in this paper, our purpose is twofold. firstly, the tensor andresiduum operations on $l-$nested systems are introduced under thecondition of complete residuated lattice. then we show that$l-$nested systems form a complete residuated lattice, which isprecisely the classical isomorphic object of complete residuatedpower set lattice. thus the new representation theorem of$l-$subsets on complete re...

This paper investigates type isomorphism in a λ-calculus with intersection and union types. It is known that in λ-calculus, the isomorphism between two types is realised by a pair of terms inverse one each other. Notably, invertible terms are linear terms of a particular shape, called finite hereditary permutators. Typing properties of finite hereditary permutators are then studied in a relevan...

3 Uniform measures of complexity 12 3.1 Metric entropy and the combinatorial dimension . . . . . . . . . 12 3.1.1 Binary valued classes . . . . . . . . . . . . . . . . . . . . . 13 3.1.2 Real valued classes . . . . . . . . . . . . . . . . . . . . . . 15 3.2 Random averages and the combinatorial dimension . . . . . . . . 17 3.3 Phase transitions in GC classes . . . . . . . . . . . . . . . . . . ...

A 1-2 model configuration is a subgraph of the hexagonal lattice, in which the edgedegree of each vertex is either 1 or 2. We prove that for any translation invariant Gibbs measure of the 1-2 model configurations on the whole-plane hexagonal lattice, almost surely there are no infinite paths. Using a measure-preserving correspondence between 1-2 model configurations on the hexagonal lattice and...

In this short note we prove that if a symplectomorphism f is C-stably shadowable, then f is Anosov. The same result is obtained for volume-preserving diffeomorphisms.

In this paper, we study the stability of a wide class of switched systems using stability preserving mappings. By considering an existing result and extending it to a general class of switched systems, we show that stability preserving mappings constitute an important and practical tool in stability analysis and design of switched systems.

Let D be a division ring and let m,n be integers ≥ 2. Let Mm×n(D) be the space of m × n matrices. In the fundamental theorem of the geometry of rectangular matrices all bijective mappings φ of Mm×n(D) are determined such that both φ and φ−1 preserve adjacency. We show that if a bijective map φ of Mm×n(D) preserves the adjacency then also φ −1 preserves the adjacency. Thus the supposition that φ...

We prove that the surface-diffusion flow and the volumepreserving mean curvature flow can drive embedded hypersurfaces to self-intersections.