Addressing a perennial apologetic and pastoral demand, the twelve Minor Prophets undertake to assert and demonstrate the goodness of God in the face of apparent evidence to the contrary. I will argue that the Twelve were intended to be read together and have the purpose of encouraging the post-exilic reader to trust Yahweh’s faithfulness to his salvation promises, even in the face of the many s...

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the identity and unity of the divine attributes in mulla sadra’s view is based on the possibility of extraction of multiple concepts from a single aspect of an instance. this possibility is not compatible with the unity of the concept with its referent and is not also compatible with the denotation of concepts. in this article, the unity of god’s essence and attributes is the main assumption be...

The effective action for type II string theory compactified on a six torus is N = 8 supergravity, which is known to have an E 7 duality symmetry. We show that this is broken by quantum effects to a discrete subgroup, E 7 (Z), which contains both the T-duality group O(6, 6; Z) and the S-duality group SL(2; Z). We present evidence for the conjecture that E 7 (Z) is an exact 'U-duality' symmetry o...

We discuss some aspects of the representation theory of the deformed Virasoro algebra Virp,q. In particular, we give a proof of the formula for the Kac determinant and then determine the center of Virp,q for q a primitive N -th root of unity. We derive explicit expressions for the generators of the center in the limit t = qp → ∞ and elucidate the connection to the Hall-Littlewood symmetric func...

1. Introduction. Let K be a number field, let p be an odd prime, and let K ∞ /K be an extension containing all p-power roots of unity whose Galois group Γ is isomorphic to Z

Representations of SO(5) q are constructed explicitly on the Chevalley basis for all q, generic and root of unity. Matrix elements of the generators are obtained for all representations depending on three variable indices, the maximal number being 4. A prescription for contraction is given such that a complete Hopf algebra is immediately obtained for the non-semisimple contracted case. For q a ...

For a finite system A = {as + nsZ}s=1 of arithmetic sequences the covering function is w(x) = |{1 6 s 6 k : x ≡ as (mod ns)}|. Using equalities involving roots of unity we characterize those systems with a fixed covering function w(x). From the characterization we reveal some connections between a period n0 of w(x) and the moduli n1, · · · , nk in such a system A. Here are three central results...

Any finite-dimensional Hopf algebra H is Frobenius and the stable category of H-modules is triangulated monoidal. To H-comodule algebras we assign triangulated module-categories over the stable category of H-modules. These module-categories are generalizations of homotopy and derived categories of modules over a differential graded algebra. We expect that, for suitable H, our construction could...