A pre-Lie product is a binary operation whose associator is symmetric in the last two variables. As a consequence its antisymmetrization is a Lie bracket. In this paper we study the symmetrization of the pre-Lie product. We show that it does not satisfy any other universal relation than commutativity. This means that the map from the free commutative-magmatic algebra to the free pre-Lie algebra...

This paper defines and investigates nonsymmetric Macdonald polynomials with values in an irreducible module of the Hecke algebra of type AN−1. These polynomials appear as simultaneous eigenfunctions of Cherednik operators. Several objects and properties are analyzed, such as the canonical bilinear form which pairs polynomials with those arising from reciprocals of the original parameters, and t...

Motivated by applications in combinatorial geometry, we consider the following question: Let $\lambda=(\lambda_1,\lambda_2,\ldots,\lambda_m)$ be an $m$-partition of a positive integer $n$, $S_i \subseteq \mathbb{C}^{\lambda_i}$ finite sets, and let $S:=S_1 \times S_2 \cdots S_m \subset \mathbb{C}^n$ multigrid defined $S_i$. Suppose $p$ is $n$-variate degree $d$ polynomial. How many zeros does h...

background and objective: serum creatinine is the most used endogenous marker of glomerular filtration rate (gfr), but it also has multiple limitations. therefore, some surrogate gfr markers, such as beta trace protein, have been introduced for gfr estimation. the aim of our study was to estimate gfr by serum beta trace protein using three available equations and compare them to dtpa gfr as the...

We consider the implications of the Revised Symmetrization Postulate 1 for states of more than two particles. We show how to create permutation symmetric state vectors and how to derive alternative state vectors that may be asymmetric for any pair by creating asymmetric interdependencies in their state descriptions. Because we can choose any pair to create such an asymmetry, the usual generaliz...

It is argued that the criticisms by Schwartz and Schwartz of Jensen's analysis of IQ data on monozygotic twins reared apart fall down on two central points, methodological and theoretical: (a) Valid inferences concerning the broad heritability of intelligence can be drawn from analysis of the combined data from several independent studies of MZ twins reared apart, even though the groups differ ...

We investigate solutions of the 2d incompressible Euler equations, linearized around steady states which are radially decreasing vortices. Our main goal is to understand smoothness what we call spectral density function associated with operator, hope will be a step towards proving full nonlinear asymptotic stability The motivation for considering that it not possible describe vorticity or strea...

[1] Schwartz [2007] recently evaluated the time constant of Earth’s climate system. However, his methodology yields to a significant underestimation of the value of t and obscures a much more interesting property of the system. Schwartz found t = 5 ± 1 years. Herein, by using an improved methodology I find that for short time scales from 0 to 2 years t is of the order of a several months and fo...