A convolutionless equation of motion for the reduced density matrix of a system coupled to its environment, where the system1 environment is closed, may be obtained using a projection-operator technique. We show that, when both the system and the environment Hilbert spaces are finite-dimensional, it is possible to eliminate the need for the partial trace over the environment states by construct...

In this paper, the Riemann–Hilbert problem, with a jump supported on an appropriate curve complex plane finite endpoint at origin, is used for study of corresponding matrix biorthogonal polynomials associated Laguerre type matrices weights—which are constructed in terms given Pearson equation. First and second order differential systems fundamental matrix, solution mentioned derived. An explici...

One of unsolved problems in quantum measurement theory is to characterize coexistence of quantum effects. In this paper, applying positive operator matrix theory, we give a mathematical characterization of the witness set of coexistence of quantum effects and obtain a series of properties of coexistence. We also devote to characterizing bijective morphisms on quantum effects leaving the witness...

This paper aims to present some inequalities for unitarily invariant norms. In section 2, we give a refinement of the Cauchy-Schwarz inequality for matrices. In section 3, we obtain an improvement for the result of Bhatia and Kittaneh [Linear Algebra Appl. 308 (2000) 203-211]. In section 4, we establish an improved Heinz inequality for the Hilbert-Schmidt norm. Finally, we present an inequality...

Let W be an operator weight taking values almost everywhere in the bounded positive invertible linear operators on a separable Hilbert space H. We show that if W and its inverse W−1 both satisfy a matrix reverse Hölder property introduced in [2], then the weighted Hilbert transform H : LW (R,H) → L 2 W (R,H) and also all weighted dyadic martingale transforms Tσ : LW (R,H)→ L 2 W (R,H) are bound...

We reduce several computations with Hilbert and Vandermonde type matrices to matrix computations of the Hankel-Toeplitz type (and vice versa). This unifies various known algorithms for computations with dense structured matrices and enables us to extend any progress in computations with matrices of one class to the computations with other classes of matrices. In particular, this enables us to c...

Cryptography is the science of using mathematics to encrypt and decrypt data. Cryptography enables you to store sensitive information or transmit it across insecure networks so that it cannot be read by anyone except the intended recipient. While cryptography is the science of securing data, cryptanalysis is the science of analyzing and breaking secure communication. Classical cryptanalysis inv...

The diagonal in a product of projective spaces is cut out by the ideal of 2×2-minors of a matrix of unknowns. The multigraded Hilbert scheme which classifies its degenerations has a unique Borel-fixed ideal. This Hilbert scheme is generally reducible, and its main component is a compactification of PGL(d)/PGL(d). For n = 2 we recover the manifold of complete collineations. For projective lines ...

The function k : Ω×Ω→ R is called a kernel on Ω if the matrix (k(xi, xj))1≤i,j≤n is positive semidefinite for all positive integers n and all x1, . . . , xn ∈ Ω. It is well-known that if k is a kernel on Ω, then there exists a Hilbert space H̃ and Φ̃ : Ω→ H̃ such that k(x, x′) = 〈Φ̃(x), Φ̃(x)〉H̃. While H̃ and Φ̃ are not uniquely determined by k, the Hilbert space of functionsHk = {〈v, Φ̃(·)〉H̃ : v ∈ H̃} i...

We describe methods for the derivation of strong asymptotics for the denominator polynomials and the remainder of Padé approximants for a Markov function with a complex and varying weight. Two approaches, both based on a Riemann-Hilbert problem, are presented. The first method uses a scalar Riemann-Hilbert boundary value problem on a two-sheeted Riemann surface, the second approach uses a matri...