Subdivision based isogeometric analysis for geometric flows

We present a new isogeometric analysis (IGA) approach based on extended Loop subdivision scheme for solving various geometric flows defined on subdivision surfaces. The studied flows include the second-order, fourth-order, and sixth-order geometric flows, such as averaged mean curvature flow, constant mean curvature flow, and minimal mean-curvature-variation flow, which are generally derived by minimizing the associate energy functionals with $L^2$-gradient flow respectively. The geometric flows are discretized by means of subdivision based IGA, where the finite element space is formulated by the limit form of the extended Loop subdivision for different initial control meshes. The basis functions, consisting of quartic box-splines corresponding to each subdivided control mesh, are utilized to represent the geometry exactly. For the cases of the evolution of open surfaces with any shape boundary, high-order continuous boundary conditions derived from the mixed variational forms of the geometric flows should be implemented to be consistent with the isogeometric concept. For time discretization, we adopt an adaptive semi-implicit Euler scheme. By several numerical experiments, we study the convergence behaviors of the proposed approach for solving the geometric flows with high-order boundary conditions. Moreover, the numerical results also show the accuracy and efficiency of the proposed method.     

Optimal carbon reduction level and ordering quantity under financial constraints

Carbon tax policy is widely adopted by many countries to curb carbon emissions. In the context of carbon tax policy, firms have more incentive to improve carbon reduction levels by reducing their carbon tax costs. However, firms need to bear carbon reduction costs that may cause shortage of capital. Thus, firms may face problems of financial constraints, which may demotivate firms to produce greener products. To address the decision‐making challenges of firms in the contexts of carbon tax policy and financial constraints, we consider a supply chain with a manufacturer who produces green products and a retailer who sells these products. Our study develops five models to investigate the two firms’ optimal wholesale price, carbon reduction level and ordering quantity, according to the manufacturer and retailer with or without financial constraints. Our goal in this study is to explore how carbon tax policy and banks’ interest rates affect the profits of the two firms, supply chain and consumer surplus. Certain managerial insights are obtained as follows. We demonstrate that carbon tax policy and banks’ interest rates demotivate the manufacturer to produce greener products and demotivate the retailer to order more products. If the interest rate to the manufacturer (retailer) is relatively low, then the manufacturer with financial constraint benefits (harms) the consumers compared with the retailer with financial constraint. Importantly, our analysis suggests that carbon tax policy harms the firms but benefits consumers, and the government in some conditions should reduce unit carbon tax.     

Multicriteria decision-making using Archimedean aggregation operators in Pythagorean hesitant fuzzy environment

In multicriteria decision-making (MCDM), the existing aggregation operators are mostly based on algebraic t-conorm and t-norm. But, Archimedean t-conorms and t-norms are the generalized forms of t-conorms and t-norms which include algebraic, Einstein, Hamacher, Frank, and other types of t-conorms and t-norms. From that view point, in this paper the concepts of Archimedean t-conorm and t-norm are introduced to aggregate Pythagorean hesitant fuzzy information. Some new operational laws for Pythagorean hesitant fuzzy numbers based on Archimedean t-conorm and t-norm have been proposed. Using those operational laws, Archimedean t-conorm and t-norm-based Pythagorean hesitant fuzzy weighted averaging operator and weighted geometric operator are developed. Some of their desirable properties have also been investigated. Afterwards, these operators are applied to solve MCDM problems in Pythagorean hesitant fuzzy environment. The developed Archimedean aggregation operators are also applicable in Pythagorean fuzzy contexts also. To demonstrate the validity, practicality, and effectiveness of the proposed method, a practical problem is considered, solved, and compared with other existing method.     

防振条约束失效对蒸汽发生器传热管面内流弹失稳的影响研究

根据防振条布置以及面内支承连续失效个数，将防振条面内约束失效分析划分为多种工况，分析了不同工况下面内约束失效对传热管面内模态的影响，采用各位置阻尼在振型函数上进行加权平均的方法计算了各阶模态的阻尼比，进而研究了防振条面内不同约束对传热管面内流弹失稳的影响。分析结果表明，随着面内支承连续失效位置的增多，弯管段面内首阶模态频率不断降低，出现在弯管段的振型越加明显；弯管段面内首阶模态不一定是最大流弹失稳比值出现的模态，最大流弹失稳比值出现模态的振型几乎都出现在弯管段；随着面内支承连续失效位置的增多，面内流弹失稳比值不断增大，当连续3个及以上防振条面内约束失效时，将出现流弹失稳现象。     

