Our goal, in this paper, is to study some equivalent deenitions of the pseudospectra of a closed linear operator. We start from two deenitions, one with strict inequality and the other with non-strict inequality. The rst deenition makes the pseudospectrum open and the second makes it closed. We will show the subtle diierence between these seemingly almost identical deenitions and the relations ...

The Crab Pulsar’s radio emission is unusual, consisting predominantly of giant pulses, with durations about a microsecond but structure down to the nanosecond level, and brightness temperatures up 1037 K. It unclear how pulses are produced, they likely originate near pulsar’s light cylinder, where corotating plasma approaches speed light. We report observations in 400–800 MHz frequency band, br...

The Heimann-Bielschowsky phenomenon (HBP) refers to coarse vertical oscillation of the eye with impaired vision. The ocular movements are strictly monocular, occurring only in the eye with amblyopia. The vertical oscillation is of equal velocity in both vertical directions, or may sometimes be greater in the downward than upward direction. HBP develops several years after loss of vision. It can...

Hydrocracking has great importance in present day refining due to strict environmental and norms of quality of fuel. In recent years the demand for middle distillate and gasoline has increased tremendously while that of heavy gas has decreased. In the present work we have modeled and then applied five lump scheme to hydrocracker reactor. The first order kinetics was assumed for the conversion i...

Self-similarity has been the paradigmatic picture for the pinch-off of a drop. Here we will show through high-speed imaging and boundary integral simulations that the inverse problem, the pinch-off of an air bubble in water, is not self-similar in a strict sense: A disk is quickly pulled through a water surface, leading to a giant, cylindrical void which after collapse creates an upward and a d...

Multiweighted energy games are two-player multiweighted games that concern the existence of infinite runs subject to a vector of lower and upper bounds on the accumulated weights along the run. We assume an unknown upper bound and calculate the set of vectors of upper bounds that allow an infinite run to exist. For both a strict and a weak upper bound we show how to construct this set by employ...

Drawing directed graphs has many applications and occurs whenever a natural flow of information is to be visualized. Given a directed acyclic graph (DAG) G, we are interested in an upward drawing of G, that is, a drawing of G in which all arcs are drawn as curves that are monotonically increasing in the vertical direction. Besides the upward property, it is desirable that the number of arc cros...