A generalized arithemtic numerical monoid is of the form S = 〈a, ah+d, ah+2d, . . . , ah+ xd〉 where the gcd(a, d) = 1 and a > x. Much is known for the arithmetic numerical monoid, when h = 1, due to known information for that specific monoid’s length set. Therefore, this paper will explore various invariants of the generalized arithmetic numerical monoid.

Cigarette smoking is associated with an increased incidence of a number of diseases. Minimal information is available at the molecular level concerning the mechanism of action of cigarette smoke. Platelet-activating factor (PAF) is one of the most potent proinflammatory agents described. PAF concentration may be regulated by the degradation of PAF as catalyzed by the plasma enzyme, PAF acetylhy...

Often A is called H-module algebra. We refer reader to [11, 6] for the basic information concerning Hopf algebras and their actions on associative algebras. Definition 1.2 The invariants of H in A is the set AH of those a ∈ A, that ha = ε(h)a for each h ∈ H. Straightforward computations show, that AH is subalgebra of A. The notion of action of Hopf algebra on associative algebra generalize the ...

the second half of the third hijri century, coinciding with the reign of three caliphs, al-mu’tamid (256-79 ah), al-mu’tadhid (279-89 ah), and al-muktafi (289-95 ah), abbasids restored their authority and renewed their organization. this reform process which was began by abu ahmad al-muwaffaq (d. 278 ah) and reached its climax at the time of abu al-abbas al-mu’tadhid stood between two decline p...

Ataxic hemiparesis (AH) is a classic lacunar syndrome associated with localized damage to the pons, internal capsule, thalamus, or corona radiata. A depression of metabolic activity known as crossed cerebellar diaschisis (CCD) is frequently observed in the cerebellar hemisphere contralateral to the site of the lesion in patients with AH. Though small cortical or subcortical lesions may result i...