explanation of the multiplicity of the world and the way it was created from the beginning of existence is one the concerns of philosophers, including mullā ṣadrā. the discourse of the emanation of multiplicity from unity would be totally different with respect to the apparent words of ṣadrā, who believes in the gradational unity of existence and according to his specific viewpoint, believing i...

We construct a canonical compactification SQ g,K of the moduli of abelian varieties over Z[ζN , 1/N ] where ζN is a primitive Nth root of unity. It is very similar to, but slightly different from the compactification SQg,K in [N99]. Any degenerate abelian scheme on the boundary of SQ g,K is one of the (torically) stable quasi-abelian schemes introduced in [AN99], which is reduced and singular. ...

We give three constructions of three-class association schemes as fusion schemes of the cyclotomic scheme, two of which are primitive.

A multi-variable theta product is examined. It is shown that, under very general choices of the parameters, the quotient of two such general theta products is a root of unity. Special cases are explicitly determined. The second main theorem yields an explicit evaluation of a sum of series of cosines, which greatly generalizes one of Ramanujan’s theorems on certain sums of hyperbolic cosines.

1. For a field F and a family of central simple F algebras we prove that there exists a regular field extension E/F preserving indices of F -algebras such that all the algebras from the family are cyclic after scalar extension by E. 2. Let A be a central simple algebra over a field F of degree n with a primitive n-th root of unity ρn. We construct a quasiaffine F -variety Symb(A) such that, for...

Let p > 2 be prime, and let n,m ∈ N be given. For cyclic extensions E/F of degree p that contain a primitive pth root of unity, we show that the associated Fp[Gal(E/F )]-modules H(GE , μp) have a sparse decomposition. When E/F is additionally a subextension of a cyclic, degree p extension E/F , we give a more refined Fp[Gal(E/F )]-decomposition of H (GE , μp).

Vazirani and the author [Electron. J. Combin., 15 (1) (2008), R130] gave a new interpretation of what we called l-partitions, also known as (l, 0)-Carter partitions. The primary interpretation of such a partition λ is that it corresponds to a Specht module S which remains irreducible over the finite Hecke algebra Hn(q) when q is specialized to a primitive l root of unity. To accomplish this we ...

OBJECTIVES Theories of patient satisfaction with treatment outcome have not been developed and tested in healthcare settings. The objectives of this study were to test a new theory linking patient satisfaction and embodiment (body--self unity) and examine it in relation to other competing theories. DESIGN We conducted a prospective cohort study. SETTING This study was conducted at a tertiar...

We prove a Morita reduction theorem for the cyclotomic Hecke algebras Hr,p,n(q,Q) of type G(r, p, n). As a consequence, we show that computing the decomposition numbers of Hr,p,n(Q) reduces to computing the psplittable decomposition numbers (see Definition 1.1) of the cyclotomic Hecke algebras Hr′,p′,n′ (Q ), where 1 ≤ r ≤ r, 1 ≤ n ≤ n, p | p and where the parameters Q are contained in a single...