Abstract This paper presents (Lagrangian) variational formulations for single and multicomponent semi-compressible fluids with both reversible (entropy-conserving) irreversible (entropy-generating) processes. Semi-compressible are useful in describing low-Mach dynamics, since they soundproof . These models find wide use many areas of fluid including geophysical astrophysical dynamics. Specifica...

We prove the topological invariance of the combinatorial Euler characteristic of ominimal sets with the help of a canonical, topologically defined stratification of o-minimal sets by locally compact ones. Introduction. Let Bn be the collection of semi-algebraic subsets of R, i.e. sets definable by a finite boolean combination of polynomial equalities and inequalities. The Bn, n ∈ N, satisfy (i)...

In the previous lectures, we have defined the Shannon Capacity of a graph, Θ(G). This lecture is concerned with the Shannon Capacity of the disjoint union G +H of two graphs G and H. The union of two graphs is, informally, what you get when you just place one graph next to the other. In 1956, Shannon conjectured [1] that Θ(G + H) = Θ(G) + Θ(H). As we will see, this is a very natural conjecture ...

In this paper, a condition which ensures the existence of fuzzy simply open sets in $P$- space is obtained. It established that disjoint $G_{\delta}$-sets $P$-space are cs dense sets. A for strongly irresolvable and globally disconnected to become hyperconnected D-Baire space. obtained extremally disconnected, semi-$P$ does not have $G_{\delta}$-sets.

The lattice Lu of upper semicontinuous convex normal functions with convolution ordering arises in studies of type-2 fuzzy sets. In 2002, Kawaguchi and Miyakoshi [Extended t-norms as logical connectives of fuzzy truth values, Multiple-Valued Logic 8(1) (2002) 53–69] showed that this lattice is a complete Heyting algebra. Later, Harding et al. [Lattices of convex, normal functions, Fuzzy Sets an...

We introduce a covering conjecture and show that it holds below ADR + “Θ is regular”. We then use it to show that in the presence of mild large cardinal axioms, PFA implies that there is a transitive model containing the reals and ordinals and satisfying ADR + “Θ is regular”. The method used to prove the Main Theorem of this paper is the core model induction. The paper contains the first applic...

We show that two open books in a given closed, oriented three-manifold admit isotopic stabilizations, where the stabilization is made by successive plumbings with Hopf bands, if and only if their associated plane fields are homologous. Since this condition is automatically fulfilled in an integral homology sphere, the theorem implies a conjecture of J. Harer, namely, that any fibered link in th...

In this paper, we introduce the notions of fuzzy γ-I-open sets and fuzzy γ-I-continuous functions to obtain a decomposition of fuzzy semi-I-continuity. We also investigated the fundamental properties of such functions.