We consider the evolution of a qubit (spin 1/2) under the simultaneous continuous measurement of three noncommuting qubit operators σ(x), σ(y), and σ(z). For identical ideal detectors, the qubit state evolves by approaching a pure state with a random direction in the Bloch vector space and by undergoing locally isotropic diffusion in the perpendicular directions. The quantum state conditioned o...

We develop a theory of existence and uniqueness for the following porous medium equation with fractional diffusion,  ∂u ∂t + (−∆)σ/2(|u|m−1u) = 0, x ∈ RN , t > 0, u(x, 0) = f(x), x ∈ RN , with data f ∈ L1(RN ) and exponents 0 < σ < 2, m > m∗ = (N − σ)+/N . An L1-contraction semigroup is constructed. Nonnegative solutions are proved to be continuous and strictly positive for all x ∈ RN , t > 0...

This note is a complement of the paper " Solving BSDE with adaptive control variate " [1]. It deals with the convergence of the approximating operator P, based on a non parametric regression technique called local averaging, and defined in Definition 1.1. Although the computations are quite standard (see [3], [2]), the specificities of the paper are the following • the support of the variables ...

*Correspondence: Andrew J. Shirk, College of the Environment, Climate Impacts Group, University of Washington, Box 355674, Seattle, WA 98195, USA e-mail: [email protected] Effective population size (Ne) is an important parameter in conservation genetics because it quantifies a population’s capacity to resist loss of genetic diversity due to inbreeding and drift. The classical approach to estimate N...

In the paper, approximation of analytic functions on compact sets strip {s=σ+it∈C∣1/2&lt;σ&lt;1} by shifts F(ζ(s+iu1(τ)),…,ζ(s+iur(τ))), where ζ(s) is Riemann zeta-function, u1,…,ur are certain differentiable increasing functions, and F a continuous operator in space considered. It obtained that set above interval [T,T+H] with H=o(T), T→∞, has positive lower density. Additionally, positivity de...

In this study, using the concept of statistical σ−convergence which is stronger than convergence and statistical convergence we prove a Korovkin-type approximation theorem for sequences of positive linear operators defined on C∗ which is the space of all 2π-periodic and continuous functions on R, the set of all real numbers. We also study the rates of statistical σ−convergence of approximating ...

This paper proposes a general method to design the noise-transfer-function of a continuous-time Σ∆ modulator having high-order passive LC loop filters. The feedback signals can have arbitrary shapes and can be applied either at internal nodes or only at the input node. As a design example, this technique is used to design a 4 order Σ∆ modulator where the internal nodes of the loop filter are re...

The critical behaviour of the one-dimensional q-state Potts model with long-range interactions decaying with distance r as r −(1+σ) has been studied in the wide range of parameters 0 < σ ≤ 1 and 1 16 ≤ q ≤ 64. A transfer matrix has been constructed for a truncated range of interactions for integer and continuous q, and finite range scaling has been applied. Results for the phase diagram and the...

In dimension three, we establish the existence of weak solutions {u,H,E} to the Landau-Lifshitz equation (1.1) coupled with the time-dependent Maxwell equation (1.2)-(1.3) such that u is Hölder continuous away from a closed set Σ, which has locally finite 3-dimensional parabolic Hausdorff measure. For two reduced Maxwell equations (1.17) and (1.18), Hölder continuity of ∇u away from Σ is also e...

and thus be represented (for σ > 1 ) as a product of terms of the form exp(a(eibt − 1)), each of which is the characteristic function of a Poisson random variable with intensity a and values in the lattice kb, k = 0, 1, 2, . . . . Cf. Gnedenko and Kolmogorov [6, p. 75]. Faced with a family of “zeta distributions” indexed by parameter σ > 1 , one is led to ask for joint distributions, i.e., for ...