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A.12. PROOF OF THEOREM 7.3.1 nC nB n n 1 A A p2 1 k p2 2 k pij1 k pij2 k p.j1 k p.j2 k .j ij = pi.. p..k j =1 j =1 p.j1 k p.j2 k i=1
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All methods defined in the home interface are referenced in the bean class. However, the methods in the bean class have the prefix ejb. Hence, in the home method, the method create is known as ejbCreate in the bean class. Notice that the prefacing of the home method name with ejb also holds for finder methods, too. Speaking of finder methods, notice that the method findByPrimaryKey coded in the home interface template returns an object of the bean class, whereas the method ejbFindByPrimaryKey returns an object of the bean s class primary key. A moment s reflection reveals the wisdom of this construct: The bean class method, invoked remotely through the home interface, should return a reference to the object. Because a primary key uniquely knows the entity bean, returning the primary key is the logical choice. However, remember that your client writes code to invoke the method on the home interface, not the bean interface. Part of the magic of EJB is the remote invocation of the bean method on the server when the client invokes the corresponding method from the home (or remote) interface. You can code finder methods for those entity beans with bean-managed persistence. Beans with containermanaged persistence implement finder methods for you. Methods described in the remote interface have the same name as the corresponding methods in the bean interface. Do not prefix remote interface methods with ejb. Entity beans require that you code an ejbPostCreate method for every create method described in your home interface. Notice the presence of two ejbPost create methods: ejbPostCreate and ejbPostAnotherCreate. The ejbPost methods execute after the create methods. The last seven methods are the entity bean s state management callback methods, which are explained in detail in the next chapter. Here, you can say that these methods notify the entity bean when a bean is created, loaded from permanent storage, or destroyed. Because javax.ebj.EntityBean is an interface, you must supply a method body for these required state management methods, but you need not do anything meaningful. Many developers use adapter classes to provide empty method bodies in those rare cases in which beans are not already extending a superclass. You can read about the state management callback methods in s 13, 14, and 15.
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A trade is built from a collection of legs and possibly a schedule of exercise decisions. The class trade in module encapsulates the concept of a trade.
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It is often said, What you don t know won t hurt you. This does not apply in business. It equally does not apply with respect to patents. Patent infringement is not a specific intent tort in layman s terms, that means that one may infringe a patent without intending to do so. Patent infringement may be innocent, but it is patent infringement nonetheless. It is not a defense to a charge of patent infringement that you were unaware of the allegedly infringed patent (although, as we will see, it
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Comparison of RSOM with SOM Quantization Error 0.038 0.022 32.588 0.081 28.855 0.246 Iteration at Which Error Converged 5000 50 8830 95 8666 102
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To nd the rank of an object a1 a2 . . . am , one should nd the number of objects preceding it. It can be found by the following function: function rank(a1 , a2 , . . . , am ) rank 1 ; for i 1 to m do for each x < ai rank rank + N(a1 , a2 , . . . , ai 1 , x). Obviously in the last for loop only such values x for which a1 a2 . . . ai 1 x can be completed to represent an instance of a combinatorial object should be considered (otherwise adding 0 to the rank does not change its value). We now consider a general procedure for unranking. It is the inverse of ranking function and can be calculated as follows. procedure unrank ( rank, n, a1 , a2 , . . . , am ) i 0; repeat i i + 1; x rst possible value; while N(a1 , a2 , . . . , ai 1 , x) rank do {rank rank N(a1 , a2 , . . . , ai 1 , x); x next possible value}; ai x until rank = 0; a1 a2 . . . am lexicographically rst object starting by a1 a2 . . . ai . We now present ranking and unranking functions for several combinatorial objects. In case of ranking combinations out of {1, 2, . . . , n}, x is ranged between ai 1 + 1 and ai 1. Any (m, n)-combination that starts with a1 a2 . . . ai 1 x is in fact a (m i, n x)- combination. The number of such combinations is C(m i, n x). Thus the ranking algorithm for combinations out of {1, 2, . . . , n} can be written as follows (a0 = 0 in the algorithm): function rankcomb (a1 , a2 , . . . , am ) rank 1 ; for i 1 to m do for x ai 1 + 1 to ai 1 do rank rank + C(m i, n x). In lexicographic order, C(4, 6) = 15 (4,6)-combinations are listed as 1234, 1235, 1236, 1245, 1246, 1256, 1345, 1346, 1356, 1456, 2345, 2346, 2356, 2456, 3456. The rank of 2346 is determined as 1 + C(4 1, 6 1) + C(4 4, 6 5) = 1 + 10 + 1 = 12 where last two summands correspond to combinations that start with 1 and 2345, respectively. Let us consider a larger example. The rank of 3578 in
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