We consider the second order nonlinear ordinary differential equation u″ (t) = u1+α (α > 0) with positive initial data u(0) = a0, u′(0) = a1, whose solution becomes unbounded in a finite time T. The finite time T is called the blow-up time. Since finite difference schemes with uniform meshes can not reproduce such a phenomenon well, adaptively-defined grids are applied. Convergence with mesh sizes of certain smallness has been considered before. However, more iterations are required to obtain an approximate blow-up time if smaller meshes are applied. As a consequence, we consider in this paper a finite difference scheme with a rather larger grid size and show the convergence of the numerical solution and the numerical blow-up time. Application to the nonlinear wave equation is also discussed.

The effect of minor transition metal (TM) additives of Ni, Co, or Zn on the interfacial reactions of the solder joints between Sn–Ag–Cu (SAC) solder and the Cu/Ni(P)/Au substrate was investigated, especially subsequent to multi-reflowing. (Cu,Ni)6Sn5 formed at the interface of all the joints except that of SAC–Ni, of which the interfacial compound was (Ni,Cu)6Sn5. The interfacial compounds of the SAC–Co and SAC–Zn contained a small amount of alloying elements of less than 3 at.%. Two P-rich layers, Ni3P and Ni–Sn–P emerged at the interface of the SAC joints. Nanoindentation analysis indicates that the hardness and Young’s modulus of these two phases were slightly higher than those of the Ni(P) substrate, which were in turn much greater than those of the Cu–Ni–Sn compounds. Worthy of notice is that with TM additions, the Ni–Sn–P phase between Ni3P and interfacial compounds was absent even after 10 reflows. For the SAC–Co joints, the growth of Ni-containing intermetallic compounds within the solder gave rise to the excess Ni dissolution, which caused a discrete Ni3P layer and over-consumed Ni(P) substrate underneath the grooves in-between (Cu, Ni)6Sn5 scallop grains at the interface. This phenomenon is presented for the first time, and the mechanism is proposed in this study.

We investigated a cluster of postoperative febrile episodes and episodes of Acinetobacter baumannii bacteremia in obstetrics and gynecology wards after an electrical blackout and loss of the water supply. The use of patient-controlled analgesia was the only independent risk factor associated with postoperative fever, and A. baumannii isolates recovered from the blood of patients who had received patient-controlled analgesia were genetically related to an isolate recovered from the diluted morphine solution used for this procedure. After inappropriate preparation of the morphine solution was identified and stopped, the outbreak ended.

A fast and accurate method for detecting the collisions of convex polyhedra in a graphical simulation environment based on a newly developed method of distance estimate is presented. By the simultaneous use of the enclosing and the enclosed ellipsoids of convex polyhedra, potential collisions can be detected more accurate than those methods using only bounding volume for object representation, and more efficient than the polyhedral methods. An approach for computing the enclosed ellipsoid of a convex polyhedron by compressing, stretching and scaling operations on its best-fit enclosing ellipsoid is introduced. Graphical simulations of two case studies (moving polyhedral objects in three-dimensional space and multiple robot arms undergoing straight line motions) are conducted to demonstrate the accuracy of the proposed algorithm for collision detection.