This paper describes the discrete Radon transform (DRT) and the exact inversion algorithm for it. Similar to the discrete Fourier transform (DFT), the DRT is defined for periodic vector-sequences and studied as a transform in its own right. Casting the forward transform as a matrix-vector multiplication, the key observation is that the matrix-although very large-has a block-circulant structure....

In this work we study fractional order Sumudu transform. In the development of the definition we use fractional analysis based on the modified Riemann Liouville derivative, then we name the fractional Sumudu transform. We also establish a relationship between fractional Laplace and Sumudu via duality with complex inversion formula for fractional Sumudu transform and apply new definition to solv...

Hafner and Stopple proved a conjecture of Zagier that the inverse Mellin transform symmetric square [Formula: see text]-function associated to Ramanujan tau function has an asymptotic expansion in terms nontrivial zeros Riemann zeta text]. Later, Chakraborty et al. extended this phenomenon for any Hecke eigenform over full modular group. In paper, we study Lambert series text] where is text]th ...

Inverting the exponential Radon transform has a potential use for SPECT (single photon emission computed tomography) imaging in cases where a uniform attenuation can be approximated, such as in brain and abdominal imaging. Tretiak and Metz derived in the frequency domain an explicit inversion formula for the exponential Radon transform in two dimensions for parallel-beam collimator geometry. Pr...

Considering a linearly ordered set, we introduce its symmetric version, and endow it with two operations extending supremum and infimum, so as to obtain an algebraic structure close to a commutative ring. We show that imposing symmetry necessarily entails non associativity, hence computing rules are defined in order to deal with non associativity. We study in details computing rules, which we e...