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... ∂s (t, s)|s=t ≡ 0. Therefore when T = R, the above theorem improves [6, Theorem 1]. Remark 2.4. Let h(t, s) = (t − s)γ , γ > 0. It is easy to see that h(t, s) satisfies (H1 ) − −(H4 ). So we get the following Kamenev-type criterion on time scales (Note that in [6] it is assumed that γ > 1.) We defin ...
... ∂s (t, s)|s=t ≡ 0. Therefore when T = R, the above theorem improves [6, Theorem 1]. Remark 2.4. Let h(t, s) = (t − s)γ , γ > 0. It is easy to see that h(t, s) satisfies (H1 ) − −(H4 ). So we get the following Kamenev-type criterion on time scales (Note that in [6] it is assumed that γ > 1.) We defin ...
STABILITY OF ANALYTIC OPERATOR
... function space integral [7]. This is the rst stability theorem for the integral as a bounded linear operator on L2 (Rn ) where n is any positive integer. In [10], Johnson and Skoug introduced stability theorems for the integral as an L(Lp (RN ); Lp (RN )) theory, 1 < p 2. Chang studied stability ...
... function space integral [7]. This is the rst stability theorem for the integral as a bounded linear operator on L2 (Rn ) where n is any positive integer. In [10], Johnson and Skoug introduced stability theorems for the integral as an L(Lp (RN ); Lp (RN )) theory, 1 < p 2. Chang studied stability ...
Chapter 3 Review HW
... _________________________________________________________ 7. Find the values of x and y given m ║ n in the diagram above, m∠ 4 = (6x – 5), m∠ 10 = (5x + 8), and m∠ 9 = (3y – 10). ...
... _________________________________________________________ 7. Find the values of x and y given m ║ n in the diagram above, m∠ 4 = (6x – 5), m∠ 10 = (5x + 8), and m∠ 9 = (3y – 10). ...
Convergence in Mean Square Tidsserieanalys SF2945 Timo Koski
... then we say that (6.5) is a causal linear process. The condition (6.6) guarantees (c.f. (5.6)) that the infinite sum in (6.5) converges in mean square. By causality we mean that the current value Xt is influenced only by values of the white noise in the past, i.e., Zt−1 , Zt−2 , . . . , and its curr ...
... then we say that (6.5) is a causal linear process. The condition (6.6) guarantees (c.f. (5.6)) that the infinite sum in (6.5) converges in mean square. By causality we mean that the current value Xt is influenced only by values of the white noise in the past, i.e., Zt−1 , Zt−2 , . . . , and its curr ...
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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.