We present a method for the direct measurement of Wigner characteristic function thermalizing harmonic oscillator that is completely inaccessible control or measurement. The strategy employs recently proposed probe-measurement-based scheme [Phys. Rev. Lett. 122, 110406 (2019)] which relies on pulsed two-level probe. generalize this to case nonunitary time evolution target oscillator, describing...

The harmonic morphisms φ : M → Nn are studied using the methods of the moving frame and exterior differential systems and three main results are achieved. The first result is a local structure theorem for such maps in the case that φ is a submersion, in particular, a normal form is found for all such φ once the metric on the target manifold N is specified. The second result is a finiteness theo...

A continuous function f u iv is a complex-valued harmonic function in a complex domain C if both u and v are real harmonic inC. In any simply connected domainD ⊆ C, we canwrite f h g, where h and g are analytic in D. We call h the analytic part and g the co-analytic part of f . Note that f h g reduces to h if the coanalytic part g is zero. For p ≥ 1, denote by H p the set of all multivalent har...

In this paper, we introduce a new labeling called one modulo three harmonic mean labeling. A graph G is said to be one modulo three harmonic mean graph if there is a function φ from the vertex set of G to {1, 3, 4, ... ,3 − 2, 3 } with φ is one-one and φ induces a bijection φ∗ from the edge set of G to {1, 4, ..., 3q 2}, where φ∗(e = uv) = ( ) ( ) ( ) ( ) or ( ) ( ) ( ) ( ) and the function φ i...

This paper presents a significant modification of our previously proposed speech recognizer’s front-end based on perceptual harmonic cepstral coefficients. The spectrum is split into two frequency bands, which correspond to the harmonic and non-harmonic components. A weighting function, which depends both on the voiced/unvoiced/ transitional classification and on the prominence of harmonic stru...

A 2p-times continuously differentiable complex-valued function f = u+ iv in a simply connected domainΩ ⊆ C is p-harmonic if f satisfies the p-harmonic equation ∆p f = 0. In this paper, we investigate the properties of p-harmonic mappings in the unit disk |z| < 1. First, we discuss the convexity, the starlikeness and the region of variability of some classes of p-harmonic mappings. Then we prove...