abstract. let r be a 2-torsion free ring with identity. in this paper, first we prove that any jordan left derivation (hence, any left derivation) on the full matrix ringmn(r) (n  2) is identically zero, and any generalized left derivation on this ring is a right centralizer. next, we show that if r is also a prime ring and n  1, then any jordan left derivation on the ring tn(r) of all n×n up...

‎let $mathcal{a}$ be a unital banach algebra‎, ‎$mathcal{m}$ be a left $mathcal{a}$-module‎, ‎and $w$ in $mathcal{z}(mathcal{a})$ be a left separating point of $mathcal{m}$‎. ‎we show that if $mathcal{m}$ is a unital left $mathcal{a}$-module and $delta$ is a linear mapping from $mathcal{a}$ into $mathcal{m}$‎, ‎then the following four conditions are equivalent‎: ‎(i) $delta$ is a jordan left de...

thoracic duct is a duct that drains the lymph from the cisterna chily into the venous angle of the cranial vena vava. thoracic duct in the horse is situated on the right side, but in rare cases the left thoracic duct has been reported. in this report the course and left position of the thoracic duct in an embalmed donkey is described. regarding many anatomical similarities between horse and don...

a 78-year-old woman was referred for coronary angiography with the chief complaint of exertional angina and dyspnea of a very long duration during routine daily physical activities. she had a history of poorly controlled hypertension and dyslipidemia. coronary angiography revealed diffuse three-vessel disease. interestingly, an unusual branch was noted originating from the mid shaft of the left...

background: early diagnosis of left ventricular mass (lvm) inappropriateness and left ventricular hypertrophy   (lvh) can result in preventing diastolic left ventricular dysfunction and its related morbidity and mortality. this study was performed to determine if diastolic dysfunction   is associated with lvh and inappropriate lvm. methods: one hundred   and twenty five uncomplicated hypertensi...