in this paper we study right $n$-engel group elements‎. ‎by modifying a group constructed by newman and nickel‎, ‎we construct‎, ‎for each integer $ngeq 5$‎, ‎a 2-generator group $g =langle a‎, ‎brangle$ with the property that $b$ is a right $n$-engel‎ ‎element but where $[b^k,_n a]$ is of infinite order when $knotin {0‎, ‎1}$‎.

We propose the first skyrmion spin ice, realized via confined, interacting liquid crystal skyrmions. Skyrmions in a chiral nematic behave as quasiparticles that can be dynamically bound, and created or annihilated individually with ease precision. show these employed to realize binary variables interact form ice-rule states. Because of their unique versatility, skyrmions open entirely novel ave...

In 1938 Marcus Rhodes provided the first genetic description of an unstable mutation, an allele of a gene required for the production of pigment in maize. This instability resulted in a variegated phenotype. Variegation describes irregular patterns of pigmentation and reflects changes in the expression of genes that control pigment production. Rhodes defined two genes required for this instabil...

The dynamics of creation, annihilation, and transformation of topological defects in a closed system with a vector-type order parameter is studied both theoretically and experimentally. The particular case of a drop of a nematic with varying boundary conditions is considered. In the theoretical part, the concept of a continuously defined topological description of surface defects (e.g., boojums...

We prove that the extended Toda hierarchy of [1] admits nonabelian Lie algebra of infinitesimal symmetries isomorphic to the half of the Virasoro algebra. The generators Lm, m ≥ −1 of the Lie algebra act by linear differential operators onto the tau function of the hierarchy. We also prove that the tau function of a generic solution to the extended Toda hierarchy is annihilated by a combination...

Under anaerobic conditions an exponentially growing culture of Escherichia coli K-12 was exposed to hydrogen peroxide in the presence of various compounds. Hydrogen peroxide (0.1 mM) together with 0.1 mM L-cysteine or L-cystine killed the organisms more rapidly than 10 mM hydrogen peroxide alone. The exposure of E. coli to hydrogen peroxide in the presence of L-cysteine inhibited some of the ca...

Let B be a real vector lattice and a Banach space under a semimonotonic norm. Suppose T is a linear operator on B which is positive and eventually compact, y is a positive vector, and A is a positive real. It is shown that (XI—TY1y is positive if, and only if, y is annihilated by the absolute value of any generalized eigenvector of T* associated with a strictly positive eigenvalue not less than...

Let g be a complex semisimple Lie algebra, with a Bore1 subalgebra b c g and Cartan subalgebra h c b. In classifying the finite dimensional representations of g, Cartan showed that any simple finite dimensional g-module has a generating element u, annihilated by n = [b, b], on which h acts by a linear form I E h*. Such an element is called a primitive vector (for the module). Harish-Chandra [9]...

Lipid and protein oxidation are well-known manifestations of free radical activity and oxidative stress. The current study investigated extermination of Leishmania tropica promastigotes induced by lipid and protein oxidation with reactive oxygen species produced by PEGylated metal-based nanoparticles. The synthesized photodynamic therapy-based doped and nondoped zinc oxide nanoparticles were ac...

Free planar electrons in a uniform magnetic field are shown to possess the symmetry of area-preserving diffeomorphisms (W -infinity algebra). Intuitively, this is a consequence of gauge invariance, which forces dynamics to depend only on the flux. The infinity of generators of this symmetry act within each Landau level, which is infinite-dimensional in the thermodynamical limit. The incompressi...