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New PDF release: The Nested Universal Relation Database Model

This monograph describes a style of knowledge modelling whose easy objective is to make databases more straightforward to exploit by way of offering them with logical information independence. to accomplish this, the nested UR (universal relation) version is outlined via extending the classical UR version to nested family. Nested family generalize flat family and make allowance hierarchically based items to be modelled at once, while the classical UR version permits the person to view the database as though it have been composed of a unmarried flat relation.

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Additional info for New Scientist (August 20, 2005)

Example text

There is an integer k such that c = kd. Since d is a sum of multiples of a and b, we may write am + bn = d. Multiplying this equation by k, we get a(mk) + b(nk) = dk = c so that x = mk and y = nk is a solution. For the “only if” part, suppose x0 and y0 is a solution of the equation. Then ax0 + by0 = c. Since d | a and d | b, then d | c. 2 (Division Theorem). 6) where a is called the dividend, q the quotient, and r the remainder. If b a, then r satisfies the stronger inequalities 0 < r < a. 18 1.

Hence, r = r1 , and also q = q1 . 1. Let a and b be integers with a = 0. We say a divides b, denoted by a | b, if there exists an integer c such that b = ac. When a divides b, we say that a is a divisor (or factor) of b, and b is a multiple of a. If a does not divide b, we write a b. If a | b and 0 < a < b, then a is called a proper divisor of b. The largest divisor d such that d | a and d | b is called the greatest common divisor (gcd) of a and b. The greatest common divisor of a and b is denoted by gcd(a, b).

The algebraic formula for computing P3 (x3 , y3 ) = P1 (x1 , y1 ) + P2 (x2 , y2 ) on E is as follows: (x3 , y3 ) = (λ2 − x1 − x2 , λ(x1 − x3 ) − y1 ), where  3x21 + a    if P1 = P2 2y1 λ= y − y1    2 otherwise. x2 − x1 The idea for fast computing Q = kP over an elliptic curve E is similar to that of computing y = xk over N. For example, to compute Q = 105P , we first let k = 105 = (1101001)2 and then perform the operations as follows starting from e6 to e0 : 1: 1: 0: 1: 0: 0: 1: Q ← P + 2Q Q ← P + 2Q Q ← 2Q Q ← P + 2Q Q ← 2Q Q ← 2Q Q ← P + 2Q ⇒ ⇒ ⇒ ⇒ ⇒ ⇒ ⇒ Q←P ⇒ c ← P + 2P ⇒ Q ← 2(P + 2P ) ⇒ Q ← P + 2(2(P + 2P )) ⇒ Q ← 2(P + 2(2(P + 2P ))) ⇒ Q ← 2(2(P + 2(2(P + 2P )))) ⇒ Q ← P + 2(2(2(P + 2(2(P + 2P ))))) ⇒ Q=P Q = 3P Q = 6P Q = 13P Q = 26P Q = 52P Q = 105P .