scholarly journals INFINITELY MANY SOLUTIONS FOR CRITICAL FRACTIONAL EQUATION WITH SIGN-CHANGING WEIGHT FUNCTION

2020 ◽  
Vol 10 (1) ◽  
pp. 131-139
Author(s):  
Wei Chen ◽  
◽  
Chun-Lei Tang
2019 ◽  
Vol 2019 ◽  
pp. 1-9
Author(s):  
Xianzhong Yao ◽  
Xia Li ◽  
Fuchen Zhang ◽  
Chunlai Mu

In this paper, we study the following Schrödinger-Poisson equations −Δu+u+ϕu=u5+λaxup−1u,x∈ℝ3,−Δϕ=u2,x∈ℝ3, where the parameter λ>0 and p∈0,1. When the parameter λ is small and the weight function ax fulfills some appropriate conditions, we admit the Schrödinger-Poisson equations possess infinitely many negative energy solutions by using a truncation technology and applying the usual Krasnoselskii genus theory. In addition, a byproduct is that the set of solutions is compact.


2002 ◽  
Author(s):  
Shyhnan Liou ◽  
Chung-Ping Cheng
Keyword(s):  

2020 ◽  
Author(s):  
Anusha Ampavathi ◽  
Vijaya Saradhi T

UNSTRUCTURED Big data and its approaches are generally helpful for healthcare and biomedical sectors for predicting the disease. For trivial symptoms, the difficulty is to meet the doctors at any time in the hospital. Thus, big data provides essential data regarding the diseases on the basis of the patient’s symptoms. For several medical organizations, disease prediction is important for making the best feasible health care decisions. Conversely, the conventional medical care model offers input as structured that requires more accurate and consistent prediction. This paper is planned to develop the multi-disease prediction using the improvised deep learning concept. Here, the different datasets pertain to “Diabetes, Hepatitis, lung cancer, liver tumor, heart disease, Parkinson’s disease, and Alzheimer’s disease”, from the benchmark UCI repository is gathered for conducting the experiment. The proposed model involves three phases (a) Data normalization (b) Weighted normalized feature extraction, and (c) prediction. Initially, the dataset is normalized in order to make the attribute's range at a certain level. Further, weighted feature extraction is performed, in which a weight function is multiplied with each attribute value for making large scale deviation. Here, the weight function is optimized using the combination of two meta-heuristic algorithms termed as Jaya Algorithm-based Multi-Verse Optimization algorithm (JA-MVO). The optimally extracted features are subjected to the hybrid deep learning algorithms like “Deep Belief Network (DBN) and Recurrent Neural Network (RNN)”. As a modification to hybrid deep learning architecture, the weight of both DBN and RNN is optimized using the same hybrid optimization algorithm. Further, the comparative evaluation of the proposed prediction over the existing models certifies its effectiveness through various performance measures.


Entropy ◽  
2021 ◽  
Vol 23 (2) ◽  
pp. 255
Author(s):  
Mario Gonzalez-Lee ◽  
Hector Vazquez-Leal ◽  
Luis J. Morales-Mendoza ◽  
Mariko Nakano-Miyatake ◽  
Hector Perez-Meana ◽  
...  

In this paper, we explore the advantages of a fractional calculus based watermarking system for detecting Gaussian watermarks. To reach this goal, we selected a typical watermarking scheme and replaced the detection equation set by another set of equations derived from fractional calculus principles; then, we carried out a statistical assessment of the performance of both schemes by analyzing the Receiver Operating Characteristic (ROC) curve and the False Positive Percentage (FPP) when they are used to detect Gaussian watermarks. The results show that the ROC of a fractional equation based scheme has 48.3% more Area Under the Curve (AUC) and a False Positives Percentage median of 0.2% whilst the selected typical watermarking scheme has 3%. In addition, the experimental results suggest that the target applications of fractional schemes for detecting Gaussian watermarks are as a semi-fragile image watermarking systems robust to Gaussian noise.


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