Convergence analysis of a weak Galerkin finite element method on a Shishkin mesh for a singularly perturbed fourth-order problem in 2D

We consider the singularly perturbed fourth-order boundary value problem $\varepsilon ^{2}\Delta ^{2}u-\Delta u=f$ on the unit square $\Omega \subset \mathbb{R}^2$, with boundary conditions $u = \partial u / \partial n = 0$ on $\partial \Omega$, where $\varepsilon \in (0, 1)$ is a small parameter. The problem is solved numerically by means of a weak Galerkin(WG) finite element method, which is highly robust and flexible in the element construction by using discontinuous piecewise polynomials on finite element partitions consisting of polygons of arbitrary shape. The resulting WG finite element formulation is symmetric, positive definite, and parameter-free. Under reasonable assumptions on the structure of the boundary layers that appear in the solution, a family of suitable Shishkin meshes with $N^2$ elements is constructed ,convergence of the method is proved in a discrete $H^2$ norm for the corresponding WG finite element solutions and numerical results are presented

Research on Safety Investment Decision Evaluation and Optimization of Network Booking Taxi Platform Enterprise based on Subjective-Objective Assessment Method

This study addresses the current problem of disproportion between the investment and return of safety operation of Network Booking Taxi Platform Enterprises (NBTPE). This study selects the more representative NBTPE in the domestic travel field, and further forms a graph of safety input law based on the impact analysis of internal and external safety inputs by applying the System Dynamics method. Based on the comprehensive use of subjective empowerment method represented by analytical hierarchy process and objective empowerment method represented by entropy weight method, the study proposes the method of determining the reasonable proportion of each safety input cost through the comprehensive Subjective-Objective Assessment Method, and evaluates the feasibility and reasonableness of the method by using the method of linear regularization. Further the study concluded that enterprises need to increase the investment in equipment and facilities in the field of safety investment, while the proportion of investment in different links was measured and suggestions were made to optimize the current proportion of safety investment in NBTPE. This study provides support for optimizing the safety investment ratio of platform companies and improving the efficiency of safety management

Rational or altruistic: the impact of social media information exposure on Chinese youth’s willingness to donate blood

BackgroundNon-remunerated blood donation is the main approach for various medical institutions to get the source of blood supply, but the blood supply shortage is still a problem in today’s society. Social media has become the main approach of information acquisition for youth groups nowadays, and the information on social media will have an impact on people’s behavioral decisions. The objective of this study was therefore to investigate the correlation between social media exposure to relevant information about blood donation and the willingness of youths to donate blood.MethodsWe collected data from 455 questionnaires through an online questionnaire and structural equation modeling was constructed for validation. Data were analyzed for reliability, validity, and demographic differences using IBM-SPSS 26.0, and IBM-SPSS-AMOS 26.0 was used for model fit analysis and path analysis.ResultsThe results of the study showed that there was a positive correlation between social media exposure to relevant blood donation information and willingness to donate blood (β = 0.262, p < 0.001), altruism (β = 0.203, p < 0.001) and self-efficacy (β = 0.170, p < 0.001). While there was also a positive correlation between attitude toward blood donation and self-efficacy (β = 0.560, p < 0.001), there was no positive correlation between it and willingness to donate blood (β = −0.180, p = 0.786). There was also a positive correlation between altruism and willingness to donate blood (β = 0.150, p < 0.05) and attitude toward blood donation (β = 0.150, p < 0.001). Similarly, there was a positive correlation between self-efficacy and willingness to donate blood (β = 0.371, p < 0.001).ConclusionExposure to more information related to blood donation on social media can increase the willingness of the youth population to donate blood, while exposure to information related to altruism and self-efficacy on social media can also enhance young people’s attitudes toward blood donation, while further strengthening their willingness to donate

Assessing the new product development process for the industrial decarbonization of sustainable economies

This study aims to find out the significant stages of new product development process for the industrial decarbonization of sustainable economies by using interval type-2 (IT2) fuzzy decision-making trial and evaluation laboratory (DEMATEL). The findings demonstrate that commercialization is the most significant process of new product generation process of industrial decarbonization. Moreover, it is also concluded that with respect to the sub-criteria, cost analysis, and performance evaluation have the highest weights. An effective cost analysis is required in the new product development process. The costs of the product development process can in some cases be much higher than anticipated. This situation eliminates the effectiveness of the newly developed product. In this context, companies need to make the necessary plans for the costs of these new products correctly. On the other hand, it is important to follow the costs in detail during the process. Otherwise, the product that does not provide a cost advantage will not be preferred by industrial companies. This will cause the actions to be taken to reduce carbon emissions to fail.Key Scientific Research Project of Colleges and Universities in Henan Province "Research on the key role of Investment in the Optimization and upgrading of Industrial structure in Henan Province"Soft Science Research Plan Project of Henan Provinc

Deep Deformable Models: Learning 3D Shape Abstractions with Part Consistency

The task of shape abstraction with semantic part consistency is challenging due to the complex geometries of natural objects. Recent methods learn to represent an object shape using a set of simple primitives to fit the target. \textcolor{black}{However, in these methods, the primitives used do not always correspond to real parts or lack geometric flexibility for semantic interpretation.} In this paper, we investigate salient and efficient primitive descriptors for accurate shape abstractions, and propose \textit{Deep Deformable Models (DDMs)}. DDM employs global deformations and diffeomorphic local deformations. These properties enable DDM to abstract complex object shapes with significantly fewer primitives that offer broader geometry coverage and finer details. DDM is also capable of learning part-level semantic correspondences due to the differentiable and invertible properties of our primitive deformation. Moreover, DDM learning formulation is based on dynamic and kinematic modeling, which enables joint regularization of each sub-transformation during primitive fitting. Extensive experiments on \textit{ShapeNet} demonstrate that DDM outperforms the state-of-the-art in terms of reconstruction and part consistency by a notable margin

Faster Ray Tracing through Hierarchy Cut Code

We propose a novel ray reordering technique to accelerate the ray tracing process by encoding and sorting rays prior to traversal. Instead of spatial coordinates, our method encodes rays according to the cuts of the hierarchical acceleration structure, which is called the hierarchy cut code. This approach can better adapt to the acceleration structure and obtain a more reliable encoding result. We also propose a compression scheme to decrease the sorting overhead by a shorter sorting key. In addition, based on the phenomenon of boundary drift, we theoretically explain the reason why existing reordering methods cannot achieve better performance by using longer sorting keys. The experiment demonstrates that our method can accelerate secondary ray tracing by up to 1.81 times, outperforming the existing methods. Such result proves the effectiveness of hierarchy cut code, and indicate that the reordering technique can achieve greater performance improvement, which worth further research