We study an inverse problem to determine a nonlinearity of an autonomous equation from a blow-up time of solutions of the equation. A local well-posedness of the inverse problem near a nonlinearity of the type $u^{1+\sigma}$, $\sigma>0$, is established. The paper also suggests that the inverse problem has a good, mathematical structure from a viewpoint of the Wiener-Hopf theory in integral equations.

In 2009~[4,5], S. Gun, M. R. Murty, P. Rath studied transcendental values of the logarithm of the gamma function. They showed that for any rational number $x$ with $0 < x < \frac{1}{2}$, the number $\log \Gamma(x) + \log \Gamma(1-x)$ is transcendental with at most one possible exception. In this paper, we study transcendental values of log double sine function using their method.

In this paper, we obtain an analog of Younis’s Theorem 5.2 in~[7] for the Dunkl transform on the real line for functions satisfying the $(\beta, \gamma)$-Dunkl Lipschitz condition in the space $\mathrm{L}^{p}(\mathbf{R}, |x|^{2\alpha+1}dx)$, where $\alpha\geq -\frac{1}{2}$.