Asymptotic preserving (AP) schemes for multiscale kinetic and hyperbolic equations: a review Abstract. Kinetic and hyperbolic equations contain small scales (mean free path/time, Debye length, relaxation or reaction time, etc.) that lead to various different asymptotic regimes, in which the classical numerical approximations become prohibitively expensive. Asymptotic-preserving (AP) schemes are...

Inspired by the imbricated scale-tissue flexible armor of elasmoid fish, we design hybrid stiff plate/soft matrix material architectures and reveal their ability to provide protection against penetration while preserving flexibility. Indentation and bending tests on bio-inspired 3D-printed prototype materials show that both protection and flexibility are highly tunable by geometrical parameters...

Dual-energy (DE) CT scans provide two sets of measurements at two different source energies. In principle, two materials can be accurately decomposed from DECT measurements. For triple-material decomposition, a third constraint, such as volume or mass conservation, is required to solve three sets of unknowns from two sets of measurements. An image-domain (ID) method [1] has been proposed recent...

Kinetic and hyperbolic equations contain small scales (mean free path/time, Debye length, relaxation or reaction time, etc.) that lead to various different asymptotic regimes, in which the classical numerical approximations become prohibitively expensive. Asymptotic-preserving (AP) schemes are schemes that are efficient in these asymptotic regimes. The designing principle of AP schemes are to p...

background: leiomyomas are the most common benign tumors of the uterus. removal of the prolapsed pedunculated submucous myoma represents a distinct entity. evaluation and treatment of such cases may need intervention via the hymen.mini-laparotomic management of a pedunculated submucous myoma while preserving hymen integrity in a virginal patient is described as a safe alternative.. case: a 30-y...

The Farey sequences can be used [1] to create the Eulers totient function φ(n), by identifying the fractions for number n that did not occur in all Farey sequences up to n-1. This function creates, when divided by n-1, what is here called the Primety measure, which is a measure of how close to being a prime number n is. P(n)=φ(n)/(n-1) has maximum 1 for all prime numbers and minimum that decrea...