‎Let $mathcal{F}$ be an field of zero characteristic and $N_{infty‎}(‎mathcal{F})$ be the algebra of infinite strictly upper triangular‎ ‎matrices with entries in $mathcal{F}$‎, ‎and $f:N_{infty}(mathcal{F}‎)rightarrow N_{infty}(mathcal{F})$ be a non-additive Lie centralizer of $‎N_{infty }(mathcal{F})$; that is‎, ‎a map satisfying that $f([X,Y])=[f(X),Y]$‎ ‎for all $X,Yin N_{infty}(mathcal{F})...

Let $mathcal{H}$ and $mathcal{K}$ be infinite dimensional Hilbert spaces, while $mathcal{B(H)}$ and $mathcal{B(K)}$ denote the algebras of all linear bounded operators on $mathcal{H}$ and $mathcal{K}$, respectively. We characterize the forms of additive mappings from $mathcal{B(H)}$ into $mathcal{B(K)}$ that preserve the nonzero idempotency of either Jordan products of operators or usual produc...

The reticulation L(R) of a commutative ring R was introduced by Joyal in 1975, then the theory developed Simmons remarkable paper published 1980. is bounded distributive algebra whose main property that Zariski prime spectrum Spec(R) and Stone SpecId (L(R)) are homeomorphic. construction lattice generalized Belluce for each unital defined axioms. In recent we algebras semidegenerate congruence-...

assume that $mathbb{d}$ is the open unit disk. applying ozaki's conditions, we consider two classes of locally univalent, which denote by $mathcal{g}(alpha)$ and $mathcal{f}(mu)$ as follows begin{equation*}  mathcal{g}(alpha):=left{fin mathcal{a}:mathfrak{re}left( 1+frac{zf^{prime prime }(z)}{f^{prime }(z)}right)

Let $\mathcal{C}_d\subset \mathbb{C}^{d+1}$ be the space of non-singular, univariate polynomials degree $d$. The Vi\`{e}te map $\mathscr{V} : \mathcal{C}_d \rightarrow Sym_d(\mathbb{C})$ sends a polynomial to its unordered set roots. It is classical fact that induced $\mathscr{V}_*$ at level fundamental groups realises an isomorphism between $\pi_1(\mathcal{C}_d)$ and Artin braid group $B_d$. F...

The problem of constructing an optimal rooted phylogenetic‎ ‎network from a set of rooted triplets is NP-hard. ‎In this paper‎, ‎we present a novel method called NCH‎, ‎which tries to construct a rooted phylogenetic network with the minimum number‎‎of reticulation nodes from an arbitrary set of rooted triplets based on the concept of the height function of a tree and a network. We report the pe...

Abstract Let $f$ be a degree $d$ bicritical rational map with critical point set $\mathcal{C}_f$ and value $\mathcal{V}_f$. Using the group $\textrm{Deck}(f^k)$ of deck transformations $f^k$, we show that if $g$ is shares an iterate $f$, then $\mathcal{C}_f = \mathcal{C}_g$ $\mathcal{V}_f \mathcal{V}_g$. this, two maps even share iterate, they second both belong to symmetry locus maps.