A novel approach on micropolar fluid flow in a porous channel with high mass transfer via wavelet frames

In this article, we present the Laguerre wavelet exact Parseval frame method (LWPM) for the two-dimensional flow of a rotating micropolar fluid in a porous channel with huge mass transfer. This flow is governed by highly nonlinear coupled partial differential equations (PDEs) are reduced to the nonlinear coupled ordinary differential equations (ODEs) using Berman's similarity transformation before being solved numerically by a Laguerre wavelet exact Parseval frame method. We also compared this work with the other methods in the literature available. Moreover, in the graphs of the velocity distribution and microrotation, we shown that the proposed scheme's solutions are more accurate and applicable than other existing methods in the literature. Numerical results explaining the effects of various physical parameters connected with the flow are discussed.

Lower Semi-frames, Frames, and Metric Operators

This paper deals with the possibility of transforming a weakly measurable function in a Hilbert space into a continuous frame by a metric operator, i.e., a strictly positive self-adjoint operator. A necessary condition is that the domain of the analysis operator associated with the function be dense. The study is done also with the help of the generalized frame operator associated with a weakly measurable function, which has better properties than the usual frame operator. A special attention is given to lower semi-frames: indeed, if the domain of the analysis operator is dense, then a lower semi-frame can be transformed into a Parseval frame with a (special) metric operator.

An Operator Based Approach to Irregular Frames of Translates

We consider translates of functions in L 2 ( R d ) along an irregular set of points, that is, { ϕ ( · − λ k ) } k ∈ Z —where ϕ is a bandlimited function. Introducing a notion of pseudo-Gramian function for the irregular case, we obtain conditions for a family of irregular translates to be a Bessel, frame or Riesz sequence. We show the connection of the frame-related operators of the translates to the operators of exponentials. This is used, in particular, to find for the first time in the irregular case a representation of the canonical dual as well as of the equivalent Parseval frame—in terms of its Fourier transform.

Frames and subspaces

This thesis will consist of three parts. In the first part we find the closest probabilistic Parseval frame to a given probabilistic frame in the 2 Wasserstein Distance. It is known that in the traditional [symbol]2 distance the closest Parseval frame to a frame [phi] = {[symbol]i} N[i=1] [symbol] R[d] is [phi[�] = {[symbol] � i }N[i]=1 = {S [-1/2][[symbol]i]} N[i=1] where S is the frame operator of [phi]. We use this fact to prove a similar statement about probabilistic frames in the 2 Wasserstein metric. In the second part, we will associate a complex vector with a rank 2 real projection. Using this association we will answer many open questions in frame theory. In particular we will prove Edidin's theorem in phase retrieval in the complex case, answer a question on mutually unbiased bases, a question on equiangular lines, and a question on fusion frames. In the last part we will give a way to calculate the exact constant for the [symbol]1 � [symbol]2 inequality and use this method to prove a couple of interesting theorems

NECESSARY AND SUFFICIENT CONDITIONS FOR PRIME PARSEVAL FRAMES

In the article we consider two disjoint classes of frames, prime and composite Parseval frames, the union of which forms a set of Parseval frames. The main goal is to obtain a description of these two classes. In this article we prove necessary and sufficient conditions for the frame to be a prime Parseval frame.