One of the drawbacks of Data Envelopment Analysis (DEA) is the problem of lack of discrimination among efficient Decision Making Units (DMUs). A method for removing this difficulty is called changing reference set proposed by Jahanshahloo and et.al (2007). The method has some drawbacks. In this paper a modified method and new method to overcome this problems are suggested. The main advantage of...

an efficient, mild and environmentally friendly method was reported for the synthesis of an efficient, mild and environmentally friendly method was reported for the synthesis of pyranopyroles from aryl aldehydes, ethyl acetoacetate, malononitrile and hydrazine hydrate in the presence of catalytic amounts of methyl imidazolium hydrogen sulfate ([hmim][hso4]) as an efficient catalyst. these synth...

There are several numerical methods for computing approximate zeros of a given univariate polynomial. In this paper, we develop a simple and novel method for determining sharp upper bounds on errors in approximate zeros of a given polynomial using Rouche's theorem from complex analysis. We compute the error bounds using non-linear optimization. Our bounds are scalable in the sense that we compu...

I n this paper we show how mathematics can illuminate the study of cake-cutting in ways that have practical implications. Specifically, we analyze cake-cutting algorithms that use a minimal number of cuts (n − 1 if there are n people), where a cake is a metaphor for a heterogeneous, divisible good, whose parts may be valued differently by different people. These algorithms not only establish th...