给定度序列图的覆盖成本和反向覆盖成本的研究

具有n个顶点且度序列为(m,2,…,2,1,…,1)(1的重数为m)的连通图不止一个(这些图均为树),而每个树对应唯一一个段序列(l₁,l₂,…,l_m).通过对任意一树移动最长段的悬挂点到最短段悬挂点的方式得到另一树,比较前后两树的覆盖成本和反向覆盖成本,给出了具有最小覆盖成本和反向覆盖成本的极树,并且进一步给出了取得最小覆盖成本和反向覆盖成本的顶点.     

Characterization and gas adsorption of a novel three‐dimensional metal–organic framework (MOF) generated from a new polydentate fluorene‐bridged ligand

A polydentate ligand bridged by a fluorene group, namely 9,9‐bis(2‐hydroxyethyl)‐2,7‐bis(pyridin‐4‐yl)fluorene (L), has been prepared under solvothermal conditions in acetonitrile. Crystals of the three‐dimensional metal–organic framework (MOF) poly[[[μ₃‐9,9‐bis(2‐hydroxyethyl)‐2,7‐bis(pyridin‐4‐yl)fluorene‐κ³N:N′:O]bis(methanol‐κO)(μ‐sulfato‐κ²O:O′)nickel(II)] methanol disolvate], {[Ni(SO₄)(C₂₇H₂₄N₂O₂)(CH₃OH)]·2CH₃OH}_n, (I), were obtained by the solvothermal reaction of L and NiSO₄ in methanol. The ligand L forms a two‐dimensional network in the crystallographic bc plane via two groups of O—H…N hydrogen bonds and neighbouring two‐dimensional planes are completely parallel and stack to form a three‐dimensional structure. In (I), the Ni^II ions are linked by sulfate ions through Ni—O bonds to form inorganic chains and these Ni‐containing chains are linked into a three‐dimensional framework via Ni—O and Ni—N bonds involving the polydentate ligand L. With one of the hydroxy groups of L coordinating to the Ni^II atom, the torsion angle of the hydroxyethyl group changes from that of the uncoordinated molecule. In addition, the adsorption properties of (I) with carbon dioxide were investigated.     

An organoantimony nitrate complex with azastibocine framework as water tolerant Lewis acid catalyst for the synthesis of 1,2-disubstitued benzimidazoles

A novel organoantimony complex of 6-cyclohexyl-6,7-dihydrodibenzo[c,f] [1,5]azastibocin-12(5H)-yl nitrate ( 2 ) was synthesized and systematically characterized by techniques such as NMR spectra, TG-DSC, and X-ray diffraction. It was found that the complex 2 exhibits relatively strong Lewis acidity (3.3 < Ho ≤ 4.8) and could be employed as a water tolerant Lewis acid catalyst for the synthesis of synthetically valuable benzimidazole derivatives starting from aldehydes and arylenediamines. This catalytic system shows excellent tolerance toward a wide variety of functional groups, such as methyl, methoxyl, fluoro, chloro, bromo, nitro, cyan, trifluoromethyl, 1-naphthaldehyde, furfural and n-butyl, together with facile reusability in 5 times scale enlarged synthesis.     

Fast,Facile and Solvent-Free Dry-Melt Synthesis of Oxovanadium(IV) Complexes: Simple Design with High Potency towards Cancerous Cells

A range of oxobis(phenyl-1,3-butanedione) vanadium(IV) complexes have been successfully synthesized from cheap starting materials and a simple and solvent-free one-pot dry-melt reaction. This direct, straightforward, fast and alternative approach to inorganic synthesis has the potential for a wide range of applications. Analytical studies confirm their successful synthesis, purity and solid-state coordination, and we report the use of such complexes as potential drug candidates for the treatment of cancer. After a 24 hour incubation of A549 lung carcinoma cells with the compounds, they reveal cytotoxicity values elevenfold greater than cisplatin and remain non-toxic towards normal cell types. Additionally, the complexes are stable over a range of physiological pH values and show the potential for interactions with bovine serum albumin.     

