A new approach for studying wave propagation phenomena in an inviscid gas is presented. This approach can be viewed as the extension of the method of characteristics to the general case of unsteady multidimensional flow. A family of spacetime manifolds is found on which an equivalent one-dimensional (1-D) problem holds. Their geometry depends on the spatial gradients of the flow, and they provi...

Abstract We consider a smooth area-preserving Anosov diffeomorphism $f\colon \mathbb T^2\rightarrow T^2$ homotopic to an automorphism L of $\mathbb . It is known that the positive Lyapunov exponent f with respect normalized Lebesgue measure less than or equal topological entropy , which, in addition, probability maximal entropy. Moreover, equalities only occur simultaneously. show these are res...

In this paper, we define a new domination-like invariant of graphs. Let $${\mathbb {R}}^{+}$$ be the set non-negative numbers. $$c\in {\mathbb {R}}^{+}-\{0\}$$ number, and let G graph. A function $$f:V(G)\rightarrow is c-self-dominating if for every $$u\in V(G)$$ , $$f(u)\ge c$$ or $$\max \{f(v):v\in N_{G}(u)\}\ge 1$$ . The c-self-domination number $$\gamma ^{c}(G)$$ defined as ^{c}(G):=\min \{...

In this paper, we define some new homomorphism-monotone parameters for hypergraphs. Using these parameters, we extend some graph homomorphism results to hypergraph case. Also, we present some bounds for some well-known invariants of hypergraphs such as fractional chromatic number,independent numer and some other invariants of hyergraphs, in terms of these parameters.

If G is the group of an oriented knot k, then the set Hom(K,Σ) of representations of the commutator subgroup K = [G,G] into any finite group Σ has the structure of a shift of finite type ΦΣ, a special type of dynamical system completely described by a finite directed graph. Invariants of ΦΣ, such as its topological entropy or the number of its periodic points of a given period, determine invari...

For a compact set of actions, an entropy Kushnirenko type is chosen in such way that it vanishes on this but takes infinite values for the typical actions. As consequence we find measure-preserving transformations are not isomorphic to isometric rearrangements finite geometric figures.