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Chapter 4 -
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... = −k(T − A), where T is the temperature of a body 1. Newton’s law of cooling: dt in an environment with ambient temperature A. d2 x 2. Gravity near the earth’s surface: m 2 = mg, where x is the height of a mass m dt above the surface of the earth. d2 x 3. Hooke’s law: m 2 = −kx, where x is the displ ...
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... The Eulerian numbers have the following combinatorial interpretation. PutZ n = {1,2, — ,A7}*and let 7r=(ai, a2, —, an) denote a permutation of Zn. A rise of IT is a pair of consecutive elements^-, a[+i such that a\ < a{+i; in addition a conventional rise to the left of at is included. Then [6, Ch. 8 ...
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... If multiplication results in poly. of degree > n-1 Reduce it by modulo some irreducible poly. m(x)  f(x) = q(x) m(x) + r(x) => r(x) = f(x) mod m(x) ...
< 1 ... 151 152 153 154 155 156 157 158 159 ... 449 >

System of polynomial equations

A system of polynomial equations is a set of simultaneous equations f1 = 0, ..., fh = 0 where the fi are polynomials in several variables, say x1, ..., xn, over some field k.Usually, the field k is either the field of rational numbers or a finite field, although most of the theory applies to any field.A solution is a set of the values for the xi which make all of the equations true and which belong to some algebraically closed field extension K of k. When k is the field of rational numbers, K is the field of complex numbers.
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