AdS/CFT correspondence [1] conjectures an equivalence between the string/gravity theory on AdS5 × S and the conformal gauge theory of N = 4 super Yang–Mills (SYM) in the four-dimensional Minkowski space, which appears as the boundary to the five-dimensional anti de Sitter (AdS5) space. With the correspondence reversed, the AdS string/gravity can be regarded as built up over the fourdimensional ...

Jung et al. [7] introduced a geometric structure on Sym+(p), the set of p×p symmetric positive-definite matrices, based eigen-decomposition. Eigenstructure determines both stratification defined by eigenvalue multiplicities, and fibers “eigen-composition” map F:M(p):=SO(p)×Diag+(p)→Sym+(p). When M(p) is equipped with suitable Riemannian metric, fiber leads to notions scaling-rotation distance b...

Let P be a convex and dominated statistical model on the measurable space (X ,A), with A minimal sufficient, and let n ∈ N. Then A⊗n sym, the σ-algebra of all permutation invariant sets belonging to the n-fold product σ-algebra A⊗n, is shown to be minimal sufficient for the corresponding model for n independent observations, Pn = {P⊗n : P ∈ P}. The main technical tool provided and used is a fun...

Let P be a convex and dominated statistical model on the measurable space (X ; A), with A minimal suucient, and let n 2 N. Then A n sym , the-algebra of all permutation invariant sets belonging to the n-fold product-algebra A n , is shown to be minimal suucient for the corresponding model for n independent observations, P n = fP n : P 2 Pg. The main technical tool provided and used is a functio...

We characterize the natural diagonal almost product (locally product) structures on the tangent bundle of a Riemannian manifold. We obtain the conditions under which the tangent bundle endowed with the determined structure and with a metric of natural diagonal lift type is a Riemannian almost product (locally product) manifold, or an (almost) para-Hermitian manifold. We find the natural diagona...

The classical n-variable Kloosterman sums over the finite field Fp give rise to a lisse Ql-sheaf Kln+1 on Gm,Fp = P 1 Fp − {0,∞}, which we call the Kloosterman sheaf. Let Lp(Gm,Fp ,Sym Kln+1, s) be the L-function of the k-fold symmetric product of Kln+1. We construct an explicit virtual scheme X of finite type over Spec Z such that the p-Euler factor of the zeta function of X coincides with Lp(...

In this paper we study qualitative features of glueballs in N = 1 SYM for models of wrapped branes in IIA and IIB backgrounds. The scalar mode, 0 is found to be a mixture of the dilaton and the internal part of the metric. We carry out the numerical study of the IIB background. The potential found exhibits a mass gap and produces a discrete spectrum without any cut-off. We propose a regularizat...

In this paper we investigate algebraic and topological properties of McAlister semigroups. We show that for a non-zero cardinal ? the group automorphisms semigroup M? is isomorphic to direct product Sym(?)×Z2, where Sym(?) permutations ?. semigroups admit unique compact Hausdorff topology. Each element semitopological isolated. It follows free inverse over singleton admits only discrete shift-c...

We investigate N = 4 noncommutative super Yang-Mills (SYM) theory. We compute the one-loop four gauge boson scattering amplitude on parallel Dp-branes, and find the corresponding contribution to the noncommutative SYM one-loop action in a momentum expansion. The result is somewhat surprising. We find that while the planar diagram can be written using the usual ∗-product, the contributions from ...

D-instantons are considered as a probe of coinciding N D3-branes. They can feel an external metric via the commutator terms in their effective action. We show that when the D-instantons are separated from the D3-branes, the metric which is probed at the one loop level, exactly coincides with that of the BPS R-R 3-brane. Interesting connection of this result to the possible explanation of the Ad...