Analysis of the strong vertices of ΣcND∗\Sigma_cND^{*} and ΣbNB∗\Sigma_bNB^{*} in QCD sum rules

The strong coupling constant is an important parameter which can help us to understand the strong decay behaviors of baryons. In our previous work, we have analyzed strong vertices $\Sigma_{c}^{*}ND$, $\Sigma_{b}^{*}NB$, $\Sigma_{c}ND$, $\Sigma_{b}NB$ in QCD sum rules. Following these work, we further analyze the strong vertices $\Sigma_{c}ND^{*}$ and $\Sigma_{b}NB^{*}$ using the three-point QCD sum rules under Dirac structures $q\!\!\!/p\!\!\!/\gamma_{\alpha}$ and $q\!\!\!/p\!\!\!/p_{\alpha}$. In this work, we first calculate strong form factors considering contributions of the perturbative part and the condensate terms $\langle\overline{q}q\rangle$, $\langle\frac{\alpha_{s}}{\pi}GG\rangle$ and $\langle\overline{q}g_{s}\sigma Gq\rangle$. Then, these form factors are used to fit into analytical functions. According to these functions, we finally determine the values of the strong coupling constants for these two vertices $\Sigma_{c}ND^{*}$ and $\Sigma_{b}NB^{*}$.Comment: arXiv admin note: text overlap with arXiv:1705.0322

A variation of a classical Turán-type extremal problem

AbstractA variation of a classical Turán-type extremal problem (Erdős on Graphs: His Legacy of Unsolved Problems (1998) p. 36) is considered as follows: determine the smallest even integer σ(Kr,s,n) such that every n-term graphic non-increasing sequence π=(d1,d2,…,dn) with term sum σ(π)=d1+d2+⋯+dn≥σ(Kr,s,n) has a realization G containing Kr,s as a subgraph, where Kr,s is a r×s complete bipartite graph. In this paper, we determine σ(Kr,s,n) exactly for every fixed s≥r≥3 when n≥n0(r,s), where m=[(r+s+1)24] andn0(r,s)=m+3s2−2s−6,ifs≤2randsis even,m+3s2+2s−8,ifs≤2randsis odd,m+2s2+(2r−6)s+4r−8,ifs≥2r+1

Tetra­kis[μ-2-(3,4-dimeth­oxy­phen­yl)acetato]-κ3 O 1,O 1′:O 1;κ3 O 1:O 1,O 1′;κ4 O 1:O 1′-bis­{[2-(3,4-dimeth­oxy­phen­yl)acetato-κ2 O 1,O 1′](1,10-phenanthroline-κ2 N,N′)erbium(III)}

In the dimeric centrosymmetric title complex, [Er2(C10H11O4)6(C12H8N2)2], the ErIII ion is nine-coordinated by five 2-(3,4-dimeth­oxy­lphen­yl)acetic acid (DMPA) ligands via seven O atoms and two N atoms from a bis-chelating 1,10-phenanthroline (phen) ligand in a distorted tricapped trigonal-prismatic geometry. The DMPA ligands are coordinated to the ErIII ion in bis-chelate, bridging and bridging tridentate modes. Relatively weak intra­molecular C—H⋯O inter­actions reinforce the stability of the mol­ecular structure. Inter­molecular C—H⋯O inter­actions are also observed