Let x, y be sets. Observe that {〈x, y〉} is one-to-one. In the sequel n denotes a natural number. One can prove the following two propositions: (1) For every non empty topological space T holds T and T ΩT are homeomorphic. (2) Let X be a non empty subspace of En T and f be a function from X into R1. Suppose f is continuous. Then there exists a function g from X into En T such that (i) for every ...

A new re¯ow parameter, heating factor (Q g), which is de®ned as the integral of the measured temperature over the dwell time above liquidus, has been proposed in this report. It can suitably represent the combined e€ect of both temperature and time in usual re¯ow process. Relationship between reliability of the micro-ball grid array (micro-BGA) package and heating factor has been discussed. The...

The paper presents an overview of the current methodology and practice in modeling and control of the grinding process in industrial ball mills. Basic kinetic and energy models of the grinding process are described and the most commonly used control strategies are analyzed and discussed.

This paper deals with the analysis of broadcast soccer video. To recognize interesting events such as a goal, estimation of ball movements is necessary. It is, however, sometimes difficult to detect a ball by a simple color and shape-based method when it overlaps with players and lines. We therefore develop a method of estimating a ball route during such overlaps by considering spatio-temporal ...

This study discusses kinematic and dynamic precession models for a rolling ball with a finite contact area and a point contact respectively. In literature, both conventions have been applied. In this paper, we discuss in detail the kinematic and dynamic models to describe the ball precession and the radius of a circular rolling path. The kinematic model can be used if the contact area and frict...

An apparatus is described for measuring the stiffness and coefficient of restitution (COR) of balls with application to softballs. While standardized test methods currently exist to measure these properties, they do not represent the displacement rate and magnitude that occur in play. The apparatus described herein involves impacting a fixed, solid cylindrical surface (matched to the diameter o...

Sn–9Zn solder joints containing Ag nano particles were prepared by mechanically mixing Ag nano particles (0.3, 0.5 and 1 wt%) with Sn–9Zn solder paste. In the monolithic Sn–Zn solder joints, scallop-shaped AuZn3 intermetallic compound layers were found at their interfaces. However, after the addition of Ag nano particles, an additional uniform AgZn3 intermetallic compound layer well adhered to ...

From an s-variate continuous function whose positive and negative parts both have infinite Lebesgue integral, we construct a continuous rearrangement whose generalized Riemann integral equals any prescribed value. The original function is assumed to be finite a.e., with domain an interval in IR. A similar result is obtained for functions defined on a ball.

For a bounded Lipschitz domain Ω, we show the existence of a measurable set D ⊂ ∂Ω of given area such that the first eigenvalue of the Laplacian with Dirichlet conditions on D and Neumann conditions on ∂Ω \D becomes minimal. If Ω is a ball, D will be a spherical cap.