Let G be a simple connected graph with n ≤ 2 vertices and m edges, and let μ1 ≥ μ2 ≥...≥μn-1 >μn=0 be its Laplacian eigenvalues. The Kirchhoff index and Laplacian-energy-like invariant (LEL) of graph G are defined as Kf(G)=nΣi=1n-1<...

the concept of right (left) quotient (or residual) of an ideal η by anideal ν of an l-subring μ of a ring r is introduced. the right (left) quotients areshown to be ideals of μ . it is proved that the right quotient [η :r ν ] of an idealη by an ideal ν of an l-subring μ is the largest ideal of μ such that[η :r ν ]ν ⊆ η . most of the results pertaining to the notion of quotients(or residual) of ...

The dominant production mechanism for heavy quark-antiquark bound states in very high energy processes is fragmentation, the splitting of a high energy parton into a quarkonium state and other partons. We show that the fragmentation functions D(z, μ) describing these processes can be calculated using perturbative QCD. We calculate the fragmentation functions for a gluon to split into S-wave qua...

the parafascicular nucleus (pfn) of thalamus, as a supraspinal structure, has an important role in processing of nociceptive information. in addition, μ-opioid receptor contributes to supraspinal modulation of nociception. in the present study, the effects of microinjection of naloxone (a non-specific opioid-receptor antagonist) and naloxonazine (a specific μ-opioid receptor antagonist) were in...