The accurate localization of S1 and S2 is essential for heart sound segmentation classification. However, current direct algorithms have poor noise immunity low accuracy. Therefore, this paper proposes a new optimal algorithm based on K-means clustering Haar wavelet transform. includes three parts. Firstly, method uses the Viola integral Shannon’s energy-based to extract function envelope energ...

Intranasal route, ensuring suitable bioavailability of medicines under circumvention of the gastrointestinal degradation and hepatic first-pass elimination, has been a popular choice for drug delivery. Among nasal dosage forms, mucoadhesive solid inserts have been shown to resist mucociliary clearance and provide a prolonged nasal residence time. Hence, the purpose of this study was the prepara...

In the paper we calculate the images of the operators of multiplication by Laurent polynomials with respect to the Harish-Chandra transform and its non-symmetric generalization due to Opdam. It readily leads to a new simple proof of the Harish-Chandra inversion theorem in the zonal case (see [HC,He1]) and the corresponding theorem from [O1]. We assume that k > 0 and restrict ourselves to compac...

I. abstract. In this note, we prove several multiplicative products of the n-dimensional Hankel transform. In fact the following formulae: H{δ (k) (u(x))}.H{δ () (u(x))} = DH δ (k++ n−2 2) (u(x)) , (III,1)

spherical granules of the superionic conductor β/β́ lizr2(po4)3 in the range of sub 100 nm sizewere synthesizedvia freeze drying methodand fully reviewed in all aspects. samples were characterized by the x-ray diffractometry (xrd), the thermal analysis (tg, dsc), thefourier transform infra-red spectroscopy (ftir) and the scanning electron microscopy (sem).their structuredepends largely on the me...

The discrete Fourier transform (DFT) maps a nite number of discrete time-domain samples to the same number of discrete Fourier-domain samples. Being practical to compute, it is the primary transform applied to real-world sampled data in digital signal processing. The DFT has special relationships with the discrete-time Fourier transform and the continuous-time Fourier transform that let it be u...

For each pair (n, k) with 1 ≤ k < n, we construct a tight frame (ρλ : λ ∈ Λ) for L(R), which we call a frame of k-plane ridgelets. The intent is to efficiently represent functions which are smooth away from singularities along k-planes in R. We also develop tools to help decide whether in fact k-plane ridgelets provide the desired efficient representation. We first construct a wavelet-like tigh...

We propose and justify a new approach to constructing optimal nonlinear transforms of random vectors. We show that the proposed transform improves such characteristics of rank-reduced transforms as compression ratio, accuracy of decompression and reduces required computational work. The proposed transform Tp is presented in the form of a sum with p terms where each term is interpreted as a part...

We give an exposition of Novodvorskii’s theorem in Banach algebra K-theory, asserting that the Gelfand transform for a commutative induces isomorphism topological K-theory.

OBJECTIVE The Fourier transform, a fundamental mathematic tool widely used in signal analysis, is ubiquitous in radiology and integral to modern MR image formation. Understanding MRI techniques requires a basic understanding of what the Fourier transform accomplishes. MR image encoding, filling of k-space, and a wide spectrum of artifacts are all rooted in the Fourier transform. CONCLUSION Th...