noise, sensitivity, digital cameras, scanners, color, colour We formalize ideas of orthogonality and inner products implicit in the development of a number of figures of merit (FOM, [1]) of colour recording filters. We show that, in negligible measurement noise, the data dependence of each FOM based on linear colour correction is equivalent to a choice of inner product (and hence of orthogonali...

We formalize ideas of orthogonality and inner products implicit in the development of a number of figures of merit (FOM) of color recording filters. We show that, in negligible measurement noise, the data dependence of each FOM based on linear color correction is equivalent to a choice of inner product (and hence of orthogonality). Further, we show that optimal sensors with respect to noise sen...

We show that any unitary transformation performed on the quantum state of a closed quantum system describes an inner, reversible, generalized quantum measurement. We also show that under some specific conditions it is possible to perform a unitary transformation on the state of the closed quantum system by means of a collection of generalized measurement operators. In particular, given a comple...

‎Let $mathscr{L}$ be a commutative subspace lattice generated by finite many commuting independent nests on a complex separable Hilbert space $mathbf{H}$ with ${rm dim}hspace{2pt}mathbf{H}geq 3$‎, ‎${rm Alg}mathscr{L}$‎ ‎the CSL algebra associated with $mathscr{L}$ and $mathscr{M}$ be an algebra containing ${rm Alg}mathscr{L}$‎. ‎This article is aimed at describing the form of‎ ‎additive mapppi...

It is shown that if the ring of constants of a restricted differential Lie algebra with a quasi-Frobenius inner part satisfies a polynomial identity (PI) then the original prime ring has a generalized polynomial identity (GPI). If additionally the ring of constants is semiprime then the original ring is PI. The case of a non-quasi-Frobenius inner part is also considered.

Tail biting trellis codes and block concatenated codes are discussed from random coding arguments. Error exponents and decoding complexity for generalized tail biting (GTB) random trellis codes, and their relationships are derived, where the GTB trellis codes consist of full tail biting (FTB) trellis codes, partial tail biting (PTB) trellis codes and direct truncated (DT) trellis codes. We show...

The aim of this paper is to give a presentation of several subjects of Schur analysis with some historical information. The class of J-inner functions plays a key role in this new mathematical eld which is situated at the seam of various mathematical disciplines (operator theory, scattering theory, complex function theory, prediction theory for stochastic processes, spectral theory for diierent...

Introducing the notions of (inner) σ-derivation, (inner) σ-endomorphism and oneparameter group of σ-endomorphisms (σ-dynamics) on a Banach algebra, we correspond to each σ-dynamics a σ-derivation named as its σ-infinitesimal generator. We show that the σ-infinitesimal generator of a σ-dynamics of inner σ-endomorphisms is an inner σ-derivation and deal with the converse. We also establish a nice...

We develop a general convergence theory for the generalized minimal residual method for least squares problems preconditioned with inner iterations. The inner iterations are performed by stationary iterative methods. We also present theoretical justifications for using specific inner iterations such as the Jacobi and SOR-type methods. The theory is improved particularly in the rankdeficient cas...