Decomposition of ideals into pseudo-irreducible ideals

A proper ideal of a commutative ring is called pseudo-irreducible if it cannot be written as a product of two comaximal proper ideals. In this paper, we give a necessary and su?cient condition for every proper ideal of a commutative ring to be a product of pairwise comaximal pseudo-irreducible ideals. Examples of such rings include Laskerian rings, or more generally J-Noetherian rings and ZD-rings. We study when certain classes of rings satisfy this condition.     

Kantorovich variant of a new kind of q‐Bernstein–Schurer operators

Ren and Zeng (2013) introduced a new kind of q‐Bernstein–Schurer operators and studied some approximation properties. Acu et al. (2016) defined the Durrmeyer modification of these operators and studied the rate of convergence and statistical approximation. The purpose of this paper is to introduce a Kantorovich modification of these operators by using q‐Riemann integral and investigate the rate of convergence by means of the Lipschitz class and the Peetre's K‐functional. Next, we introduce the bivariate case of q‐Bernstein–Schurer–Kantorovich operators and study the degree of approximation with the aid of the partial modulus continuity, Lipschitz space, and the Peetre's K‐functional. Finally, we define the generalized Boolean sum operators of the q‐Bernstein–Schurer–Kantorovich type and investigate the approximation of the Bögel continuous and Bögel differentiable functions by using the mixed modulus of smoothness. Furthermore, we illustrate the convergence of the operators considered in the paper for the univariate case and the associated generalized Boolean sum operators to certain functions by means of graphics using Maple algorithms. Copyright © 2017 John Wiley & Sons, Ltd.     

Complete Caps in with Both N and q Odd

In this work, an inductive method to construct complete caps in affine spaces is provided. Using this tool, for odd and q odd, complete caps smaller than all already known ones are obtained.     

A Simple Homoleptic Gallium(I) Olefin Complex: Mimicking Transition‐Metal Chemistry at a Main‐Group Metal?

The earth‐metal olefin complex [Ga ^I (COD)₂]⁺[Al(OR^F)₄]^? (COD=1,5‐cyclooctadiene; R^F=C(CF₃)₃) constitutes the first homoleptic olefin complex of any main‐group metal accessible as a bulk compound. It is straight forward to prepare in good yield and constitutes an olefin complex of a main‐group metal that—similar to many transition‐metals—may adopt the +1 and +3 oxidation states opening potential applications. Crystallographic‐, vibrational‐ and computational investigations give an insight to the atypical bonding between an olefin and a main‐group metal. They are compared to classical transition‐metal relatives.     

Direct Comparison of Subvalent,Polycationic Group 13 Cluster Compounds: Lessons learned on Isoelectronic DMPE Substituted Gallium and Indium Tetracation Salts

The tetracationic, univalent cluster compounds [{M(dmpe)}₄]⁴⁺ (M=Ga, In; dmpe=bis(dimethylphosphino)ethane) were synthesized as their pf salts ([pf]⁻=[Al(OR^F)₄]⁻; R^F=C(CF₃)₃). The four-membered ring in [{M(dmpe)}₄]⁴⁺ is slightly puckered for M=Ga and almost square planar for M=In. Yet, although structurally similar, only the gallium cluster is prevalent in solution, while the indium cluster forms temperature dependent equilibria that include even the monomeric cation [In(dmpe)]⁺. This system is the first report of one and the same ligand inducing formation of isoelectronic and isostructural gallium/indium cluster cations. The system allows to study systematically analogies and differences with thermodynamic considerations and bonding analyses, but also to outline perspectives for bond activation using cationic, subvalent group 13 clusters.     

Molybdenum(VI) Bis(imido) Complexes: From Frustrated Lewis Pairs to Weakly Coordinating Cations

Molybdenum(VI) bis(imido) complexes [Mo(NtBu)₂(L^R)₂] (R=H 1 a ; R=CF₃ 1 b ) combined with B(C₆F₅)₃ ( 1 a /B(C₆F₅)₃, 1 b /B(C₆F₅)₃) exhibit a frustrated Lewis pair (FLP) character that can heterolytically split H−H, Si−H and O−H bonds. Cleavage of H₂ and Et₃SiH affords ion pairs [Mo(NtBu)(NHtBu)(L^R)₂][HB(C₆F₅)₃] (R=H 2 a ; R=CF₃ 2 b ) composed of a Mo(VI) amido imido cation and a hydridoborate anion, while reaction with H₂O leads to [Mo(NtBu)(NHtBu)(L^R)₂][(HO)B(C₆F₅)₃] (R=H 3 a ; R=CF₃ 3 b ). Ion pairs 2 a and 2 b are catalysts for the hydrosilylation of aldehydes with triethylsilane, with 2 b being more active than 2 a . Mechanistic elucidation revealed insertion of the aldehyde into the B−H bond of [HB(C₆F₅)₃]⁻. We were able to isolate and fully characterize, including by single-crystal X-ray diffraction analysis, the inserted products Mo(NtBu)(NHtBu)(L^R)₂][{PhCH₂O}B(C₆F₅)₃] (R=H 4 a ; R=CF₃ 4 b ). Catalysis occurs at [HB(C₆F₅)₃]⁻ while [Mo(NtBu)(NHtBu)(L^R)₂]⁺ (R=H or CF₃) act as the cationic counterions. However, the striking difference in reactivity gives ample evidence that molybdenum cations behave as weakly coordinating cations (WCC).     

The movement and thermal history of an aluminium particle in a RF plasma generator

In previous studies on plasma-particle interaction, as far as we know, the rf plasma flow and temperature fields are all simulated by the non-self-consistent one-dimensional electromagnetic (1-D EM) field model. In the present paper, the complete self-consistent two-dimensional electromagnetic (2-D EM) field model incorporating the axial Lorentz force component, which is neglected in the 1-D model, is firstly adopted to calculate the aluminium particle trajectory and thermal history in atmospheric rf Ar plasma with the particle evaporation effect included. The crucial effect of reverse flow within the coil region on the particle trajectory is discovered and the results show that the 2-D EM field model must be adopted instead of the 1-D model when the plasma-particle interaction is studied. The effect of carrier gas flux on the particle movement and heating are also studied, resulting in some useful conclusions for both plasma theory and application. recommended by Prof. Wu Chengkang The project supported by the National Natural Science Foundation of China     

钢-混凝土组合梁受扭性能全过程分析

在合理假定的基础上，根据混凝土、钢梁和钢筋的本构关系，利用平衡及变形协调条件，推导出了适用于组合梁受扭全过程分析的一系列方程式，并提出了组合梁受扭分析的简化算法。然后，用VC 6．0编制了分析程序，制作了输入和输出的可视化界面。最后，对实验和理论分析结果进行了对比，结果表明方法合理，精度满足要求。     

可压缩流体中封闭薄球壳的自由振动

通过引入位移函数，成功地研究了薄球壳在可压缩流体中的自由振动。发现存在两类自由振动：第一类与外界流体无关；第二类则受到流体性质的影响．证明了第二类振动的频率方程具有多项式形式并只存在复频率（除ｎ＝１时有Ω＝０）．求解ｎ＝０，１和２时的频率方程，并讨论参数的影响及给出根轨迹图。最后就小阻尼系数法作了对比分析。