On the analysis and application of an ion size-modified Poisson–Boltzmann equation

Dynamics analysis on a class of delayed neural networks involving inertial terms

“…Remark 2.1 In Theorem 2.1, x(t) and x (t) are exponentially convergent to y(t) and y (t), respectively. This suggests that the stability on system (1.1) is in accordance with the exponential stability definition adopted in [15][16][17][18][19][20][21]29].…”

“…Remark 1.2 Assumption (T 2 ) means that a i and b i are large enough and satisfy the above matrix inequalities which are adopted to guarantee the stability of system (1.1). Clearly, the above matrix inequalities are weaker than those used in [15][16][17][18][19][20][21], where |a ib i | is assumed to be small enough.…”

Association of Jensen’s inequality for s-convex function with Csiszár divergence

“…for all ξ i ∈ I and α i ≥ 0 with n i=1 α i = 1. Convex function has wide applications in pure and applied mathematics, physics, and other natural sciences [1][2][3][4][5][6][7][8][9][10][11][12][13][14][15][16][17][18][19][20]; it has many important and interesting properties [21][22][23][24][25][26][27][28][29][30][31][32][33][34][35][36][37] such as monotonicity, continuity, and differentiability. Recently, many generalizations and extensions have been made for the convexity, for example, s-convexity [38], strong convexity [39][40][41], preinvexity [42], GA-convexity [43], GG-convexity [44], Schur convexity [45][46][47][48]…”

Stability of antiperiodic recurrent neural networks with multiproportional delays

“…Remark To the author's knowledge, the issue of antiperiodic RNNs involving proportional delays has never been investigated. Obviously, the corresponding conclusions in Shao, Tan, Gong, Cao, Li, Zhou, Yang, Wang, Peng and Wang, Cai et al, Li et al, Kudu, Hu et al, Hu and Zou, Huang et al, and Hu et al and the references cited therein cannot be used to deal with the exponential convergence on the antiperiodic phenomenon for system .…”