Are Buchberger’s criteria necessary for the chain condition?

Are Buchberger's criteria necessary for the chain condition?

Buchberger’s Gröbner basis theory plays a fundamental role in symbolic computation. The resulting algorithms essentially carry out several S-polynomial reductions. In his PhD thesis and later publication Buchberger showed that sometimes one can skip S-polynomial reductions if the leading terms of polynomials satisfy certain criteria. A question naturally arises: Are Buchberger’s criteria also n...

A Necessary Condition for Weyl-Heisenberg Frames

A necessary condition for multiple objective fractional programming

In this paper, we establish a proof for  a  necessary condition for  multiple objective fractional programming. In order to derive the set of necessary conditions, we employ an equivalent parametric problem. Also, we  present the related semi parametric model.

The value of lateral lymphoscintigraphy images of the pelvis for gynecological cancers: Are they necessary?

Introduction: In the current study we evaluated the incremental value of lateral pelvic lymphoscintigraphy imaging of endometrial or cervical cancer patients who underwent sentinel node mapping. Methods: Operable endometrial and cervical cancer patients without clinical or paraclinical evidence of lymph node involvement were included in the study. The day before surgery the patients were sent ...

Necessary condition for the quantum adiabatic approximation

A gapped quantum system that is adiabatically perturbed remains approximately in its eigenstate after the evolution. We prove that, for constant gap, general quantum processes that approximately prepare the final eigenstate require a minimum time proportional to the ratio of the length of the eigenstate path to the gap. Thus, no rigorous adiabatic condition can yield a smaller cost. We also giv...