Semi-Special Permutations on [p q r]

(P, Q)-Special Functions

It is suggested that the (p, q)-hypergeometric series studied by Burban and Klimyk (in Integral Transforms and Special Functions 2 (1994) 15-36) can be considered as a special case of a more general (P, Q)-hypergeometric series. 1. Introduction I propose a general (P, Q)-hypergeometric series. In this, I am inspired mainly by the paper of Burban and Klimyk [1] titled " P, Q-differentiation, P, ...

Towards large r from [ p , q ] - inflation

The recent discovery of B-mode polarizations in the CMB by the BICEP2 collaboration motivates the study of large-field inflation models which can naturally lead to significant tensor-to-scalar ratios. A class of such models in string theory are axion monodromy models, where the shift symmetry of an axion is broken by some branes. In type IIB string theory such models so far utilized NS5 branes ...

Branes in L (p,q,r)

We have found the solution to the back reaction of putting a stack of coincident D3 and D5 branes in R×M6, where M6 is constructed from an infinite class of Sasaki-Einstein spaces, L. The non-zero fluxes associated to 2 and 3-form suggests the presence of non-contractible 2 and 3-cycles in this geometry. The radial part of the warp factor has the usual form and possess the cascading feature. We...

New Attacks on RSA with Moduli N = p r q

We present three attacks on the Prime Power RSA with modulus N = pq. In the first attack, we consider a public exponent e satisfying an equation ex − φ(N)y = z where φ(N) = pr−1(p − 1)(q − 1). We show that one can factor N if the parameters |x| and |z| satisfy |xz| < N r(r−1) (r+1)2 thereby extending the recent results of Sakar [16]. In the second attack, we consider two public exponents e1 and...

ANALYSIS ON THE MINIMAL REPRESENTATION OF O(p, q) – III. ULTRAHYPERBOLIC EQUATIONS ON R p−1,q−1