Rigorous bounds on the storage capacity of the dilute Hopfield model

We study a neural network model consisting ofN neurons where a dendritic connection between each pair of neurons exists with probabilityp and is absent with probability 1-p. For the Hopfield Hamiltonian on such a network, we prove that ifp c[(lnN)/N]^1/2, the model can store at leastm= _cpN patterns, where _c 0.027 ifc 3 and decreases proportional to 1/(–lnc) forc small. This generalizes the results of Newman for the standard Hopfield model.     

可变色形状记忆材料

以聚乙烯醇和单宁酸为原料制备出了形状记忆水凝胶,以乙二胺四乙酸、二水合氯化铜、六水合氯化镁、氧化铝为原料制备出了无机热致变色材料,以结晶紫内酯、硼酸、十六醇为原料制备出了有机热致变色材料,并将形状记忆材料与热致变色材料结合,成功制备出了两种既能记忆形状又能变色的新型复合高分子材料。本实验原料简单易得,方法简便,并与本科阶段有机化学、无机化学、仪器分析、精细化学品化学等课程中所学习的自由基聚合反应、化学交联、络合反应等知识结合,可作为本科教学的一个综合实验,提高学生的动手能力,激发学生学习化学的兴趣和热情。     

Molecular shape recognition capability of liquid-crystal bonded phases in reversed-phase high performance liquid chromatography

Summary The chromatographic retention behaviour of two liquidcrystal bonded phases have been evaluated using polycyclic aromatic hydrocarbons (PAHs) as the probe samples in reversed-phase high performance liquid chromatography (RP-HPLC). The results clearly indicate that these phases have better planarity and shape recognition capabilities than commercially-avaialble polymeric octadecylsilica (ODS) phases whose strong planarity and shape selectivities were found earlier. It can also be concluded from the chromatographic observations that the shape recognition capability of these phases is dependent on both mobile phase composition and column temperature, but that the effect of mobile phase and temperature on the shape selectivity work independently. The retention behaviour can be explained by changes in the phase structure with changes of eluent composition and temperature.     

Evaluation of the surface tension measurement of axisymmetric drop shape analysis (ADSA) using a shape parameter

A quantitative criterion called “shape parameter” to evaluate the quality of surface tension measurement of Axisymmetric Drop Shape Analysis (ADSA) is presented. ADSA is a powerful technique for the measurement of interfacial tensions and contact angles of pendant drops, sessile drops, and bubbles. Despite the general success of ADSA, deficient results may be obtained for drops close to spherical shape. Therefore, the “shape parameter” was used to determine the range of drop shapes in which ADSA succeeds or fails. The “shape parameter” is a dimensionless parameter that expresses quantitatively the difference in shape between a given experimental profile and an inscribed circle. The surface tension measurements of ADSA were evaluated for both pendant drop and constrained sessile drop configurations using the shape parameter. Different shapes of the pendant drop were studied using different sizes and materials of holders. For each drop configuration, a “critical shape parameter” was defined based on the minimum value of the shape parameter that guarantees an error of less than ±0.1 mJ/m². Furthermore, the effects of the type of liquid and constellation on the “critical shape parameter” were studied.     

Investigation of nu(N-H) and nu(C-N) stretching modes of propylamine (C3H7NH2) in a binary system C3H7NH2 + CH3OH via concentration dependent Raman study and ab initio calculations

Raman spectra of propylamine (C3H7NH2) and its binary mixtures, C3H7NH2 + CH3OH with varying mole fractions of the reference system, C3H7NH2, C were recorded in two widely apart wavenumber regions, 3100-3600 cm(-1) and 1225-1325 cm(-1). In the former region, the two Raman bands at approximately 3305 and approximately 3326 cm(-1), obtained after the line shape analysis, which were assigned to symmetric nu(N-H) and anti-symmetric nu(N-H) stretching modes, respectively, show a downshift upon dilution. However, whereas the nu(N-H) anti-symmetric mode shows a shift of 18.6 cm(-1), the nu(N-H) symmetric mode shows a much smaller shift (5.7 cm(-1)) between neat liquid and high dilution, C = 0.1. This aspect has been explained using the optimized geometries calculated employing ab initio theory (MP2 level) for the neat C3H7NH2 and its different hydrogen-bonded complexes. The linewidth versus concentration plot for the nu(N-H) anti-symmetric stretching mode, however exhibits a distinct maxima at C = 0.4, which has been explained as a slight departure from the concentration fluctuation model. In the latter region, a symmetric peak is observed, which corresponds to nu(C-N) stretching mode, which shows an upshift upon dilution and an almost linear concentration dependence. This has also been explained in terms of the parameters obtained from the optimized geometries of the different hydrogen-bonded complexes.     

