we show that a recently introduced lax pair of the sawada-kotera equation is nota new one but is trivially related to the known old lax pair. using the so-called trivialcompositions of the old lax pairs with a differentially constrained arbitrary operators,we give some examples of trivial lax pairs of kdv and sawada-kotera equations.

‎we introduce a generalization of the notion of‎ depth of an ideal on a module by applying the concept of‎ local cohomology modules with respect to a pair‎ ‎of ideals‎. ‎we also introduce the concept of $(i,j)$-cohen--macaulay modules as a generalization of concept of cohen--macaulay modules‎. ‎these kind of modules are different from cohen--macaulay modules‎, as an example shows‎. ‎also an art...

Assume that $(N,L)$, is a pair of finite dimensional nilpotent Lie algebras, in which $L$ is non-abelian and $N$ is an ideal in $L$ and also $mathcal{M}(N,L)$ is the Schur multiplier of the pair $(N,L)$. Motivated by characterization of the pairs $(N,L)$ of finite dimensional nilpotent Lie algebras by their Schur multipliers (Arabyani, et al. 2014) we prove some properties of a pair of nilpoten...

the ion-pair association constant values, related to the reaction +  were determined by means of the nmr spectroscopy. the values of the thermodynamic functions of the ion pairing process were calculated on the basis of the nmr results. in addition, the association entropy was found to be dependent on the temperature. comparing the experimental data and the fuoss theory it is found that  ion-pa...

In this paper, we give connection between the order of the generalized Baer-invariant of a pair of finite groups and its factor groups, when ? is considered to be the specific variety. Moreover, we give a necessary and sufficient condition in which the generalized Baer-invariant of a pair of groups can be embedded into the generalized Baer-invariant of pair of its factor groups.

using the gaussian 2003 software and mp2 /6 – 311+ g method for the c2h4 : o2, co:cl2 andco2:co2 pairs and mp2/6-311++g** method for the co2:h2o pair and b3lyp/6-31g methodfor the o2:o2 pair the optimized interaction energies between two considered pair molecules ofstudied gases(c2h4:o2, co:cl2, co2:h2o, o2:o2 and co2:co2 pairs) as a function of thedistances between the centers of two considere...

this research has been carried out to study and find a rather general description for a lone pairorbital in molecules. since the orbital parameters must be manageable in advance, and correctgeometry of the molecule (bond lengths) is depend on the appropriate lone pair description; thefsgo method including optimization has been used to obtain orbital parameters and energy. theproposed models for...