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We define a novel time-frequency analyzing tool, namely linear canonical wavelet transform (LCWT) and study some of its important properties like inner product relation, reconstruction formula and also characterize its range. We obtain Donoho-Stark's and Lieb's uncertainty principle for the LCWT and give a lower bound for the measure of its essential support. We also give Shapiro's mean dispersion theorem for the proposed LCWT.

Analysis of the fetal heart rate during pregnancy is essential for monitoring the proper development of the fetus. Current fetal heart monitoring techniques lack the accuracy in fetal heart rate monitoring and features acquisition, resulting in diagnostic medical issues. The challenge lies in the extraction of the fetal ECG from the mother's ECG during pregnancy. This approach has the advantage of being a reliable and non-invasive technique. For this aim, we propose in this paper a wavelet/multi-wavelet method allowing to extract perfectly the feta ECG parameters from the abdominal mother ECG. The method is essentially due to the exploitation of Clifford wavelets as recent variants in the field. We prove that these wavelets are more efficient and performing against classical ones. The experimental results are therefore due to two basic classes of wavelets and multi-wavelets. A first-class is the classical Haar Schauder, and a second one is due to Clifford valued wavelets and multi-wavelets. These results showed that wavelets/multiwavelets are already good bases for the FECG processing, provided that Clifford ones are the best., Comment: 21 pages, 8 figures, 1 table

Capturing solution near the singular point of any nonlinear SBVPs is challenging because coefficients involved in the differential equation blow up near singularities. In this article, we aim to construct a general method based on orthogonal polynomials as wavelets. We discuss multiresolution analysis for wavelets generated by orthogonal polynomials, e.g., Hermite, Legendre, Chebyshev, Laguerre, and Gegenbauer. Then we use these wavelets for solving nonlinear SBVPs. These wavelets can deal with singularities easily and efficiently. To deal with the nonlinearity, we use both Newton's quasilinearization and the Newton-Raphson method. To show the importance and accuracy of the proposed methods, we solve the Lane-Emden type of problems and compare the computed solutions with the known solutions. As the resolution is increased the computed solutions converge to exact solutions or known solutions. We observe that the proposed technique performs well on a class of Lane-Emden type BVPs. As the paper deals with singularity, non-linearity significantly and different wavelets are used to compare the results.

The conformal gravity fit to observed galactic rotation curves requires {\gamma}>0. On the other hand, conventional method for light deflection by galaxies gives a negative contribution to Schwarzschild value for {\gamma}>0, which is contrary to observation. Thus, it is very important that the contribution to bending should in principle be positive, no matter how small its magnitude is. Here we show that the Rindler-Ishak method gives a positive contribution to Schwarzschild deflection for {\gamma}>0, as desired. We also obtain the exact local coupling term derived earlier by Sereno. These results indicate that conformal gravity can potentially test well against all astrophysical observations to date., Comment: 6 pages

After the work of Rindler and Ishak, it is now well established that the bending of light is influenced by the cosmological constant {\Lambda} appearing in the Schwarzschild-de Sitter spacetime. We show that their method, when applied to the galactic halo gravity parametrized by a constant {\gamma}, yields exactly the same {\gamma}- correction to Schwarzschild bending as obtained by standard methods. Different cases are analyzed, which include some corrections to the special cases considered in the original paper by Rindler and Ishak., Comment: 15 pages