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In this paper we present a recurrent relation for counting meaningful compositions of the higher-order differential operations on the space $R^{n}$ (n=3,4,...) and extract the non-trivial compositions of order higher than two.
In this paper we consider successive iterations of the first-order differential operations in space ${bf R}^3.$
Let $R^{n+1, n}$ be the vector space $R^{2n+1}$ equipped with the bilinear form $(X,Y)=X^t C_n Y$ of index $n$, where $C_n= sum_{i=1}^{2n+1} (-1)^{n+i-1} e_{i, 2n+2-i}$. A smooth $gamma: Rto R^{n+1,n}$ is {it isotropic} if $gamma, gamma_x, ldots, gam
Some of the observational aspects related to the evolutionary status and dust production in R Cor Bor stars are discussed. Recent work regarding the surface abundances, stellar winds and evidence for dust production in these high luminosty hydrogen d
Langer and Perline proved that if x is a solution of the geometric Airy curve flow on R^n then there exists a parallel normal frame along x(. ,t) for each t such that the corresponding principal curvatures satisfy the (n-1) component modified KdV (vm
Let $C^{[M]}$ be a (local) Denjoy-Carleman class of Beurling or Roumieu type, where the weight sequence $M=(M_k)$ is log-convex and has moderate growth. We prove that the groups ${operatorname{Diff}}mathcal{B}^{[M]}(mathbb{R}^n)$, ${operatorname{Diff