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.     

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.     

Casorati Inequalities for Statistical Submanifolds in Kenmotsu Statistical Manifolds of Constant ϕ-Sectional Curvature with Semi-Symmetric Metric Connection

In this paper, we prove some inequalities between intrinsic and extrinsic curvature invariants, namely the normalized δ-Casorati curvatures and the scalar curvature of statistical submanifolds in Kenmotsu statistical manifolds of constant ϕ-sectional curvature that are endowed with semi-symmetric metric connection. Furthermore, we investigate the equality cases of these inequalities. We also describe an illustrative example.     

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.     

Metric inequalities for routings on direct connections with application to line planning

We consider multi-commodity flow problems in which capacities are installed on paths. In this setting, it is often important to distinguish between flows on direct connection routes, using single paths, and flows that include path switching. We derive a feasibility condition for path capacities supporting such direct connection flows similar to the well-known feasibility condition for arc capacities in ordinary multi-commodity flows. The condition can be expressed in terms of a class of metric inequalities for routings on direct connections. We illustrate the concept on the example of the line planning problem in public transport and present an application to large-scale real-world problems.     

Automatic Search Dense Connection Module for Super-Resolution

The development of display technology has continuously increased the requirements for image resolution. However, the imaging systems of many cameras are limited by their physical conditions, and the image resolution is often restrictive. Recently, several models based on deep convolutional neural network (CNN) have gained significant performance for image super-resolution (SR), while extensive memory consumption and computation overhead hinder practical applications. For this purpose, we present a lightweight network that automatically searches dense connection (ASDCN) for image super-resolution (SR), which effectively reduces redundancy in dense connection and focuses on more valuable features. We employ neural architecture search (NAS) to model the searching of dense connections. Qualitative and quantitative experiments on five public datasets show that our derived model achieves superior performance over the state-of-the-art models.     

变截面双帽箱型横截面点焊薄壁构件的扭转问题

提出沿构件长度方向截面尺寸发生缓慢变化时双帽箱型横截面点焊薄壁构件扭转特性的分析方法,并利用此方法讨论了变截面等焊点间隔构件和变截面非等焊点间隔构件的翘曲扭转问题并得到如下结论:①变截面构件长度越长,扭转刚度越小,其刚度下降率与等截面构件几乎相等;②采用变截面构件,不仅保持一定刚度,还可以减少焊点数目,降低焊接成本;③若右半部分的焊点间隔p2对左半部分的焊点间隔p1的变化范围小于25%,则其传递剪力变化不大。仿真结果与实验值以及利用cosmos/m而得到的数值解相比较吻合得较好,完全满足工程精度要求。此研究为解决实际车体结构的设计问题,具有有益的参考价值。