The Bohr phenomenon for analytic functions on shifted disks

In this paper, we investigate the Bohr phenomenon for the class of analytic functions defined on the simply connected domain \(\Omega_{\gamma}=\bigg\{z\in\mathbb{C} \colon \bigg|z+\frac{\gamma}{1-\gamma}\bigg|<\frac{1}{1-\gamma}\bigg\}\) for \(0\leq \gamma<1.\) We study improved Bohr radius, Bohr-Rogosinski radius and refined Bohr radius for the class of analytic functions defined in \(\Omega_{\gamma}\), and obtain several sharp results.

Modelling of density of states and energy level of chalcogenide quantum dots

Quantum dots (QDs) or semiconductor nanocrystals are luminous materials with unique optical properties that can be fine-tuned by varying the size of the material. Chalcogenide QDs show strong quantum confinements effects owing to the fact that the exciton Bohr radius is much larger than the particle size, and tunable energy bandgap leads to widespread technological interest in near-infrared optical devices. In this communication, one dimensional Cu2SnS3 and PbSexS1-x QDs is modeled by a particle in a box model which was used to compute energies and density of states. The density of states and the energy level of QDs are determined as a function of the strengths of the potential walls of the inner box. The results exhibit that the density of states decreases exponentially with an increase in the energy level of QDs. The density of states at lower energy levels is more significant than what is observed in higher energy levels.

On Bohr Radius of Certain Analytic Functions with Negative Coefficients

The key purpose of this paper is to investigate the Bohr radius for several subclasses of analytic functions with negative coefficients. Our investigation with the Bohr radius correlates with the classes of generalized Janowski type functions. Under this novel strategy, we develop Bohr’s phenomenon for a generalized class associated with q-functions having q ∈ (0, 1). In the applications viewpoint, our consequences have shown the applicability in the class inaugurated by Bessel functions.

Bohr phenomenon for operator-valued functions

We establish Bohr inequalities for operator-valued functions, which can be viewed as analogues of a couple of interesting results from scalar-valued settings. Some results of this paper are motivated by the classical flavour of Bohr inequality, while others are based on a generalized concept of the Bohr radius problem.