The synthesis of some new N-[1-(2,5-dichlorophenyl)-5-methyl-1,2,3-triazol-4-yl]-carbamic acid ester derivatives are reported in this paper. The yielded products 6a-l were confirmed by Elemental analyses, NMR, MS, and IR spectra.
We apply the continuation theorem of Mawhin to ensure that a fourth-order nonlinear difference equation of the form Δ 4 u k − 2 − a k u α k + b k u β k = 0 with periodic boundary conditions possesses at least one nontrivial positive solution, where Δ u k = u k + 1 − u k is the forward difference operator, α > 0 , β > 0 and α ≠ β , a k , b k are T -periodic functions and a k b k > 0 . As applications, we give some examples to illustrate the application of these theorems.
The complemented triangulation graph of a graph G, denoted by CT(G), is defined as the graph obtained from G by adding, for each edge uv of G, a new vertex whose neighbours are the vertices of G other than u and v. In this paper, we first obtain the A-spectra, the L-spectra, and the Q-spectra of the complemented triangulation graphs of regular graphs. By using the results, we construct infinitely many pairs of A-cospectral graphs, L-cospectral graphs, and Q-cospectral graphs. We also obtain the number of spanning trees and the Kirchhoff index of the complemented triangulation graphs of regular graphs.
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