Separation of variables for quantum integrable models related to Uq(sl^N) U_q(\hat{sl}_N)

In this paper we construct separated variables for quantum integrable models related to the algebra $U_q(\hat{sl}_N)$. This generalizes the results by Sklyanin for $N=2,3$.Comment: 12 pages, Latex, AMS font

Solutions to Knizhnik-Zamolodchikov equations with coefficients in non-bounded modules

We explicitly write dowm integral formulas for solutions to Knizhnik-Zamolodchikov equations with coefficients in non-bounded -- neither highest nor lowest weight -- \gtsl_{n+1}-modules. The formulas are closely related to WZNW model at a rational level.Comment: 13 page

KINEMATICS OF MATERIAL REMOVAL AND FORMING OF SURFACE AT GRINDING

The mathematical model of kinematics of material removal and a forming of surfaces isdeveloped at grinding. Conditions of increase of productivity of processing are defined and newkinematic schemes of high-performance grinding are offere

Slimness of graphs

Slimness of a graph measures the local deviation of its metric from a tree metric. In a graph $G=(V,E)$, a geodesic triangle $\bigtriangleup(x,y,z)$ with $x, y, z\in V$ is the union $P(x,y) \cup P(x,z) \cup P(y,z)$ of three shortest paths connecting these vertices. A geodesic triangle $\bigtriangleup(x,y,z)$ is called $\delta$-slim if for any vertex $u\in V$ on any side $P(x,y)$ the distance from $u$ to $P(x,z) \cup P(y,z)$ is at most $\delta$, i.e. each path is contained in the union of the $\delta$-neighborhoods of two others. A graph $G$ is called $\delta$-slim, if all geodesic triangles in $G$ are $\delta$-slim. The smallest value $\delta$ for which $G$ is $\delta$-slim is called the slimness of $G$. In this paper, using the layering partition technique, we obtain sharp bounds on slimness of such families of graphs as (1) graphs with cluster-diameter $\Delta(G)$ of a layering partition of $G$, (2) graphs with tree-length $\lambda$, (3) graphs with tree-breadth $\rho$, (4) $k$-chordal graphs, AT-free graphs and HHD-free graphs. Additionally, we show that the slimness of every 4-chordal graph is at most 2 and characterize those 4-chordal graphs for which the slimness of every of its induced subgraph is at most 1