This paper aims to improve the alternative formulation of the fifth- and sixth-order accurate weighted essentially non-oscillatory (AWENO) finite difference schemes. The first is to derive the AWENO scheme with sixth-order accuracy in the smooth region of the solution. Second, a new weighted polynomial functions combining the perturbed forms with conserved variable to the AWENO is constructed; the new form of tunable functions are invented to maintain non-oscillatory property. Detailed numerical experiments are presented to illustrate the behavior of the new perturbational AWENO schemes. The performance of the present scheme is evaluated in terms of accuracy and resolution of discontinuities using a variety of one and two-dimensional test cases. We show that the resulted perturbational AWENO schemes can achieve fifth- and sixth-order accuracy in smooth regions while reducing numerical dissipation significantly near singularities.

The unsteady dynamics of the starting flow of a flat plate is studied by using a vortex shedding model. The model describes the body and separated vortex from the trailing edge of the plate by vortex sheets, retaining a singularity at the leading edge. The model is applied to simulate the flow of an accelerated plate for small angles of attack. For numerical computations, we take two representative cases of the translational velocity of a plate: impulsive translation and uniform acceleration. The model successfully demonstrates the formation of wakes shed from the plate. The wake behind the plate is stronger for a larger angle of attack. Predictions for the lifting force from the model are in agreement with results of Navier-Stokes simulations.

In this paper we discuss some recovery of H(div)-conforming flux approximations from the equilibrated fluxes of Ainsworth and Oden for quadratic finite element methods of second-order elliptic problems. Combined with the hypercircle method of Prager and Synge, these flux approximations lead to a posteriori error estimators which provide guaranteed upper bounds on the numerical error. Furthermore, we prove some superconvergence results for the flux approximations and asymptotic exactness for the error estimator under proper conditions on the triangulation and the exact solution. The results extend those of the previous paper for linear finite element methods.

We study the numerical analysis for the Cahn-Hilliard (CH) equation using the decoupled projection (DP) method. The CH equation is a fourth order nonlinear partial differential equation that is hard to solve. Therefore, various of numerical schemes have been proposed to solve the CH equation. To verify the relation of each existing scheme for the CH equation, we consider the DP method for linear convex splitting schemes. We present the numerical experiments to demonstrate our analysis. Throughout this study, it is expected to construct a novel numerical scheme using the relation with existing numerical schemes.

This study aims to establish and analyze a mathematical model for the transmission dynamics of male adolescent smoking and to determine an optimal control strategy to reduce male adolescent smoking. We consider three groups in the population: smokers, non-smokers, and temporary nonsmokers. In our model to which optimal control theory was applied, the number of smokers decreased sharply and the number of non-smokers increased significantly. Our simulation results under various control scenarios reveal that integrated control measures(such as prevention, education, and treatment) may be necessary to reduce the growth rate of adolescent smoking. Moreover, we concluded that efforts to encourage current smokers and temporary quitters to quit should be sustained longer than efforts to reduce the rate at which nonsmokers become smokers through smoking prevention education.

In this paper, we derive the Γ-limit of functionals pertaining to some optimal material distribution problems that involve a variable exponent, as the exponent goes to infinity. In addition, we prove a relaxation result for supremal optimal design functionals with respect to the weak-∗ L^∞(Ω; [0, 1])× W^1,p0 (Ω;ℝ^m) weak topology.

This paper introduces the industrial problem, the solution, and the results of the research conducted with Define Inc. The client company wanted to improve the performance of an object detection model on the floor plan dataset. To solve the problem, we analyzed the operational principles, advantages, and disadvantages of the existing object detection model, identified the characteristics of the floor plan dataset, and proposed to use of YOLO v5 as an appropriate object detection model for training the dataset. We compared the performance of the existing model and the proposed model using mAP@60, and verified the object detection results with real test data, and found that the performance increase of mAP@60 was 0.08 higher with a 25% shorter inference time. We also found that the training time of the proposed YOLO v5 was 71% shorter than the existing model because it has a simpler structure. In this paper, we have shown that the object detection model for the floor plan dataset can achieve better performance while reducing the training time. We expect that it will be useful for solving other industrial problems related to object detection in the future. We also believe that this result can be extended to study object recognition in 3D floor plan dataset.

Topological data analysis (TDA) is a data analysis technique, recently developed, that investigates the overall shape of a given dataset. The mapper algorithm is a TDA method that considers the connectivity of the given data and converts the data into a mapper graph. Compared to persistent homology, another popular TDA tool, that mainly focuses on the homological structure of the given data, the mapper algorithm is more of a visualization method that represents the given data as a graph in a lower dimension. As it visualizes the overall data connectivity, it could be used as a prediction method that visualizes the new input points on the mapper graph. The existing mapper packages such as Giotto-TDA, Gudhi and Kepler Mapper provide the descriptive mapper algorithm, that is, the final output of those packages is mainly the mapper graph. In this paper, we develop a simple predictive algorithm. That is, the proposed algorithm identifies the node information within the established mapper graph associated with the new emerging data point. By checking the feature of the detected nodes, such as the anomality of the identified nodes, we can determine the feature of the new input data point. As an example, we employ the fraud credit card transaction data and provide an example that shows how the developed algorithm can be used as a node prediction method.