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coating sheds particles that impinge upon the turbine blades and cause erosion. Blade failures: Resonant vibrations cause mechanical stress in blades near inlet. Sealed bearing failure: Vibrations during start-up cause stress on the sealed bearings that seal the shaft as it detrudes from the turbine. This creates leaks in the seal.
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Given a point set V , the Delaunay triangulation is obtained by all triangles T = (u, v, w) V 3 that satisfy that there exists no further node x V that is contained in the disk U(u, v, w) passing through the nodes u, v, and w. The geometric graph formed by a Delaunay triangulation is planar and is known to be a spanner with respect to the Euclidean distance metric [9,18]. It is thus an ideal candidate planar graph routing schemes might be applied on. However, Delaunay triangulation requires knowledge of the entire node set, and, moreover, might contain arbitrarily long edges, that is, edges that are longer than the communication range of its end points. It has been observed that the intersection of the Delaunay triangulation and UDG over a node set V , which is referred as unit Delaunay triangulation UDel(V ), preserves the spanning property; that is, with respect to the Euclidean distance metric for two given nodes the shortest path in UDel(V ) is at most a constant longer than the shortest path in the UDG [14,28]. Thus, Delaunay triangulation is an interesting candidate for constructing planar, spanning topologies in a localized manner. In the method described by Gao et al. [14], each node locally constructs a Delaunay triangulation over all its one-hop neighbor nodes and announces this triangulation to its one-hop neighbors. Based on this information a node u checks for each incident Delaunay triangulation edge (u, v) if there exists a one-hop neighbor w that is connected to v but does not contain the edge (u, v) in its local Delaunay triangulation. In this case, the edge (u, v) is removed at node u. It is shown that this topology construction method always produces a planar graph that preserves all edges of UDel(V ) [14]. The topology is thus a spanner as well. Li et al. [28] introduced the concept of k-localized Delaunay triangulation LDelk (V ), which denotes the topology obtained by preserving each node Gabriel graph edges and edges of all k-localized Delaunay triangles. The latter refers to all triangles (u, v, w) that satisfy that u, v, and w can reach each other in the underlying UDG and that the disk U(u, v, w) does not contain any k-hop neighbor of u, v, or w. It is observed that LDelk (V ) may be nonplanar for k = 1 while it is always planar for k > 2. Moreover, it is shown that LDelk (V ) is a spanner. LDelk (V ) can be used for localized topology control since it requires only local neighborhood information. However, the communication cost will be high for k > 1. For this reason the planarized LDel1 (V ) method PLDel(V ) described in the work by Li et al. [28] rst locally constructs the nonplanar topology LDel1 (V ) and then removes intersecting edges by the following scheme. In a previous step, a node u removes a triangle (u, v, w) from LDel1 (V ) if one edge of a neighbor nodes triangle (x, y, z) is lying in the circle U(u, v, w). Afterward, node u keeps all incident edges that are either a Gabriel graph edge or an edge from a triangle (u, v, w) that was kept by each triangle nodes u, v, and w. The partial Delaunay triangulation PDT described by Li et al. [29] employs an alternative de nition of Delaunay triangulation in a localized way. It is easy to show that the edges (u, v) of a Delaunay triangulation are exactly those edges that satisfy that there exists a circle having u and v on its boundary that does not contain any other nodes. A node u running the PDT method keeps an edge (u, v) if the empty circle rule
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the checklist for package selection. This includes the ability to exchange data with other information systems, the capacity of the package (both with regard to the number of simultaneous users and the number of transactions), the data model used in the package, and such issues as support during implementation, user guides, and training.
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of nearby wifi hotspots, stock quotes, directions, and more. Services like 4INFO (http://4info.net/howto/index.jsp tag=fr_hp_btm_nav) and Google Mobile s SMS search (http://google.com/intl/en_us/mobile/sms/) make it easy. For example, text wifi 80222 to 4INFO (44636) for hotspots in zip code 80222 or flight UAL 696 to GOOGLE (466453) for United 696 flight status. Add an item to your to-do list or calendar. Set up a to-do list on Gubb (gubb.net) and you can add items by SMS. Add events to your 30Boxes (30boxes.com) or Google Calendar (calendar.google.com) by just texting the details to the short code, like 8/8 8am meet with John. Check your daily agenda. Google Calendar makes it easy to find out what s on your schedule. Text next to GVENT (48368) to get your next appointment, day to get that day s agenda, or nday to get tomorrow s agenda. Remind yourself. Online calendars will send you text message reminders of upcoming events. Remember the Milk to-do lists (rememberthemilk .com) will remind you by SMS too. You can also use a dedicated reminder service like PingMe (gopingme.com). Read your voice mail. Get the gist of a voicemail message by SMS, with CallWave s Vtxt service (http://www.callwave.com/widgets/ureg.aspx). You won t get an exact transcription less important comments like hello and ummmm will be left out but that keeps the message down to about the size of a text message. Get email by text message. All the carriers offer email gateways to SMS; check the list at http://www.tipmonkies.com/2005/09/22/sms-toe-mail-the-complete-guide/ to see what yours is. Figure out what yours is and you can forward selected email to your phone. If you want to get certain urgent emails, you can tell the senders to put a code word into the subject and use a filter to send only those messages to SMS.
