Graphs whose critical groups have larger rank

The critical group C(G) of a graph G is a refinement of the number of spanning trees of the graph and is closely connected with the Laplacian matrix. Let r(G) be the minimum number of generators (i.e., the rank) of the group C(G) and β(G) be the number of independent cycles of G. In this paper, some forbidden induced subgraphs are given for r(G) = n − 3 and all graphs with r(G) = β(G) = n − 3 are characterized.     

固定接触界面法向静弹性刚度

基于Hertz接触理论推导了两个微凸体之间互相作用的法向接触静弹性刚度.根据修正后的一个微接触点的平截面积尺寸分布,给出了界面的总法向接触静弹性条件刚度、总条件载荷的解析解.将法向静弹性刚度的解析解嵌入到有限元软件中,获得整机的理论模态.通过实验对解析解进行了定量验证.以机床结合部为研究对象,在理论振型与实验振型一致的...     

恰有两个子群共轭类长的有限群

设G是有限群,Ns(G)表示G的子群共轭类长构成的集合.本文研究Ns(G)中只有两个元素时有限群G的结构,在非幂零情形时给出了G的完全分类,在幂零情形时获得了G的一些性质.     

M-群的正规子群

构造了一类新的可解群,使得其中的每个成员均不能同构于M-群的正规子群,推广了R.W.van der Waall关于M-群的一个类似结果.     

The critical group of <Emphasis Type="Italic">K</Emphasis><Subscript><Emphasis Type="Italic">m</Emphasis></Subscript> × <Emphasis Type="Italic">C</Emphasis><Subscript><Emphasis Type="Italic">n</Emphasis></Subscript>

In this paper, the structure of the critical group of the graph K _m × C _n is determined, where m, n ≥ 3.     

Characterization of bifurcating non-linear normal modes in piecewise linear mechanical systems

The non-linear modal properties of a vibrating 2-DOF system with non-smooth (piecewise linear) characteristics are investigated; this oscillator can suitably model beams with a breathing crack or systems colliding with an elastic obstacle. The system having two discontinuity boundaries is non-linearizable and exhibits the peculiar feature of a number of non-linear normal modes (NNMs) that are greater than the degrees of freedom. Since the non-linearities are concentrated at the origin, its non-linear frequencies are independent of the energy level and uniquely depend on the damage parameter. An analysis of the NNMs has been performed for a wide range of damage parameter by employing numerical procedures and Poincaré maps. The influence of damage on the non-linear frequencies has been investigated and bifurcations characterized by the onset of superabundant modes in internal resonance, with a significantly different shape than that of modes on fundamental branch, have been revealed.     

杆弹侵彻钢纤维混凝土实验研究

采用DOP实验方法,进行了35CrMnSiA杆弹对不同钢纤维体积含量的钢纤维混凝土的侵彻实验.分别研究了杆弹着速和钢纤维体积含量对钢纤维混凝土杭侵彻性能的影响.实验表明,随着弹速增加,不同钢纤维含量的钢纤维混凝土侵彻深度都会增加,但钢纤维混凝土中弹体便深增加较素混凝土缓慢;而钢纤维能增强混凝土的抗侵彻性能,且随钢纤维体...     

Atom Exchange Versus Reconstruction: (GexAs4−x)x− (x=2, 3) as Building Blocks for the Supertetrahedral Zintl Cluster [Au6(Ge3As)(Ge2As2)3]3−

The Zintl anion (Ge₂As₂)^2? represents an isostructural and isoelectronic binary counterpart of yellow arsenic, yet without being studied with the same intensity so far. Upon introducing [(PPh₃)AuMe] into the 1,2‐diaminoethane (en) solution of (Ge₂As₂)^2?, the heterometallic cluster anion [Au₆(Ge₃As)(Ge₂As₂)₃]^3? is obtained as its salt [K(crypt‐222)]₃[Au₆(Ge₃As)(Ge₂As₂)₃]?en?2 tol ( 1 ). The anion represents a rare example of a superpolyhedral Zintl cluster, and it comprises the largest number of Au atoms relative to main group (semi)metal atoms in such clusters. The overall supertetrahedral structure is based on a (non‐bonding) octahedron of six Au atoms that is face‐capped by four (Ge_xAs_4?x)^x? (x=2, 3) units. The Au atoms bind to four main group atoms in a rectangular manner, and this way hold the four units together to form this unprecedented architecture. The presence of one (Ge₃As)^3? unit besides three (Ge₂As₂)^2? units as a consequence of an exchange reaction in solution was verified by detailed quantum chemical (DFT) calculations, which ruled out all other compositions besides [Au₆(Ge₃As)(Ge₂As₂)₃]^3?. Reactions of the heavier homologues (Tt₂Pn₂)^2? (Tt=Sn, Pb; Pn=Sb, Bi) did not yield clusters corresponding to that in 1 , but dimers of ternary nine‐vertex clusters, {[AuTt₅Pn₃]₂}^4? (in 2 – 4 ; Tt/Pn=Sn/Sb, Sn/Bi, Pb/Sb), since the underlying pseudo‐tetrahedral units comprising heavier atoms do not tend to undergo the said exchange reactions as readily as (Ge₂As₂)^2?, according to the DFT calculations.     

A novel three‐dimensional tetranuclear CoII coordination polymer with water hexamers based on the V‐shaped tetracarboxylate ligand 4‐(2,4‐dicarboxylatophenoxy)phthalate

A new coordination polymer (CP), namely, poly[[diaquatris[μ₂‐1,4‐bis(1H‐imidazol‐1‐yl)benzene]bis[μ₆‐4‐(2,4‐dicarboxylatophenoxy)phthalato]tetracobalt(II)] hexahydrate], {[Co₄(C₁₆H₆O₉)₂(C₁₂H₁₀N₄)₃(H₂O)₂]·6H₂O}_n, has been synthesized by solvothermal reaction. The CP was fully characterized by IR spectroscopy, elemental analysis, thermogravimetric analysis, and powder and single‐crystal X‐ray diffraction. It presents a three‐dimensional (3D) structure based on tetranuclear Co^II secondary building units (SBUs) with a tfz‐d net and point symbol (4³)₂(4⁶·6¹⁸·8⁴). The 4‐(2,4‐dicarboxyphenoxy)phthalic acid (H₄dcppa) ligands are completely deprotonated and link {Co₄(COO)₄}^4? SBUs into two‐dimensional (2D) layers. Furthermore, adjacent layers are connected by 1,4‐bis(1H‐imidazol‐1‐yl)benzene (bib) ligands, giving rise to a 3D supramolecular architecture. Interestingly, there are numerous elliptical cavities in the CP where isolated unique discrete hexameric water clusters have been observed. The results of thermogravimetric and magnetic analyses are described in detail.     

推导粒子数态波函数的厄米多项式算符法

引入厄米多项式算符并用其正规乘积展开式推导出了粒子数态|n〉在坐标表象和动量表象下的波函数,并由此得出了坐标和动量本征态的福克(Fock)表示形式,这是一个简洁而全新的推导方法.