Continuous Event Graphs (CEGs), a subclass of Continuous Petri Nets, are defined as the limiting cases of timed event graphs and Timed Event Multigraphs. A set of dioid algebraic linear equations will be inferred as a novel method of analyzing a special class of CEG, if treated the cumulated token consumed by transitions as state-variables, endowed the monotone nondecreasing functions pointwise...

This paper is concerned with the existence, uniqueness and globally asymptotic stability of traveling wave fronts in the quasi-monotone reaction advection diffusion equations with nonlocal delay. Under bistable assumption, we construct various pairs of superand subsolutions and employ the comparison principle and the squeezing technique to prove that the equation has a unique nondecreasing trav...

We aim, in this work, to demonstrate the existence of minimal and maximal coupled quasi-solutions for nonlinear Caputo fractional differential systems with order q ∈ (1,2). Our approach is based on mixed monotone iterative techniques developed under concept lower upper quasi-solutions. results extend those obtained ordinary equations ones.

The notion of causal operators is extended to periodic boundary value problems with nonlinear boundary conditions in this paper. By utilizing the monotone iterative technique and the method of lower and upper solutions (resp. weakly coupled lower and upper solutions), we establish the existence of the extremal solutions (resp. weakly coupled extremal quasi-solutions) for nonlinear periodic boun...

This paper deals with the existence of L-quasi-solutions for impulsive periodic boundary value problems in an ordered Banach space E. Under a new concept of upper and lower solutions, a new monotone iterative technique on periodic boundary value problems of impulsive differential equations has been established. Our result improves and extends some relevant results in abstract differential equat...

The notions of a quasi-monotone operator and of a cyclically quasi-monotone operator are introduced, and relations between such operators and quasi-convex functions are established.

Some new inequalities are obtained relating to the generalized trapezoid and midpoint rules for the Riemann–Stieltjes integral with a convex integrand and monotone nondecreasing integrator. Results are deduced for the special case of weighted Riemann integrals. Mathematics subject classification (2000): Primary 26D15, Secondary 26D10..

We study subsets of [1, x] on which the Euler φ-function is monotone (nondecreasing or nonincreasing). For example, we show that for any > 0, every such subset has size < x, once x > x0( ). This confirms a conjecture of the second author.

We prove an exponential lower bound on the length of cutting plane proofs. The proof uses an extension of a lower bound for monotone circuits to circuits which compute with real numbers and use nondecreasing functions as gates. The latter result is of independent interest, since, in particular, it implies an exponential lower bound for some arithmetic circuits.

This paper studies the global output convergence of a class of recurrent neural networks with globally Lipschitz continuous and monotone nondecreasing activation functions and locally Lipschitz continuous time-varying inputs. We establish two sufficient conditions for global output convergence of this class of neural networks. Symmetry in the connection weight matrix is not required in the pres...