Let R be an associative ring in which an identity element is not assumed. A right quotient ring of P is an overring 5 such that for each aQS there corresponds rQR such that arQR and ar 9*0. A theorem of R. E. Johnson [l ] states that R possesses a right quotient ring S which is a (von Neumann) regular ring if and only if P has vanishing right singular ideal. In this case P possesses a unique (u...

The matching of energy supply and demand under hypoxic conditions is critical for sustaining myocardial function. Numerous reports indicate that basal energy requirements and ion handling may differ between the ventricles. We hypothesized that ventricular response to hypoxia shows interventricular differences caused by the heterogeneity in glucose metabolism and expression and activity of ion t...

The Zygmund sums of a function $f\in L_{1}$ are trigonometric polynomials the form $$Z^{s}_{n-1}(f;t):=\frac{a_{0}}{2}+\sum_{k=1}^{n-1}\Big(1-\big(\frac{k}{n}\big)^{s}\Big) \big(a_{k}(f)\cos kt+b_{k}(f)\sin kt\big), s>0,$$ where $a_{k}(f)$ and $b_{k}(f)$ Fourier coefficients $f$. We establish exact-order estimates uniform approximations by $Z^{s}_{n-1}$ $2\pi$-periodic continuous functions f...

when addition and multiplication are defined in the obvious way, form a ring, the group-ring of G over K, which will be denoted by R (G, K). Henceforward, we suppose that K has the modulus 1, and we denote the identity in G by e0. Then R(G,K) has the modulus l.e0. Since no confusion can arise thereby, the element 1. e in R(G, K) will be written as e, and whenever it is convenient, the elements ...

We show that for every 1 ≤ k d/(log d)C, some absolute constant C, finite transitive set of unit vectors in ℝd lies within distance $$O\left({1/\sqrt {\log \left({d/k} \right)}} \right)$$ codimension subspace, and this bound is best possible. This extends a result Ben Green, who proved it = 1.