Does a given system of linear equations Ax = b have a nonnegative integer solution? This is a fundamental question in many areas, such as operations research, number theory, and statistics. In terms of optimization, this is called an integer feasibility problem. A generalized integer feasibility problem is to find b such that there does not exist a nonnegative integral solution in the system wi...

ÐHigh-speed multiplication is frequently used in general-purpose and application-specific computer systems. These systems often support integer multiplication, where two n-bit integers are multiplied to produce a 2n-bit product. To prevent growth in word length, processors typically return the n least significant bits of the product and a flag that indicates whether or not overflow has occurred...

Background The recently published method SMART1Map[1] has proposed a new true T1 measurement technique. It consists in a 2D saturation-recovery prepared balancedSSFP sequence which allows different acquisition schemes depending on the number of repetition (shot) used. Single-shot acquisition duration is short but cardiac motion blur can occur due to long acquisition window duration. Two-shot ac...

BACKGROUND Focus group studies are increasingly published in health related journals, but we know little about how researchers use this method, particularly how they determine the number of focus groups to conduct. The methodological literature commonly advises researchers to follow principles of data saturation, although practical advise on how to do this is lacking. Our objectives were firstl...

Reliable data on electron backscattering in different media are not available in literature, even more for electrons of continuum spectrum. Material's parameters that depend or could be inferred from those data might have some uncertainties. Back in 1978, K. K. Sharma and M. Singh determined the value of saturation thickness for backscattered electrons and attenuation coefficient in some metals...

We present a setup capable of overcoming the saturation output power of semiconductor optical amplifiers operating in the pulsed regime. The concept is to couple different time delays to orthogonal polarization modes, amplify the pulses multiplexed in time, and use the polarization information to recombine them into a single high-power optical pulse. Making use of a single amplifier and two pol...

It is shown that current saturation in semiconducting carbon nanotubes is indistinguishable from metallic nanotubes if the carrier density is above a critical value determined by the bandgap and the optical phonon energy. This feature stems from the higher number of current-carrying states in the semiconducting tubes due to the van Hove singularity at the band edge. Above this critical carrier ...

Let C be a family of edge-colored graphs. A t-edge colored graph G is (C, t)saturated if G does not contain any graph in C but the addition of any edge in any color in [t] creates a copy of some graph in C. Similarly to classical saturation functions, define satt(n, C) to be the minimum number of edges in a (C, t) saturated graph. Let Cr(H) be the family consisting of every edge-colored copy of...

In this work, we propose a new statistical randomness test, the Saturation Point Test, which can be applied to integer sequences as well as binary sequences and is designed to increase the number of tests for short sequences. The subject of Saturation Point Test is the index of integer, denoted by SP , where all possible integers occur in the given sequence. We evaluate the probability Pr(SP = ...

There have been extensive studies on the performance of IEEE 802.11 networks, most of which focus on the saturation regime where user queues are always full. This paper departs from prior work in that we focus on non-saturated regimes. Specifically, we consider two scenarios: one consisting of a mixture of saturated and non-saturated users, the other consisting of users of buffer size one. In b...