Time-dependent Lyapunov matrix equation (TDLME) plays a central role in the control of linear and nonlinear systems. Existing models, including the classical zeroing neural dynamics (ZNDs) model and its variants, have been used to address the TDLME problem. However, those models require time-dependent matrix inversion, which is computationally demanding, and they primarily focus on measurement-related noise, overlooking other sources of system uncertainty. To overcome these challenges, we propose an inverse-free reciprocal-type ZND (RTZND) model. This model integrates an energy-based error function with the ZND framework, eliminating the need for matrix inversion and incorporating error-feedback-related noise through its closed-loop control structure. We establish the convergence and robustness of the RTZND model using Lyapunov stability theory and assess its performance under external disturbances. Numerical simulations confirm its effectiveness and improved computational efficiency in solving the TDLME problem. We further confirm its applicability through two case studies, a time-dependent linear system and a nonlinear system modeled by the single machine infinite bus (SMIB) system, highlighting the RTZND model’s practical value in addressing TDLME problems.

In this study, the authors propose two fourth‐order partial differential equations (PDEs) to inpaint the image. By analysing those anisotropic fourth‐order PDEs and comparing their diffusion images, the authors confirm they are forward diffusion or backward diffusion. A numerical algorithm is presented using a finite‐difference method and analyse the stability of discretisation. Finally, they show various experimental results and conclude that the proposed new models are better than the second‐order and third‐order PDEs, especially for weakening the blocky effects.

Online/offline signatures are used in a particular scenario where the signer must respond quickly once the message to be signed is presented. In this paper, we present a general method to efficiently convert a trapdoor hash family into an online/offline signature scheme without resorting to any additional signature scheme. We prove that the new scheme is secure in the randomoraclemodel if the underlying trapdoor hash family is collision resistant. Compared to Shamir and Tauman's paradigm, there is an almost 50% reduction in overall computational cost by using the new scheme.

We reveal some drawbacks in Ghodosi's scheme and present an improved RSA-based access control scheme for hierarchical groups. The proposed scheme enjoys the following properties: 1. The size of an individual's share sequence is bounded by a small constant times the size of the RSA modulus corresponding to that group. 2. The delegation of information flow from higher-level groups to lower-level groups is completely non-interactive. 3. It doesn't require an online trusted authority to upgrade the system as soon as communication happened. 4. The proposed scheme is resistant to conspiracy.