We explain how to construct solutions to the self-dual Einstein vacuum equations from solutions of various two-dimensional integrable systems by exploiting the fact that the Lax formulations of both systems can be embedded in that of the self-dual Yang–Mills equations. We illustrate this by constructing explicit self-dual vacuum metrics on R × Σ, where Σ is a homogeneous space for a real subgro...

In this paper branching rules for the fundamental representations of the symplectic groups in positive characteristic are found. The submodule structure of the restrictions of the fundamental modules for the group Sp2n(K) to the naturally embedded subgroup Sp2n−2(K) is determined. As a corollary, inductive systems of fundamental representations for Sp∞(K) are classified. The submodule structure...

(using the restricted product topology ensures that a 7→ a−1 is continuous, which is not true of the subspace topology). As a topological group, IK is locally compact and Hausdorff. The multiplicative group K× is canonically embedded as a discrete subgroup of IK via the diagonal map x 7→ (x, x, x, . . .), and the idele class group is the quotient CK := IK/K, which is locally compact but not com...

Let Cox(Sr) be the homogeneous coordinate ring of the blow-up Sr of P 2 in r general points, i.e., a smooth Del Pezzo surface of degree 9 − r. We prove that for r ∈ {6, 7}, Proj(Cox(Sr)) can be embedded into Gr/Pr, where Gr is an algebraic group with root system given by the primitive Picard lattice of Sr and Pr ⊂ Gr is a certain maximal parabolic subgroup.

Introduction: Indomethacin increases generation of mitochondrial reactive oxygen species (ROS) which have a crucial role in the indomethacin-induced gastric ulcer. Coenzyme Q10 has an antioxidant activity on mitochondria and cell membranes and protects lipids from oxidation and is essential for stabilizing biological membranes. Superoxide dismutase (SOD) acts as one of the defense mechanisms ag...

In this paper, persents the definitions of strongly prime ideal, strongly prime N-subgroup, Pseudo-valuation near ring and Pseudo-valuation N-group. Some of their properties have also been proven by theorems. Then it is shown that, if N be near ring with quotient near-field K and P be a strongly prime ideal of near ring N, then is a strongly prime ideal of ‎‎, for any multiplication subset S of...

in this paper, we will give necessary and sufficient conditions for certain hnnextensions of subgroup separable groups with normal associated subgroup to be conjugacyseparable. in fact, we will show that these hnn extensions are conjugacy separable if and onlyif the normalizer of one of its associated subgroup is conjugacy separable.

let $g$ be a finite group with the identity $e$‎. ‎the subgroup intersection graph $gamma_{si}(g)$ of $g$ is the graph with vertex set $v(gamma_{si}(g)) = g-e$ and two distinct vertices $x$ and $y$ are adjacent in $gamma_{si}(g)$ if and only if $|leftlangle xrightrangle capleftlangle yrightrangle|>1$‎, ‎where $leftlangle xrightrangle $ is the cyclic subgroup of $g$ generated by $xin g$‎. ‎in th...