平台框架部件刚度的简化计算

利用卡氏定理,对惯性平台框架部件的刚度进行简化计算。通过微机编程获得数据,为结构设计初期合理选取结构参数提供参考。     

Graceful Signed Graphs

A (p, q)-sigraph S is an ordered pair (G, s) where G = (V, E) is a (p, q)-graph and s is a function which assigns to each edge of G a positive or a negative sign. Let the sets E ⁺ and E ^– consist of m positive and n negative edges of G, respectively, where m + n = q. Given positive integers k and d, S is said to be (k, d)-graceful if the vertices of G can be labeled with distinct integers from the set {0, 1, ..., k + (q – 1)d such that when each edge uv of G is assigned the product of its sign and the absolute difference of the integers assigned to u and v the edges in E ⁺ and E ^– are labeled k, k + d, k + 2d, ..., k + (m – 1)d and –k, – (k + d), – (k + 2d), ..., – (k + (n – 1)d), respectively.In this paper, we report results of our preliminary investigation on the above new notion, which indeed generalises the well-known concept of (k, d)-graceful graphs due to B. D. Acharya and S. M. Hegde.     

一些包含Lucas数的恒等式

利用第一类Chebyshev多项式的性质以及其与Lucas数的关系得到了关于Lucas数立方的一些恒等式.     

Synthesis and characterization of 6‐ and 12‐arm star polymers by nitroxide‐mediated radical polymerization of St and MA from dendritic TIPNO‐based hexafunctional and dodecafunctional macroinitiators

Dendritic multifunctional macroinitiators having six and 12 TIPNO‐based alkoxyamines, TIPNO‐6 and TIPNO‐12 , were synthesized and used in the living radical polymerization of styrene (St), methyl acrylate (MA), N,N‐dimethylacrylamide (DMAAm), and isoprene (IP). The polymerizations of St initiated with TIPNO‐6 gave 6‐arm star polymers with narrow polydispersities of 1.14–1.18. In the polymerizations of MA initiated with TIPNO‐6 and TIPNO‐12 , the influences of added TIPNO on the polydispersity indexes (PDIs) of the resulting star polymers were first investigated, and this led to the successful formation of poly(MA) star polymers with narrow polydispersities (1.10–1.18). Moreover, the polymerizations of DMAAm and IP from TIPNO‐6 in the presence or absence of TIPNO were briefly investigated. The benzyl ether bonds of the poly(St) and poly(MA) star polymers were cleaved by treating with Me₃SiI or Pd/C, and the resulting arm's parts were analyzed with SEC. The PDIs of the resulting arm parts were low (1.19–1.23), and the M_ns agreed with the M_n,theor, indicating that the poly(St) and poly(MA) star polymers had well‐controlled arms. © 2007 Wiley Periodicals, Inc. J Polym Sci Part A: Polym Chem 45: 4364–4376, 2007     

A general Hsu-Robbins-Erdős Type estimate of tail probabilities of sums of independent identically distributed random variables

Periodica Mathematica Hungarica - Let X 1,X 2,... be a sequence of independent and identically distributed random variables, and put % MATHTYPE!MTEF!2!1!+-%...     

Maximal σ‐polynomials of connected 3‐chromatic graphs

In the set of graphs of order n and chromatic number k the following partial order relation is defined. One says that a graph G is less than a graph H if c_i(G) ≤ c_i(H) holds for every i, k ≤ i ≤ n and at least one inequality is strict, where c_i(G) denotes the number of i‐color partitions of G. In this paper the first ? n/2 ? levels of the diagram of the partially ordered set of connected 3‐chromatic graphs of order n are described. © 2003 Wiley Periodicals, Inc. J Graph Theory 43: 210–222, 2003     

一个素变数丢番图不等式

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Using the new in–in method for the synthesis of polyisoprene/polystyrene heteroarm star polymers

The basis of the two‐step in–in method is as follows: star polymers with poly(divinyl benzene) cores, synthesized by the arm‐first method, include many unreacted double bonds in their core, and these double bonds can be attacked by the carbanions of some monomers such as styrene and dienes. In this work, linear polyisoprene chains were used to attack the double bonds existing in the poly(divinyl benzene) cores of polystyrene star polymers, so that a heteroarm star polymer with polystyrene and polyisoprene arms was synthesized. It was later well characterized with size exclusion chromatography, light scattering, viscometry, UV spectroscopy, dynamic mechanical thermal analysis, and ¹H NMR. © 2002 Wiley Periodicals, Inc. J Polym Sci Part A: Polym Chem 41: 135–142, 2003     

Thermolyzable polymer networks and star polymers containing a novel,compact, degradable acylal‐based dimethacrylate cross‐linker: Synthesis,characterization, and thermolysis

A compact, cleavable acylal dimethacrylate cross‐linker, 1,1‐ethylenediol dimethacrylate (EDDMA), was synthesized from the anhydrous iron(III) chloride‐catalyzed reaction between methacrylic anhydride and acetaldehyde. The ability of EDDMA to act as cross‐linker was demonstrated by using it for the preparation of one neat cross‐linker network, four star polymers of methyl methacrylate (MMA), and four randomly cross‐linked MMA polymer networks using group transfer polymerization (GTP). For comparison, the corresponding polymer structures based on the commercially available ethylene glycol dimethacrylate (EGDMA) cross‐linker (isomer of EDDMA) were also prepared via GTP. The number of arms of the EDDMA‐based star polymers was lower than that of the corresponding EGDMA polymers, whereas the degrees of swelling in tetrahydrofuran of the EDDMA‐based MMA networks were higher than those of their EGDMA‐based counterparts. Although none of the EDDMA‐containing polymers could be cleanly hydrolyzed under basic or acidic conditions, they could be thermolyzed at 200 °C within 1 day giving lower molecular weight products. © 2007 Wiley Periodicals, Inc. J Polym Sci Part A: Polym Chem 45: 5811–5823, 2007     

Ring resonators with N × M couplers

Multiple-zero multiple-pole optical filter transfer functions may be implemented more efficiently in an integrated optics architecture if higher order N × M optical couplers are utilized. For example, a coherent ring resonator made from two 3×3 couplers offers some advantages over the three mirror Fabry-Perot etalon, which is its analog. To this end we develop the formalism for obtaining the transfer functions and scattering matrices of ring resonators made from two N × M couplers. We then present a methodology for analyzing serial and parallel systems of N × M optical coupler ring resonators.