The quantum constraint equations for a relativistic three-dimensional harmonic oscillator are shown to find concise expression in terms of Lorentz covariant ladder operators. These ladder operators consist of two conjugate 4-vectors that are each constrained to generate three linearly independent combinations of ladder operator components for raising and lowering the eigenstates of the oscillat...

Researchers at Washington State University conducted an independent evaluation of the first year of the Washington State Early Childhood Education Career and Wage Ladder Pilot Program. The evaluation, which compared ladder centers with a control group, verified that the career and wage ladder works to improve the quality of early childhood education by reducing teacher turnover and encouraging ...

This paper gives a comprehensive analysis of Montgomery powering ladder. Initially developed for fast scalar multiplication on elliptic curves, we extend the scope of Montgomery ladder to any exponentiation in an abelian group. Computationally, the Montgomery ladder has the triple advantage of presenting a Lucas chain structure, of being parallelized, and of sharing a common operand. Furthermor...

A ladder is a 2 × k grid graph. When does graph class $${\cal C}$$ exclude some as minor? We show that this the case if and only all graphs G in admit proper vertex coloring with bounded number of colors such for every 2-connected subgraph H G, there color appears exactly once H. This type relaxation notion centered coloring, where connected must be The minimum treedepth it known classes are th...