Abstract Let T: V W be a surjective real linear isometry between full real Hilbert C-modules over real C-algebras A and B, respectively. We show that the following conditions are equivalent:(a) T is a 2-isometry;(b) T is a complete isometry;(c) T preserves ternary products;(d) T preserves inner products;(e) T is a module map. When A and B are commutative, we give a full description of the structure of T.

In this paper, gold ball wire bonding at low temperature using a high frequency transducer was evaluated. The substrates used were FR-4 laminates with two different gold-plated surface finishes: electrolytic and immersion gold-plated. Bonding temperatures of 120/spl deg/C, 80/spl deg/C and 40/spl deg/C were investigated with 1 mil fine pitch gold wire. Prior to wire bonding, the laminates and dice were plasma treated. The surfaces were analyzed prior to and after plasma treatment before wire bonding using XPS and AFM. Bonded areas were also analyzed using SEM. Design of experiment (DOE) techniques have been employed to optimize the bonding parameters at each temperature. The response of the DOE was evaluated by using bond shear and bond pull. The results show that bonding at low temperature is viable with the use of a high frequency transducer wire bonder.

In this paper we deal with the following generalized vector quasi-equilibrium problem: given a closed convex set K in a normed space K , a subset K in a Hausdorff topological vector space K , and a closed convex cone K in K . Let K , K be two multifunctions and K be a single-valued mapping. Find a point K such that\begin {gather}(\hat x,\hat y)\in\Gamma (\hat x)\times\Phi (\hat x),\,\,{\rm and}\,\,\{f (\hat x,\hat y, z): z\in\Gamma (\hat x)\}\cap (-{\rm Int} C)=\emptyset.\notag\end {gather} We prove some existence theorems for the problem in which K can be discontinuous and K can be unbounded.

Let <i>C</i> be a nonempty closed convex subset of a real Hilbert space <i>H</i>. Let <i>S</i> : <i>C</i> <i>C</i> be an asymptotically nonexpansive map in the intermediate sense with the fixed point set <i>F</i>(<i>S</i>). Let <i>A</i> : <i>C</i> <i>H</i> be a Lipschitz continuous map, and <i>VI</i>(<i>C, A</i>) be the set of solutions <i>u</i> <i>C</i> of the variational inequality

Necessary conditions of optimality are derived for multiobjective optimal control problems with pathwise state constraints, in which the dynamics constrain is modeled as a differential inclusion. The obtained result extends results of [2] and [29].