we study the set of all determinants of adjacency matrices of graphs with a given number of vertices. using brendan mckay's data base of small graphs, determinants of graphs with at most $9$ vertices are computed so that the number of non-isomorphic graphs with given vertices whose determinants are all equal to a number is exhibited in a table. using an idea of m. newman, it is proved that if $...

‎for any integer $kgeq 1$‎, ‎a set $s$ of vertices in a graph $g=(v,e)$ is a $k$-‎tuple total dominating set of $g$ if any vertex‎ ‎of $g$ is adjacent to at least $k$ vertices in $s$‎, ‎and any vertex‎ ‎of $v-s$ is adjacent to at least $k$ vertices in $v-s$‎. ‎the minimum number of vertices of such a set‎ ‎in $g$ we call the $k$-tuple total restrained domination number of $g$‎. ‎the maximum num...

The family G of connected graphs with second largest Laplacian eigenvalue at most θ, where θ = 3.2470 is the largest root of the equation μ−5μ+6μ−1 = 0, is characterized by Wu, Yu and Shu [Y.R. Wu, G.L. Yu and J.L. Shu, Graphs with small second largest Laplacian eigenvalue, European J. Combin. 36 (2014) 190–197]. Let G(a, b, c, d) be a graph with order n = 2a + b + 2c + 3d + 1 that consists of ...

Introducing various pendant functional groups and building blocks of interest to polypeptides in a highly efficient, controlled manner is crucial to access polypeptide materials with desired structures and functions. In this study, we synthesized γ-(4-vinylbenzyl)-(L)-glutamate N-carboxyanhydride (VB-Glu-NCA), which was readily obtained and purified in large quantity. VB-Glu-NCA monomer was sub...

In the title compound, C(24)H(24)Cl(4)N(2)O(4)S(2), the dihedral angles between the central benzene ring and the pendant rings are 58.09 (10) and 62.59 (10)°. The dihedral angle between the pendant rings is 81.64 (9)°. Both sulfonamide groups lie to the same side of the central ring but the C-S-N-C torsion angles [73.09 (16) and -117.35 (14)] and S-N-C-C torsion angles [-143.80 (14) and -111.45...

We report here the efficient reduction of CO2 to CO by cobalt aminopyridine macrocycles. The effect of the pendant amines on catalysis was investigated. Several cobalt complexes based on the azacalix[4](2,6)pyridine framework with different substitutions on the pendant amine groups have been synthesized (R = H (1), Me (2), and allyl (3)), and their electrocatalytic properties were explored. Und...

In the title compound, C(26)H(24)Cl(4)N(2)O(4)S(2), the dihedral angles between the central benzene ring and the pendant rings are 70.07 (12) and 59.07 (12)°. The equivalent angle between the pendant rings is 79.24 (12)°. Both sulfonamide groups lie to the same side of the central ring but the pendant chains have very different conformations, as indicated by their C-S-N-C torsion angles [104.66...

Teach pendant is the most widely used means of robot teaching at present. Despite the difficulties of using the motion command buttons on the teach pendant, it is an economical, robust, and effective device for robot teaching task. This paper presents the development of a force/moment direction sensor named COSMO that can improve the teach pendant based robot teaching. Robot teaching experiment...