let $mathcal m$ be a factor von neumann algebra. it is shown that every nonlinear $*$-lie higher derivation$d={phi_{n}}_{ninmathbb{n}}$ on $mathcal m$ is additive. in particular, if $mathcal m$ is infinite type $i$factor, a concrete characterization of $d$ is given.

We develop the formalism of finite modular group Γ4′≡S4′, a double cover permutation Γ4≃S4, for theories flavour. The integer weight k>0 level 4 forms indispensable can be even or odd. explicitly construct lowest-weight (k=1) in terms two Jacobi theta constants, denoted as ε(τ) and θ(τ), τ being modulus. show that these furnish 3D representation S4′ not present S4. Having derived multiplication...

The famous Leftover Hash Lemma (LHL) states that (almost) universal hash functions are good randomness extractors. Despite its numerous applications, LHL-based extractors suffer from the following two limitations: – Large Entropy Loss: to extract v bits from distribution X of minentropy m which are ε-close to uniform, one must set v ≤ m − 2 log (1/ε), meaning that the entropy loss L def = m − v...

Let $mathfrak{A}$ be a Banach algebra. We say that a sequence ${D_n}_{n=0}^infty$ of continuous operators form $mathfrak{A}$ into $mathfrak{A}$ is a textit{local higher derivation} if to each $ainmathfrak{A}$ there corresponds a continuous higher derivation ${d_{a,n}}_{n=0}^infty$ such that $D_n(a)=d_{a,n}(a)$ for each non-negative integer $n$. We show that if $mathfrak{A}$ is a $C^*$-algebra t...

The Lie derivation of multivector fields along multivector fields has been introduced by Schouten (see cite{Sc, S}), and studdied for example in cite{M} and cite{I}. In the present paper we define the Lie derivation of differential forms along multivector fields, and we extend this concept to covariant derivation on tangent bundles and vector bundles, and find natural relations between them and...

Four coordination networks based on the {ε-PMo(V)(8)Mo(VI)(4)O(40)(OH)(4)Zn(4)} Keggin unit (εZn) have been synthesized under hydrothermal conditions. (TBA)(3){PMo(V)(8)Mo(VI)(4)O(36)(OH)(4)Zn(4)}[C(6)H(4)(COO)(2)](2) (ε(isop)(2)) is a 2D material with monomeric εZn units connected via 1,3 benzenedicarboxylate (isop) linkers and tetrabutylammonium (TBA) counter-cations lying between the planes....

– We consider the scattering of particles (kinetic energy ε) by an obstacle which tunnels coherently between two positions (tunnel splitting ∆), for arbitrary values of ε/∆ and scattering strength U . The obstacle mimics two classical scatterers at fixed positions when ε ∆. Interference disappears when ε ∆, but can be recovered if the elastic-scattering channel is detected only. At intermediate...

DNA polymerase (pol) ε is thought to be the leading strand replicase in eukaryotes, whereas pols λ and β are believed to be mainly involved in re-synthesis steps of DNA repair. DNA elongation by the human pol ε is halted by an abasic site (apurinic/apyrimidinic (AP) site). In this study, we present in vitro evidence that human pols λ, β, and η can perform translesion synthesis (TLS) of an AP si...