... interconnection network under link failure. The minimum dominating set of sites plays an important role in the network for it dominates the whole network with the minimum cost. So we must consider whether its function remains good when the network is attacked. Suppose that someone such as a saboteur ...
Calculus Lecture 2
... taking x sufficiently close but to the right of c. lim+ f (x) = −∞ means that f (x) can be made as small as we wish by x→c ...
... taking x sufficiently close but to the right of c. lim+ f (x) = −∞ means that f (x) can be made as small as we wish by x→c ...
Elementary Number Theory
... n · 1 > n · k despite that fact that k is positive and so 1 ≤ k. This is impossible because it violates the same Property of Inequalities. qed 1.3 Definition An integer n is even (or has even parity) if it is divisible by 2 and is odd (or is of odd parity) otherwise. 1.4 Lemma Recall that |a| equals ...
... n · 1 > n · k despite that fact that k is positive and so 1 ≤ k. This is impossible because it violates the same Property of Inequalities. qed 1.3 Definition An integer n is even (or has even parity) if it is divisible by 2 and is odd (or is of odd parity) otherwise. 1.4 Lemma Recall that |a| equals ...
Understanding Calculus II: Problems, Solutions, and Tips
... estimate the age of a fossil using carbon dating. In each of these cases, calculus is needed to solve the problem. Although precalculus mathematics (geometry, algebra, and trigonometry) also deals with velocities, accelerations, tangent lines, slopes, and so on, there is a fundamental difference bet ...
... estimate the age of a fossil using carbon dating. In each of these cases, calculus is needed to solve the problem. Although precalculus mathematics (geometry, algebra, and trigonometry) also deals with velocities, accelerations, tangent lines, slopes, and so on, there is a fundamental difference bet ...
and let A,B be finitely generated graded S-modules. If T is a
... the ideals I generated by quadrics such that m2 ⊂ I + L for every ideal L generated by n − q − 1 independent linear forms. In Section 7 we study powers of linearly presented ideals. The following conjecture sparked this entire paper: CONJECTURE 1.1 (Eisenbud and Ulrich). If I ⊂ S is a linearly prese ...
... the ideals I generated by quadrics such that m2 ⊂ I + L for every ideal L generated by n − q − 1 independent linear forms. In Section 7 we study powers of linearly presented ideals. The following conjecture sparked this entire paper: CONJECTURE 1.1 (Eisenbud and Ulrich). If I ⊂ S is a linearly prese ...
Fundamental theorem of calculus
The fundamental theorem of calculus is a theorem that links the concept of the derivative of a function with the concept of the function's integral.The first part of the theorem, sometimes called the first fundamental theorem of calculus, is that the definite integration of a function is related to its antiderivative, and can be reversed by differentiation. This part of the theorem is also important because it guarantees the existence of antiderivatives for continuous functions.The second part of the theorem, sometimes called the second fundamental theorem of calculus, is that the definite integral of a function can be computed by using any one of its infinitely-many antiderivatives. This part of the theorem has key practical applications because it markedly simplifies the computation of definite integrals.