Reversible Activation of Water by an Air- and Moisture-Stable Frustrated Rhodium Nitrogen Lewis Pair

[Cp*Rh(κ³N,N′,P- L )][SbF₆] (Cp*=C₅Me₅), bearing a guanidine-derived phosphano ligand L , behaves as a “dormant” frustrated Lewis pair and activates H₂ and H₂O in a reversible manner. When D₂O is employed, a facile H/D exchange at the Cp* ring takes place through sequential C(sp³)−H bond activation.     

Effects of substituents on bridging ligands on the single‐molecule magnet properties of Zn2Dy2 cluster complexes

Two new Zn₂Dy₂ complexes were constructed from Zn (II) salen‐type Schiff base complex fragment and 2,6‐pyridinedimethanol (H₂pdm) or its Br‐substituted analogue (4‐bromopyridine‐2,6‐diyl)dimethanol (H₂Brpdm); their molecular formulas are [Zn₂Dy₂(L)₂(pdm)₂(MeOH)₂](ClO₄)₂ [ 1 , H₂L = N, N′‐ bis(3‐methoxysalicylidene)‐1,3‐diaminopropane] and [Zn₂Dy₂(L)₂(Brpdm)₂(MeOH)₂](ClO₄)₂ [ 2 ], the Dy (III) ions of which have a NO₇ triangular dodecahedral coordination sphere. The two complexes show not only ferromagnetic interaction but also field‐induced single‐molecule magnet (SMM) behavior, which are rare Dy (III)‐containing cluster complexes with the NO₇ triangular dodecahedral coordination sphere that can show good magnetic relaxation. The energy barrier value of complex 2 is higher than those of complex 1 and the Dy (III) complexes with the DyNO₇ triangular dodecahedral coordination configuration reported in the literature.     

基于利他偏好的电商供应链最优决策与契约协调

构建了由一个占主导地位的电商平台和一个处于跟随地位的制造商组成的Stackelberg主从博弈模型,研究了电商平台有无利他偏好时电商供应链的最优决策和契约协调问题,并通过数值算例验证了本文的主要结论.研究表明:电商平台的利他偏好行为能够促使自身服务水平提高、正向影响制造商的最优销售价格并削弱自身利润.但电商平台的让利行为能够提高制造商的利润水平、缓和供应链冲突并改善供应链整体绩效."销售佣金比例+服务成本共担"契约能够完美的协调电商供应链,使双方最优利润获得帕累托改进,从而保证电商平台有足够的激励执行利他偏好行为.另外,进一步分析发现电商平台的利他偏好正向影响制造商支付给电商平台的固定技术服务费、制造商占有的电商供应链利润份额和服务成本分担比例,负向影响自身的销售佣金比例.     

Bis-4,4′-biphenyl Ring Embedded Octaphyrin with Three Distinct Conformational Structures

Three distinct conformational structures of carbaoctaphyrins were prepared by incorporating bis-4,4'-biphenyl units in the macrocyclic core. The free-base form adopts a figure-eight conformation, whereas the protonation triggers a conformational change with a pyrrole ring inversion and acquires an open-framework structure. The insertion of bis-Rh^I metal ion in the macrocyclic core affords a singly twisted conformational structure. Furthermore, the local aromaticity in the bis-4,4'-biphenyl ring dominates the overall macrocyclic aromaticity in all three forms, and thus adopts nonaromatic characteristics. These results are supported by spectral as well as theoretical studies, and they are unambiguously confirmed by X-ray crystal analyses.     

