Why Is an Integral an Accurate Value?

The derivative and integral in calculus are both exact values. To explain this reason, the integration interval can be infinitely subdivided. The difference in area between curved trapezoids and rectangles can be explained by the theory of higher-order infinitesimal, leading to the conclusion that the difference between the two is an infinitesimal value. From this, it can be inferred that the result obtained by integration is indeed an accurate value.

The Theoretical Significance and Reality of Imaginary Number

It is a fact that imaginary numbers do not have practical significance. But the role of imaginary numbers is very broad and enormous, due to the existence of Euler’s formula. Due to Euler’s formula, imaginary numbers have been applied in many theoretical theories. One of the biggest functions of imaginary numbers is to represent changes in phase, which is indispensable in signal analysis theory. The imaginary numbers in quantum mechanics pose a greater mystery: do the imaginary numbers really exist? This question still needs further scientific development to be answered.

Why Are There as Many Elements in the Cantor Set as There Are Real Numbers?

There are many important concepts in linear algebra, such as linear correlation and linear independence, eigenvalues and eigenvectors, and so on. The article provides a graphical explanation of how to distinguish between the concepts of linear correlation and linear independence. The conclusion points out that linear independence means that there are no two (base) vectors with the same direction in a vector graph;otherwise, it is a linear correlation.

The Meaning of Divergence

The concept of the divergence is fundamental in electromagnetic field theory, yet they are especially difficult mathematical concepts. Understanding this concept requires strong spatial and abstract thinking. When teaching, through the graphical and quantitative methods presented herein, the significance of the divergence is displayed by a quantitative method for the first time. Through these methods, the concepts of the divergence can be grasped more easily. These explanations will be helpful for students to strengthen the understanding of this concept and has a certain reference significance.

Classification of hyperspectral images using fusion of CNN and MiniGCN with SVM

Convolutional neural networks(CNNs)have gained popularity for categorizing hyperspectral(HS)images due to their ability to capture representations of spatial-spectral features.However,their ability to model relationships between data is limited.Graph convolutional networks(GCNs)have been introduced as an alternative,as they are effective in representing and analyzing irregular data beyond grid samplingconstraints.WhileGCNs have traditionally.been computationally intensive,minibatch GCNs(miniGCNs)enable minibatch training of large-scale GCNs.We have improved the classification performance by using miniGCNs to infer out-of-sample data without retraining the network.In addition,fuzing the capabilities of CNNs and GCNs,through concatenative fusion has been shown to improve performance compared to using CNNs or GCNs individually.Finally,support vector machine(SvM)is employed instead of softmax in the classification stage.These techniques were tested on two HS datasets and achieved an average accuracy of 92.80 using Indian Pines dataset,demonstrating the effectiveness of miniGCNs and fusion strategies.