في هذا العمل قدمنا تعاريف لمفاهيم جديدة والتي تسمى : الاشتقاقات اليسارية وتعميم الحلقات المقتربة الاولية الثلاثية. اضافة الى ذلك قمنا بدراسة ابدالية الثلاثية عند وجود بعض المتطابقات الجبرية على تعميم اليسارية.

LetN be a zero-symmetric left near-ring, not necessarily with amultiplicative identity element; and letZ be its multiplicative center. DefineN to be 3-prime if for all a, b ∈ N\{0}, aNb / {0}; and callN 2-torsion-free if N, has no elements of order 2. A derivation onN is an additive endomorphism D of N such that D xy xD y D x y for all x, y ∈ N. A generalized derivation f with associated deriva...

Critical Dirac operators are those which have eigenfunctions and/or resonances for E = m. We estimate the behavior of the generalized eigenfunctions of critical Dirac operators under small perturbations of the potential. The estimates are done in the L∞-norm. We show that for small k the generalized eigenfunctions are in leading order multiples of the respective eigenfunctions and/or resonances...

Let N be a near ring. An additive mapping f : N → N is said to be a right generalized (resp., left generalized) derivation with associated derivation d onN if f(xy) = f(x)y + xd(y) (resp., f(xy) = d(x)y + xf(y)) for all x, y ∈ N. A mapping f : N → N is said to be a generalized derivation with associated derivation d onN iff is both a right generalized and a left generalized derivation with asso...

Background and Objectives: Identification of surgical instruments in laparoscopic video images has several biomedical applications. While several methods have been proposed for accurate detection of surgical instruments, the accuracy of these methods is still challenged high complexity of the laparoscopic video images. This paper introduces a Surgical Instrument Detection Framework (SIDF) for a...

We show that the exact distribution of a positive linear combination of independent Gumbel random variables can be written as the sum of a linear combination of independent log Gamma distributions, and an independent shifted Generalized Integer Gamma distribution. Given the complexity of this exact distribution, we develop a near-exact distribution using a shifted Generalized Near-Integer Gamma...