N → Sn coordination in the complexes of tin halides with pyridine: A comparison between Sn(II) and Sn(IV)

The experimentally well‐known complexation of tin(II) and tin(IV) halides with pyridine (py) leads to structures showing N → Sn coordination. In the present work, the complexes SnX_n·mpy (where X = F, Cl, Br, I; n = 2, 4; m = 1, 2) possessing this kind of coordination were studied using a computational quantum chemical approach. Various aspects in the theoretical picture of these complexes were examined to find similarities and differences in their N → Sn coordination. The aspects included, among others, the physical nature of intermolecular interactions, and their role in establishing the structure and energetic stabilization of the complexes. In this context, the effect of tin valency was inspected in great detail. As proven by several theoretical methods, a largely ionic character with a certain covalent component can be attributed to the studied N → Sn coordination, irrespective of tin valency. All complexes are destabilized by py‐py and three‐body interactions, but the Sn(II) complexes experience it to a greater extent. Marked differences are observed in the structural behavior of N → Sn and SnX_n during complex formation. This affects the energetics of complexation and, in consequence, the penta‐coordinated Sn(IV) center shows a higher propensity to expand its coordination number, compared with the tri‐coordinated Sn(II) center. The present study supplements the experimental characterization of SnX_n·mpy and, in general, it sheds light on the coordination of heteroaromatic nitrogen to tin. The survey of the Cambridge Structural Database revealed that such coordination occurred in a number of crystal structures.     

Syntheses and structures of two novel fluorescent metal–organic frameworks generated from a tridentate donor–acceptor motif ligand

The tridentate organic ligand 4,4′,4′′‐(4,4,8,8,12,12‐hexamethyl‐8,12‐dihydro‐4H‐benzo[9,1]quinolizino[3,4,5,6,7‐defg]acridine‐2,6,10‐triyl)tribenzoic acid ( H₃L ) has been synthesized (as the methanol 1.25‐solvate, C₄₈H₃₉NO₆·1.25CH₃OH). As a donor–acceptor motif molecule, H₃L possess strong intramolecular charge transfer (ICT) fluorescence. Through hydrogen bonds, H₃L molecules construct a two‐dimensional (2D) network, which pack together into three‐dimensional (3D) networks with an ABC stacking pattern in the crystalline state. Based on H₃L and M(NO₃)₂ salts (M = Cd and Zn) under solvothermal conditions, two metal–organic frameworks (MOFs), namely, catena‐poly[[triaquacadmium(II)]‐μ‐10‐(4‐carboxyphenyl)‐4,4′‐(4,4,8,8,12,12‐hexamethyl‐8,12‐dihydro‐4H‐benzo[9,1]quinolizino[3,4,5,6,7‐defg]acridine‐2,6‐diyl)dibenzoato], [Cd(C₄₈H₃₇NO₆)(H₂O)₃]_n, I , and poly[[μ₃‐4,4′,4′′‐(4,4,8,8,12,12‐hexamethyl‐8,12‐dihydro‐4H‐benzo[9,1]quinolizino[3,4,5,6,7‐defg]acridine‐2,6,10‐triyl)tribenzoato](μ₃‐hydroxido)zinc(II)], [Zn₂(C₄₈H₃₆NO₆)(OH)]_n, II , were synthesized. Single‐crystal analysis revealed that both MOFs adopt a 3D structure. In I , partly deprotonated HL ^2? behaves as a bidentate ligand to link a Cd^II ion to form a one‐dimensional chain. In the solid state of I , the existence of weak interactions, such as O—H…O hydrogen bonds and π–π interactions, plays an essential role in aligning 2D nets and 3D networks with AB packing patterns for I . The deprotonated ligand L ^3? in II is utilized as a tridentate building block to bind Zn^II ions to construct 3D networks, where unusual Zn₄O₁₄ clusters act as connection nodes. As a donor–acceptor molecule, H₃L exhibits fluorescence with a photoluminescence quantum yield (PLQY) of 70% in the solid state. In comparison, the PL of both MOFs is red‐shifted with even higher PLQYs of 79 and 85% for I and II , respectively.