In this paper, we consider the relationship between the binding number and the existence of fractional k-factors of graphs. The binding number of G is defined by Woodall as bind(G)=min{ | NG(X) || X |:∅≠X⊆V(G) }. It is proved that a graph G has a fractional 1-factor if bind(G)≥1and has a fractional k-factor if bind(G)≥k−1k. Furthermore, it is showed that both results are best possible in some sense.
Hydrophobic Val derivative Schiff base copper(II) complexes and dipeptide (AlaAla, GlyGly) derivative Schiff base copper(II) complexes were introduced into egg white lysozyme. X-ray crystal structure analysis revealed amino acid derivative Schiff base copper(II) complexes were obtained. Herein we discuss primarily on the binding mode of copper(II) of the complexes obtained with egg white lysozyme. The electron density of copper(II) ions was confirmed by X-ray crystal structure analysis. The Val derivative Schiff base copper(II) complex was weakly bound at Arg114 of egg white lysozyme. In other copper(II) complexes, binding of copper(II) ions with dissociated ligands to various residues was observed. The binding sites of copper(II) ions were compared with computational scientific predictions.
Kou TakahashiRyotaro MiyazakiDaisuke NakaneTemitayo O. AiyelabolaTakashiro Akitsu
The basis functions of the translation invariant shell model are used to construct the ground state nuclear wave functions of 3H. The used residual two-body interactions consist of central, tensor, spin orbit and quadratic spin orbit terms with Gaussian radial dependence. The parameters of these interactions are so chosen in such a way that they represent the long-range attraction and the short-range repulsion of the nucleon-nucleon interactions. These parameters are so chosen to reproduce good agreement between the calculated values of the binding energy, the root mean-square radius, the D-state probability, the magnetic dipole moment and the electric quadrupole moment of the deuteron nucleus. The variation method is then used to calculate the binding energy of triton by varying the oscillator parameter which exists in the nuclear wave function. The obtained nuclear wave functions are then used to calculate the root mean-square radius and the magnetic dipole moment of the triton.
