The main aim of this paper is to introduce a neurosophic subsethood measure for single valued neutrosophic sets. For this purpose, we first introduce a system of axioms for subsethood measure of single valued neutrosophic sets. Then we give a simple subsethood measure based to distance measure. Finally, to show effectiveness of intended subsethood measure, an application is presented in multicr...

We study general state-space Markov chains that depend on a parameter, say, . Sufficient conditions are established for the stationary performance of such a Markov chain to be differentiable with respect to . Specifically, we study the case of unbounded performance functions and thereby extend the result on weak differentiability of stationary distributions of Markov chains to unbounded mapping...

We prove the weak-strong uniqueness for measure-valued solutions of the incompressible Euler equations. These were introduced by R.DiPerna and A.Majda in their landmark paper [10], where in particular global existence to any L initial data was proven. Whether measure-valued solutions agree with classical solutions if the latter exist has apparently remained open. We also show that DiPerna’s mea...

This paper considers some measure-valued processes {Xt : t ∈ [0, T ]} based on an underlying critical branching particle structure with random branching rates. In the case of constant branching these processes are Dawson-Watanabe processes. Sufficient conditions on functionals Φ of the process are given that imply that the expectations E(Φ(XT )) are comparable to the constant branching case. Ap...

We consider strong and weak topologies on the space of orbits from the unit interval to the set of probability measures on a given domain. In particular, we are interested in periodic orbits of probability measures on the circle. We show that a real-valued rotation number can be defined in a natural way for all smooth enough orbits whose range is composed of probability measures supported on th...

This paper addresses the problem of sensitivity analysis for finite-horizon performance measures of general Markov chains. We derive closed-form expressions and associated unbiased gradient estimators for the derivatives of finite products of Markov kernels by measure-valued differentiation (MVD). In the MVD setting, the derivatives of Markov kernels, called D-derivatives, are defined with resp...

In this paper, we firstly invoke gradual Hausdorff metric to define a new additive fuzzy-valued measure on the ordinary measurable space. Then, from the view of a fuzzy number as a crisp interval of gradual numbers, we show that the new fuzzy-valued measure can be characterized by two gradual number-valued measures. Finally, we investigate some of its properties and structural characterizations.

The semigroup-valued integral of M. Sion [S] is reformulated for a general notion of approximation by sums of values taken by a set function integrand. A convergence in measure theorem is established, which yields both his pointwise dominated convergence theorem as well as an integrability criterion which specializes to his existence theorem. In [S] M. Sion introduced and developed an "integral...

In this work, we study concentration properties for vector valued maps. In particular, we describe inequalities which capture the exact dimensional behavior of Lipschitz maps with values in Rk. To this task, we study in particular a domination principle for projections which might be of independent interest. We further compare our conclusions to earlier results by Pinelis in the Gaussian case, ...

We give a comprehensive treatment of Sturm–Liouville operators whose coefficients are measures including a full discussion of self-adjoint extensions and boundary conditions, resolvents, and Weyl–Titchmarsh–Kodaira theory. We avoid previous technical restrictions and, at the same time, extend all results to a larger class of operators. Our operators include classical Sturm– Liouville operators,...