1 + - Mathematical Association of America
... for any α ∈ R. We classify the convergence behavior of the one-parameter family f α (x) = (1 + x1 )x+α , thus obtaining an elementary example that’s in keeping with the general principle—especially espoused by Grothendieck in algebraic geometry—that an object only reveals itself fully in “dynamics”. ...
... for any α ∈ R. We classify the convergence behavior of the one-parameter family f α (x) = (1 + x1 )x+α , thus obtaining an elementary example that’s in keeping with the general principle—especially espoused by Grothendieck in algebraic geometry—that an object only reveals itself fully in “dynamics”. ...
erbpetsa
... and give some sufficient conditions for nonoscillation. Recently Bohner and Saker [5] considered (1.1) and used Riccati techniques to give some sufficient conditions for oscillation when (1.3) or (1.4) hold. They obtain some sufficient conditions which guarantee that every solution oscillates or con ...
... and give some sufficient conditions for nonoscillation. Recently Bohner and Saker [5] considered (1.1) and used Riccati techniques to give some sufficient conditions for oscillation when (1.3) or (1.4) hold. They obtain some sufficient conditions which guarantee that every solution oscillates or con ...
ON THE UNIQUENESS OF CLASSICAL SOLUTIONS OF CAUCHY
... of at most linear growth due to the assumption that g is of at most linear growth. Proof of sufficiency. This follows from Theorem 1. Proof of necessity. If (3) is violated, then t → Xt is a strict local martingale on each time interval (0, T ), T ∈ (0, ∞); see [4], [2] and especially the remark after ...
... of at most linear growth due to the assumption that g is of at most linear growth. Proof of sufficiency. This follows from Theorem 1. Proof of necessity. If (3) is violated, then t → Xt is a strict local martingale on each time interval (0, T ), T ∈ (0, ∞); see [4], [2] and especially the remark after ...
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.