We study an action of the skew divided difference operators on the Schubert polynomials and give an explicit formula for structural constants for the Schubert polynomials in terms of certain weighted paths in the Bruhat order on the symmetric group. We also prove that, under certain assumptions, the skew divided difference operators transform the Schubert polynomials into polynomials with posit...

Abstract. In this expository and survey paper, along one of main lines of bounding the ratio of two gamma functions, we look back and analyse some inequalities, the complete monotonicity of several functions involving ratios of two gamma or q-gamma functions, the logarithmically complete monotonicity of a function involving the ratio of two gamma functions, some new bounds for the ratio of two ...

Received (Day Month Year) Revised (Day Month Year) Communicated by (xxxxxxxxxx) Fractional B-splines are a natural extension of classical B-splines. In this short paper, we show their relations to fractional divided differences and fractional difference operators , and present a generalized Hermite-Genochi formula. This formula then allows the definition of a larger class of fractional B-splines.

1 Divided Power Algebra—October 31, 2016 1 1.1 Divided Power Structure . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1 1.2 Extension of Divided Power Structure . . . . . . . . . . . . . . . . . . . . . . . 3 1.3 Compatible Divided Power structure . . . . . . . . . . . . . . . . . . . . . . . 4 1.4 Divided Power Algebra Associated to a Module . . . . . . . . . . . . . . . . . 5 1.5...

Decision tree methodology is a commonly used data mining method for establishing classification systems based on multiple covariates or for developing prediction algorithms for a target variable. This method classifies a population into branch-like segments that construct an inverted tree with a root node, internal nodes, and leaf nodes. The algorithm is non-parametric and can efficiently deal ...

The piecewise-constant exponential model is a semi-parametric continuous time duration model.1 The model is semi-parametric in the sense that the shape of the hazard rate with respect to time is not specified a priori but is determined by the data. The basic idea underlying the PCE model is that the duration time can be divided up into discrete units in each of which the hazard rate is assumed ...