虚拟手交互中约束类物体操作研究

虚拟手技术是虚拟现实技术中的一种交互方式，是指通过手势识别技术将人的真实手映射到虚拟环境中并与虚拟物体进行交互操作的人机交互方式。主要应用于虚拟训练、虚拟手术和虚拟装配等领域。对虚拟手交互的约束类对象进行了研究，提出了基于运动学的约束类物体操作方法，解决了阀门类有约束物体交互中虚拟手姿态不真实、操作不可控的问题。设计实验验证了基于运动学的方法能以符合实际操作的效果完成虚拟现实系统中的操作任务，可以应用到虚拟训练、虚拟装配等仿真平台。     

Copy-move forgery detection of duplicated objects using accurate PCET moments and morphological operators

This paper presents a new method for copy-move forgery detection of duplicated objects. A bounding rectangle is drawn around the detected object to form a sub-image. Morphological operator is used to remove the unnecessary small objects. Highly accurate polar complex exponential transform moments are used as features for the detected objects. Euclidian distance and correlation coefficient between the feature vectors are calculated and used for searching the similar objects. A set of 20 forged images with duplicated objects is carefully selected from previously published works. Additional 80 non-forged images are edited by the authors and forged by duplicating different kinds of objects. Numerical simulation is performed where the results show that the proposed method successfully detect different kinds of duplicated objects. The proposed method is much faster than the previously existing methods. Also, it exhibits high robustness to various attacks such as additive white Gaussian noise, JPEG compression, rotation, and scaling.     

ZerNet: Convolutional Neural Networks on Arbitrary Surfaces Via Zernike Local Tangent Space Estimation

In this paper, we propose a novel formulation extending convolutional neural networks (CNN) to arbitrary two-dimensional manifolds using orthogonal basis functions called Zernike polynomials. In many areas, geometric features play a key role in understanding scientific trends and phenomena, where accurate numerical quantification of geometric features is critical. Recently, CNNs have demonstrated a substantial improvement in extracting and codifying geometric features. However, the progress is mostly centred around computer vision and its applications where an inherent grid-like data representation is naturally present. In contrast, many geometry processing problems deal with curved surfaces and the application of CNNs is not trivial due to the lack of canonical grid-like representation, the absence of globally consistent orientation and the incompatible local discretizations. In this paper, we show that the Zernike polynomials allow rigourous yet practical mathematical generalization of CNNs to arbitrary surfaces. We prove that the convolution of two functions can be represented as a simple dot product between Zernike coefficients and the rotation of a convolution kernel is essentially a set of 2 × 2 rotation matrices applied to the coefficients. The key contribution of this work is in such a computationally efficient but rigorous generalization of the major CNN building blocks.     

A cash-constrained stochastic inventory model with consumer loans and supplier credits: the case of nanostores in emerging markets

We consider a small traditional retailer that is managing its inventory under strict cash constraints, mainly because typically informal loans are offered to customers. These stores are widely present in emerging markets, and we refer to them as nanostores (also called ‘mom-and-pop stores’). As the suppliers require immediate payments for goods delivered, a nanostore can only replenish products to the level for which it has on-hand cash available. To improve delivery efficiency, a supplier might offer a nanostore credit for its replenishments. However, currently, suppliers are often reluctant to do so as these nanostores quickly go bankrupt or disappear, hence defaulting on all outstanding credits. The objective of this paper is to determine when it is beneficial to offer supplier credits. We propose a multi-period, stochastic inventory model, and numerically compare scenarios with and without supplier credits. Our study shows that even in the presence of this risk, suppliers often have good incentives to provide these credits, even if interest is not incurred. For this to hold, the operations of the retailer should be (a little) profitable in the first place, for which we provide analytical conditions.     

立体几何褶皱织物的成型与织造

为拓宽立体几何褶皱织物的设计思路,设计具有立体几何效果的褶皱织物,对立体几何褶皱织物的成型原理进行了研究和探讨。提出了在二维织物面料铺设折叠线,形成一定规律的几何图案,并将几何图案按折叠线划分成上凸折叠区、下凹折叠区及非折叠区,在不同折叠区填充不同组织并以弹性纱和非弹性纱交替引纬,以此作为设计立体几何褶皱织物的基础。结果显示:设计好几何图案,选择不同的纬二重组织填充不同折叠区域,选用蚕丝为经纱、涤纶低弹丝与氨纶丝包覆的弹力丝与涤纶全拉丝为纬纱进行织造,所得的织物能形成具有明显立体几何形状的褶皱。