A note on continuous fractional wavelet transform in ℝn

In this paper, we study the continuous fractional wavelet transform (CFrWT) in [Formula: see text]-dimensional Euclidean space [Formula: see text] with scaling parameter [Formula: see text] such that [Formula: see text]. We obtain inner product relation and reconstruction formula for the CFrWT depending on two wavelets along with the reproducing kernel function, involving two wavelets, for the image space of CFrWT. We obtain Heisenberg’s uncertainty inequality and Local uncertainty inequality for the CFrWT. Finally, we prove the boundedness of CFrWT on the Morrey space [Formula: see text] and estimate [Formula: see text]-distance of the CFrWT of two argument functions with respect to different wavelets.

Point Distribution and Perfect Directions in 𝔽p2\mathbb{F}_p^2

Let p ≥ 3 be a prime, S \subseteq \mathbb{F}_p^2 a nonempty set, and w:\mathbb{F}_p^2 \to R a function with supp w = S. Applying an uncertainty inequality due to András Bíró and the present author, we show that there are at most {1 \over 2}\left| S \right| directions in \mathbb{F}_p^2 such that for every line l in any of these directions, one has \sum\limits_{z \in l} {w\left( z \right) = {1 \over p}\sum\limits_{z \in \mathbb{F}_p^2} {w\left( z \right),} } except if S itself is a line and w is constant on S (in which case all, but one direction have the property in question). The bound {1 \over 2}\left| S \right| is sharp.As an application, we give a new proof of a result of Rédei-Megyesi about the number of directions determined by a set in a finite affine plane.

Heisenberg uncertainty inequality for certain Lie groups

We establish analogues of Heisenberg uncertainty inequality for some classes of Lie groups, such as connected and simply connected nilpotent Lie groups, diamond Lie groups and Heisenberg motion groups.

Heisenberg–Pauli–Weyl inequality for connected nilpotent Lie groups

The purpose of this paper is to formulate and prove an analogue of the classical Heisenberg–Pauli–Weyl uncertainty inequality for connected nilpotent Lie groups with noncompact center. Representation theory and a localized Plancherel formula play an important role in the proof.

Human resources management in context of corporate social responsibility

The globalization of economic activities in the last decade brings changes in the world of work; there is uncertainty, inequality, new risks. The new requirements apply to the management of human resources and the sustainability development. To make the company successful in the long term, it must meet the new expectations of their surroundings, which necessarily include the responsible behaviour towards the society in which it operates. Man limits reliability of the features of the system. As a result of the failure to adapt labour conditions humans began to appear health, economic and social consequences. Through human resources and people management can be designed to target the working system and increasing the efficiency of human labour. The paper focuses on the sustainable management of human resources in the context of the requirements of social responsibility, identifying current problems in this area in practice and proposes solutions. Keywords: Human resources; Management; Corporate social responsibility