Related papers: Alternative Numerical Techniques
This note introduces a new class of integer factoring algorithms. Two versions of this method will be described, deterministic and probabilistic. These algorithms are practical, and can factor large classes of balanced integers N = pq, p <…
The purpose of this note is to provide an alternative proof of two quadratic transformation formulas contiguous to that of Gauss using a differential equation approach.
Discrete Fourier transform (DFT) is the base of modern signal or information processing. 1-Dimensional fast Fourier transform (1D FFT) and 2D FFT have time complexity O(NlogN) and O(N^2logN) respectively. Quantum 1D and 2D DFT algorithms…
The problem of infinities in quantum field theory (QRT) is a long standing problem in physics.For solving this problem, different renormalization techniques have been suggested but the problem still persists. Here we suggest another…
Quantum computing is a promising new area of computing with quantum algorithms offering a potential speedup over classical algorithms if fault tolerant quantum computers can be built. One of the first applications of the classical computer…
The \textit{Temporal Fusion Transformer} (TFT), proposed by Lim \textit{et al.}, published in \textit{International Journal of Forecasting} (2021), is a state-of-the-art attention-based deep neural network architecture specifically designed…
The Lie algebras over the algebra of dual numbers are introduced and investigated.
I give a brief overview of fault-tolerant quantum computation, with an emphasis on recent work and open questions.
In this paper, we identify two different sets of problems. The first covers the problems that the iterative proportional fitting (IPF) algorithm was developed to solve. These concern completing a population table by using a sample. The…
The Quantum Fourier Transformation (QFT) is a well-known subroutine for algorithms on qubit-based universal quantum computers. In this work, the known QFT circuit is used to derive an efficient circuit for the multidimensional QFT. The…
The nonlinear Fourier transform (NLFT) extends the classical Fourier transform by replacing addition with matrix multiplication. While the NLFT on $\mathrm{SU}(1,1)$ has been widely studied, its $\mathrm{SU}(2)$ variant has only recently…
The quantum Fourier transform (QFT) has been implemented on a three bit nuclear magnetic resonance (NMR) quantum computer, providing a first step towards the realization of Shor's factoring and other quantum algorithms. Implementation of…
Some Caputo q-fractional difference equations are solved. The solutions are expressed by means of a new introduced generalized type of q-Mittag-Leffler functions. The method of successive approximation is used to obtain the solutions. The…
The fractional quantum and statistical mechanics have been developed via new path integrals approach.
The quadratic phase Fourier transform (QPFT) is a generalization of several well-known integral transforms, including the linear canonical transform (LCT), fractional Fourier transform (FrFT), and Fourier transform (FT). This paper…
This paper presents new results in the theory of number theoretic Hilbert (NHT) transforms. New polymorphic solutions have been found for the 14-point and 16-point transforms. Several transform pairs are computed and solutions found for…
We construct the new q-extension of Bernoulli numbers and polynomials in this paper. Finally we consider the q-zeta functions which interpolate the new q-extension of Bernoulli numbers and polynomials.
These are notes from a 15 week course aimed at graduate mathematicians. They provide an essentially self-contained introduction to some of the ideas and terminology of QFT.
The alternative approach to QCD analysis of the structure function F2gamma is presented. It differs from the conventional one by the presence of the terms, which in conventional approach appear in higher orders. The numerical results show…
In an earlier paper we introduced the notion of 'bifurcating continued fractions' in a heuristic manner. In this paper a formal theory is developed for the 'bifurcating continued fractions'.