Following Anders and Archer, we say that an unordered rooted labeled forest avoids the pattern σ∈Sk if in each tree, sequence of labels along shortest path from root to a vertex does not contain subsequence with same relative order as σ. For permutation σ∈Sk−2, construct bijection between n-vertex forests avoiding (σ)(k−1)k≔σ(1)⋯σ(k−2)(k−1)k (σ)k(k−1)≔σ(1)⋯σ(k−2)k(k−1), giving common generaliza...

Let σ={σi:i∈I} be a partition of the set all prime numbers. A subgroup H finite group G is said to σ-subnormal in if can joined by chain subgroups H=H0⊆H1⊆⋯⊆Hn=G where, for every j=1,⋯,n, Hj−1 normal Hj or Hj/CoreHj(Hj−1) σi-group some i∈I. B soluble normalising Nσ-residual non-σ-subnormal G, where Nσ saturated formation σ-nilpotent groups. We show that normalises does not have section σ-residu...

In this paper, we introduce the property (h) on Banach lattices and present its characterization in terms of disjoint sequences. Then, an example is given to show that order-to-norm continuous operator may not be σ-order continuous. Suppose T:E→F order-bounded from Dedekind σ-complete lattice E into complete F. We prove T σ-order-to-norm if only both order weakly compact addition, can represent...

In this research at the first Enalapril drug and its fullerene derivative were optimized. NBO calculations and NMR for the complexes were carried out at the B3LYP/6-31G* quantum chemistry level. Different parameters such as energy levels, the amount of Chemical Shift in different atoms, the amount of HOMO/LUMO, chemical potential (µ ), chemical hardness (η), the coefficients of hybrid bonds (π,...

The quantum-chemical calculations on the conformational properties of 2-flouro-2-oxo- 1,3,2-dioxaphosphorinane (1), 2-choloro-2-oxo-1,3,2-dioxaphosphorinane (2) and 2-bromo- 2-oxo-1,3,2-dioxaphosphorinane (3) have been investigated by means of ab initio molecular orbital (HF/6-311+G**) and hybrid density functional theory (B3LYP/6-311+G**) based methods and Natural Bond Orbital (NBO) interpreta...

Now a day study on boron nitrid nanotubes are in considerable attetion due to their unique properties in different field of science. In this letter, after final optimization, thermodynamic properties analysis, stabilities, electronic structure and nuclear magnetic resonance parameters including σ isotropic and σ anisotropic tensors and asymmetric parameters of 15N and 11B nuclei are calculated....