In this work we present a ``modest'' holographic reconstruction of the bulk geometry in asymptotically flat spacetime using two-point correlators boundary quantum field theory (QFT) spacetime. The QFT lives on null spacetime, namely infinity and/or Killing horizons. relies two unrelated results: (i) there is bulk-to-boundary type correspondence between free fields living manifold and its bounda...

All equivalence classes of Hadamard matrices of order at most 28 have been found by 1994. Order 32 is where a combinatorial explosion occurs on the number of inequivalent Hadamard matrices. We find all equivalence classes of Hadamard matrices of order 32 which are of certain types. It turns out that there are exactly 13,680,757 Hadamard matrices of one type and 26,369 such matrices of another t...

A complex Hadamard matrix, C, of order n has elements 1, -1, i, i and satisfies CC* = nIn where C* denotes the conjugate transpose of C. Let C = [cij] be a complex Hadamard matrix of order n. S(C) = ∑ cij is called the sum of C. 0(C) = │S(C)│ is called the excess of C. We study the excess of complex Hadamard matrices. As an application many real Hadamard matrices of large and maximal excess are...

Recently Loeb and Walsh [3] established several results concerning the Royden boundary in the axiomatic setting. This in effect generalizes theorems about H D-f unctions, Dirichlet-finite harmonic functions on surfaces to Riemannian manifolds, which are the most general carriers of these functions. Their results are however restricted to bounded H D-f unctions. Whether Nakai's [4] characterizat...

Homological invariants “at infinity” and (coarse) isoperimetric inequalities are basic tools in the study of large-scale geometry (see e.g., [Gr]). The purpose of this paper is to combine these two ideas to construct a family divk(X ), 0 ≤ k ≤ n − 2 , of geometric invariants for Hadamard manifolds X 1 . The divk(X ) are meant to give a finer measure of the spread of geodesics in X ; in fact the...

A Z2Z4-linear Hadamard code of length α+2β = 2 is a binary Hadamard code which is the Gray map image of a Z2Z4-additive code with α binary coordinates and β quaternary coordinates. It is known that there are exactly b t−1 2 c and b t 2 c nonequivalent Z2Z4-linear Hadamard codes of length 2, with α = 0 and α 6= 0, respectively, for all t ≥ 3. In this paper, it is shown that each Z2Z4-linear Hada...

in the first part of this paper, some theorems are given for a riemannian manifold with semi-symmetric metric connection. in the second part of it, some special vector fields, for example, torse-forming vector fields, recurrent vector fields and concurrent vector fields are examined in this manifold. we obtain some properties of this manifold having the vectors mentioned above.

A trade in a complex Hadamard matrix is a set of entries which can be changed to obtain a different complex Hadamard matrix. We show that in a real Hadamard matrix of order n all trades contain at least n entries. We call a trade rectangular if it consists of a submatrix that can be multiplied by some scalar c 6= 1 to obtain another complex Hadamard matrix. We give a characterisation of rectang...