Effect of concentration on surfactant micelle shapes —A molecular dynamics study

Many aspects of the behavior of surfactants have not been well understood due to the coupling of many different mechanisms. Computer simulation is, therefore, attractive in the sense that it can explore the effect of different mechanisms separately. In this paper, the shapes, structures and sizes of sodium dodecylbenzenesulfonate (SDBS) micelles under different concentrations in an oil/water mixture were studied via molecular dynamics (MD) simulations using a simplified atomistic model which basically maintains the hydrophile and lipophile properties of the surfactant molecules. Above the critical micellar concentration (cmc), surfactant molecules aggregate spontaneously to form a wide variety of assemblies, from spherical to rodlike, wormlike and bilayer micelles. Changes in their ratios of the principle moments of inertia (g₁/g₃, g₂/g₃) indicated the transition of micelle shapes at different concentrations. The aggregation number of micelle is found to have a power-law dependence on surfactant concentration.     

Seed‐Mediated Synthesis of Gold Tetrahedra in High Purity and with Tunable,Well‐Controlled Sizes

We report a facile synthesis of Au tetrahedra in high purity and with tunable, well‐controlled sizes via seed‐mediated growth. The success of this synthesis relies on the use of single‐crystal, spherical Au nanocrystals as the seeds and manipulation of the reaction kinetics to induce an unsymmetrical growth pattern for the seeds. In particular, the dropwise addition of a precursor solution with a syringe pump, assisted by cetyltrimethylammonium chloride and bromide at appropriate concentrations, was found to be critical to the formation of Au tetrahedra in high purity. Their sizes could be readily tuned in the range of 30–60 nm by simply varying the amount of precursor added to the reaction solution. The current strategy not only enables the synthesis of Au tetrahedra with tunable and controlled sizes but also provides a facile and versatile approach to reducing the symmetry of nanocrystals made of a face‐centered cubic lattice.     

A novel design of membrane mirror with small deformation and imaging performance analysis in infrared system

A method of diminishing the shape error of membrane mirror is proposed in this paper. The inner inflating pressure is considerably decreased by adopting the pre-shaped membrane. Small deformation of the membrane mirror with greatly reduced shape error is sequentially achieved. Primarily a finite element model of the above pre-shaped membrane is built on the basis of its mechanical properties. Then accurate shape data under different pressures can be acquired by iteratively calculating the node displacements of the model. Shape data are applicable to build up deformed reflecting surfaces for the simulative analysis in ZEMAX. Finally, ground-based imaging experiments of 4-bar targets and nature scene are conducted. Experiment results indicate that the MTF of the infrared system can reach to 0.3 at a high spatial resolution of 10l p/mm, and texture details of the nature scene are well-presented. The method can provide theoretical basis and technical support for the applications in lightweight optical components with ultra-large apertures.     

Invariance principles for hybrid systems with memory

Hybrid systems with memory are dynamical systems exhibiting both delayed and hybrid dynamics. Such systems can be described by hybrid functional inclusions. Classical invariance principles play an instrumental role in proving stability and convergence of dynamical systems. Invariance principles for general hybrid systems with delays, however, remain an open topic. In this paper, we prove invariance principles for hybrid systems with memory, using both Lyapunov–Razumikhin function and Lyapunov–Krasovskii functional methods. These invariance principles are then applied to derive two stability results as corollaries.     

聚甲基丙烯酸甲酯/星形聚乙二醇半互穿聚合物网络的形状记忆性能和分子机理

采用非共价复合方法,设计并合成了具有星形结构的聚甲基丙烯酸甲酯/星形聚乙二醇半互穿聚合物网络(PMMA/SPEG)和聚甲基丙烯酸甲酯/线性聚乙二醇半互穿聚合物网络(PMMA/LPEG).研究了PEG分子量对PMMA/SPEG和PMMA/LPEG的热性能、机械性能、动态机械性能和形状记忆性能的影响.结果表明,与PMMA/LPEG相比,星形结构的嵌入显著提高了PMMA/SPEG复合物的机械性能、形状回复率和回复速度.采用Edwards管道模型理论对其形状记忆效应的分子机理进行了阐释,利用材料的应力松弛特性对机理分析进行了验证.