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...

We proceed further in the investigation of Robin problem $$({\text{P}_\alpha })\;\;\;\;\;\left\{ {\begin{array}{*{20}{c}} { - \vartriangle u = a(x){u^q}}&{\text{in}}&\Omega \\ {u \geqslant 0\;\;\;\;\;\;\;\;}&{\text{in}}&\Omega {{\partial _v}u \alpha u\;\;\;\;}&{\text{on}}&{\partial \Omega }, \end{array}} \right.$$ on a smooth bounded domain Ω ⊂ ℝN, with sign-changing and 0 < q 1. Assuming exist...

We describe a Jordan-algebraic version of results related to convexity of images of quadratic mappings as well as related results on exactness of symmetric relaxations of certain classes of nonconvex optimization problems. The exactness of relaxations is proved based on rank estimates. Our approach provides a unifying viewpoint on a large number of classical results related to cones of Hermitia...

We call a finitely complete category diexact if every difunctional relation admits a pushout which is stable under pullback and itself a pullback. We prove three results relating to diexact categories: firstly, that a category is a pretopos if and only if it is diexact with a strict initial object; secondly, that a category is diexact if and only if it is Barr-exact, and every pair of monomorph...

In this paper, we principally explore flat modules over a commutative ring with identity. We do this in relation to projective and injective modules with the help of derived functors like Tor and Ext. We also consider an extension of the property of flatness and induce analogies with the “special cases” occurring in flat modules. We obtain some results on flatness in the context of a noetherian...

Completions of (small) categories under certain kinds of colimits and exactness conditions have been studied extensively in the literature. When the category that we complete is not left exact but has some weaker kind of limit for finite diagrams, the universal property of the completion is usually stated with respect to functors that enjoy a property reminiscent of flatness. In this fashion no...

this article presents a unified approach to the abstract notions of partial convolution and involution in $l^p$-function spaces over semi-direct product of locally compact groups. let $h$ and $k$ be locally compact groups and $tau:hto aut(k)$ be a continuous homomorphism.  let $g_tau=hltimes_tau k$ be the semi-direct product of $h$ and $k$ with respect to $tau$. we define left and right $tau$-c...

PURPOSE We aimed to compare the intra- and interoperator variability of lobar volumetry and emphysema scores obtained by semi-automated and manual segmentation techniques in lung emphysema patients. MATERIALS AND METHODS In two sessions held three months apart, two operators performed lobar volumetry of unenhanced chest computed tomography examinations of 47 consecutive patients with chronic ...