A certain class of mixed states artificially constructed that is used in quantum cryptography is crucial for representation of signals. This correspondence shows that the square-root measurement gives the optimal measurement for such a class of mixed states.

This paper presents an O(n2 log n) algorithm for computing the symmetric singular value decomposition of square Hankel matrices of order n, in contrast with existing O(n3) SVD algorithms. The algorithm consists of two stages: first, a complex square Hankel matrix is reduced to a complex symmetric tridiagonal matrix using the block Lanczos method in O(n2 log n) flops; second, the singular values...

This contribution describes a Square Block, SB, format for storing a banded symmetric matrix. This is possible by rearranging “in place” LAPACK Band Layout to become a SB layout: store submatrices as a set of square blocks. The new format reduces storage space, provides higher locality of memory accesses, results in regular access patterns, and exposes parallelism.

We study scattering properties of a PT -symmetric square well potential with real depth larger than the threshold of particle-antiparticle pair production as the time component of a vector potential in the Dirac equation. Spontaneous pair production inside the well becomes tiny beyond the strength at which discrete bound states with real energies disappear, consistently with a spontaneous break...

We find a lower bound in terms of N for the number of newforms of weight k and level N whose symmetric square L-functions are non-vanishing at a fixed point s0 with 1 2 < Re(s0) < 1 or s0 = 1 2 .

A square matrix is called line-sum-symmetric if the sum of elements in each of its rows equals the sum of elements in the corresponding column. Let A be an n x n nonnegative matrix and let X and Y be n x n diagonal matrices having positive diagonal elements. Then the matrices XA, XAXand XA Yare called a row-scaling, a similarity-scaling and an equivalence-scaling of A. The purpose of this paper...

We exhibit a spectral identity involving L(s,Symf) for f on SL2. Perhaps contrary to expectations, we do not treat L(s,Symf) directly as a GL3 object. Rather, we take advantage of the coincidence that the standard L-function for SL2 is the symmetric square for a cuspform on GL2 restricted to SL2. [1] As SL2 = Sp2, the integral identities obtained from Sp2n × Sp2n ⊂ Sp4n produce standard L-funct...

Correlation of heat transfer coefficients for air flow through the regenerator constructed from randomly paked spheres is reported for the symmetric-balanced mode of operation. The experimental results have been correlated by the least square regression has been obtained.The present correlation has been compared with the heat transfer coefficient correlations in the literature.

3 Koszul duality 22 3.1 Quadratic algebras . . . . . . . . . . . . . . . . . . . . . . . . . . 22 3.2 Dual coalgebra and algebra . . . . . . . . . . . . . . . . . . . . . 23 3.3 Some more examples . . . . . . . . . . . . . . . . . . . . . . . . . 28 3.3.1 The free algebra . . . . . . . . . . . . . . . . . . . . . . . 28 3.3.2 An example from Fröberg . . . . . . . . . . . . . . . . . . 28 3.3.3 ...

The Gaussian curvature tern in the expression for the energy density in bending of a lipid bilayer can be decomposed in two terns one symmetric and the other one antisymmetric in the principal curvatures. The symmetric tern is proportional to the square of the mean local curvature. A similar tern has exclusively been used to calculate the equilibrium shape of bilayer structures the topology of ...