When the reduced twisted $C^*$-algebra $C^*_r(\mathcal{G}, c)$ of a non-principal groupoid $\mathcal{G}$ admits Cartan subalgebra, Renault's work on subalgebras implies existence another description c)$. In an earlier paper, joint with Reznikoff and Wright, we identified situations where such subalgebra arises from subgroupoid $\mathcal{S}$ $\mathcal{G}$. this study relationship between origina...

we consider the concept of fuzzy quasi-contractions initiated by '{c}iri'{c} in the setting of fuzzy metric spaces and establish fixed point theorems for quasi-contractive mappings and for fuzzy $mathcal{h}$-contractive mappings on m-complete fuzzy metric spaces in the sense of george and veeramani.the results are illustrated by a representative example.

We describe some new and recent results that allow for the analysis and representation of reticulate evolution by non-tree networks. In particular, we (1) present a simple result to show that, despite the presence of reticulation, there is always a well-defined underlying tree that corresponds to those parts of life that do not have a history of reticulation; (2) describe and apply new theory f...

The notion of extriangulated category was introduced by Nakaoka and Palu giving a simultaneous generalization exact categories triangulated categories. Our first aim is to provide an extension Auslander's formula: for some $\mathcal{C}$, there exists localization sequence $\operatorname{def}\mathcal{C} \to \mod\mathcal{C} \operatorname{lex}\mathcal{C}$, where $\operatorname{lex}\mathcal{C}$ den...

In phylogenetics, phylogenetic trees are rooted binary trees, whereas phylogenetic networks are rooted arbitrary acyclic digraphs. Edges are directed away from the root and leaves are uniquely labeled with taxa in phylogenetic networks. For the purpose of validating evolutionary models, biologists check whether or not a phylogenetic tree is contained in a phylogenetic network on the same taxa. ...

Chalinidae is a family of haplosclerid sponges with a delicate reticulated chaonosomal skeleton of uni-, paucior multispicular primary lines which are connected by unispicular secondary lines, and with an ectosomal skeleton, if present, formed by a regular hexagonal, unispicular, tangential reticulation (Weerdt 2002). Currently, the family harbors only five valid genera (Chalinula, Cladocroce, ...

In studies of molecular evolution, phylogenetic trees are rooted binary trees, whereas phylogenetic networks are rooted acyclic digraphs. Edges are directed away from the root and leaves are uniquely labeled with taxa in phylogenetic networks. For the purpose of validating evolutionary models, biologists check whether or not a phylogenetic tree (resp. cluster) is contained in a phylogenetic net...

We consider cyclic codes $\mathcal{C}_\mathcal{L}$ associated to quadratic trace forms in $m$ variables $Q_R(x) = \operatorname{Tr}_{q^m/q}(xR(x))$ determined by a family $\mathcal{L}$ of $q$-linearized polynomials $R$ over $\mathbb{F}_{q^m}$, and three related $\mathcal{C}_{\mathcal{L},0}$, $\mathcal{C}_{\mathcal{L},1}$ $\mathcal{C}_{\mathcal{L},2}$. describe the spectra for all these when is ...