Curvature of curvilinear 4-webs and pencils of one forms: Variation on a theorem of Poincaré, Mayrhofer and Reidemeister

A curvilinear d-web W = (F ₁ , . . . , F _d ) is a configuration of d curvilinear foliations F _i on a surface. When d = 3, Bott connections of the normal bundles of F _i extend naturally to equal affine connection, which is called Chern connection. For 3 < d, this is the case if and only if the modulus of tangents to the leaves of F _i at a point is constant. A d-web is associative if the modulus is constant and weakly associative if Chern connections of all 3-subwebs have equal curvature form. We give a geometric interpretation of the curvature form in terms of fake billiard in §2, and prove that a weakly associative d-web is associative if Chern connections of triples of the members are non flat, and then the foliations are defined by members of a pencil (projective linear family of dim 1) of 1-forms. This result completes the classification of weakly associative 4-webs initiated by Poincaré, Mayrhofer and Reidemeister for the flat case. In §4, we generalize the result for n + 2-webs of n-spaces. Received: September 23, 1996     

Difference discrete connection and curvature on cubic lattice Dedicated to Professor Sheng GONG on the occasion of his 75th birthday

In a way similar to the continuous case formally, we define in different but equivalent manners the difference discrete connection and curvature on discrete vector bundle over the regular lattice as base space. We deal with the difference operators as the discrete counterparts of the derivatives based upon the differential calculus on the lattice. One of the definitions can be extended to the case over the random lattice. We also discuss the relation between our approach and the lattice gauge theory and apply to the discrete integrable systems.     

The double exponential map and covariant derivation

We study the double exponential map which is a composition of a special form of two exponential maps on a manifold with connection. We relate this map and the composition of covariant derivations as well as the composition of pseudodifferential operators on these manifolds.     

Homogeneity and Canonical Connections of Isoparametric Manifolds

On every isoparametric submanifold M a connection with parallel second fundamental form is constructed geometrically such that M is an orbit of an s-representation if and only if the connection is a canonical one. If the rank of M is greater than one this connection is in case of homogeneity the canonical connection of the reductive decomposition given by the orbit of s-representation. This revised version was published online in June 2006 with corrections to the Cover Date.     

A Galois Connection

The connection presented in this paper mirror-links two metamathematical structures, the finitary closure operators, and the compact consistency properties, in such a way that a specification of one structure induces a provably equivalent specification of the other. Mathematics Subject Classification (2000): Primary 06A15, Secondary 28E10 03B22     

All-glass open-split interface for capillary GC/MS

This paper describes a design for an all-glass GC/MS interface. The design has advantages due to low dead volume, lack of column effluent adsorption and degradation, simple interface production and installation, and ease of column mounting/dismounting.     

Optimized Selection of Water Resource Allocation Schemes Based on Improved Connection Entropy in Beijing’s Southern Plain

Increased urbanization has caused problems such as increasing water consumption and the continuous deterioration of the groundwater environment. It is necessary to consider the groundwater quality in the water resource optimization system and increase the rate of reclaimed water development to reduce the amount of groundwater exploitation and achieve sustainable development of water resources. This study used the Daxing District, a region of Beijing’s southern plain, as an example to evaluate water quality by analyzing water quality data of surface and groundwater from 2012 to 2016 and actual water-use schemes from 2006 to 2016. Three groundwater extraction modes were set up based on NO₃–N concentrations, water resources were optimized under three extraction modes, and water resource optimization schemes were determined based on the improved connection entropy. The results show that (1) the surface water quality was poor, and the proportion of V₄ type water in the indexes of NH₃–N and chemical oxygen demand (COD) was the largest. The surface water can only be used for agricultural irrigation. The pollution sources contributing most to NH₃–N and COD were domestic and agricultural pollution sources. (2) The groundwater quality was good. The NO₃–N index was primarily type I–III water, accounting for 95.20% of the total samples. Severe NH₃–N pollution areas were mainly in the northern region, and most regional groundwater can be used for various purposes. (3) Taking 2016 as an example, three groundwater exploitation modes were set to optimize water resource allocation, and the results showed that the rate of groundwater development and NO₃–N pollution decreased significantly after optimization. (4) Connection entropy is an evaluation method that combines connection numbers and entropy, including identify, difference, and opposition entropy. As connection entropy being a kind of complete entropy, which can reflect the difference of the system in different states, based on the improved connection entropy, the connection entropies of optimal water resource allocation and actual water-use schemes were calculated. The connection entropy of groundwater exploitation mode 3 was less than that of groundwater exploitation modes 1 and 2 and actual water-use schemes from 2006 to 2016. Therefore, exploitation mode 3’s water resource optimization scheme was recommended. In the paper, satisfactory results have been obtained. As a kind of complete entropy, connection entropy has great research value in dealing with complex hydrological problems. This study’s research methods and outcomes can provide methodological and theoretical lessons for water management in freshwater-deficient areas.     

螺栓连接的梁–弹簧模型及各齿承载分布

螺栓各齿承载分布严重不均,内外螺纹啮合的第一齿承载较大且齿根存在应力集中,易造成螺栓杆横断失效。本文通过对螺栓连接的受力变形分析,建立梁–弹簧模型,推导了理论模型的力学方程组,并基于此模型编程计算,求解得到螺栓连接件在使用过程中各齿承载的分布情况和齿根应力集中系数。最后进行有限元仿真,对比理论模型和有限元的结果,两者误差在工程可接受范围之内。研究表明,螺栓连接的组合梁–弹簧模型是合理有效的。

     

抑制大型折叠腔结构光斑抖动技术的研究

针对光腔镜盒的真空变形和振动对精密光学系统的影响,分析了传统刚性连接的光学调整架平台以及球关节连接结构在减振降噪设计的不足,从支撑和柔性密封连接的角度,设计了隔离振动和光腔镜盒真空变形的精密光学调整架平台,对应用于大型折叠腔的双层光学调整架平台的动力学特性进行ANSYS仿真,并完成了光斑抖动验证实验。结果显示框架式双层光学调整架平台的第一阶弹性体频率可达到126.5,172.3 Hz,很好地满足折叠腔光学调整架平台的使用要求;应用在大型折叠腔,抽真空试验前后He-Ne导引光输出光斑位置无变化,形状变化很小,出光过程中输出抖动角均方根值为3.73,隔离振动传递效果明显。     

并联换热系统中冷媒分配的优化分析

为减小并联换热系统的质量,本文在一定的简化和假设之上,建立了其流动与传热的物理和数学模型;并以系统总换热面积最小为优化目标,通过对分配系数的变量转换,提出了一种可准确求解最佳分配系数的方法,并对计算结果进行了讨论,发现分配系数的结果与势容耗散最大基本一致.根据计算结果.本文给出了支路较少时分配系数与换热支路效能之间的近似关联式.