We consider whether the “inequality-splitting” property established in the Brøndsted– Rockafellar theorem for the subdifferential of a proper convex lower semicontinuous function on a Banach space has an analog for arbitrary maximal monotone multifunctions. We introduce the maximal monotone multifunctions of type (ED), for which an “inequality-splitting” property does hold. These multifunctions...

in this article, we investigate sufficient conditions for existence of maximal and minimalsolutions to a coupled system of highly nonlinear differential equations of fractional order with mixedtype boundary conditions. to achieve this goal, we apply monotone iterative technique togetherwith the method of upper and lower solutions. also an error estimation is given to check theaccuracy of the me...

A networked dynamical system is composed of subsystems interconnected via prescribed interactions. In many engineering applications, however, one subsystem can also affect others “unintended” interactions that significantly change the intended network's behavior. Although unintended be modeled as disturbance inputs to subsystems, these disturbances depend on states. Thus, a attenuation property...

Let P be a graph property. For k ≥ 1, a graph G has property Pk iff every induced k-vertex subgraph of G has P. For a graph G we denote by NPk(G) the number of induced k-vertex subgraphs of G having P. A property is called spanning if it does not hold for graphs that contain isolated vertices. A property is called connected if it does not hold for graphs with more than one connected component. ...

1. Overview This paper talks about that monotone circuit is P-Complete. Decision problem that include P-Complete is mapping that classify input with a similar property. Therefore equivalence relation of input value is important for computation. But monotone circuit cannot compute the equivalence relation of the value because monotone circuit can compute only monotone function. Therefore, I make...

A function f : {0, 1} → {0, 1} is said to be k-monotone if it flips between 0 and 1 at most k times on every ascending chain. Such functions represent a natural generalization of (1-)monotone functions, and have been recently studied in circuit complexity, PAC learning, and cryptography. Our work is part of a renewed focus in understanding testability of properties characterized by freeness of ...

We present an efficient computational procedure for finite abstraction of discrete-time mixed monotone systems by considering a rectangular partition of the state space. Mixed monotone systems are decomposable into increasing and decreasing components, and significantly generalize the well known class of monotone systems. We tightly overapproximate the one-step reachable set from a box of initi...