Following Weyl’s account in The Classical Groups we develop an analogue of the (first and second) Fundamental Theorems of Invariant Theory for rings of differential operators: when V is a k-dimensional complex vector space with the standard SLkC action, we give a presentation of the ring of invariant differential operators D(C[V n])SLkC and a description of the ring of differential operators on...

Let R be a ring and V be a matrix valuation on R. It is shown that, there exists a correspondence between matrix valuations on R and some special subsets ?(MVPR) of the set of all square matrices over R, analogous to the correspondence between invariant valuation rings and abelian valuation functions on a division ring. Furthermore, based on Malcolmson’s localization, an alternative proof for t...

for any reduced commutative $f$-ring with identity and bounded inversion, we show that a condition which is obviously necessary for the socle of the ring to coincide with the socle of its bounded part, is actually also sufficient. the condition is that every minimal ideal of the ring consist entirely of bounded elements. it is not too stringent, and is satisfied, for instance, by rings of conti...

for a fixed positive integer , we say a ring with identity is n-generalized right principally quasi-baer, if for any principal right ideal of , the right annihilator of is generated by an idempotent. this class of rings includes the right principally quasi-baer rings and hence all prime rings. a certain n-generalized principally quasi-baer subring of the matrix ring are studied, and connections...

We study the category of wheeled PROPs using tools from Invariant Theory. A typical example a PROP is mixed tensor algebra V=T(V)⊗T(V⋆), where T(V) on an n-dimensional vector space over field K characteristic 0. First we classify all ideals initial object Z in PROPs. show that non-degenerate sub-wheeled V are exactly subalgebras form VG G closed, reductive subgroup general linear group GL(V). W...

Here, p(: Ω→ R) is the pressure, ∂Ω is the boundary, and n is the unit outward normal vector on ∂Ω. In the axisymmetric case, the existence of solutions to (1.2) was discussed as the problem of vortex rings in, for example, [2, 4, 5, 8]. Their methods were based on a variational principle for kinetic energy. By contrast, Vallis et al. [13] proposed a completely different approach to the solvabi...

Partial difference sets with parameters (v,k,k,/x) = (v,(v— l)/2,(v — 5)/4,(v— l)/4) are called Paley partial difference sets. By using finite local rings, we construct a family of Paley PDSs for abelian/7-groups with any given exponent. Furthermore, we prove some non-existence results on Paley PDSs. Using these results, we prove that Paley PDSs exist in a rank 2 abelian group if and only if th...

Adenosine (ADO), an endogenous regulator of coronary vascular tone, enhances vasorelaxation in the presence of nucleoside transport inhibitors such as dipyridamole. We tested the hypothesis that coronary smooth muscle (CSM) contains a high-affinity transporter for ADO. ADO-mediated relaxation of isolated large and small porcine coronary artery rings was enhanced 12-fold and 3.4-fold, respective...

Motivated by recent results of Tao–Ziegler [Discrete Anal. 2016] and Greenfeld–Tao (2022 preprint) on concatenating affine-linear functions along subgroups an abelian group, we show three recovering affine linearity $$f: V \rightarrow W$$ from their restrictions to lines, where V, W are $${\mathbb {F}}$$ -vector spaces $$\dim \geqslant 2$$ . First, if < |{\mathbb {F}}|$$ {\mathbb is when restri...

An significant milestone study in coding theory recognized to be the paper written by Hammons at al. [1]. Fields are useful area for constructing codes but after the study [1] finite ring have received a great deal of attention. Most of the studies are concentrated on the case with codes over finite chain rings. However, optimal codes over nonchain rings exist (e.g see [2].) In [3], et al. stud...