We propose a q-analog of classical plethystic conjectures due to Foulkes. In our conjectures, a divided difference of plethysms of Hall-Littlewood polynomials Hn(x; q) replaces the analogous difference of plethysms of complete homogeneous symmetric functions hn(x) in Foulkes’ conjecture. At q = 0, we get back the original statement of Foulkes, and we show that our version holds at q = 1. We dis...

This is a study of Favard interpolation—in which the nth derivatives of the interpolant are bounded above by a constant times the nth divided differences of the data—in the case the data is given on some subset of a rectangular lattice in R k. In some instances, depending on the geometry of this subset, we construct a Favard interpolant, and in other instances, we prove that none exists.

Baiocchi et al. generalized a few years ago a classical theorem of Ingham and Beurling by means of divided differences. The optimality of their assumption has been proven by the third author of this note. The purpose of this note to extend these results to vector coefficient sums.

In this paper we derive a formula for divided differences of composite functions of several variables with respect to rectangular grids of points. Letting the points coalesce yields a chain rule for partial derivatives of multivariate functions. Math Subject Classification: 41A05, 65D05, 26A06

Abstract In the expository and survey paper, along one of main lines of bounding the ratio of two gamma functions, the author looks back and analyses 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...

By analyzing the monitoring data of excavation foundation, maximum lateral displacement depth and top vertical retaining wall, column are studied. Research indicates that 3rd power polynomial curve can better fit change law deformation wall at each point；the fourth support demolition has great influence on wall. The third layer greatly increased After second is removed, to negative. gradually d...

virulence of the opportunistic yeast, candida albieans, involves the interplay of many complex changes including the yeast-hyphae transition, which mainly involves protein changes. cell wall mannoproteins are found to be the main cause of adherence of c. albieans to epithel ial cells in the first step of an infection process. in the present study, cell wall mannoproteins of intact yeast were pu...

We interpret divided power structures on the homotopy groups of simplicial commutative rings as having a counterpart in divided power structures on chain complexes coming from a non-standard symmetric monoidal structure.

By a result of H. Cartan (cf. 5]), the homotopy of a simplicial commutative algebra is equipped with divided power operations. In this paper, we provide a general approach to the construction of Cartan operations in the context of simplicial algebras over an operad.

A 5-amino-8-hydroxyquinoline (AHQ)-modified gold nanoparticle (GNP) layer was fabricated on an inner wall of a silica capillary column by alternatively passing a citrate-stabilized GNP solution and an AHQ solution in a repeating fashion. The observations by a field emission scanning electron microscope showed that the thickness of the resulting GNP layer was about 0.15 microm. This column was t...