Notes on pedal and contrapedal curves of fronts in the Euclidean plane

A pedal curve (a contrapedal curve) of a regular plane curve is the locus of the feet of the perpendiculars from a point to the tangents (normals) to the curve. These curves can be parametrized by using the Frenet frame of the curve. Yet provided that the curve has some singular points, the Frenet frame at these singular points is not well‐defined. Thus, we cannot use the Frenet frame to examine pedal or contrapedal curves. In this paper, pedal and contrapedal curves of plane curves, which have singular points, are investigated. By using the Legendrian Frenet frame along a front, the pedal and contrapedal curves of a front are introduced and properties of these curves are given. Then, the condition for a pedal (and a contrapedal) curve of a front to be a frontal is obtained. Furthermore, by considering the definitions of the evolute, the involute, and the offset of a front, some relationships are given. Finally, some illustrated examples are presented.     

Thermal Methods in the Synthesis of New Ordered Mesoporous Adsorbents

The synthesis of new ordered mesoporous adsorbents, specifically of the MCM-41 type, involves a step of thermal elimination of the template (a surfactant) where CRTA is shown to provide a 'soft chemistry' route. Once the mesoporous (i.e. 2 to 50 nm pore width) material is obtained, the pore size is determined by thermoporometry, a convenient application for low temperature DSC. Finally, the hydrophobic - hydrophilic properties of the pore walls are explored by immersion microcalorimetry in water. This revised version was published online in July 2006 with corrections to the Cover Date.     

On H‐immersions

For a fixed multigraph H, possibly containing loops, with V(H) = {h₁,…, h_k}, we say a graph G is H‐linked if for every choice of k vertices v₁,…,v_k in G, there exists a subdivision of H in G such that v_i represents h_i (for all i). An H‐immersion in G is similar except that the paths in G, playing the role of the edges of H, are only required to be edge disjoint. In this article, we extend the notion of an H‐linked graph by determining minimum degree conditions for a graph G to contain an H‐immersion with a bounded number of vertex repetitions on any choice of k vertices. In particular, we extend results found in [2,3,5]. © 2007 Wiley Periodicals, Inc. J Graph Theory 57: 245–254, 2008     

硼酸和γ—氧化铝作为Lewis酸性固体模型物的热化学研究

本文用热化学方法研究某些ⅢA族元素的含氧化合物与多种有机碱类的相互作用,试建立Lewis酸性的固体模型,探讨复相酸碱反应的机理。硼酸在室温是一种稳定的固体酸,在水溶液中的酸性来源于水中OH~-离子在中心硼原子上的配位,而不是硼酸分子自身解离给出质子。这显示了典型的Lewis酸性。固体硼酸也可能成为一个Lewis酸的固体模型。与硼同族的     

Calorimetric determination of activated carbons in aqueous solutions

The interactions among five samples of activated carbons, obtained from different lignocellulosic materials with different degrees of activation of approximately 20% and aqueous solutions of phenol and 4-nitro phenol are studied by means of the determination of immersion enthalpies. It is established that the obtained activated carbons are of a basic character and show values for the pH at the point of zero charge, pH_PZC, that range from 7.4 to 9.7 and, in all cases, higher total basicity contents than the values obtained for total acidity. The immersion heat of the activated carbons in CCl₄ and water is determined obtaining values which are higher for CCl₄ immersion and vary from 31.4 to 48.6 J g⁻¹. The hydrophobic factor, hf, it is calculated from the relation between of the immersion heat of the activated carbons in CCl₄ and the immersion heat in water, the obtained values were 2.98 and 6.75, which are greater than 1 due to the greater values obtained in CCl₄ when compared to the values obtained in water. Immersion enthalpies in phenol solution range from 7.6 to 13.9 J g⁻¹ and for the case of 4-nitro phenol such enthalpies range from 12.7 to 20.5 J g⁻¹; all the 5 samples studied showed a higher value for the heat of immersion in aqueous solutions of 4-nitro phenol.     

半球形固体浸没透镜显微系统的透射光场研究

应用高数值孔径系统的矢量衍射理论研究了半球形固体浸没透镜(SIL)球面表面的反射对SIL系统透射场的影响.研究结果表明,半球形SIL球面表面的反射对SIL显微系统的透射光强产生很大的影响.然而,这种反射不改变半球形SIL显微系统的分辨率.SIL球面介质界面材料的折射率失配越大,透射光强减小越多.在SIL的球面表面涂上减反膜或者在物镜和SIL之间填充折射率较大（但比SIL的折射率小）的介质可以提高系统的透射光强.     

表面凹陷对等离子体浸没离子注入均匀性的影响

利用二维流体模型和数值计算方法模拟了等离子体浸没离子注入（ＰⅢ）Ｋ ,具有圆弧凹槽的平面靶周围的鞘层扩展情况,计算了鞘层扩展过程中的电热分布、离子速度和离子密度变化获得了沿靶表面的离子入射角度和注入剂量的分布情况,为等离子体浸没离子注入处理复杂形状靶提供了理论基础。     

On nonpositively curved Euclidean submanifolds: splitting results

In this article, we prove that a n–dimensional, non–positively curved Euclidean submanifold with codimension p and with minimal index of relative nullity is (in an open dense subset) locally the product of p hypersurfaces. Received: October 21, 1997     

铝表面前处理及化学沉积镍初期行为

利用开路电位-时间(EOCP-t)曲线,研究铝表面经浸镍和化学预镀镍前处理后,化学沉积镍的初期行为;通过扫描电子显微镜(SEM)观察铝表面经前处理后的表面形貌.结果表明:未经及经前处理的铝表面,化学沉积镍的初期行为都经历去氧化膜、活化、混合控制以及化学沉积过程.经过浸镍和化学预镀镍前处理后的铝表面附着细小的镍颗粒.依据EOCP-t和SEM的最佳实验结果,在含有络合剂和还原剂的碱性预镀镍溶液中,经二次化学预镀镍前处理,成功实现铝基底弱酸性化学镀镍.所获得的化学镀镍层与铝基底结合牢固,呈团颗粒状形貌和非晶态结构.     

Structural, mechanical and hydrophobic properties of fluorine-doped diamond-like carbon films synthesized by plasma immersion ion implantation and deposition (PIII–D)

Fluorine-doped diamond-like carbon (a-C:F) films with different fluorine content were fabricated on Si wafer by plasma immersion ion implantation and deposition (PIII–D). Film composition and structure were characterized by X-ray photoelectron spectroscopy (XPS) and Raman scattering spectroscopy. Surface morphology and roughness were analyzed by atomic force microscopy (AFM). Hardness and scratch resistance were measured by nano-indentation and nano-scratch, respectively. Water contact angles were measured by sessile drop method. With the increase of the CF₄ flux, fluorine content was gradually increased to the film. Raman spectra indicates that these films have a diamond-like structure. The addition of fluorine to diamond-like carbon films had a critical influence on the film properties. The film surface becomes more smoother due to the etching behavior of F⁺. Hardness was significantly reduced, while the scratch resistance results show that these films have a fairly good adhesion to the substrate. Evident improvements of the hydrophobicity have been made to these films, with contact angles of double-stilled water approaching that of polytetrafluoroethylene (PTFE). Our study suggests that broad application regions of the fluorine-doped amorphous carbon films with diamond-like structure, synthesized by PIII–D, can be extended by combining the non-wetting properties and mechanical properties which are far superior to those of PTFE.