in this paper we study necessary and sufficient conditions for some types of linear combinations of wave packet frames to be a frame for l^2(r^d). further, we illustrate our results with some examples and applications.

This note explores some properties of a notion of linear combination of partial order relations over a given set. A bilinear form is used to represent compatibility of orders, and we study combinations up to equivalence through this form. A precise description of the quotient space is provided according to the nature of the semiring of coefficients.

‎In this paper,  the sufficient conditions for the linear combinations of slanted half-plane harmonic mappings to be univalent and convex in the direction of $(-gamma) $ are studied. Our result improves some recent works. Furthermore, a illustrative example and imagine domains of the linear combinations satisfying the desired conditions are enumerated.