Monotonicity under coarse-graining is a crucial property of the quantum relative entropy. The aim of this paper is to investigate the condition of equality in the monotonicity theorem and in its consequences as the strong sub-additivity of von Neumann entropy, the Golden-Thompson trace inequality and the monotonicity of the Holevo quantitity. The relation to quantum Markov states is briefly ind...

We analyze the problem of fully implementing a social choice set in ex post equilibrium. We identify an ex post monotonicity condition that is necessary and in economic environments su¢ cient for full implementation in ex post equilibrium. We also identify an ex post monotonicity no veto condition that is su¢ cient. Ex post monotonicity is satis…ed in all single crossing environments with stric...

The monotonicity, convexity, log-convexity and complete monotonicity properties for some special functions are proved, and some inequalities are established.

<p style='text-indent:20px;'>The theory of Mean Field Game Controls considers a class mean field games where the interaction is through joint distribution state and control. It well known that, for standard games, certain monotonicity conditions are crucial to guarantee uniqueness equilibria then global wellposedness master equations. In literature condition could be Lasry–Lions monotonic...

The relaxation of the property monotonicity is a trend in theory aggregation and fusion functions several generalized forms have been introduced, most which are based on notion directional monotonicity. In this paper, we propose general framework for that encompasses different can find literature. Additionally, introduce various new not Specifically, dilative monotonicity, requires function inc...

We propose a notion of operator monotonicity for functions of several variables, which extends the well known notion of operator monotonicity for functions of only one variable. The notion is chosen such that a fundamental relationship between operator convexity and operator monotonicity for functions of one variable is extended also to functions of several variables.

The authors insist that monotonicity is a necessary property of a good cohesion metric and the violation of the monotonicity property limits the application of CBMC. They also state that the augmented CBMC can also be used as a guideline for quality evaluation and restructuring of poorly designed classes. This paper raises the question about the necessity of monotonicity by analyzing the reason...

It is well known that there are a great number of interesting results in Fourier analysis established by assuming monotonicity of coefficients, and many of them have been generalized by loosing the condition to quasi-monotonicity, O-regularly varying quasi-monotonicity, etc.. Generally speaking, it has become an important topic how to generalize monotonicity. Recently, Leindler [5] defined a ne...

In this paper nonlinear monotonicity and boundedness properties are analyzed for linear multistep methods. We focus on methods which satisfy a weaker boundedness condition than strict monotonicity for arbitrary starting values. In this way, many linear multistep methods of practical interest are included in the theory. Moreover, it will be shown that for such methods monotonicity can still be v...