We shall discuss further regularity properties of null-additive fuzzy measure on metric spaces following the previous results. Under the null-additivity condition, some properties of the inner/outer regularity and the regularity of fuzzy measure are shown. Also the strong regularity of fuzzy measure is discussed on complete separable metric spaces. As an application of strong regularity, we pre...

We examine three primal space local Hölder type regularity properties of finite collections of sets, namely, [q]-semiregularity, [q]-subregularity, and uniform [q]-regularity as well as their quantitative characterizations. Equivalent metric characterizations of the three mentioned regularity properties as well as a sufficient condition of [q]-subregularity in terms of Fréchet normals are estab...

The paper investigates the stability of the solutions of linearquadratic optimal control problems with bang-bang controls in terms of metric sub-regularity and bi-metric regularity. New sufficient conditions for these properties are obtained, which strengthen the known conditions for sub-regularity and extend the known conditions for bi-metric regularity to Bolza-type problems.

Until very recently, regularity accounts of causation have virtually vanished from the scene. Problems encountered within other theoretical frameworks have lately induced philosophers working on causation – as e.g. Hall (2004) or Beebee (2006) – to direct their attention back to regularity theoretic analyses. In light of the most recent proposals of regularity theories, the essay at hand will t...

1. Ultrafilters, ultraproducts and ultralimits 1 1.1. Filters and ultrafilters 1 1.2. Ultralimits 2 1.3. Some model-theoretic notation 3 1.4. Ultraproducts of first-order structures 3 1.5. References 6 2. Graph regularity and measures on ultraproducts 6 2.1. Szemerédi’s regularity lemma 6 2.2. Finitely additive measures 7 2.3. Obtaining countable additivity 9 2.4. Integration for charges (signe...

We discuss Matijevic–Roberts type theorem on strong F -regularity, F -purity, and Cohen–Macaulay F -injective (CMFI for short) property. Related to this problem, we also discuss the base change problem and the openness of loci of these properties. In particular, we define the notion of F -purity of homomorphisms using Radu–André homomorphisms, and prove basic properties of it. We also discuss a...

Texture regularity is one of the important visual characteristics. It can be used to determine differences in the surface between two objects. Several methods of measurement have been produced by previous researchers.However, in this paper the authors offer a new formula for calculating the regularity of texture features. Regularity is measured by the intensity of the pixels of grayscale images...

In the present paper, we define regularity and normality like strong S1 regularity, S1 regularity, weak S1 regularity, strong S1 normality, S1 normality as well as weak S1 normality on L-topological spaces. Also we investigate some of their properties and the relations between them. 2010 Mathematics Subject Classification: 54A40, 54D10, 54D15, 54D65, 03E72.

The one-to-one relation between the points fulfilling the KKT conditions of an optimization problem and the zeros of the corresponding Kojima function is well-known. In the present paper we study the interplay between metric regularity and strong regularity of this a priori nonsmooth function in the context of semidefinite programming. Having in mind the topological structure of the positive se...