In communication networks there is a growing need for ensuring that networks maintain service despite failures. To meet the need, the concept of δ-reliable channel is introduced; it is a set of communication channels along a set of paths. The δ-reliable channel meets the requirement that if a link or node fails, failure is limited to a maximum of δ f (f total capacity of the channels, and 0<δ 1). The max-flow min-cut theorem of δ-reliable flow has been proved for the single-commodity case. In this paper we give a method for evaluating the maximum δ-reliable flow between a specified pair of vertices for single commodity case. The method consists of a maximum of 1/δ iterations of calculations of the maximum flow value.

A new silicon capacitive pressure sensor with center clamped diaphragm is presented. The sensor has a silicon-glass structure and is fabricated by batch-fabrication processes. Since deformed diaphragm has a doughnut-shape, parallel-like displacement is realized and therefore better linearity of 0.7% which is half of the conventional flat diaphragm sensor is obtained. It is clarified both analytically and experimentally that the capacitive pressure sensor with center clamped diaphragm is advantageous in terms of linearity.

The problem of finding the location of the center and the problem of finding the median in a graph are important and basic among many network location problems. In connection with these two problems, the following two theorems are well-known. One is proved by Jordan and Sylvester, and it shows that the center of every tree consists of either one vertex or two adjacent vertices. The other is proved by Jordan and it shows that the centroid (median) of every tree consists of either one vertex or two adjacent vertices. These theorems have been generalized by many researchers so far. Harary and Norman proved that the center of every connected graph G lies in a single block of G. Truszczynski proved that the median of every connected graph G lies in a single block of G. Slater defined k-centrum, which can express both center and median, and proved that the k-centrum of every tree consists of either one vertex or two adjacent vertices. This paper discusses generalization of these theorems. We define the -blocks of a graph G as a generalization of the blocks of G, where is a subset of the vertex set of G; and define the -centroid of G as a generalization of the centroid of G. First, we prove that the -centroid of G is included in an -block of G. This is a generalization of the above theorems concerning centroid, by Jordan and Truszczynski. Secondly, we define the -centrum of G as a generalization of the k-centrum of G and prove some theorems concerning the location of -centrum. Using one of theorems proved here, we can easily obtain the theorem showing that the k-centrum of every connected graph G lies in a single block of G. This theorem is a generalization of the above theorem by Slater.