The (Non-Iterative) Partial Differential Equation Method: Application to Electron-Molecule Scattering

1995 ◽  
pp. 191-212 ◽  
Author(s):  
A. Temkin ◽  
C. A. Weatherford
Keyword(s):  
Differential Equation ◽  
Partial Differential Equation ◽  
Equation Method ◽  
Partial Differential ◽  
Molecule Scattering ◽  
Differential Equation Method

scholarly journals Partial Differential Equations-Based Iterative Denoising Algorithm for Movie Images

2021 ◽  
Vol 2021 ◽  
pp. 1-10
Author(s):  
Pingli Sun ◽  
Chenxia Wang ◽  
Min Li ◽  
Lanqi Liu
Keyword(s):  
Differential Equation ◽  
Partial Differential Equation ◽  
Noise Reduction ◽  
Video Processing ◽  
Gaussian Noise ◽  
Video Image ◽  
Equation Method ◽  
Partial Differential ◽  
Iterative Denoising ◽  
Differential Equation Method

Film video noise can usually be defined as the error information visible on the video image, caused by the digital signal system. This distortion is inevitably present in the video obtained by various camera equipment. Noise reduction techniques are important preprocessing processes in many video processing applications, and its main goal is to reduce the noise contained in a video image while preserving as much of its edge and texture information as possible. In this paper, we describe in detail the principles of the space-time noise reduction filter, propose a 3D-filter algorithm for Gaussian noise, an improved 3D-filter algorithm based on the 3D-BDP (bloom-deep-split) filter for mixed noise, and a filter algorithm for luminance and color noise in low-brightness scenes. By dissecting the partial differential equation (PDE) denoising process, we establish a new iterative denoising algorithm. The partial differential equation method can be considered as the iterative denoising of the filter, and the first stage of the new algorithm uses wavelet-domain adaptive Wiener filter as the filtering base and achieves good results by adjusting the parameters. The proposed model in this paper is compared with the existing denoising model, and the analysis results show that the model proposed in this section can effectively remove multiplicative noise. The experimental report shows that the parameters set by the algorithm have some stability and can achieve good processing results for multiple images, which is an advantage over the partial differential equation method for denoising. The second stage of the algorithm uses the appropriate partial differential equation method to remove the pseudo-Gibbs in the first stage, which further improves the performance of the algorithm. After the image containing Gaussian noise is processed by the new algorithm, the pseudo-Gibbs effect, which often occurs in wavelet denoising, is eliminated, and the step effect, which occurs in partial differential equation denoising, is avoided; the details are better preserved, and the peak signal-to-noise ratio is improved, and a large number of experiments show that it is an effective denoising method.

scholarly journals An Odor Interaction Model of Binary Odorant Mixtures by a Partial Differential Equation Method

Sensors ◽  
2014 ◽  
Vol 14 (7) ◽  
pp. 12256-12270 ◽  
Author(s):  
Luchun Yan ◽  
Jiemin Liu ◽  
Guihua Wang ◽  
Chuandong Wu
Keyword(s):  
Differential Equation ◽  
Partial Differential Equation ◽  
Interaction Model ◽  
Equation Method ◽  
Partial Differential ◽  
Differential Equation Method

scholarly journals Structured Assessment of Student Outcomes “a” and “e” in Mathematics and Science Courses for Engineering Students

2019 ◽  
Vol 8 (9) ◽  
pp. 215-218
Keyword(s):  
Differential Equation ◽  
Partial Differential Equation ◽  
Quality Assurance ◽  
Student Outcomes ◽  
Engineering Students ◽  
Equation Method ◽  
Partial Differential ◽  
Science Courses ◽  
Mathematics And Science ◽  
Differential Equation Method

Skills, performance, and ability attributes are known as student outcomes that are gained during graduation. In order to evaluate quality assurance of these outcomes, a set of specific and targeted curriculum and extra-curriculum activities must be used for precise as-assessment. Meeting the required outcomes, a set of desired courses have to be selected to insure that the desired outcome is highly satisfied. “Highly” covered can be identified using Bloom’s levels, number of covered hours, weight of its assessment and others. Student outcomes are directly linked to course goals that are identified using a set of measurable verbs. In this paper, we will be using two outcomes “a” and “e” to structurally assess both direct and indirect outcomes in mathematics and other scientific courses using a partial differential equation method by defining appropriate measurable course goals. The strategy to assess the outcome is also explained.

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