Hyperspectral Image Super-Resolution Network Based on Reinforcing Inter-Spectral Incremental Information

Hyperspectral images typically have high spectral resolution but low spatial resolution,which impacts the reliability and accuracy of subsequent applications,for example,remote sensingclassification and mineral identification.But in traditional methods via deep convolution neural net-works,indiscriminately extracting and fusing spectral and spatial features makes it challenging toutilize the differentiated information across adjacent spectral channels.Thus,we proposed a multi-branch interleaved iterative upsampling hyperspectral image super-resolution reconstruction net-work(MIIUSR)to address the above problems.We reinforce spatial feature extraction by integrat-ing detailed features from different receptive fields across adjacent channels.Furthermore,we pro-pose an interleaved iterative upsampling process during the reconstruction stage,which progres-sively fuses incremental information among adjacent frequency bands.Additionally,we add twoparallel three dimensional(3D)feature extraction branches to the backbone network to extractspectral and spatial features of varying granularity.We further enhance the backbone network’sconstruction results by leveraging the difference between two dimensional(2D)channel-groupingspatial features and 3D multi-granularity features.The results obtained by applying the proposednetwork model to the CAVE test set show that,at a scaling factor of×4,the peak signal to noiseratio,spectral angle mapping,and structural similarity are 37.310 dB,3.525 and 0.9438,respec-tively.Besides,extensive experiments conducted on the Harvard and Foster datasets demonstratethe superior potential of the proposed model in hyperspectral super-resolution reconstruction.

CRITICAL EXTINCTION EXPONENTS FOR POLYTROPIC FILTRATION EQUATIONS WITH NONLOCAL SOURCE AND ABSORPTION

In this article, by applying the super-solution and sub-solution methods, instead of energy estimate methods, the authors investigate the critical extinction exponents for a polytropic filtration equation with a nonlocal source and an absorption term, and give a classification of the exponents and coefficients for the solutions to vanish in finite time or not, which improve one of our results （Applicable Analysis, 92（2013）, 636-650） and the results of Zheng et al （Math. Meth. Appl. Sci., 36（2013）, 730-743）.

An ecological model with the p-Laplacian and diffusion

We study the existence of positive solutions of a population model with diffusion of the form {-△pu=aup-1-f（u）-c/ua,x∈Ω,u=0,x∈Ω where △p denotes the p-Laplacian operator defined by △pz =div（｜z｜P-2z）, p 〉 1, Ω is a bounded domain of RN with smooth boundary, α∈ C （0, 1）, a and e are positive constants. Here f ： [0, ∞） → R is a continuous function. This model arises in the studies of population biology of one species with u representing the concentration of the species. We discuss the existence of positive solution when f satisfies certain additional conditions. We use the method of sub- and super-solutions to establish our results.

Existence and Boundary Behavior of Positive Solutions of Quasi-linear Elliptic Singular Equations with a Gradient term

Existence of positive solutions of a class of quasi-linear elliptic equation with a gradient term is obtained by using super-solution and sub-solution method. In par- ticular, we study the asymptotic behavior of the solution near the boundary up to the second order under various assumptions on the growth of the coefficients of the equa- tion. The results of this paper is new and extend previously known results.