Centre. Thanks are also due to R. Miles for suggestions regarding the extension of the results to multidimensional regions, and to P. A. P. Moran and R. Brent for suggestions regarding the evaluation of the integral ₀ ¹ ... ^0/1 (x ₁ ² + ... +x _n ^/2 )^1/2 dx ₁ ...dx _n.     

Dynamics of Hopfield-Type Neural Networks with Modulo Periodic Unpredictable Synaptic Connections,Rates and Inputs

In this paper, we rigorously prove that unpredictable oscillations take place in the dynamics of Hopfield-type neural networks (HNNs) when synaptic connections, rates and external inputs are modulo periodic unpredictable. The synaptic connections, rates and inputs are synchronized to obtain the convergence of outputs on the compact subsets of the real axis. The existence, uniqueness, and exponential stability of such motions are discussed. The method of included intervals and the contraction mapping principle are applied to attain the theoretical results. In addition to the analysis, we have provided strong simulation arguments, considering that all the assumed conditions are satisfied. It is shown how a new parameter, degree of periodicity, affects the dynamics of the neural network.     

Molecular Engineering of Quinone-Based Nickel Complexes and Polymers for All-Organic Li-Ion Batteries

All-organic Li-ion batteries appear to be a sustainable and safer alternative to the currently-used Li-ion batteries but their application is still limited due to the lack of organic compounds with high redox potentials toward Li⁺/Li⁰. Herein, we report a computational design of nickel complexes and coordination polymers that have redox potentials spanning the full voltage range: from the highest, 4.7 V, to the lowest, 0.4 V. The complexes and polymers are modeled by binding low- and high-oxidized Ni ions (i.e., Ni(II) and Ni(IV)) to redox-active para-benzoquinone molecules substituted with carboxyl- and cyano-groups. It is found that both the nickel ions and the quinone-derived ligands are redox-active upon lithiation. The type of Ni coordination also has a bearing on the redox potentials. By combining the complex of Ni(IV) with 2-carboxylato-5-cyano-1,4-benzoquinones as a cathode and Ni(II)-2,5-dicarboxylato-3,6-dicyano-1,4-benzoquinone coordination polymer as an anode, all-organic Li-ion batteries could be assembled, operating at an average voltage exceeding 3.0 V and delivering a capacity of more than 300 mAh/g.     

Nonlinear dynamical magnetosonic wave interactions and collisions in magnetized plasma

The one-dimensional nonlinear dynamical wave interactions in a system of quasineutral two-fluid plasma in a constant magnetic field are investigated.The existence of the travelling wave solutions is discussed.The modulation stability of linear waves and the modulation instability of weakly nonlinear waves are presented.Both suggest that the Korteweg-de Vries(KdV) system is modulationally stable.Besides,the wave interactions including the periodic wave interaction and the solitary wave interactio...     

离散交换群上Toeplitz算子代数的一个正合列

在引进几乎不变子集的基础上定义一般的离散交换群上的广义Toeplitz算子,研究该算子的一些性质,得到了几乎不变子集的一个刻画以及由该广义Toeplitz算子生成的C*-代数的一个正合序列。