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...

Parseval's formula and inversion formula for the S-transform are given. A relation between the S-transform and pseudodifferential operators is obtained. The S-transform is studied on the spaces S(ℝn) and S'(ℝn).

We give a new combinatorial interpretation of the noncommutative Lagrange inversion formula, more precisely, of the formula of Brouder-FrabettiKrattenthaler for the antipode of the noncommutative Faà di Bruno algebra.

In this note, we consider the minimum number of NOT operators in a Boolean formula representing a Boolean function. In circuit complexity theory, the minimum number of NOT gates in a Boolean circuit computing a Boolean function f is called the inversion complexity of f . In 1958, Markov determined the inversion complexity of every Boolean function and particularly proved that ⌈log 2 (n + 1)⌉ NO...

In two dimensions, the exponential X-ray transform has been wellstudied due to its applications of correcting attenuation effects in Single Photon Emission Computed Tomography (SPECT). Explicit inversion formulas have been known for over 15 years. The threedimensional (3D) case has not been as thoroughly examined, and inversion formulas are available for only a few of the wide range of possible...

In many numerical examples it has been demonstrated that the saddlepoint approximation for the cumulative distribution function of a general nor-malised statistic behaves better in comparison with the third order Edge-worth expansion. The eeect is especially pronounced in the tails. Here we are dealing with the inverse problem of quantile evaluation. The inversion 1 of the Lugannani-Rice approx...

INTRODUCTION T diagnosis of food allergy can be challenging and many conditions can mimic food allergy. It is imperative to differentiate true food allergy from the ‘mimics’ of food allergy, particularly in children eliminating multiple foods from their diet. This case report describes a child with features of Auriculotemporal (Frey’s) syndrome, posing as multiple food allergies. The child was ...