In this paper, we define both the upper and lower order of a sense-preserving harmonic mapping in D . We generalize to case some known results about holomorphic functions with positive show consequences function having finite order. addition, improve related result when there is equality distortion theorem for mappings Some examples are provided illustrate developed theory.

Sentential adverbs are often assumed to be situated in front of the verb phrase in arbitrary order. In a recent monograph, however, Cinque (1999) claims that the relative order of sentential adverbs may, in principle, be universally fixed. In this paper I first give a brief presentation of Cinque’s proposal. Then I present a pilot study of sentential adverbs in English and Swedish. This study i...

The pancake problem is a famous search problem where the objective is to sort a sequence of objects (pancakes) through a minimal number of prefix reversals (flips). The best approaches for the problem are based on heuristic search with abstraction (pattern database) heuristics. We present a new class of abstractions for the pancake problem called relative-order abstractions. Relative-order abst...

Relative worst-order analysis is a technique for assessing the relative quality of online algorithms. We survey the most important results obtained with this technique and compare it with other quality measures.

A semi-batch crystallization system is used to determine growth kinetics and morphology of barium carbonate crystals, under a constant pH value and constant temperature in the various relative supersaturations. Results show that crystal growth rate satisfies a first-order kinetic expression at high relative supersaturation, while at relative supersaturation values lower than 3,  the k...

<p style='text-indent:20px;'>We construct Green's functions for second order parabolic operators of the form <inline-formula><tex-math id="M1">\begin{document}$ Pu = \partial_t u-{\rm div}({\mathbf A} \nabla u+ {\mathbf b}u)+ c} \cdot u+du $\end{document}</tex-math></inline-formula> in id="M2">\begin{document}$ (-\infty, \infty) \times \Omega $\end{document}<...

data envelope analysis (dea) is an approach to estimate the relative efficiency of decision making units (dmus). several studies were conducted in order to prioritize efficient units and some useful models such as cross-efficiency matrix (cem) were presented.  besides, a number of dea models with interval data have been developed and ranking dmus with such data was solved. however, presenting a...