We consider subrings S of rings R such that R = S⊕V with V either two sided invariant under multiplication by S or invariant under the commutator with S. We show that some important properties of R are inherited by S under such conditions. One is the FCR-property which says that every finite dimensional representation is completely reducible. Another application gives a characterization (in cha...

Superconducting thin-film rings smaller than the film penetration depth ~the Pearl length! are considered. The current distribution, magnetic moment, and thermodynamic potential F(H ,N ,v) for a flat, washer-shaped annular ring in a uniform applied field H perpendicular to the film are solved analytically within the London approach for a state with winding number N and a vortex at radius v betw...

We use character sums to confirm several recent conjectures of V. I. Arnold on the uniformity of distribution properties of a certain dynamical system in a finite field. On the other hand, we show that some conjectures are wrong. We also analyze several other conjectures of V. I. Arnold related to the orbit length of similar dynamical systems in residue rings and outline possible ways to prove ...

For a nontrivial connected graph G with no isolated vertex, nonempty subset D \(\subseteq\) V (G) is rings dominating set if and for each vertex \(\upsilon\) \(\in\) \ adjacent to at least two vertices in D. Thus, the of all D, \(\mid\)N(\(\upsilon\)) \(\cap\) (V D)\(\mid\) \(\ge\) 2. Moreover, called minimum smallest size given graph. The cardinality domination number G, denoted by \(\gamma\)r...

In this work, we define three composite matrices derived from group rings. We employ these to create generator of the form $ [I_n \ | \Omega(v)], where I_n is identity matrix and \Omega(v) a search for binary self-dual codes with parameters [36,18, 6 \text{or} 8]. next lift over ring R_1 = \mathbb{F}_2+u\mathbb{F}_2 obtain whose images are [72,36,12]. Many turn out have weight enumerators that ...

Let the finite group G act linearly on the vector space V over the field k of arbitrary characteristic, and let H < G be a subgroup. The extension of invariant rings k[V ] ⊂ k[V ] is studied using modules of covariants. An example of our results is the following. Let W be the subgroup of G generated by the reflections in G. A classical theorem due to Serre says that if k[V ] is a free k[V ]-mod...

Let the finite group G act linearly on the vector space V over the field k of arbitrary characteristic and let H < G be a subgroup. The extension of invariant rings k[V ] ⊂ k[V ] is studied using modules of covariants. An example of our results is the following. Let W be the subgroup of G generated by the reflections in G. A classical theorem due to Serre says that if k[V ] is a free k[V ]-modu...

In this paper we define a new type of rings ”almost powerhermitian rings” (a generalization of almost hermitian rings) and establish several sufficient conditions over a ring R such that, every regular matrix admits a diagonal power-reduction.

Crocus sativus L. (saffron) is a widely used food additive for its color and taste. The hypotensive effects of saffron have been shown in previous studies. The aim of this study was to evaluate the mechanism of vasodilatory effects induced by saffron on isolated rat aorta.To study the vasodilatory effects of saffron aqueous extract (0.5, 1 and 2 mg/mL), isolated rat thoracic aorta rings were co...

To determine if radiocontrast impairs vascular relaxation of the renal artery, segments (4-5 mm in length) of canine renal artery were suspended in vitro in organ chambers to measure isometric force (95% O2/5% CO2, at 37 C). Arterial segments with and without endothelium were placed at the optimal point of their length-tension relation and incubated with 10 microM indomethacin to prevent synthe...