Let X be a smooth hypersurface of degree n ≥ 3 in P. We prove that the log canonical threshold of H ∈ |−KX| is at least n−1 n . Under the assumption of the Log minimal model program, we also prove that a hyperplane section H of X is a cone in P over a smooth hypersurface of degree n in P if and only if the log canonical threshold of H is n−1 n . Bibliography : 20 titles.

The idea of generating skewed distributions from normal has been of great interest among researchers for decades. This paper proposes four families of generalized normal distributions using the T -X framework. These four families of distributions are named as T -normal families arising from the quantile functions of (i) standard exponential, (ii) standard log-logistic, (iii) standard logistic a...

We establish the preserving log-convexity property for the generalized Pascal triangles. It is an extension of a result of H. Davenport and G. Pólya “On the product of two power series”, who proved that the binomial convolution of two log-convex sequences is log-convex.

In this paper we study the log structures on generalized semistable varieties, generalize the result by F. Kato and M. Olsson, and prove the canonicity of log structure when it can be expected. In out text we first give the definitions of local chart and weakly normal crossing morphism. Then we study the invariants of complete noetherian local ring coming from weakly normal crossing morphisms. ...

We discuss generalized proximity operators (GPO) and their associated generalized projection problems. On inputs of size n, we show how to efficiently apply GPOs and generalized projections for separable norms and distance-like functions to accuracy in O(n log(1/ )) time. We also derive projection algorithms that run theoretically in O(n log n log(1/ )) time but can for suitable parameter range...

Oxime extractants 3-tert-butyl-2-hydroxy-5-methyl benzaldehyde oxime (HL1) and 3-tert-butyl-2-hydroxy-5-methoxy benzaldehyde oxime (HL2) were synthesized and characterized by conventional spectroscopic methods. Suitable lipophilic nature of the prepared extractants allowed examining the ability of these molecules for extr...

We prove the termination of flips for pseudo-effective NQC log canonical generalized pairs dimension 4. As main ingredients, we verify 3-dimensional pairs, and show that which admit weak Zariski decompositions follows from in lower dimensions.