Let $\mathcal{A}= \{A_t \}_{t \in G}$ and $\mathcal{B}= \{B_t \}_{t\in be $C^*$-algebraic bundles over a finite group $G$. $C=\oplus_{t G}A_t$ $D=\oplus_{t\in G}B_t$. Also, let $A=A_e$ $B=B_e$, where $e$ is the unit element in We suppose that $C$ $D$ are unital $A$ $B$ have elements $D$, respectively. In this paper, we shall show if there an equivalence $\mathcal{A}-\mathcal{B}$-bundle $G$ with...

Let $mathcal {A}$ be an abelian category with enough projective objects and $mathcal {X}$ be a full subcategory of $mathcal {A}$. We define Gorenstein projective objects with respect to $mathcal {X}$ and $mathcal{Y}_{mathcal{X}}$, respectively, where $mathcal{Y}_{mathcal{X}}$=${ Yin Ch(mathcal {A})| Y$ is acyclic and $Z_{n}Yinmathcal{X}}$. We point out that under certain hypotheses, these two G...

‎Let $mathcal{A}$ be a commutative Banach algebra and $mathscr{X}$ be a left Banach $mathcal{A}$-module‎. ‎We study the set‎ ‎${rm Dec}_{mathcal{A}}(mathscr{X})$ of all elements in $mathcal{A}$ which induce a decomposable multiplication operator on $mathscr{X}$‎. ‎In the case $mathscr{X}=mathcal{A}$‎, ‎${rm Dec}_{mathcal{A}}(mathcal{A})$ is the well-known Apostol algebra of $mathcal{A}$‎. ‎We s...

A sequence ${T_n}_{n=1}^{infty}$ of bounded linear  operators on a separable infinite dimensional Hilbert space $mathcal{H}$ is called subspace-diskcyclic with respect to the closed subspace $Msubseteq mathcal{H},$ if there exists a vector $xin mathcal{H}$ such that the disk-scaled orbit ${alpha T_n x: nin mathbb{N}, alpha inmathbb{C}, | alpha | leq 1}cap M$ is dense in $M$. The goal of t...

Processes such as hybridization, horizontal gene transfer, and recombination result in reticulation which can be modeled by phylogenetic networks. Earlier likelihood-based methods for inferring phylogenetic networks from sequence data have been encumbered by the computational challenges related to likelihood evaluations. Consequently, they have required that the possible network hypotheses be g...

Motivation: A major unresolved problem in phylogeny is to reconstruct the evolutionary history of a set of species when it cannot be modeled by a simple tree. When a reticulation event, such as hybrid speciation or horizontal transfer, occurs, separate regions of a species’ genetic data may evolve along different trees. Our approach uses the gene trees for each region to solve the inverse probl...

The DSC method has been employed to monitor the kinetics of reticulation of aqueous polyurethane systems without catalysts, and with the commercial catalyst of zirconium (CATXC-6212) and the highly selective manganese catalyst, the complex Mn(III)diacetylacetonemaleinate (MAM). Among the polyol components, the acrylic emulsions were used for reticulation in this research, and as suitable reticu...

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.