The purpose of this article is to study determinants of matrices which are known as generalized Pascal triangles (see R. Bacher. Determinants of matrices related to the Pascal triangle. J. Théor. Nombres Bordeaux, 14:19–41, 2002). This article presents a factorization by expressing such a matrix as a product of a unipotent lower triangular matrix, a Toeplitz matrix, and a unipotent upper triang...

In this paper, we investigate the general case of black hole at horizon by the method of Damour-Ruffini-Zhao. The proof of identification of the location of horizons determined both by Damour-Ruffini-Zhao’s (D-R-Z) method and by equation of null super-surface is given. The formula of temperature on the horizon for general black holes is obtained and is successfully checked by a variety of model...