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Let G be a simple graph of order n with vertex set V (G) = { v 1 , v 2 , ... , v n } and edge set E (G). The arithmetic–geometric matrix A AG (G) = (h i j) of G is a matrix of order n defined by h i , j = 1 2 d i d j + d j d i if v i v j ∈ E (G) and 0 otherwise, where d i stands for the degree of the vertex v i in G. The arithmetic–geometric characteristic polynomial of G is the characteristic polynomial of A AG (G). The arithmetic–geometric energy ℰ AG (G) of G is the sum of absolute values of all eigenvalues of A AG (G). In this paper, we obtain the arithmetic–geometric characteristic polynomial and arithmetic–geometric energy of some specific graphs. In addition, we also consider the arithmetic–geometric characteristic polynomial and arithmetic–geometric energy change of these graphs when one edge is deleted. [ABSTRACT FROM AUTHOR]

For two graphs G and H, the corona product G ∘ H is the graph obtained by taking one copy of G and | V G | copies of H, and joining the ith vertex of G with every vertex of the ith copy of H. In this paper, we study the state transfer of corona relative to the signless Laplacian matrix. We explore some conditions that guarantee the signless Laplacian perfect state transfer in G ∘ H . We prove that G ∘ K m has no signless Laplacian perfect state transfer for some special m. We also show that K 2 ∘ H has pretty good state transfer but no perfect state transfer relative to the signless Laplacian matrix for a regular graph H. Furthermore, we show that n K 2 ¯ ∘ K 1 has signless Laplacian pretty good state transfer, where n K 2 ¯ is the cocktail party graph. [ABSTRACT FROM AUTHOR]

Abstract: In this paper, the problem of when the sub-direct sum of two strictly diagonally dominant P-matrices is a strictly diagonally dominant P-matrix is studied. In particular, it is shown that the subdirect sum of overlapping principal submatrices of strictly diagonally dominant P-matrices is a strictly diagonally dominant P-matrix. It is also established that the 2-subdirect sum of two totally nonnegative matrices is a totally nonnegative matrix under some conditions. It is obtained that a partial totally nonnegative matrix, whose graph of the specified entries is a monotonically labeled 2-chordal graph, has a totally nonnegative completion. Finally, a positive answer to the question (IV) in Fallat and Johnson [Shaun M. Fallat, C.R. Johnson, J.R. Torregrosa, A.M. Urbano, P-matrix completions under weak symmetry assumptions, Linear Algebra Appl. 312 (2000) 73–91] is given for P 0-matrices. [Copyright &y& Elsevier]

With the expansion of global energy problems and the deepening of research on oxygen reduction reaction (ORR) in alkaline media, the development of low cost and high electrocatalytic performance catalysts has become a research hotspot. In this study, a hexagonal Pd-C-MnOOH composite catalyst was prepared by using the triblock copolymer P123 as the reducing agent and protective agent, sucrose as the carbon source and self-made MnOOH as the carrier under hydrothermal conditions. When the Pd load is 20% and the C/MnOOH ratio is 1 : 1, the 20% Pd-C-MnOOH-1 : 1 catalyst obtained by the one-step method has the highest ORR activity and stability in the alkaline system. At 1600 rpm, the limiting diffusion current density and half-wave potential of the 20% Pd-C-MnOOH-1 : 1 electrocatalyst are -4.78 mA cm -2 and 0.84 V, respectively, which are better than those of the commercial 20%Pd/C catalyst. According to the Koutecky-Levich (K-L) equation and the linear fitting results, the electron transfer number of the 20%Pd-C-MnOOH-1 : 1 electrocatalyst for the oxygen reduction reaction is 3.8, which is similar to that of a 4-electron process. After 1000 cycles, the limiting diffusion current density of the 20%Pd-C-MnOOH-1 : 1 catalyst is -4.61 mA cm -2 , which only decreases by 3.7%, indicating that the 20%Pd-C-MnOOH-1 : 1 catalyst has good stability. The reason for the improvement of the ORR performance of the Pd-C-MnOOH composite catalyst is the improvement of the conductivity of the carbon layer formed by original carbonization, the regular hexagonal highly active Pd particles and the synergistic catalytic effect between Pd and MnOOH. The method of introducing triblock copolymers in the synthesis of oxides and metal-oxide composite catalysts is expected to be extended to other electrocatalysis fields.