Localizations of Transfors

Let be n-dimensional teisi, i.e., higher-dimensional Gray-categorical structures. The following questions can be asked. Does a left q-transfor , i.e., a functor 2 _q , induce a right q-transfor , i.e., a functor More generally, does a functor induce a functor For k-arrows c and whose (k – 1)-sources and targets agree, does a q-transfor induce a q-transfor , for appropriate k-arrows For k-arrows c and whose (k – 1)-sources and targets agree, does a q-transfor induce a (q + k + 1)-transfor , for appropriate k-arrows I give answers to these questions in the cases where n-dimensional teisi and their tensor product have been defined, i.e., for n 3, and for n up to 5 in some cases that do not need all data and axioms of n-dimensional teisi.I apply the above to compositions in teisi, in particular to braidings and syllepses. One of the results is that a braiding on a monoidal 2-category induces a pseudo-natural transformation , where is the reverse of ? –, which is almost, but not quite, equal to – ?. However, in higher dimensions need not be reversible, so a braiding on a higher-dimensional tas can not be seen as a transfor A B B A.     

Fusion Operators and Cocycloids in Monoidal Categories

The Yang–Baxter equation has been studied extensively in the context of monoidal categories. The fusion equation, which appears to be the Yang–Baxter equation with a term missing, has been studied mainly in the context of Hilbert spaces. This paper endeavours to place the fusion equation in an appropriate categorical setting. Tricocycloids are defined; they are new mathematical structures closely related to Hopf algebras.     

纺织结构复合材料力学性能的实验研究

本文通过实验测定了三维编织结构复合材料侧边未切割、受切割和中央钻孔试件的拉伸性能，对比了受切割和未切割纤维对于试件侧边拉伸应变的影响，并且讨论了拉伸失效的机理和原因．发现受切割和钻孔试件的拉伸性能低于未加工试件的性能，受切割侧边的拉伸应变高于未切割侧边的拉伸应变，三维编织结构复合材料的拉伸失效主要由纤维断裂引起的．文中还对三维编织结构复合材料的孔边应力集中现象进行了研究，并进行了深入分析，得到一个重要结论，即四步法复合材料的孔边应力集中系数比传统层板复合材料和金属材料的低．从这个意义上说，三维编织结构复合材料适合于作为含孔结构的连接件．     

纵横步进编织规律的数学描述及其证明

对于纵横编织步进编织中的步长选取规律用精确的数学语言描述 ,并给出其严格的数学证明 ,为进一步设计和实现纵横编织技术提供了理论基础 .     

超高速弹丸撞击三维编织C/SiC复合材料双层板结构的实验研究

 目前在航天器防护结构设计中,采用的方案仍是双层（或多层）屏蔽结构 。双层板屏蔽结构由前板、后板和空隙组成。实验采用一种新型三维四向碳纤维织物结构增强SiC陶瓷基复合材料（简写为3DBC/SiC）做前板,其在超高速弹丸冲击作用下发生粉末化,和铝板做前板相比,所形成的碎片云团中有效碎片数目大大减少,减轻了对后板的破坏作用。结果表明：3DBC/SiC是航天器防护结构设计中一种比较理想的防护材料。     

Acoustic emission characterization of tensile damage in 3D braiding composite shafts

The acoustic emission (AE) method was used to monitor the tensile damage in a 3D braiding composite shaft. The 3D braiding composite shaft was manufactured via Vacuum Assisted Resin Transfer Moulding (VARTM) and the tensile experiment was conducted accompanied by AE monitoring. The AE signals were analyzed using the wavelet transformation for time-frequency analysis. The characteristic values of the AE signals were decomposed by the principal component analysis (PCA). The damage mode of the 3D braiding composite shaft under tension was identified and classified by the fuzzy clustering method (FCM). The results showed that the AE method could monitor the damage evolution process of the 3D braiding composite shaft under tension and the FCM combined with the PCA effectively divided the damage mode of the 3D braiding composite shaft. The results will provide an effective method for health monitoring of the 3D braiding composite shaft within engineering.     

Qubit Approach to the Topological Degeneracy of 4 and 6-Quasihole Pfaffian Paired Hall State

By virtue of the two-layer picture of Pfaffian pair Hall state, a qubit representation of topological degeneracy for quasiholes excitation is displayed. The non-Abelian feature of states can be manifested readily by the new wave functions. The virtue of this approach is that one does not need to find the equalities of Pfaffians, which is a so tedious task as exemplified for the case of six quasiholes. Then the braiding matrices are also constructed readily by just permutating single-qubit states, which are unitary and hermite.     

Spatial braiding of cylindrical articles

The effective deformative characteristics of spatially reinforced composites made by spatial braiding along the generatrices of a one-sheet hyperboloid are analyzed. The geometrical relationships determining the structure of a unit cell of a braided composite are derived. The effective thermoelastic characteristics are calculated by the method of orientational averaging. The dependences of the bending and torsional stiffnesses of thick-walled cylindrical rods — made by the method suggested and by winding — on the braiding/winding angle are compared. The numerical estimations are given for rods made of carbon (CFRP) and aramid (AFRP) epoxy plastics. Submitted to the 11th International Conference on Mechanics of Composite Materials (Riga, June 11–15, 2000). Translated from Mekhanika Kompzitnykh Materialov, Vol. 36, No. 3, pp. 341–354, May–June, 2000.     

Proposed Entanglement Swapping in Continuous Variable Systems via Braiding

We study entanglement swapping in continuous variable systems by using braiding transformations. It is found that entanglement swapping in two-mode squeezed vacuum states and squeezed coherent states can be realized based on the braiding operators.     

Composites in offshore technology in the next century

The advisability of application of advanced composites in deep-water offshore technology is shown using risers and tendons as examples. Numerical estimations of the parameters of multilayered metal-composite risers are obtained. Two new processes of spatial braiding for creating the external jackets of compound tendons are considered. Advanced composites are the only possible choice for exploitation of deposits at depths greater than 1500 m. That is why they are the most promising structural materials for offshore technology in the next century. This report was presented at the Symposium “Composites for the Next Millennium” in honor of Stephen Tsai's 70th birthday, Tours, France, 2–3 July, 1999. Institute of Polymer Mechanics, University of Latvia, Riga, LV-1006 Latvia. Translated from Mekhanika Kompozitnykh Materialov, Vol. 35, No. 5, pp. 549–560, September–October, 1999.