A Free Boundary Problem for Some Modified Predator-Prey Model in a Higher Dimensional Environment

Applications of Mathematics - We focus on the free boundary problems for a Leslie-Gower predator-prey model with radial symmetry in a higher dimensional environment that is initially well populated...     

Face-Directed Assembly of Molecular Cubes: In Situ Substitution of a Predetermined Concave Cluster

Systematic design and self-assembly of metal–organic polyhedra with predictable configurations has been a long-standing challenge in crystal engineering. Herein a concave polyoxovanadate cluster, [V₆O₆(OCH₃)₉(SO₄)₄]⁵⁻, which can be generated in situ under specific reaction conditions, is reported. Based on this cluster, a potential trivalent molecular building block, [V₆O₆(OCH₃)₉(SO₄)(CO₂)₃]²⁻, can be obtained by the bridging-ligand-substitution strategy and it possesses appropriate angle information for the design of molecular cubes. Utilizing the face-directed assembly of the trivalent molecular building block and a diverse set of tetratopic carboxylate linkers, a series of metal–organic cubes ( VMOC-1 – VMOC-5 ) with the same topology but different functionalities and dimensions were designed and constructed. An inclusion study using VMOC-3 shows that they are potential molecular receptors for selective capture of size-matching polycyclic aromatic hydrocarbon guest molecules.     

基于ABAQUS的微细电火花超声振动主轴 仿真研究*

微细电火花技术凭借自身的特点和优势,在航空航天、医疗器械等领域发挥着重要的作用。超声振动辅助电火花加工在传统电火花加工中引入超声振动,加工精度和加工效率明显提高。作为核心部件,超声振动主轴的设计尤为重要。但传统设计过程,大大延长了研发周期和增加了成本,,因此,采用仿真方式进行研究具有重要的意义。本文对设计的微细电火花超声振动主轴的进行了仿真研究,通过ABAQUS进行了模态分析和谐响应分析,得到了超声振动主轴的谐振频率和输出振幅等参数。超声振动主轴的测试实验验证了仿真结果的正确性。     

Synthesis, structure, and luminescent property of a heterometallic metal-organic framework constructed from rod-shaped secondary building blocks

A new heterometallic MOF compound, [ZnNa(m-BDC)2].NH2(CH3)2 (MOF-CJ2), has been solvothermally synthesized and characterized by single-crystal X-ray diffraction, X-ray powder diffraction, ICP, TGA, IR, and photoluminescence spectroscopy analyses. It crystallizes in monoclinic space group C2/c (No. 15) with a=13.277(6) A, b=14.323(7) A, c=11.328(6) A, and beta=111.73(2) degrees. Its framework is constructed from M-O-C (M=Na and Zn) rods composed of alternating six-coordinated Na(I) centers and four-coordinated Zn(II) centers. These rods are linked by m-BDC links to form primitive cubic (pcu) type rod packing. This framework exemplifies the first open-framework heterometallic MOF structure based on the assembly of infinite rod building units.     

ON GRAMMATICAL COMPLEXITY OF A CLASS OF ATTRACTORS

ＯＮＧＲＡＭＭＡＴＩＣＡＬＣＯＭＰＬＥＸＩＴＹＯＦＡＣＬＡＳＳＯＦＡＴＴＲＡＣＴＯＲＳＬｕＱｉｎｈｅ（卢钦和）（ＤｅｐａｒｔｍｅｎｔｏｆＭａｔｈｅｍａｔｉｃｓ．ＳｕｚｈｏｕＵｎｉｖｅｒｓｉｔ｝＇．Ｓｕｚｈｏｕ２１５００６．Ｐ．Ｒ．Ｃｈｉｎａ）Ａｂｓｔ...     

A pilot study (APMP.QM-P19) for the measurement of melamine in milk powder

A pilot study (APMP.QM-P19) of the Asia Pacific Metrology Program for the determination of melamine at two different levels in milk powder was organized in 2010. It was the first interlaboratory comparison programme in measuring melamine in food matrices for metrology institutes in the region. Melamine was chosen as the target analyte because of the recent crises that happened in 2007 and 2008 had caused substantial concern from consumers, food manufacturers, policy makers on food safety and the food testing communities. The objectives of APMP.QM-P19 were to evaluate the testing capability of participants on the quantification of trace level melamine in milk and milk products and to investigate the degree of equivalence with respect to the assigned values. In total, 19 laboratories (11 metrology institutes and eight food testing institutes) enrolled in the study. Analytical techniques reported by participants included liquid chromatography with ultra-violet and tandem mass spectrometry, gas chromatography with high-resolution mass spectrometry and enzyme-linked immunosorbent assay. Dispersion of analytical data in the two test materials was significant, and normal Gaussian distribution of data was not observed. The median was agreed to be used as the assigned values in the programme. Metrology institutes who employed isotope dilution mass spectrometry technique were found to give more consistent results and higher degree of equivalence than others. The performance of most of the food testing institutes was not satisfactory, and they were encouraged to have a thorough review of their validation procedure and estimation of uncertainty.     

Reversed Cation Selectivity of G8‐Octamer and G16‐Hexadecamer towards Monovalent and Divalent Cations

A reverse‐binding‐selectivity between monovalent and divalent cations was observed for two different self‐assembly G₁₆‐hexadecamer and G₈‐octamer systems. The dissociation constant between G₄‐quadruplex and monomer was calculated via VT‐¹H NMR experiments. Quantitative energy profiles revealed entropy as the key factor for the weaker binding toward Ba²⁺ compared with K⁺ in the G₈‐octamer system despite stronger ion‐dipole interactions. This study is the first direct comparison of the G₄‐quartet binding affinity between mono and divalent cations and will benefit future applications of G‐quadruplex‐related research. Further competition experiments between the G₈‐octamer and 18‐crown‐6 with K⁺ demonstrated the potential of this G₈ system as a new potassium receptor.     

Chiral layered zincophosphate [d-Co(en)3]Zn3(H0.5PO4)2(HPO4)2 assembled about d-Co(en)(3)3+ complex cations

A new chiral layered zincophosphate [d-Co(en)3]Zn3(H(0.5)PO4)2(HPO4)2, designated ZnPO-CJ16, has been hydrothermally synthesized by using the optically pure chiral metal complex d-Co(en)3I3 as the template. It contains 4.6-net sheets which array in a helical fashion with an ABCDEF stacking sequence along the [001] direction. The chiral d-Co(en)3(3+) complex cations reside in the interlayer regions. Interestingly, there exist symmetrical O...H...O H-bonds between inorganic sheets, which results in a pseudo-three-dimensional open-framework structure stabilized by strong H-bonds. The crystal data are as follows: ZnPO-CJ16, [d-Co(en)3]Zn3(H(0.5)PO4)2(HPO4)2; M = 818.26; hexagonal; P6(5)22 (No. 179); a = 8.5832(12) A; c = 52.610(11) A; U = 3356.6(9) A(3); T = 293(2) K; Z = 6; R1 = 0.0415 (I > 2sigma(I)); wR2 = 0.1383 (all data); Flack parameter, 0.04(4).