On integrable natural Hamiltonian systems on the suspensions of toric automorphism

We point out a mistake in the main statement of \cite{liu} and suggest and proof a correct statement.Comment: 5 pages, no figure

Breach procedure for axillary hyperhidrosis.

Dear Editor, We read with interest the communication on ‘A simple and practical method for axillary osmidrosis resection’ by Liu X, Mao T, Lei Z, Fan D appeared on JPRAS 2009.1 We found the description of the technique very useful with the support of intra-operative pictures. The use of artery clips to evert the skin flaps can be easily reproduced. However it is surprising that the Authors did not consider and mention in the References a paper by Mr N Breach appeared in the Annals of the Royal College of Surgeons of England in the late 70ies,2 when he was Senior Registrar at the Plastic Surgery Department of the Queen Victoria Hospital, East Grinstead, UK. Since then this latter procedure for surgical treatment of axillary hyperhidrosis has been widely adopted, [3], [4] and [5] especially in the Western world and in the UK where is known as the ‘Breach’ procedure. The main difference with the technique described in the paper by Liu X et al. consists in the number of incisions that has now been minimized

On Packing Colorings of Distance Graphs

The {\em packing chromatic number} $\chi_{\rho}(G)$ of a graph $G$ is the least integer $k$ for which there exists a mapping $f$ from $V(G)$ to $\{1,2,\ldots ,k\}$ such that any two vertices of color $i$ are at distance at least $i+1$. This paper studies the packing chromatic number of infinite distance graphs $G(\mathbb{Z},D)$, i.e. graphs with the set $\mathbb{Z}$ of integers as vertex set, with two distinct vertices $i,j\in \mathbb{Z}$ being adjacent if and only if $|i-j|\in D$. We present lower and upper bounds for $\chi_{\rho}(G(\mathbb{Z},D))$, showing that for finite $D$, the packing chromatic number is finite. Our main result concerns distance graphs with $D=\{1,t\}$ for which we prove some upper bounds on their packing chromatic numbers, the smaller ones being for $t\geq 447$: $\chi_{\rho}(G(\mathbb{Z},\{1,t\}))\leq 40$ if $t$ is odd and $\chi_{\rho}(G(\mathbb{Z},\{1,t\}))\leq 81$ if $t$ is even