instability of standing wave, global existence and blowup for the klein-gordon-zakharov system with different-degree nonlinearities

This paper discusses the Klein–Gordon–Zakharov system with different-degree nonlinearities in two and three space dimensions. Firstly, we prove the existence of standing wave with ground state by applying an intricate variational argument. Next, by introducing an auxiliary functional and an equivalent minimization problem, we obtain two invariant manifolds under the solution flow generated by the Cauchy problem to the aforementioned Klein–Gordon–Zakharov system. Furthermore, by constructing a type of constrained variational problem, utilizing the above two invariant manifolds as well as applying potential well argument and concavity method, we derive a sharp threshold for global existence and blowup. Then, combining the above results, we obtain two conclusions of how small the initial data are for the solution to exist globally by using dilation transformation. Finally, we prove a modified instability of standing wave to the system under study.

Optimization of Global Signal Networks for Island-Style FPGAs

We present a staggered buffer connection method that provides flexibility for buffer insertion while designing global signal networks using the tile-based FPGA design methodology. An exhaustive algorithm is used to analyze the trade-off between area and speed of the global signal networks for this staggered buffer insertion scheme, and the criterion for determining the design parameters is presented. The comparative analytic result shows that the methods in this paper are proven to be more efficient for FPGAs with a large array size.

Global stability of Hopfield neural networks

This paper gives a condition for the global stability of a continuous-time hopfield neural network when its activation function maybe not monotonically increasing.