Related papers: Quantum approach on linear combination of harmonic…
In the present paper, we derive several conditions of linear combinations and convolutions of harmonic mappings to be univalent and convex in one direction, one of them gives a partial answer to an open problem proposed by Dorff. The…
In the present paper, we introduce a family of univalent harmonic functions, which map the unit disk onto domains convex in the direction of the imaginary axis. We find conditions for the linear combinations of mappings from this family to…
For $k=1,2$, let $f_k=h_k+\overline{g_k}$ be normalized harmonic right half-plane or vertical strip mappings. We consider the convex combination $\hat{f}=\eta f_1+(1-\eta)f_2 =\eta h_1+(1-\eta)h_2 +\overline{\overline{\eta}…
Let $\mathcal{H}$ denote the class of all complex-valued harmonic functions $f$ in the open unit disk normalized by $f(0)=0=f_{z}(0)-1=f_{\bar{z}}(0)$, and let $\mathcal{A}$ be the subclass of $\mathcal{H}$ consisting of normalized analytic…
We construct sense-preserving univalent harmonic mappings which map the unit disk onto a domain which is convex in the horizontal direction, but with varying dilatation. Also, we obtain minimal surfaces associated with such harmonic…
The fractional q-calculus is the q-extension of the ordinary fractional calculus and dates back to early 20-th century. The theory of q-calculus operators are used in various areas of science such as ordinary fractional calculus, optimal…
In a 1+1 dimensional model of plane gravitational waves the flux-holonomy algebra of loop quantum gravity is modified in such a way that the new basic operators satisfy canonical commutation relations. Thanks to this construction it is…
One of the fundamental conditions for one-way quantum computation (1WQC) is the ability to make sequential measurements on isolated qubits that comprise the highly entangled resource for 1WQC, the cluster state. This has been a significant…
We show that the convolution of the harmonic function $f=h+\bar{g}$, where $h(z)+{e}^{-2{i}\gamma}g(z)=z/(1-{e}^{{i}\gamma}z)$ having analytic dilatation ${e}^{{i}\theta} z^n (0\leq\theta<2\pi)$, with the mapping…
We develop a quantum harmonic analysis framework for the affine group. This encapsulates several examples in the literature such as affine localization operators, covariant integral quantizations, and affine quadratic time-frequency…
Canonical quantization relies on Cartesian, canonical, phase-space coordinates to promote to Hermitian operators, which also become the principal ingredients in the quantum Hamiltonian. While generally appropriate, this procedure can also…
We consider the class univalent log-harmonic mappings on the unit disk. Firstly, we obtain necessary and sufficient conditions for a complex-valued continuous function to be starlike or convex in the unit disk. Then we present a general…
The paper is devoted to integral quantization, a procedure based on operator-valued measure and resolution of the identity. We insist on covariance properties in the important case where group representation theory is involved. We also…
The first author proved that the harmonic convolution of a normalized right half-plane mapping with either another normalized right half-plane mapping or a normalized vertical strip mapping is convex in the direction of the real axis.…
Quantum algorithms offer significant speedups over their classical counterparts for a variety of problems. The strongest arguments for this advantage are borne by algorithms for quantum search, quantum phase estimation, and Hamiltonian…
A bicovariant calculus of differential operators on a quantum group is constructed in a natural way, using invariant maps from \fun\ to \uqg\ , given by elements of the pure braid group. These operators --- the `reflection matrix' $Y \equiv…
Harmonic functions are abundant in nature, appearing in limiting cases of Maxwell's, Navier-Stokes equations, the heat and the wave equation. Consequently, there are many applications of harmonic functions from industrial process…
We present a quantum algorithm for systems of (possibly inhomogeneous) linear ordinary differential equations with constant coefficients. The algorithm produces a quantum state that is proportional to the solution at a desired final time.…
Fundamental matrix operations and solving linear systems of equations are ubiquitous in scientific investigations. Using the "Sender-Receiver" model, we propose quantum algorithms for matrix operations such as matrix-vector product,…
This paper is one of a series of papers on coherent spaces and their applications, defined in the recent book 'Coherent Quantum Mechanics' by the first author. The paper studies coherent quantization -- the way operators in the quantum…