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The approach of case-based reasoning can be contrasted with that used in other knowledge-based systems, such as rule-based or combined frame-rule-based systems. In rule-based systems, one has a rule base consisting of a set of production rules of the form: IF A, THEN B, where A is a condition and B is an action. If the condition A holds true, the action B is carried out. Condition A can be a composite condition consisting of, say, a conjunction of premises A1 ; A2 ; . . . ; An . In addition, a rule-based system has an inference engine that compares the data it holds in working memory with the condition parts of rules to determine which rules to re. Combined frame-rule-based systems also utilize frames, in addition to rules, to capture stereotypical knowledge. Frames consist of slots that can have default values, actual values, or attached daemons. Frames use a procedure or a rule set to determine the values required when they are triggered. Rule-based and combined frame-rule-based systems require one to acquire the symbolic knowledge that is represented in these rules or frames using manual knowledge engineering or automated knowledge acquisition tools. Sometimes, one utilizes a model of the problem
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debt issue. If the value of the assets, at maturity of the debt issue, is greater than the face value of the debt (the exercise price ), then the owners of the rm will pay the debt holders and keep the remaining value. However, if assets are insuf cient to pay the debt, the owners of the equity will exercise their default option and put the remaining assets to the debt holders. In this simple framework, the post-default value of the debt is equal to the value of the rm s remaining assets. This implies that, at maturity of the debt (i.e., at expiration of the default option ), the value of the default-risky debt is 0; If V (T ) > F D(T ) = F F V (T ); If V (T ) F where F is the face value of the (zero coupon) debt issue and V(T) is the value of the rm s assets at maturity. As we discussed in 3, in a structural model, the value of the default-risky debt is equivalent to the value of a risk-free zero coupon of equal maturity minus the value of the default option. D(t ) = Value of Risk-Free Debt Value of Default Option = F DFt f [V (t ), T , r , F, v ] So it follows that pricing credit risk is an exercise in valuing the default option. As implied in the preceding equation, this valuation could be accomplished using standard option-valuation techniques where the price of
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Frequency moments represent useful statistical information on a data set and are widely used in database applications. In particular, F0 and F1 represent the number of distinct values in the data stream and the length of the stream, respectively. F2 , also known as Gini s index, provides valuable information about the skew of the data. F , nally, is related to the maximum frequency element in the data stream, that is, maxi U fi . 8.3.2.1 Probabilistic Counting We begin our discussion from the estimation of F0 . The problem of counting the number of distinct values in a data set using small space has been studied since the early 1980s by Flajolet and Martin [29,30], who proposed a hash-based probabilistic counter. We rst note that a na ve approach to compute the exact value of F0 would use a counter c(i) for each value i of the universe U, and would therefore require O(1) processing time per item, but linear space. The probabilistic counter of Flajolet and Martin [29,30] relies on hash functions to nd a good approximation of F0 using only O(log u) bits of memory, where u is the size of the universe U. The counter consists of an array C of log u bits. Each stream item is mapped to one of the log u bits by means of the combination of two functions h and t. The hash function h : U [0, u 1] is drawn from a set of strongly 2-universal hash functions: it transforms values of the universe into integers suf ciently uniformly distributed over the set of binary strings of length log u. The function t, for any integer i, gives the number t(i) of trailing zeros in the binary representation of i. Updates and queries work as follows: Counter update: Upon seeing a stream value x, set C[t(h(x))] to 1. Distinct values query: Let R be the position of the rightmost 1 in the counter C, with 1 R log u. Return 2R . Notice that all stream items by the same value will repeatedly set the same counter bit to 1. Intuitively, the fact that h distributes items uniformly over [0, u 1] and the use of function t guarantee that counter bits are selected in accordance with a geometric distribution; that is, 1/2 of the universe items will be mapped to the rst counter bit, 1/4 will be mapped to the second counter bit, and so on. Thus, it seems reasonable to expect that the rst log F0 counter bits will be set to 1 when the stream contains
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