Netlike partial cubes, V: Completion and netlike classes

We define a completion of a netlike partial cube G by replacing each convex 2n-cycle C of G with n≥3 by an n-cube admitting C as an isometric cycle. We prove that a completion of G is a median graph if and only if G has the Median Cycle Property (MCP) (see N. Polat, Netlike partial cubes III. The Median Cycle Property, Discrete Math.). In fact any completion of a netlike partial cube having the MCP is defined by a universal property and turns out to be a minimal median graph containing G as an isometric subgraph. We show that the completions of the netlike partial cubes having the MCP preserves the principal constructions of these graphs, such as: netlike subgraphs, gated amalgams and expansions. Conversely any netlike partial cube having the MCP can be obtained from a median graph by deleting some particular maximal finite hypercubes. We also show that, given a netlike partial cube G having the MCP, the class of all netlike partial cubes having the MCP whose completions are isomorphic to those of G share different properties, such as: depth, lattice dimension, semicube graph and crossing graph.     

A 4D Composite Reinforced along Cube Diagonals with a Small Content of Yarns under Large Tensile Deformations

The deformation behavior of a 4D composite reinforced along cube diagonals under large tensile deformations is examined. The investigation is based on an applied theory which allows one to perform a macromechanical analysis of composite materials with small volume contents of reinforcing yarns with an accuracy sufficient in practice. It is found that, under large deformations, the properties of composites reinforced along cube diagonals differ qualitatively from their properties under small deformations. The evolution of the structural geometry of the deformed composite material is traced.     

关于正整数的立方部分

对于任意正整数n，定义u(n)为不大于n的最大立方数，v(n)为不小于n的最小立方数．研究了数列{u(n))和{v(n)}的性质，并给出了两个有趣的渐近公式．     

On Combinatorial Cubes

A sequence of positive integers with positive lower density contains a Hilbert (or combinatorial) cube size c log log n up to n. We prove this bound is sharp for some thinner sequence.     

The Same Upper Bound for Both: The 2‐page and the Rectilinear Crossing Numbers of the n‐Cube

We present two main results: a 2‐page and a rectilinear drawing of the n‐dimensional cube . Both drawings have the same number of crossings, even though they are given by different constructions. The first improves the current best general 2‐page drawing, while the second is the first nontrivial rectilinear drawing of .     

热轧对涂层导体用镍基带立方织构形成的影响

热机械加工制备的立方织构Ni及其合金带材广泛用于YBCO涂层导体的基带。涂层导体的制备要求基带具有强的立方织构和小的晶界角。通过在冷轧前进行热轧制备了强立方织构的镍基带。用三维取向分布函数（ODF）研究了轧制织构和再结晶织构，通过扫描电镜EBSD的观测，分析了晶粒取向分布和立方织构晶界微取向角分布。结果表明，冷轧前进行热轧有利于形成很强的立方织构和小的晶界微取向角。     

反应溅射法在立方织构镍基底上制备CeO2缓冲层

采用反应溅射的方法在具有立方织构的Ni基底上制备了 CeO2缓冲层.以Ar/H2混合气体为预沉积气体,有效地抑制了基底的氧化.在基片温度为650 ℃,气压为26 Pa的条件下沉积的CeO2薄膜具有纯c轴取向.X射线θ-2θ扫描、极图分析、Φ扫描结果表明,CeO2薄膜有良好的立方织构,其Φ扫描半高宽(FWHM)为9.0°.扫描电镜观察表明,薄膜致密且没有裂纹.     

Theoretical investigation on confinement of ions in a cube‐shaped ion trap

The confinement of ions in a cube‐shaped ion trap and the mathematical formalism governing the behavior of ions in the trap is investigated theoretically. Afterwards, the stability regions are computed using the fourth‐order Rung–Kutta method. Consequently, the influence of the direction of ions, injected into the trap from its center on the stability region, is numerically discussed. Moreover, the maximum angle of injection with respect to the vertical axis of the cube for which the ions could be confined in the trap without invoking any direct current component of voltage (henceforth referred to as limiting angle) was calculated. Strong linear correlation between the angle of injection and the ratio of the stability region areas is confirmed. A nonlinear feature of a cube‐shaped ion trap is demonstrated with a focus on the equations of motion for an ion confined into the trap. It is worthwhile to note that the stability region of our cubic ion trap, which has its own boundary conditions and electrodynamics, has been theoretically investigated for the first time. Besides, the limiting angle as well as the aforementioned strong linear correlation has not been reported in the literature previously. Copyright © 2015 John Wiley & Sons, Ltd.     

On based-free actions of compact lie groups on the hilbert cube

It is proved that a based-free action α of a given compact Lie groupG on the Hilbert cubeQ is equivalent to the standard based-free action σ if and only if the orbit spaceQ ₀/α of the free partQ ₀=Q* is aQ-manifold having the proper homotopy type of the orbit spaceQ ₀/σ. The existence of an equivariant retraction (Q ₀, σ)→(Q ₀, α) is established. It is proved that for any TikhonovG-spaceX the family of all equivariant mapsX→ conG separates the points and the closed sets inX. Translated fromMatematicheskie Zametki, Vol. 65, No. 2, pp. 163–174, February, 1999.     

M－连续格到Hilbert方体的嵌入

本文主要讨论Ｍ－连续格到Ｈｉｌｂｅｒｔ方体的嵌入问题．我们建立了Ｍ－连续格的次直积表示理论，推广并统一了Ｒａｎｅｙ，Ｂｒｕｎｓ，Ｌａｗｓｏｎ，Ｂａｎｄｅｌｔ和Ｅｒｎｅ等人的相应工作．Ｒｅｎａｙ与Ｂｒｕｎｓ的经典方法是建立在对相应的弱辅助关系的极大完备链作深入分析之上的，富于技巧性，且有局限性．与之相比，本文所使用的方体则相当朴素而自然，但却能处理更为广泛的情形．