Solvability of Some Boundary Value Problems for Fractional -Laplacian Equation

This paper considers the existence of solutions for two boundary value problems for fractional -Laplacian equation. Under certain nonlinear growth conditions of the nonlinearity, two new existence results are obtained by using Schaefer's fixed point theorem. As an application, an example to illustrate our results is given

Function and Structure of Human Left Fusiform Cortex Are Closely Associated with Perceptual Learning of Faces

SummaryTraining can lead to long-lasting improvement in our perceptual ability, which is referred to as perceptual learning. Unraveling its neural mechanisms has proved difficult. With functional and structural magnetic resonance imaging (MRI), we addressed this issue by searching for the neural correlates of perceptual learning of face views over a long time course. Human subjects were trained to perform a face view discrimination task. Their behavioral performance and MRI signals were measured before, immediately after, and 1 month after training. We found that, across individual subjects, their behavioral learning effects correlated with the stability improvement of spatial activity pattern in the left fusiform cortex immediately after and 1 month after training. We also found that the thickness of the left fusiform cortex before training could predict subjects’ behavioral learning effects. These findings, for the first time, not only suggest that, remarkably, the improved pattern stability contributes to the long-term mechanisms of perceptual learning, but also provide strong and converging evidence for the pivotal role of the left fusiform cortex in adaptive face processing

Ground state solutions of Kirchhoff-type fractional Dirichlet problem with p-Laplacian

Abstract We consider the Kirchhoff-type p-Laplacian Dirichlet problem containing the left and right fractional derivative operators. By using the Nehari method in critical point theory, we obtain the existence theorem of ground state solutions for such Dirichlet problem

Solvability of periodic boundary-value problems for second-order nonlinear differential equation involving fractional derivatives

This article concerns the existence of solutions to periodic boundary-value problems for second-order nonlinear differential equation involving fractional derivatives. Under certain linear growth condition of the nonlinearity, we obtain solutions, by using coincidence degree theory. An example illustrates our results

Hyper-Chaotic Color Image Encryption Based on Transformed Zigzag Diffusion and RNA Operation

With increasing utilization of digital multimedia and the Internet, protection on this digital information from cracks has become a hot topic in the communication field. As a path for protecting digital visual information, image encryption plays a crucial role in modern society. In this paper, a novel six-dimensional (6D) hyper-chaotic encryption scheme with three-dimensional (3D) transformed Zigzag diffusion and RNA operation (HCZRNA) is proposed for color images. For this HCZRNA scheme, four phases are included. First, three pseudo-random matrices are generated from the 6D hyper-chaotic system. Second, plaintext color image would be permuted by using the first pseudo-random matrix to convert to an initial cipher image. Third, the initial cipher image is placed on cube for 3D transformed Zigzag diffusion using the second pseudo-random matrix. Finally, the diffused image is converted to RNA codons array and updated through RNA codons tables, which are generated by codons and the third pseudo-random matrix. After four phases, a cipher image is obtained, and the experimental results show that HCZRNA has high resistance against well-known attacks and it is superior to other schemes