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The assumption that f is not constant is necessary, as otherwise the oscillations are all zero and var (f ) = 0 In this case, the graph is a horizontal segment and the value of its dimension is 1 Proof A proof [TRI 99] using geometric arguments consists of estimating the area of the Minkowski -sausage ( ) We show that this is equivalent to that of the union of the horizontal segments t J [t , t + ] {z(t)} centered on the graph This is equal to the variation var (z) EXAMPLE 17 The graph of a self-af ne function de ned on J = [a, b] may be obtained as the attractor of an iterated functions system, like the self-similar curves of Example 12 (see also s 9 and 10) For this, it is suf cient to de ne: an integer N 2; N + 1 points in the plane A1 = (x1 , y1 ), , AN +1 = (xN +1 , yN +1 ), such that x1 = a < < xi < < xN +1 = b; N af ne triangular applications of the plane T1 , ,TN , such that, for each Ti , the image of the segment A1 AN +1 is the segment Ai Ai+1 These may be written as: Ti = i hi 0 i +

Page 20 customer expectations requires us to look at the project from the customer s perspective In the world of global business and tightening competition, only those firms that excel in mastering the details of their business can be highly successful For project developer firms, this means a great challenge through requiring continuous learning and process improvements, usually in very complicated business environments This is where product thinking comes into the picture It helps the firm to focus on the details that are critical for their success The project firms that adopt the concept of product thinking can more easily build their quality standard, supply chain management, project management, and customer relationship management the successful framework in Figure 14 Figure 15 presents the product as a combination of the product concept and the delivery process of getting the physical product to the customer The customer is weighing two separate considerations in deciding whether or not to award us the job and then in evaluating our performance First, the customer is keenly interested in the product concept that we are offering Here the concepts of technical validity, organizational validity, and organizational effectiveness come

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The Sybil attack [2] consists of a node assuming several node identities while using only one physical device The additional identities can be obtained either by impersonating other nodes or by making use of false identities These identities can all be used simultaneously or over a period of time This attack can impact several services in ad hoc networks For example it can impact multipath routing [75], where a set of supposedly disjoint paths can all be passing through the same malicious node which is using several Sybil identities This attack can also impact data aggregation where the same node can contribute multiple readings each using a different identity [76] Fair resource allocation mechanisms will also be affected since a node can claim more than its fair share by using the various Sybil identities Mechanisms based on trust, voting, and so on, are also affected by this attack A simple approach for detecting the Sybil identities could be to issue a public-key certi cate to each of the identities The problem, though, is the need for a central authority that can distribute the certi cates In addition, this solution requires higher computational capabilities than might be available on resource constrained devices such as sensor nodes Resource testing was suggested as an approach to prevent Sybil attacks in [2] This approach makes use of the fact that each node is limited in some resources The test then veri es if each identity has the proper amount of the tested resource Thus, the implicit assumption here is that every identity has the same quantity of the tested resource The resources suggested in [2] are computation, storage, and communication, but these resources might not be the right ones to test for in ad hoc and sensor networks because of the heterogeneity possible in such networks due to which different physical devices have different values for the quantity of the tested resource Another resource suggested in [76] is the radio Here the assumption is that every physical device has only one radio that is incapable of simultaneously transmitting and receiving on more than one channel Thus, a node that desires to verify if any of its neighbors are.

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