We give an efficient construction of constant-degree, constant-gap quantum k-tensor product expanders. The key ingredients are an efficient classical tensor product expander and the quantum Fourier transform. Our construction works whenever k = O(n/ logn), where n is the number of qubits. An immediate corollary of this result is an efficient construction of approximate unitary k-designs on n qu...

For a number field K with ring of integers O K , we prove an analogue over finite rings of the form O K /P m of the Fundamental Theorem on the Fourier transform of a relative invariant of prehomogeneous vector spaces, where P is a big enough prime ideal of O K and m > 1. In the appendix, F. to the functional equation of L-functions of Dirichlet type associated with prehomogeneous vector spaces.

Sets K in d-dimensional Euclidean space are constructed with the property that the inverse Fourier transform of the characteristic function 1 K is a single dyadic orthonormal wavelet. The construction is characterized by its generality in terms of a quantitative iterative procedure, by its computational implementation, and by its simplicity. The general case in which the inverse Fourier transfo...

although elzaki transform is stronger than sumudu and laplace transforms to solve the ordinary differential equations withnon-constant coefficients, but this method does not lead to finding the answer of some differential equations. in this paper, a method is introduced to find that a differential equation by elzaki transform can be ‎solved?‎

We aim to introduce extended generalized Mittag-Leffler function (EGMLF) via the Beta and obtain certain integral differential representation of them. Further, we present some formulas Riemann-–Liouville fractional integration differentiation operators. Also, derive various transforms, including Euler transform, Laplace Whittakar transform K-transform. The operator images are expressed in terms...

A quick and accurate way to rotate and shift nuclear magnetic resonance (NMR) images using the two-dimensional chirp-z transform is presented. When the desired image grid is rotated and shifted from the original grid due to patient motion, the chirp-z transform can reconstruct NMR images directly onto the ultimate grid instead of reconstructing onto the original grid and then applying interpola...

A new method of parameter identification based on linear time-frequency representation and Hilbert transform is proposed in this paper to identify modal parameters of linear time-varying systems from measured vibration responses. With Gabor expansion and synthesis theory, measured responses are represented in time-frequency domain and modal components are reconstructed by time-frequency filteri...

We establish some reiteration theorems for limiting K-interpolation methods, thereby obtaining new limiting variants of the classical reiteration theorem. An application to the Fourier transform is given.

The Fast Fourier Transform (FFT) is the most efficiently known way to compute the Discrete Fourier Transform (DFT) of an arbitrary n-length signal, and has a computational complexity of O(n log n)1. If the DFT ~ X of the signal ~x has only k non-zero coefficients (where k < n), can we do better? In [1], we presented a novel FFAST (Fast Fourier Aliasing-based Sparse Transform) algorithm that cle...

in this paper cufe2o4, nanocrystalline powders were prepared. also, the supported cu ferrite was obtained by impregnation of the supports with cu and fe nitrates solutions, for calcination temperature 450 ºc. the samples were characterized by x-ray powder diffraction (xrd) and fourier transform-infrared spectroscopy (ft-ir). in this investigation photocatalytic degradation of acid red 206 in wa...