Abstract We investigate quantum lens spaces, $C(L_q^{2n+1}(r;\underline {m}))$ , introduced by Brzeziński and Szymański as graph $C^*$ -algebras. give a new description of -algebras amending an error in the original paper Szymański. Furthermore, for $n\leq 3$ we number-theoretic invariant, when all but one weight are coprime to order acting group r . This builds upon work Eilers, Restorff, Ruiz...

In this paper we will extend the method of balanced truncation using normalised right coprime factors of the system transfer matrix by Meyer [7] to balanced truncation with preservation of half line dissipativity. Special cases are preservation of positive realness and bounded realness. We consider a half line dissipative input-output system, with quadratic supply rate given by a nonsingular sy...

Coprime array, which utilizes a coprime pair of uniform linear subarrays, is an attractive structure to achieve sparse array configurations. Alternatively, effective coprime array configurations can be implemented using a uniform linear array with two coprime sensing frequencies. This enables the integration of the coprime array and filter concepts to achieve high capabilities in meeting system...

This paper is concerned with the factorization approach to control systems. We consider the models in which some plants admit or do not admit coprime factorization. In the case where the plants admits only one-side coprime factorization, it is known that the plant with additional zeros admits both side coprime factorizations. However we show that in the case where the plant do not admit coprime...

The coprime graph of a group G is Γ_G with its set vertices and any two distinct are adjacent if only their order relatively prime. Let p be prime number, then G_p denotes the multiplicative 2×2 upper unitriangular matrices over ring integers modulo p. purposes this research to study Γ_(G_p ) find first second Zagreb eccentricity indices for p≥3. results as follows. First index )isE_1 (Γ_(G_p )...

Prime objects were defined as generalization of simple objects in the categories of rings (modules). In this paper we introduce and investigate what turns out to be a suitable generalization of simple corings (simple comodules), namely fully coprime corings (fully coprime comodules). Moreover, we consider several primeness notions in the category of comodules of a given coring and investigate t...

A study is presented of right (left) coprime decompositions of a collection of N -periodic rational matrices, with some ordered structure. From a block-ordered right coprime decomposition of a rational matrix of the given periodic collection, the corresponding block-ordered right coprime decompositions of the remaining matrices of the collection are constructed. In addition, those decomposition...

We start up the study of stability general graph pairs. This notion is a generalization concept graphs. say that pair graphs $(\Gamma,\Sigma)$ stable if $Aut(\Gamma\times\Sigma) \cong Aut(\Gamma)\times Aut(\Sigma)$ and unstable otherwise, where $\Gamma\times\Sigma$ direct product $\Gamma$ $\Sigma$. An said to be nontrivially $\Sigma$ are connected coprime graphs, at least one them non-bipartite...