— For given positive integers a, b, q we investigate the density of solutions (x, y) ∈ Z to congruences ax+ by ≡ 0 mod q.

In the paper, the authors present an explicit form for a family of inhomogeneous linear ordinary differential equations, find a more significant expression for all derivatives of a function related to the solution to the family of inhomogeneous linear ordinary differential equations in terms of the Lerch transcendent, establish an explicit formula for computing all derivatives of the solution t...

In a recent publication we presented a method to obtain highly resolved NMR spectra in the presence of an inhomogeneous B(0) field with the help of a matched RF gradient. If RF gradient pulses are combined with "ideal" 90 degrees pulses to form inhomogeneous z rotation pulses, the line broadening caused by the B(0) gradient can be refocused, while the full chemical shift information is maintain...

In this paper, we consider computational methods for optimizing a multivariate inhomogeneous polynomial function over a compact set. The focus is on the design and analysis of polynomial-time approximation algorithms. The references on approximation algorithms for inhomogeneous polynomial optimization problems are extremely scarce in the literature. To the best of our knowledge, the only result...

In medical image processing, robust segmentation of inhomogeneous targets is a challenging problem. Because of the complexity and diversity in medical images, the commonly used semiautomatic segmentation algorithms usually fail in the segmentation of inhomogeneous objects. In this study, we propose a novel algorithm imbedded with a seed point autogeneration for random walks segmentation enhance...

Inhomogeneous recombination can give rise to perturbations in the electron number density which can be a factor of 5 larger than the perturbations in baryon density. We do a thorough analysis of the second order anisotropies generated in the cosmic microwave background due to perturbations in the electron number density. We show that solving the second order Boltzmann equation for photons is eq...

We consider a cosmology in which a spherically symmetric large scale inhomogeneous enhancement or a void are described by an inhomogeneous metric and Einstein’s gravitational equations. For a flat matter dominated universe the inhomogeneous equations lead to luminosity distance and Hubble constant formulas that depend on the location of the observer and a deceleration parameter that can differ ...

Time reversal of ultrasonic fields represents a way to focus through an inhomogeneous medium. This may be acomplished by a time-reversal mirror ("M) made from an array of transmit-receive transducers that respond linearly and allow the incident acoustic pressure to be sampled. The pressure field is then time-reversed and re-emitted. This process can be used to focus through inhomogeneous media ...

*Correspondence: Colin J. R. Sheppard, Department of Nanophysics, Istituto Italiano di Tecnologia, Via Morego 30, 16163 Genova, Italy e-mail: [email protected] We review Fourier methods used in the disciplines of electromagnetism and signal processing, with a view to reconciling differences in approach. In particular, Fourier methods well known in signal processing are applied to three-...