PURPOSE Quantitative analysis of hyperautofluorescent rings and progression in subjects with retinitis pigmentosa associated with retinitis pigmentosa GTPase regulator (RPGR) gene mutations. METHODS Prospective observational study of 46 subjects. Ring area, horizontal and vertical diameter measurements taken from outer and inner ring borders. Intraobserver repeatability, baseline measurements...

In the combination of 5-fluorophenyl-1, 3, 7, 9-tetra methylpyrido [2, 3, d, d, 5, 6 dipyrimidine -2, 4, 6, and 8 tetron, there are 4 rings, respectively, ring that is attached to the halogen ring A and, respectively, a ring The lower and the right to the left of the ring A are called C, B, and D. Calculations and studies show that the amount of aromatics in halogen-ring A in all cases has the ...

The twisted homogeneous coordinate ring is one of the basic constructions of the noncommutative projective geometry of Artin, Van den Bergh, and others. Chan generalized this construction to the multi-homogeneous case, using a concept of right ampleness for a finite collection of invertible sheaves and automorphisms of a projective scheme. From this he derives that certain multi-homogeneous rin...

a module m is called epi-retractable if every submodule of m is a homomorphic image of m. dually, a module m is called co-epi-retractable if it contains a copy of each of its factor modules. in special case, a ring r is called co-pli (resp. co-pri) if rr (resp. rr) is co-epi-retractable. it is proved that if r is a left principal right duo ring, then every left ideal of r is an epi-retractable ...

The directional dynamics of the resonant Rayleigh scattering from a semiconductor microcavity is investigated. When optically exciting the lower polariton branch, the strong dispersion results in a directional emission on a ring. The coherent emission ring shows a reduction of its angular width for increasing time after excitation, giving direct evidence for the time-energy uncertainty in the d...

An R-module M is called strongly noncosingular if it has no nonzero Rad-small (cosingular) homomorphic image in the sense of Harada. It is proven that (1) an R-module M is strongly noncosingular if and only if M is coatomic and noncosingular; (2) a right perfect ring R is Artinian hereditary serial if and only if the class of injective modules coincides with the class of (strongly) noncosingula...

For an arbitrary ring $R$, the zero-divisor graph of $R$, denoted by $Gamma (R)$, is an undirected simple graph that its vertices are all nonzero zero-divisors of $R$ in which any two vertices $x$ and $y$ are adjacent if and only if either $xy=0$ or $yx=0$. It is well-known that for any commutative ring $R$, $Gamma (R) cong Gamma (T(R))$ where $T(R)$ is the (total) quotient ring of $R$. In this...

For a non-commutative ring R, we consider factorizations of polynomials in R[t] where t is central variable. A pseudo-root polynomial p(t)=p0+p1t+?pktk an element ??R, for which there exist q1,q2 such that p=q1(t??)q2. We investigate the rational relationships hold among pseudo-roots p(t) by using diamond operations cover graphs modular lattices. When R division ring, each finite subset S corre...