Proof of a conjecture on monomial graphs

Let e be a positive integer, p be an odd prime, $q=p^e$, and ${\mathbb{F}}_q$ be the finite field of q elements. Let $f,g\in {\mathbb{F}}_q[X,Y]$. The graph $G_q(f,g)$ is a bipartite graph with vertex partitions $P={\mathbb{F}}_q^3$ and $L={\mathbb{F}}_q^3$, and edges defined as follows: a vertex $(p)=(p_1,p_2,p_3)\in P$ is adjacent to a vertex $[l]=[l_1,l_2,l_3]\in L$ if and only if $p_2+l_2=f(p_1,l_1)$ and $p_3+l_3=g(p_1,l_1)$. If $f=XY$ and $g=X{Y}^2$, the graph $G_q(XY,X{Y}^2)$ contains no cycles of length less than eight and is edge-transitive. Motivated by certain questions in extremal graph theory and finite geometry, people search for examples of graphs $G_q(f,g)$ containing no cycles of length less than eight and not isomorphic to the graph $G_q(XY,X{Y}^2)$, even without requiring them to be edge-transitive. So far, no such graphs $G_q(f,g)$ have been found. It was conjectured that if both f and g are monomials, then no such graphs exist. In this paper we prove the conjecture.     

气动八作动器隔振平台的主动隔振研究

多自由度隔振平台可以有效地隔离运载器传递到卫星的振动载荷。本文采用气动八作动器隔振平台实现卫星的六自由度隔振。首先应用牛顿欧拉法建立了气动八作动器隔振平台的动力学模型,设计了平台的主动控制律,然后对平台的主、被动隔振特性进行了仿真分析。仿真分析和实验结果显示主动隔振使平台各方向的低频隔振性能均得到改善。     

MACCEPA,The mechanically adjustable compliance and controllable equilibrium position actuator: A 3DOF joint with two independent compliances

The MACCEPA is a straightforward and easy to construct rotational actuator in which the compliance can be controlled separately from the equilibrium position. A 3DOF joint with adaptable compliance is presented. The generated torque is a linear function of the compliance and of the angle between the equilibrium position and actual position. This makes this actuator perfectly suitable for dynamic walking, human-robotic interfaces, and robotic rehabilitation devices Published in Prikladnaya Mekhanika, Vol. 43, No. 4, pp. 130–142, April 2007.     

智能结构有限元动力模型的建立及主动振动控制和抑制

采用一种新的压电板单元，建立了含有分布压电传感元件和执行元件结构（智能结构）的有限元动力模型。利用两种反馈控制律，研究了智能结构振动控制与抑制的问题，并提出了智能结构主动振动控制和抑制的一种方法。最后，提供了数值示例，说明本文提出方法的应用。     

一个新的八节点非协调曲边四边形平面单元

本文在文[1]和文[2]的基础上,提出构造非协调有限元的新方法。该方法不用一般的变分原理,可适用任意变系数正定和非正定偏微分方程。利用这一方法得到一个新的八节点四边形平面应力单元。与一般有限元相比,位移和应力可提高一阶收敛精度。形成单刚矩阵时,不需要进行数值积分。单元之间的协调条件容易满足,文中给出收敛性证明。文末给出数值算例,表明利用本文的方法,应力和位移均可获得满意的数值精度。     

Oxidation‐Responsive Aliphatic Polycarbonates from N‐Substituted Eight‐Membered Cyclic Carbonate: Synthesis and Degradation Study

Oxidation‐responsive aliphatic polycarbonates represent a promising branch of functional biodegradable polymers. This paper reports the synthesis and ring‐opening polymerization (ROP) of an eight‐membered cyclic carbonate possessing phenylboronic pinacol ester ( C3 ) and the H₂O₂‐triggered degradation of its polymer ( PC3 ). C3 is prepared from the inexpensive and readily available diethanolamine with a moderate yield and undergoes the well‐controlled anionic ROP with a living character under catalysis of 1,8‐diazabicyclo[5.4.0]undec‐7‐ene. It can also be copolymerized with l ‐lactide, trimethylene carbonate, and 5‐ter‐butyloxycarbonylamino trimethylene carbonate, affording the copolymers with a varied distribution of the repeating units. To clearly demonstrate the oxidative degradation mechanism of PC3 , this paper first investigates the H₂O₂‐induced decomposition of small‐molecule model compounds by proton nuclear magnetic resonance (¹H NMR). It is found that the adduct products formed by the in‐situ‐generated secondary amines and p‐quinone methide (QM) are thermodynamically unstable and can decompose slowly back to QM and the amines. On this basis, this paper further studies the H₂O₂‐accelerated degradation of PC3 nanoparticles that are prepared by the o/w emulsion method. A sequential process of oxidation of the phenylboronic ester, 1,6‐elimination of the in‐situ‐generated phenol, releasing CO₂ and intramolecular cyclization or isomerization is proposed as the degradation mechanism of PC3 .     

Equivalent dynamic thermoviscoelastic modeling of ionic polymers

Ionic polymers have attracted considerable attention due to their interesting sensing and actuating behavior which make them a proper choice for use in a wide range of applications including biomimetic robots and biomedical devices. The complicated electro‐chemo‐mechanical dynamics of ionic polymer actuators is a drawback for their applications in functional devices. Therefore, establishing a mathematical model which could effectively predict the actuators' dynamic behavior is of great interest. In this paper, a mathematical model, named equivalent dynamic thermoviscoelastic (EDT) model, based on thermal analogy and beam theory is proposed for dynamic analysis of bending‐type ionic polymer actuators. Then, the developed model is extended for analyzing the performance of the actuator in finite element software. The finite element analysis of the actuator enables consideration of material and geometric nonlinearities and facilitates modeling of functional devices based on the ionic polymer actuators. The proposed modeling approach is validated using experimental data. Copyright © 2015 John Wiley & Sons, Ltd.     

Towards the Design of Synthetic-jet Actuators for Full-scale Flight Conditions

Despite the proven capability of synthetic-jet actuators in delaying boundary-layer separation in laboratory experiments, a capability that allows the geometry and operating conditions of these devices to be designed and selected for maximum flow-control effectiveness in full-scale flight conditions has yet to be developed. In this two-part paper, the key results obtained during a 3-year research programme aiming at establishing such a capability based on a better understanding of the fluid mechanics of synthetic jets and an improved modelling capacity are reported. In Part 1 of this paper, the experimental studies of the behaviour of synthetic jets in both quiescent flow and a boundary layer are described. The work has led to an improved understanding of the dimensionless parameters that determine the formation and development of vortex rollup and how the strength of rollup can be enhanced by optimizing the geometry and operating condition. Based on the study of the nature of vortical structures produced as the result of the interaction with a boundary layer and their impact in the near-wall region where flow control is desired, the conditions for producing effective vortical structures for delaying flow separation were established. The finding from this work forms the basis of a number of criteria used for designing synthetic jet actuators for full-scale flight condition to be presented in Part 2.