This paper presents a new result on absolute exponential stability (AEST) of a class of continuous-time recurrent neural networks with locally Lipschitz continuous and monotone nondecreasing activation functions. The additively diagonally stable connection weight matrices are proven to be able to guarantee AEST of the neural networks. The AEST result extends and improves the existing absolute s...

In this paper, the authors prove some existence results of solutions for a new class of generalized bi-quasi-variational inequalities (GBQVI) for quasi-pseudo-monotone type I operators in non-compact settings in locally convex Hausdorff topological vector spaces. In obtaining these results on GBQVI for quasi-pseudo-monotone type I operators in non-compact settings, we shall use the concept of e...

‎In this paper‎, ‎some properties of pre-monotone operators are proved‎. ‎It is shown that in a reflexive Banach space‎, ‎a full domain multivalued $sigma$-monotone operator with sequentially norm$times$weak$^*$ closed graph is norm$times$weak$^*$ upper semicontinuous‎. ‎The notion of $sigma$-convexity is introduced and the‎ ‎relations between the $sigma$-monotonicity and $sigma$-convexity is i...

This paper investigates set-valued differential equations with fractional-like Hukuhara derivatives. Firstly, a novel comparison principle is given by introducing the upper quasi-monotone increasing functions. Then, stability criteria of Lipschitz and practical such different initial time are obtained via new vector Lyapunov

This paper deals with maximization of set f'unctions delined as minimum values of monotone linkage functions. In previous research, it has been shown that such a set function can be maximized by a greedy type algorithm over a family of all subsets of a finite set. ln this paper, we extend this finding to meet-semilattices. We show that the class of functions defined as minimum values of monoton...

Abstract The invariant Galton–Watson (IGW) tree measures are a one-parameter family of critical with respect to large class reduction operations. Such operations include the generalized dynamical pruning (also known as hereditary in real setting) that eliminates descendant subtrees according value an arbitrary subtree function is monotone nondecreasing isometry-induced partial order. We show th...

It is well-known that the generating function for tableaux of a given skew shape with r rows where the parts in the i'th row are bounded by some nondecreasing upper and lower bounds which depend on i can be written in form of a determinant of size r. We show that the generating function for tableaux of a given skew shape with r rows and c columns where the parts in the i'th row are bounded by n...

We analyze the consequences of strategically sophisticated bidding without assuming equilibrium behavior. In particular, we characterize interim rationalizable bids in symmetric first-price auctions with interdependent values and affiliated signals. We show that (1) every non-zero bid below the equilibrium is rationalizable, (2) some bids above the equilibrium are rationalizable, (3) the upper ...

By reformulating a learning process of a set system L as a game between Teacher and Learner, we define the order type of L to be the order type of the game tree, if the tree is well-founded. The features of the order type of L (dim L in symbol) are (1) We can represent any well-quasi-order (wqo for short) by the set system L of the upper-closed sets of the wqo such that the maximal order type o...

By recasting the Klein–Gordon equation as an eigen-equation in coupling parameter [Formula: see text] basic comparison theorem may be written text], where and are monotone nondecreasing shapes of two central potentials on text]. Meanwhile, corresponding parameters that functions energy We weaken sufficient condition for ground-state spectral ordering by proving (for example dimension) if coupli...