The energy-critical, focusing nonlinear Schrödinger equation in the nonradial case reads as follows: i∂tu = −∆u− |u| 4 N−2 u, u(x, 0) = u0 ∈ H(R ), N ≥ 3. Under a suitable assumption on the maximal strong solution, using a compactness argument and a virial identity, we establish the global well-posedness and scattering in the nonradial case, which gives a positive answer to one open problem pro...

Let be the Laplace-d'Alembert operator on a pseudo-Riemannian manifold (M; g). We derive a series expansion for the fundamental solution G(x; y) of + H , H 2 C 1 (M), which behaves well under various symmetric space dualities. The qualitative properties of this expansion were used in our paper in Invent. Math. 129 (1997) 63{74, to show that the property of vanishing logarithmic term for G(x; y)...

Smart Table Tennis Racket In article number 2100535, Mengying Zhang, Jinbo Wu, and coworkers invent a smart table tennis racket with tunable stiffness based on electrorheological elastomers. The face is multilayer structure of rubber, soft electrode, anisotropic elastomer copper electrode. By applying an electric field, the successfully changed trajectory balls, reduced ejection angle increased...

Warren was a philosopher and scientist. As a freshman at Haverford College he told the Quaker philosopher Rufus Jones that all he wanted to know was: "What is a number that a man may know it; and a man, that he may know a number?" To this the Quaker famously replied: "Friend, thee will be busy as long as thee lives." Warren acknowledged in his last days that the prophecy had been fulfilled, and...

This paper presents the object management facilities being designed into a next-generation data manager, POSTGRES. This system is unique in that it does not invent a new data model for support of objects but chooses instead to extend the relational model with a powerful abstract data typing capability and procedures as full-fledged data base objects. The reasons to remain with the relational mo...

During content planning, a typical discourse generation system receives as input a library of facts and selects facts to include as the content for utterances. However, storytellers do not need to be completely constrained by a set of facts and instead can invent facts which support the storytellers goals, subsequently constructing the storyworld around those facts. We present a discourse-drive...

The present paper proves that all limit points of sequences of renormalized solutions of the Boltzmann equation in the limit of small, asymptotically equivalent Mach and Knudsen numbers are governed by Leray solutions of the Navier-Stokes equations. This convergence result holds for hard cutoff potentials in the sense of H. Grad, and therefore completes earlier results by the same authors [Inve...