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 (respectively, copri) if RR (respectively, 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 R-module. A co-pli strongly prime RING R is a simple RING. A left self-injective co-pli RING R is left Noetherian if and only if R is a left perfect RING. It is shown that a cogenerator RING R is a pli RING if and only if it is a co-pri RING. Moreover, if R is a left perfect RING such that every projective R-module is co-epi-retractable, then R is a quasi-Frobenius RING.

Leber HEREDITARY Optic Neuropathy (LHON) is the commonest primary mitochondrial disease associated with bilateral optic neuropathies. It is recognized as the most frequent cause of isolated blindness in young men.Maternally-transmitted LHON pedigrees show incomplete penetrance with a male preponderance for visual loss. Age of onset is variable ranging from the first to eighth decade.Visual loss associated with LHON is characteristically subacute, central and painless. Typically visual loss occurs in isolation. Visual field defects consistent with central or cecocentral defects are typical. Colour vision dysfunction may be an early and severe feature of LHON-associated visual loss. Pupillary function is relatively preserved. Fundoscopic changes are characterized by peripapillary telangiectatic microangiopathy or circumpapillary nerve fiber layer swelling (pseudooedema) in the early stages, later followed by non-specific optic atrophy with nerve fiber layer drop out, especially in the papillomacular bundle.Although LHON is typically associated with isolated visual loss, neurological and multisystem organ involvement has been recognized in association with a multiple-sclerosis-like illness (usually in women), dystonia, myelopathy, neuropathy, severe encephalomyelopathy and cerebellar ataxia.One of three mtDNA point mutations account for up to 95% of known cases of LHON: m.3460G>A, m.11778G>A, m.14484T>C all of which occur in mitochondrial-encoded structural subunits of complex I. Younger age-atonset (less than 15 years) and mutation type appear to dictate visual outcome, patients with the m.14484T>C MTND6 mutation have a better visual prognosis with 60% attaining some visual improvement compared to only 5% of those harbouRING the m.11778G>A MTND4 gene mutation.

Background: Bruxism is a parafunctional disorder. The prevalence of this rhythmic activity of rodent muscles is reported to be about %8. This disease can compromise the life quality of a person’ s general performance. The aim of this study is to gather information upon genetic factors, which contribute to the pathogenesis of the disease. Materials and Methods: All related articles published in 1966 onward from google scholar such as ISI, PubMed, Scopus and Ovid within the databases were searched using English keywords ‘ Bruxism and Genetics’ . 300 articles were found. 252 articles were removed due to content duplication and irrelevance. Results: The review of selected articles finally showed that in addition to other factors such as psychological factors, local factors, systemic factors, etc., the genetic factors also play a significant role in pathogenesis of bruxism. Among the influential genes are rs6313 polymorphism from the 5HT2A gene and rs6313 polymorphism from the HTR2A gene. Conclusion: Evidence suggests that genetic factors play an important role in the pathology and development of bruxism, however the main causing mechanism still largely remains unknown.

Using fixed point methods, we prove the stability of orthogonally RING homomorphism and orthogonally RING derivation in Banach algebras.