Ricci curvature bounds in Riemannian geometry are known to be equivalent to the weak convexity (convexity along at least one geodesic between any two points) of certain functionals in the space of probability measures. We prove that the weak convexity can be reinforced into strong (usual) convexity, thus solving a question left open in [4].

Explicit expressions for the occupation time distribution of Brownian bridge, excursion and meander are derived using Kac’s formula and results of [4]. The first two distributions appeared in [8], and were derived using weak convergence of simple random walk.

In this work we continue our investigations of a compressible gas-liquid model with special focus on inclusion of external frictional forces in the momentum balance. The model is often used for multiphase well flow modeling important for different well control operations. The frictional forces have a major impact on the pressure gradient, which determines the pressure distribution along the wel...

We study Lascar strong types and Galois types and especially their relation to notions of type which have finite character. We define a notion of a strong type with finite character, so called Lascar type. We show that this notion is stronger than Galois type over countable sets in simple and superstable finitary AECs. Furthermore we give and example where the Galois type itself does not have f...

We present results of a weak gravitational lensing survey of six X-ray selected high-redshift clusters of galaxies. We find that the masses of the clusters derived from weak lensing are comparable to those derived from the X-ray observations. We show that many of the clusters have significant substructure not observed in the X-ray observations and that for the more massive clusters a singular i...

We have introduced, in a previous paper, the fundamental lax 2-category of a ‘directed space’ X. Here we show that, when X has a T1-topology, this structure can be embedded into a larger one, with the same objects (the points of X), the same arrows (the directed paths) and the same cells (based on directed homotopies of paths), but a larger system of comparison cells. The new comparison cells a...

In this paper we shall repair some errors and fill some gaps in the inner model theory of [2]. The problems we shall address affect some quite basic definitions and proofs. We shall be concerned with condensation properties of canonical inner models constructed from coherent sequences ~ E of extenders as in [2]. Condensation results have the general form: if x is definable in a certain way over...

In this paper we introduce the “do not touch” condition for squares in the discrete plane. We say that two squares “do not touch” if they do not share any vertex or any segment of an edge. Using this condition we define a covering of the discrete plane, the covering can be strong or weak, regular or non-regular. For simplicity, in this article, we will restrict our attention to regular covering...

In [3] and [6] the concepts of smooth closure, smooth interior, smooth α-closure and smooth α-interior of a fuzzy set were introduced and some of their properties were obtained. In this paper, we introduce the concepts of several types of weak smooth compactness and weak smooth α-compactness in terms of these concepts introduced in [3] and [6] and investigate some of their properties.

Let H be a countable infinite homogeneous relational structure. If H is indivisible then it is weakly indivisible and if it is weakly indivisible then it is age indivisible. There are examples of countable infinite homogeneous structures which are weakly indivisible but not indivisible. It is a natural question to ask for examples of countable age indivisible homogenous structures which are not...