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I’d like to get the inverse Laplace transform of a symbolic expression. The output of my code is equal to the input? How can I modify the code to obtain the correct result? All k and V1 are positives. InverseLaplaceTransform[(s + Subscript[k, 2] + Subscript[k, 12])/ Subscript[V, 1][ s^2 + s[Subscript[k, 1] + Subscript[k, 2]Read more

Inverse functions give X as the answer when either function is inputted to the other. For example fgx where f = X + 2 and g = X – 2 = X – 2 + 2 = X and vice versa. How can this rule be proved for arcsine where we input √1- X squaredRead more

For which morphisms of schemes $ f : X\rightarrow Y$ do we have $ f^{-1}\mathcal{O}_Y = \mathcal{O}_X$ ? (note that I don’t mean $ f^*$ , I really just mean the basic inverse image sheaf as a sheaf of rings/abelian groups/sets) This is obviously true if $ f$ is an open immersion, and intuitively IRead more

Let $ F=(F_1,\dots,F_n)\in\mathbb{C}[X_1,\dots,X_n]^n$ be a polynomial automorphism $ \mathbb{C}^n\to\mathbb{C}^n$ with inverse $ G=(G_1,\dots,G_n)$ . Let $ d:=\deg F:=\max_{1\leq i\leq n}\deg F_i$ be the degree of $ F$ . It is then known that $ \deg G\leq C(n,d):=d^{n-1}$ . Is there a known or a conjectured lower bound $ c:=c(n,d):=c(n,d,\dots)$ , i.e. possibly depending on otherRead more