Tetrahedron Equation and Quantum R Matrices for Spin Representations of $${B^{(1)}_n}$$ B n ( 1 ) , $${D^{(1)}_n}$$ D n ( 1 ) and $${D^{(2)}_{n+1}}$$ D n + 1 ( 2 )

On the nature of solutions of the difference equation $mathbf{x_{n+1}=x_{n}x_{n-3}-1}$

We investigate the long-term behavior of solutions of the difference equation[ x_{n+1}=x_{n}x_{n-3}-1 ,, n=0 ,, 1 ,, ldots ,, ]noindent where the initial conditions $x_{-3} ,, x_{-2} ,, x_{-1} ,, x_{0}$ are real numbers.  In particular, we look at the periodicity and asymptotic periodicity of solutions, as well as the existence of unbounded solutions.

K-Matrices, and D(2) n+1 Reflection

Dichlorido[(R,R)-N 1,N 1,N 2-tribenzyl­cyclo­hexane-1,2-diamine-κ2 N 1,N 2]copper(II)

In the title compound, [CuCl(2)(C(27)H(32)N(2))], which bears a chiral diamine ligand, viz (R,R)-N,N,N''- tribenzyl-cyclo-hexane-1,2-diamine, the Cu(II) ion is ligated by two N and two Cl atoms in a distorted square-planar geometry. The coordination of the ligands to the Cu(II) ion results in the formation of a five-membered heterocyclic ring and a chiral center at the monosubstituted nitro-gen...

Dynamics of higher order rational difference equation $x_{n+1}=(alpha+beta x_{n})/(A + Bx_{n}+ Cx_{n-k})$

The main goal of this paper is to investigate the periodic character, invariant intervals, oscillation and global stability and other new results of all positive solutions of the equation$$x_{n+1}=frac{alpha+beta x_{n}}{A + Bx_{n}+ Cx_{n-k}},~~ n=0,1,2,ldots,$$where the parameters $alpha$, $beta$, $A$, $B$ and $C$ are positive, and the initial conditions $x_{-k},x_{-k+1},ldots,x_{-1},x_{0}$ are...

Necessary and sufficient conditions for the chain rule in W 1 , 1 loc ( R N ; R d ) and BV loc ( R N ; R d )

In this paper we prove necessary and sufficient conditions for the validity of the classical chain rule in the Sobolev space W 1,1 loc ( R ;R ) and in the space of functions of bounded variation BVloc ( R ;R ) .