mulla sadra uses his own principles in the debate over unity, multiplicity and graded unity of being to develop a profound interpretation from the noble tradition “there is no compulsion and volition but something in between”. this approach is formed via exposing the meaning of hierarchy in sadra’s theosophy, human deeds are attributed both to the individual himself and the divine will. his bre...

The Liouville function is defined by λ(n) := (−1)Ω(n) where Ω(n) is the number of prime divisors of n counting multiplicity. Let ζm := e2πi/m be a primitive m–th root of unity. As a generalization of Liouville’s function, we study the functions λm,k(n) := ζ kΩ(n) m . Using properties of these functions, we give a weak equidistribution result for Ω(n) among residue classes. More formally, we sho...

One of the fundamental problems of theoretical mysticism is how to explain the difference between God and the world on the basis of the idea of wahdat al-wujud (the unity of existence). Following the explanation of certain necessary premises, this paper presents the theory of divine manifestation as one that can explain and analyze multiplicity. In this article we especially seek t...

Let E be an elliptic curve defined over a number field K. We show that for each root of unity ζ, the set Σζ of σ ∈ Gal(K/K) such that ζ is an eigenvalue of infinite multiplicity for σ acting on E(K)⊗ C has non-empty interior. For the eigenvalue −1, we can show more: for any σ in Gal(K/K), the multiplicity of the eigenvalue −1 is either 0 or ∞. It follows that Σ −1 is open.

There is no single answer to the unity-multiplicity problem regarding the self for the simple reason that the term "self" is used by too many different theorists in too many different ways. In fact, there are several important substantive topic areas that need to be distinguished and studied scientifically. The topic areas I examine in this article are reflexivity, unit coherence, agency, and s...

one of the consequences of accepting personal unity of existence as well as the philosophical rule of “al-wahid” is wujud-e munbasit (the extended existence). sayyid haydar amuli explains origination of multiplicity from the one on the basis of wujud-e munbasit. according to him the first emanation from being is universal and extendedand contains all degrees of contingent world. by depicting of...

This paper is concerned with the determination of the Jordan canonical form and D1/,2-norm of the SOR iterative matrix derived from the coefficient matrix A having the form *-& t) with D\ and Di symmetric and positive definite. The theoretical results show that the Jordan form is not diagonal, but has only q principal vectors of grade 2 and that the D1//2-norm of J2?Ub (u^, the optimum paramete...

the idea that the distinction of sciences has to be based on topics is facing serious criticisms and objections, since both arguments of the followers of this approach are violable and the history of science is replete with many examples that do not fit into this tight framework. this issue prompted some scholars such as muḥaqqiq khurāsānī to move toward distinction based on objective. this app...