The schema calculus of Z provides a means for expressing structured, modular specifications. Extending this modularity to program development requires the monotonicity of these operators with respect to refinement. This paper provides a thorough mathematical analysis of monotonicity with respect to four schema operations for three notions of operation refinement. The mathematical connection bet...

We extend the concept of relaxed α-monotonicity to mixed relaxed α-β-monotonicity. The concept of mixed relaxed α-β-monotonicity is more general than many existing concepts of monotonicities. Finally, we apply this concept and well known KKM-theory to obtain the solution of generalized equilibrium problem.

We describe an algorithm for proving termination of programs abstracted to systems of monotonicity constraints in the integer domain. Monotonicity constraints are a nontrivial extension of the well-known size-change termination method. While deciding termination for systems of monotonicity constraints is PSPACE complete, we focus on a well-defined and significant subset, which we call MCNP (for...

Problem statement: When analyzing random variables it is useful to measure the degree of their monotone dependence or compare pairs of random variables with respect to their monotonicity. Existing coefficients measure general or linear dependence of random variables. Developing a measure of monotonicity is useful for practical applications as well as for general theory, since monotonicity is an...

In this paper, the generalized -centroidal mean and its dual form in 2 variables are introduced. Also, studied some properties and prove their monotonicity. Further, shown that various means are partic- ular cases of generalized $bf{alpha}$-centroidal mean.

We evaluate data on choices made from convex time budgets (CTB) in Andreoni and Sprenger (Am Econ Rev 102(7):3333-3356, 2012a) and Augenblick et al. (Q J Econ 130(3):1067-1115, 2015), two influential studies that proposed and applied this experimental technique. We use the weak axiom of revealed preference (WARP) to test for external consistency relative to pairwise choice, and demand, wealth a...

We consider linear multistep methods that possess general monotonicity and boundedness properties. Strict monotonicity, in terms of arbitrary starting values for the multistep schemes, is only valid for a small class of methods, under very stringent step size restrictions. This makes them uncompetitive with the strong-stability-preserving (SSP) Runge– Kutta methods. By relaxing these strict mon...

in this note we are going to survey several invariants of finite groups related either to their orders or to generating sets or to lattices of subgroups. some relations among these invariants will be exhibited. special attention will be paid to monotonicity of them.

Monotonicity of the equilibrium bidding strategy is a key property of structural auction models. Traditional nonparametric estimators provide a flexible means of uncovering salient features of auction data, but do not formally impose the monotonicity assumption that is inherent in the models they are trying to estimate. Here we develop a nonparametric estimator which imposes the monotonicity as...

In this note we define generalized monotonicity which is a generalized version of monotonicity due to Muller and Satterthwaite (1979) for a social choice function under individual preferences which permit indifference, and shall show that generalized monotonicity and strategy−proofness are equivalent. I would like to thank Bhaskar Dutta and the anonymous referee for helpful comments. Citation: ...