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 modified Mellin transform Zk(s) = ∫ ∞ 1 |ζ( 1 2 + ix)|x dx (k ∈ N) is used to obtain estimates for

This paper describes the temporal spatio-velocity (TSV) transform for extracting pixel velocities from binary image sequences. The TSV transform is derived from the Hough transform over windowed spatio-temporal images. We present the methodology of the transform and its implementation in an iterative computational form. The intensity at each pixel in the TSV image represents a measure of the li...

This paper presents a new approach for power signal time series data mining using S-transform based K-means clustering technique. Initially the power signal time series disturbance data are pre-processed through an advanced signal processing tool such as S-transform and various statistical features are extracted, which are used as inputs to the K-means algorithm for disturbance event detection....

The Transferable Belief approach to the Theory of Evidence is based on the pignistic transform which, mapping belief functions to probability distributions, allows to make “precise” decisions on a set of disjoint hypotheses via classical utility theory. In certain scenarios, however, such as medical diagnosis, the need for an “imprecise” approach to decision making arises, in which sets of poss...

— We consider Hermitian N ×N random matrices H distributed according to a probability density dμN(H) = e−N Tr V (H)dH with analytic and uniformly convex V . From work by Zinn-Justin, Collins, and Guionnet & Maida it is known that the large-N limit of the scaled logarithm N−1 lnΩ(NK) of the Fourier transform Ω(K) of dμN(H) for K of finite rank, is a linear functional of the Voiculescu R-transfor...

The sort transform (ST) is a modification of the Burrows-Wheeler transform (BWT). Both transformations map an arbitrary word of length n to a pair consisting of a word of length n and an index between 1 and n. The BWT sorts all rotation conjugates of the input word, whereas the ST of order k only uses the first k letters for sorting all such conjugates. If two conjugates start with the same pre...

We show that the Hurwitz zeta function, ζ(ν, a), and the Legendre chi function, χν(z), defined by ζ(ν, a) = ∞ ∑ k=0 1 (k + a)ν , 0 < a ≤ 1, Re ν > 1, and χν(z) = ∞ ∑ k=0 z2k+1 (2k + 1)ν , |z| ≤ 1, Re ν > 1 with ν = 2, 3, 4, . . . , respectively, form a discrete Fourier transform pair. Many formulae involving the values of these functions at rational arguments, most of them unknown, are obtained...

This article explores the efficiency of motion-compensated three-dimensional transform coding, a compression scheme that employs a motion-compensated transform for a group of pictures. We investigate this coding scheme experimentally and theoretically. The practical coding scheme employs in temporal direction a wavelet decomposition with motion-compensated lifting steps. Further, we compare the...

The Special Affine Fourier Transform or the SAFT generalizes a number of well known unitary transformations as well as signal processing and optics related mathematical operations. Unlike the Fourier transform, the SAFT does not work well with the standard convolution operation. Recently, Q. Xiang and K. Y. Qin introduced a new convolution operation that is more suitable for the SAFT and by whi...