The dynamical system (f,R) is introduced and some of its properties are investigated. It is proven that there is an invariant set Λ on which the periodic points of f are dense.

We construct, for the Weil representation associated with any discriminant form, an explicit basis in which action of involves algebraic integers over its field definition. The a general element $${\text {SL}}_{2}(\mathbb {Z})$$ on many parts these bases is simple and explicit, fact that we use determining dimension space invariants some families forms.

in this paper, we prove some coupled coincidence point theorems for mappings satisfying generalized contractive conditions under a new invariant set in ordered cone metric spaces. in fact, we obtain sufficient conditions for existence of coupled coincidence points in the setting of cone metric spaces. some examples are provided to verify the effectiveness and applicability of our results.

For a separable rearrangement invariant space X on [0, 1] of fundamental type we identify the set all $$p\in [1,\infty ]$$ such that $$\ell ^p$$ is finitely represented in way unit basis vectors ( $$c_0$$ if $$p=\infty $$ ) correspond to pairwise disjoint and equimeasurable functions. This can be treated as follow up paper by first-named author related spaces $$(0,\infty )$$ .

The present paper proposes a novel method for 3D model content-based search based on the 3D Generalized Radon Transform. A set of descriptor vectors is extracted, which represent significant shape characteristics and completely invariant in terms of translation, scaling and rotation. Experimental results show that the proposed method can be used for 3D model search and retrieval in a highly eff...

This paper presents a new synthesis procedure (design algorithm) for cellular neural networks (CNN’s) with a space-invariant cloning template with applications to associative memories. In the present synthesis procedure, the design problem is formulated as a set of linear inequalities, and the inequalities are solved using the well-known perceptron training algorithm. When desired memory patter...

| This paper presents a new synthesis procedure (design algorithm) for cellular neural networks with space-invariant cloning template with applications to associative memories. In the present synthesis procedure, the design problem is formulated as a set of linear inequalities and the inequalities are solved using the well-known percep-tron training algorithm. When desired memory patterns are g...

In this paper, we introduce a new entropy-like invariant, named Hausdorff metric entropy, for finitely generated semigroups acting on compact metric spaces from a set-valued view and study its properties. We establish the relation between Hausdorff metric entropy and topological entropy of a semigroup defined by Bis. Some examples with positive or zero Hausdorff metric entropy are given. Moreov...